Bishop Basement Model

Import packages

# set EPSG for plotting functions
import os
import pathlib
import pickle
import string

import numpy as np
import polartoolkit as ptk
import scipy as sp
import verde as vd
import xarray as xr

import invert4geom

os.environ["POLARTOOLKIT_EPSG"] = "10598"

Get data

Here we will load a commonly used synthetic gravity and basement topography model, called the Bishop Model. It includes topography of the Moho and the sediment-basement contact, and the forward modelled gravity effect of each, providing a synthetic observed gravity dataset. The forward gravity is calculated with 6 layers of sediment which increase in density from 2100 kg/m3 at 0m to 2600 kg/m3 at the basement surface. Then 3 layers of increasing density from 2700 kg/m3 to 3300 kg/m3 at the Moho surface.

grid = invert4geom.load_bishop_model(coarsen_factor=50)

grid = grid.rename({"gravity": "gravity_anomaly_no_noise"})

# contaminate gravity with 0.2 mGal of random noise
grid["gravity_anomaly"], stddev = invert4geom.contaminate(
    grid.gravity_anomaly_no_noise,
    stddev=0.2,
    percent=False,
    seed=0,
)
grid["uncert"] = xr.full_like(grid.gravity_anomaly, stddev)
grid["upward"] = xr.full_like(grid.gravity_anomaly, 10)
grid

<xarray.Dataset> Size: 74kB
Dimensions:                   (northing: 40, easting: 38)
Coordinates:
  * northing                  (northing) float64 320B 1.459e+05 ... 5.359e+05
  * easting                   (easting) float64 304B 6.9e+03 ... 3.769e+05
Data variables:
    basement_topo             (northing, easting) float64 12kB -6.199e+03 ......
    moho_topo                 (northing, easting) float64 12kB -2.767e+04 ......
    gravity_anomaly_no_noise  (northing, easting) float64 12kB 99.08 ... 107.0
    gravity_anomaly           (northing, easting) float64 12kB 99.11 ... 106.9
    uncert                    (northing, easting) float64 12kB 0.2 0.2 ... 0.2
    upward                    (northing, easting) float64 12kB 10.0 ... 10.0

xarray.Dataset

• Dimensions:
  • northing: 40
  • easting: 38
• Coordinates: (2)
  • northing
    (northing)
    float64
    1.459e+05 1.559e+05 ... 5.359e+05

    array([145900., 155900., 165900., 175900., 185900., 195900., 205900., 215900.,
           225900., 235900., 245900., 255900., 265900., 275900., 285900., 295900.,
           305900., 315900., 325900., 335900., 345900., 355900., 365900., 375900.,
           385900., 395900., 405900., 415900., 425900., 435900., 445900., 455900.,
           465900., 475900., 485900., 495900., 505900., 515900., 525900., 535900.])

  • easting
    (easting)
    float64
    6.9e+03 1.69e+04 ... 3.769e+05

    array([  6900.,  16900.,  26900.,  36900.,  46900.,  56900.,  66900.,  76900.,
            86900.,  96900., 106900., 116900., 126900., 136900., 146900., 156900.,
           166900., 176900., 186900., 196900., 206900., 216900., 226900., 236900.,
           246900., 256900., 266900., 276900., 286900., 296900., 306900., 316900.,
           326900., 336900., 346900., 356900., 366900., 376900.])

• Data variables: (6)
  • basement_topo
    (northing, easting)
    float64
    -6.199e+03 ... -8.133e+03

    n_bytes_per_element :

    1028

    sign_flag :

    2

    shape_e :

    1901

    shape_v :

    2011

    ordering :

    1

    spacing_e :

    200.0

    spacing_v :

    200.0

    x_origin :

    2000.0

    y_origin :

    141000.0

    rotation :

    0.0

    base_value :

    0.0

    data_factor :

    1.0

    map_projection :

    0

    units_x :

    0

    units_y :

    0

    units_z :

    0

    n_valid_points :

    3822911

    grid_min :

    -9373.0

    grid_max :

    -85.0

    grid_median :

    0.0

    grid_mean :

    -6124.91357421875

    grid_variance :

    5270999.66244486

    process_flag :

    0

    array([[-6198.80626797, -6314.1976    , -6346.16559883, ...,
            -9213.5805332 , -9234.41866914, -9289.55720469],
           [-6354.59640117, -6399.13360293, -6320.50480137, ...,
            -9144.74746914, -9142.90706133, -9161.72506445],
           [-6481.59159531, -6430.78919863, -6486.14240254, ...,
            -9065.88639687, -9078.29266875, -9121.70640352],
           ...,
           [-1217.62866726, -1487.03106606, -1539.66719946, ...,
            -7758.9817334 , -8162.7999998 , -8190.46759863],
           [ -762.60108667, -1019.52691563, -1113.25669357, ...,
            -7915.75693223, -8113.40840137, -8170.89066504],
           [ -407.28640803,  -787.09218821,  -940.5566342 , ...,
            -7989.36653242, -8078.67013555, -8133.17440273]], shape=(40, 38))

  • moho_topo
    (northing, easting)
    float64
    -2.767e+04 ... -2.548e+04

    n_bytes_per_element :

    4

    sign_flag :

    2

    shape_e :

    1901

    shape_v :

    2011

    ordering :

    1

    spacing_e :

    200.0

    spacing_v :

    200.0

    x_origin :

    2000.0

    y_origin :

    141000.0

    rotation :

    0.0

    base_value :

    0.0

    data_factor :

    1.0

    map_projection :

    0

    units_x :

    0

    units_y :

    0

    units_z :

    0

    n_valid_points :

    3822911

    grid_min :

    -33038.265625

    grid_max :

    -22185.619140625

    grid_median :

    0.0

    grid_mean :

    -26822.080078125

    grid_variance :

    5140738.63260409

    process_flag :

    0

    array([[-27674.87131016, -27389.37727188, -27118.21926172, ...,
            -22871.305725  , -22645.08870312, -22397.35763359],
           [-27698.96175938, -27408.35757734, -27133.57459141, ...,
            -23047.29887109, -22813.36748984, -22556.99189297],
           [-27741.59617266, -27446.75021016, -27168.88301563, ...,
            -23211.45822109, -22971.30322422, -22707.97822891],
           ...,
           [-32890.81950469, -32671.98336719, -32438.51520703, ...,
            -25370.80920313, -25291.03895313, -25206.62383828],
           [-32913.43191719, -32693.22443359, -32459.83736563, ...,
            -25516.38592031, -25429.54635937, -25337.240425  ],
           [-32927.07117031, -32704.76180469, -32470.96455781, ...,
            -25677.29917969, -25582.00070625, -25480.29128672]],
          shape=(40, 38))

  • gravity_anomaly_no_noise
    (northing, easting)
    float64
    99.08 99.3 100.9 ... 108.4 107.0

    n_bytes_per_element :

    1028

    sign_flag :

    2

    shape_e :

    1901

    shape_v :

    2011

    ordering :

    1

    spacing_e :

    200.0

    spacing_v :

    200.0

    x_origin :

    2000.0

    y_origin :

    141000.0

    rotation :

    0.0

    base_value :

    0.0

    data_factor :

    1.0

    map_projection :

    0

    units_x :

    0

    units_y :

    0

    units_z :

    0

    n_valid_points :

    3822911

    grid_min :

    90.6748046875

    grid_max :

    155.69775390625

    grid_median :

    0.0

    grid_mean :

    115.25214385986328

    grid_variance :

    87.2583089744567

    process_flag :

    0

    array([[ 99.0815248 ,  99.30119297, 100.87978047, ..., 129.26890879,
            130.27280234, 130.73130176],
           [ 98.59668379,  99.25809258, 101.48744785, ..., 128.95925859,
            130.06447988, 130.60332461],
           [ 97.67210547,  98.67830664, 100.74405449, ..., 128.22095352,
            129.35892949, 129.91174082],
           ...,
           [128.74747168, 123.38446191, 123.32262598, ..., 111.70508008,
            109.12466875, 107.44659629],
           [139.02674629, 132.78660293, 132.3670291 , ..., 110.69648105,
            108.57331738, 107.03401445],
           [148.65024492, 139.52451621, 136.74348926, ..., 109.95311074,
            108.37658359, 107.03840918]], shape=(40, 38))

  • gravity_anomaly
    (northing, easting)
    float64
    99.11 99.28 101.0 ... 108.3 106.9

    array([[ 99.10993716,  99.2780383 , 101.01113131, ..., 129.34324964,
            130.14530293, 130.70864534],
           [ 98.75674519,  99.56004511, 101.23890105, ..., 128.83894349,
            130.43214846, 130.34250472],
           [ 97.54306617,  98.86858295, 100.75713172, ..., 128.24607576,
            129.34705549, 129.95543001],
           ...,
           [128.88446291, 123.50464077, 123.47574706, ..., 111.73921047,
            108.9421862 , 107.22506643],
           [139.01720897, 132.8545919 , 132.47092979, ..., 110.59122849,
            108.59302893, 107.09916454],
           [148.64070544, 139.49105054, 136.85364554, ..., 109.9121394 ,
            108.28657782, 106.87372322]], shape=(40, 38))

  • uncert
    (northing, easting)
    float64
    0.2 0.2 0.2 0.2 ... 0.2 0.2 0.2 0.2

    array([[0.2, 0.2, 0.2, ..., 0.2, 0.2, 0.2],
           [0.2, 0.2, 0.2, ..., 0.2, 0.2, 0.2],
           [0.2, 0.2, 0.2, ..., 0.2, 0.2, 0.2],
           ...,
           [0.2, 0.2, 0.2, ..., 0.2, 0.2, 0.2],
           [0.2, 0.2, 0.2, ..., 0.2, 0.2, 0.2],
           [0.2, 0.2, 0.2, ..., 0.2, 0.2, 0.2]], shape=(40, 38))

  • upward
    (northing, easting)
    float64
    10.0 10.0 10.0 ... 10.0 10.0 10.0

    array([[10., 10., 10., ..., 10., 10., 10.],
           [10., 10., 10., ..., 10., 10., 10.],
           [10., 10., 10., ..., 10., 10., 10.],
           ...,
           [10., 10., 10., ..., 10., 10., 10.],
           [10., 10., 10., ..., 10., 10., 10.],
           [10., 10., 10., ..., 10., 10., 10.]], shape=(40, 38))

fig = ptk.plot_grid(
    grid.basement_topo,
    fig_height=10,
    title="True basement model",
    reverse_cpt=True,
    cmap="rain",
    cbar_label="m",
    hist=True,
    frame=["nSWe", "xaf10000", "yaf10000"],
)

fig = ptk.plot_grid(
    grid.moho_topo,
    fig=fig,
    origin_shift="x",
    fig_height=10,
    title="True moho model",
    reverse_cpt=True,
    cmap="rain",
    cbar_label="m",
    hist=True,
    frame=["nSwE", "xaf10000", "yaf10000"],
)

fig = ptk.plot_grid(
    grid.gravity_anomaly,
    fig=fig,
    origin_shift="x",
    fig_height=10,
    title="Observed gravity",
    reverse_cpt=True,
    cmap="viridis",
    cbar_label="mGal",
    hist=True,
    frame=["nSwE", "xaf10000", "yaf10000"],
)

fig.show()

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

Define model domain parameters

To account for edge effects (decreasing gravity towards the edge of prism model), we will use a buffer region so the prism model edge is further away from the inversion domain (the gravity data extent).

# get full region of gravity data
full_region = vd.get_region((grid.easting.values, grid.northing.values))
full_region

(np.float64(6900.0),
 np.float64(376900.0),
 np.float64(145900.0),
 np.float64(535900.0))

# zoom in by 10 km from each side
inversion_region = vd.pad_region(full_region, -10e3)
inversion_region

(np.float64(16900.0),
 np.float64(366900.0),
 np.float64(155900.0),
 np.float64(525900.0))

grav_grid = grid[["gravity_anomaly", "uncert", "upward"]]

# only retain data within the inversion region
grav_grid = grav_grid.sel(
    easting=slice(inversion_region[0], inversion_region[1]),
    northing=slice(inversion_region[2], inversion_region[3]),
)

Observed gravity data

In this scenario, we are treating the area as having no surface topography (surface elevation is flat and equal to the ellipsoid). In this case, there is no terrain mass effect, and therefore the gravity disturbance is equal to the topo-free disturbance.

grav_data = invert4geom.create_data(grav_grid)

print(f"Gravity region (W,E,S,N): {grav_data.region}")
print(f"Gravity spacing: {grav_data.spacing} m")

grav_data

Gravity region (W,E,S,N): (16900.0, 366900.0, 155900.0, 525900.0)
Gravity spacing: 10000.0 m

<xarray.Dataset> Size: 33kB
Dimensions:          (northing: 38, easting: 36)
Coordinates:
  * northing         (northing) float64 304B 1.559e+05 1.659e+05 ... 5.259e+05
  * easting          (easting) float64 288B 1.69e+04 2.69e+04 ... 3.669e+05
Data variables:
    gravity_anomaly  (northing, easting) float64 11kB 99.56 101.2 ... 108.6
    uncert           (northing, easting) float64 11kB 0.2 0.2 0.2 ... 0.2 0.2
    upward           (northing, easting) float64 11kB 10.0 10.0 ... 10.0 10.0
Attributes:
    region:        (16900.0, 366900.0, 155900.0, 525900.0)
    spacing:       10000.0
    buffer_width:  40000.0
    inner_region:  (56900.0, 326900.0, 195900.0, 485900.0)
    dataset_type:  data
    model_type:    prisms
    coord_names:   ('easting', 'northing')

xarray.Dataset

• Dimensions:
  • northing: 38
  • easting: 36
• Coordinates: (2)
  • northing
    (northing)
    float64
    1.559e+05 1.659e+05 ... 5.259e+05

    array([155900., 165900., 175900., 185900., 195900., 205900., 215900., 225900.,
           235900., 245900., 255900., 265900., 275900., 285900., 295900., 305900.,
           315900., 325900., 335900., 345900., 355900., 365900., 375900., 385900.,
           395900., 405900., 415900., 425900., 435900., 445900., 455900., 465900.,
           475900., 485900., 495900., 505900., 515900., 525900.])

  • easting
    (easting)
    float64
    1.69e+04 2.69e+04 ... 3.669e+05

    array([ 16900.,  26900.,  36900.,  46900.,  56900.,  66900.,  76900.,  86900.,
            96900., 106900., 116900., 126900., 136900., 146900., 156900., 166900.,
           176900., 186900., 196900., 206900., 216900., 226900., 236900., 246900.,
           256900., 266900., 276900., 286900., 296900., 306900., 316900., 326900.,
           336900., 346900., 356900., 366900.])

• Data variables: (3)
  • gravity_anomaly
    (northing, easting)
    float64
    99.56 101.2 105.6 ... 110.6 108.6

    array([[ 99.56004511, 101.23890105, 105.5987079 , ..., 127.78634026,
            128.83894349, 130.43214846],
           [ 98.86858295, 100.75713172, 104.67398857, ..., 126.67145025,
            128.24607576, 129.34705549],
           [ 96.98707742,  99.47059045, 102.8264169 , ..., 125.59145588,
            127.40070836, 128.21826281],
           ...,
           [119.83623532, 115.66234054, 119.81503406, ..., 115.62119403,
            112.40428418, 109.9784768 ],
           [123.50464077, 123.47574706, 131.94682596, ..., 115.36890678,
            111.73921047, 108.9421862 ],
           [132.8545919 , 132.47092979, 136.76288088, ..., 113.71432015,
            110.59122849, 108.59302893]], shape=(38, 36))

  • uncert
    (northing, easting)
    float64
    0.2 0.2 0.2 0.2 ... 0.2 0.2 0.2 0.2

    array([[0.2, 0.2, 0.2, ..., 0.2, 0.2, 0.2],
           [0.2, 0.2, 0.2, ..., 0.2, 0.2, 0.2],
           [0.2, 0.2, 0.2, ..., 0.2, 0.2, 0.2],
           ...,
           [0.2, 0.2, 0.2, ..., 0.2, 0.2, 0.2],
           [0.2, 0.2, 0.2, ..., 0.2, 0.2, 0.2],
           [0.2, 0.2, 0.2, ..., 0.2, 0.2, 0.2]], shape=(38, 36))

  • upward
    (northing, easting)
    float64
    10.0 10.0 10.0 ... 10.0 10.0 10.0

    array([[10., 10., 10., ..., 10., 10., 10.],
           [10., 10., 10., ..., 10., 10., 10.],
           [10., 10., 10., ..., 10., 10., 10.],
           ...,
           [10., 10., 10., ..., 10., 10., 10.],
           [10., 10., 10., ..., 10., 10., 10.],
           [10., 10., 10., ..., 10., 10., 10.]], shape=(38, 36))

• Attributes: (7)

  region :

  (16900.0, 366900.0, 155900.0, 525900.0)

  spacing :

  10000.0

  buffer_width :

  40000.0

  inner_region :

  (56900.0, 326900.0, 195900.0, 485900.0)

  dataset_type :

  data

  model_type :

  prisms

  coord_names :

  ('easting', 'northing')

Create “a-priori” basement measurements

# create grid of 36 points
coords = vd.grid_coordinates(
    region=vd.pad_region(inversion_region, -30e3),
    shape=(6, 6),
)
da = vd.make_xarray_grid(coords, data=np.ones_like(coords[0]), data_names="upward")
constraint_points = vd.grid_to_table(da).drop(columns=["upward"])

# sample true topography at these points
constraint_points = invert4geom.sample_grids(
    constraint_points,
    grid.basement_topo,
    "true_upward",
)

constraint_points["upward"] = constraint_points.true_upward

# re-sample depths with uncertainty to emulate measurement errors
# set each points uncertainty equal to 2% of depth
uncert = np.abs(0.02 * constraint_points.upward)
constraint_points.loc[constraint_points.index, "true_uncert"] = uncert

constraint_points = invert4geom.randomly_sample_data(
    seed=0,
    data_df=constraint_points,
    data_col="upward",
    uncert_col="true_uncert",
)

# create weights column
constraint_points["weight"] = 1 / (constraint_points.true_uncert**2)

# create estimated uncertainty column
uncert = np.abs(0.02 * constraint_points.upward)
constraint_points.loc[constraint_points.index, "uncert"] = uncert

constraint_points.head()

	northing	easting	true_upward	upward	true_uncert	weight	uncert
0	185900.0	46900.0	-6209.559082	-6193.944497	124.191182	0.000065	123.878890
1	185900.0	104900.0	-6719.067441	-6736.819871	134.381349	0.000055	134.736397
2	185900.0	162900.0	-7276.991871	-7183.784863	145.539837	0.000047	143.675697
3	185900.0	220900.0	-8420.454391	-8402.788258	168.409088	0.000035	168.055765
4	185900.0	278900.0	-8821.850945	-8916.362853	176.437019	0.000032	178.327257

Create starting basement model

# grid the sampled values using verde
starting_topography_kwargs = dict(
    method="splines",
    region=full_region,
    spacing=grav_data.spacing,
    constraints_df=constraint_points,
    # dampings=np.logspace(-40, 0, 200),
    dampings=None,
    # weights=constraint_points.weight,
)

starting_topography = invert4geom.create_topography(
    **starting_topography_kwargs,
)

_ = ptk.grid_compare(
    grid.basement_topo,
    starting_topography.upward,
    region=inversion_region,
    grid1_name="True topography",
    grid2_name="Starting topography",
    robust=True,
    hist=True,
    inset=False,
    verbose="q",
    title="difference",
    reverse_cpt=True,
    cmap="rain",
    points=constraint_points,
    points_style="x.3c",
)

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

# sample the inverted topography at the constraint points
constraint_points = invert4geom.sample_grids(
    constraint_points,
    starting_topography.upward,
    "starting_topography",
)

rmse = invert4geom.rmse(
    constraint_points.true_upward - constraint_points.starting_topography
)
print(f"RMSE: {rmse:.2f} m")

RMSE: 84.87 m

# create model object
model = invert4geom.create_model(
    zref=constraint_points.upward.mean(),
    density_contrast=2800 - 2300,
    topography=starting_topography,
)
model.inv.plot_model(
    color_by="density",
    zscale=20,
)

Gravity misfit

All inversions in Invert4Geom are based on a gravity misfit, not a gravity anomaly. This means before the inversion, we must create a starting prism model, forward model it’s gravity effect, remove it from the gravity anomaly, and get a gravity misfit.

However, if we know nothing about the starting model, it can simply be a flat layer of zero thickness, as we will use here. In this case, the forward gravity would just be zero so there is no need to perform the forward modelling. The misfit is therefore just equal to the topo-free disturbance.

Forward gravity of starting prism layer

# calculate forward gravity of starting prism layer
grav_data.inv.forward_gravity(model)

_ = ptk.grid_compare(
    grav_data.gravity_anomaly,
    grav_data.forward_gravity,
    grid1_name="Observed gravity",
    grid2_name="Starting gravity",
    robust=True,
    hist=True,
    inset=False,
    verbose="q",
    title="Gravity misfit",
    rmse_in_title=False,
    points=constraint_points,
    points_style="x.3c",
)

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

Regional estimation - constraint point minimization

# use the constraints to find the best regional field
regional_grav_kwargs = dict(
    method="constraints",
    grid_method="eq_sources",
    constraints_df=constraint_points,
    # constraints_weights_column="weight",
    cv=True,
    cv_kwargs=dict(
        n_trials=50,
        damping_limits=(1e-60, 10),
        depth_limits=(100, 1000e3),
        progressbar=False,
        fname="../tmp/bishop_model_regional_sep",
    ),
    # damping=None,
    # depth="default",
    block_size=None,
)

grav_data.inv.regional_separation(
    **regional_grav_kwargs,
)

grav_data.inv.df.describe()

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 1.234691372574397e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 6.358838325841549e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 2.5717393541537776e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 9.25130121831585e-19.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 1.217038357095467e-16.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 1.0744814406688332e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 1.0792494071332609e-16.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 2.212367716133033e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 9.594888696632468e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 7.910748452622797e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 5.446830061638979e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 2.2850622677273476e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 3.1007257377437036e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 7.168256907828392e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 9.262979225994475e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 2.35851449831592e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 6.108639005261266e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T

	northing	easting	gravity_anomaly	uncert	upward	forward_gravity	misfit	reg	res	starting_forward_gravity	starting_misfit	starting_reg	starting_res
count	1368.000000	1368.000000	1368.000000	1.368000e+03	1368.0	1368.000000	1368.000000	1368.000000	1368.000000	1368.000000	1368.000000	1368.000000	1368.000000
mean	340900.000000	191900.000000	115.021219	2.000000e-01	10.0	0.896367	114.124852	114.416236	-0.291384	0.896367	114.124852	114.416236	-0.291384
std	109698.662868	103920.936691	8.668170	8.329718e-17	0.0	40.280643	39.807129	39.790285	5.693573	40.280643	39.807129	39.790285	5.693573
min	155900.000000	16900.000000	91.608025	2.000000e-01	10.0	-59.217044	32.942960	32.821090	-22.503406	-59.217044	32.942960	32.821090	-22.503406
25%	245900.000000	104400.000000	109.730411	2.000000e-01	10.0	-27.678731	80.084974	81.943867	-2.608942	-27.678731	80.084974	81.943867	-2.608942
50%	340900.000000	191900.000000	115.379669	2.000000e-01	10.0	-8.689017	122.087862	122.760979	-0.354759	-8.689017	122.087862	122.760979	-0.354759
75%	435900.000000	279400.000000	120.316522	2.000000e-01	10.0	35.669196	144.293965	142.991692	2.096234	35.669196	144.293965	142.991692	2.096234
max	525900.000000	366900.000000	142.955701	2.000000e-01	10.0	82.655013	179.574375	178.433873	34.071069	82.655013	179.574375	178.433873	34.071069

grav_data.inv.plot_anomalies()

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

Single inversion

Perform a single inversion to experiment with values of stopping criteria.

# setup the inversion
inv = invert4geom.Inversion(
    grav_data,
    model,
    solver_damping=0.01,
    # set stopping criteria
    l2_norm_tolerance=0.5,
    delta_l2_norm_tolerance=1.008,
)

# run the inversion
inv.invert(
    plot_dynamic_convergence=True,
    results_fname="../tmp/bishop_model",
)

inv.stats_df

	iteration	rmse	l2_norm	delta_l2_norm	iter_time_sec
0	0.0	4.279788	2.068765	inf	NaN
1	1.0	1.477773	1.215637	1.701795	0.781548
2	2.0	0.722208	0.849828	1.430450	0.243836
3	3.0	0.447648	0.669065	1.270173	0.281018
4	4.0	0.324995	0.570084	1.173626	0.193301
5	5.0	0.259985	0.509888	1.118057	0.389423
6	6.0	0.220166	0.469219	1.086674	0.191454

inv.plot_inversion_results(
    iters_to_plot=2,
)

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

_ = ptk.grid_compare(
    grid.basement_topo,
    inv.model.topography,
    region=inversion_region,
    grid1_name="True topography",
    grid2_name="Inverted topography",
    robust=True,
    hist=True,
    inset=False,
    verbose="q",
    title="difference",
    reverse_cpt=True,
    cmap="rain",
    points=constraint_points,
    points_style="x.3c",
)

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

Damping parameter cross validation

inv.reinitialize_inversion()

# resample data at 1/2 spacing to include test points for cross-validation
inv.data = invert4geom.add_test_points(inv.data)

damping_cv_obj = inv.optimize_inversion_damping(
    damping_limits=(0.001, 1),
    n_trials=8,
    fname="../tmp/bishop_model_damping_cv",
)
inv.solver_damping

0.0041265208051870905

inv.plot_convergence()

inv.plot_inversion_results(iters_to_plot=2)

_ = ptk.grid_compare(
    grid.basement_topo,
    inv.model.topography,
    grid1_name="True topography",
    grid2_name="Inverted topography",
    robust=True,
    hist=True,
    inset=False,
    title="difference",
    reverse_cpt=True,
    cmap="rain",
    points=constraint_points,
    points_style="x.3c",
)

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

# sample the inverted topography at the constraint points
constraint_points = invert4geom.sample_grids(
    constraint_points,
    inv.model.topography,
    "inverted_topography",
)

rmse = invert4geom.rmse(
    constraint_points.true_upward - constraint_points.inverted_topography
)
print(f"RMSE: {rmse:.2f} m")

RMSE: 129.82 m

Density contrast / zref optimization

Since this optimization uses the inversion error at constraint points, we can’t use the constraint point minimization technique to estimate the regional field since that inherently sets the inversion error at constraints to zero, invalidating the optimization scores.

There are two options for how to get around this issue:

1. use a different regional estimation technique while finding the optimal density contrast and zref values, then use the found optimal values with the constraint point minimization regional estimation technique afterwards.

2. separate the constraints into testing and training sets, so that only the training set is used during the regional separation, and only the testing set is used for scoring the density contrast and zref optimization.

Well just use the 1st option below.

Density optimization

inv.reinitialize_inversion()

# run the optimization for the density contrast
density_optimization_obj = inv.optimize_inversion_zref_density_contrast(
    constraints_df=constraint_points,
    density_contrast_limits=(100, 600),
    n_trials=10,
    regional_grav_kwargs={
        "method": "constant",
        "constant": inv.data.reg.mean(),
    },
    starting_topography=starting_topography,
    plot_scores=True,
    fname="../tmp/bishop_model_density_optimization",
)

Best density_contrast value (600) is at the limit of provided values (600, 100) and thus is likely not a global minimum, expand the range of values tested to ensure the best parameter value is found.
'reg' already a column of `grav_df`, but is being overwritten since calculate_regional_misfit is True

# The optimal value has been saved as the Model's density contrast for future inversions
print(inv.model.density_contrast)

600

Zref optimization

inv.reinitialize_inversion()

# run the optimization for the zref
zref_optimization_obj = inv.optimize_inversion_zref_density_contrast(
    constraints_df=constraint_points,
    zref_limits=(-8e3, 0),
    n_trials=10,
    regional_grav_kwargs={
        "method": "constant",
        "constant": inv.data.reg.mean(),
    },
    starting_topography=starting_topography,
    plot_scores=True,
    fname="../tmp/bishop_model_zref_optimization",
)

'reg' already a column of `grav_df`, but is being overwritten since calculate_regional_misfit is True

# The optimal value has been saved as the model's density contrast for future inversions
print(inv.model.zref)

-6089.837118983269

Redo regional separation and inversion with optimal values

# recreate model with optimal zref and density contrast
model = invert4geom.create_model(
    zref=inv.model.zref,
    density_contrast=inv.model.density_contrast,
    topography=starting_topography,
)

# calculate forward gravity of starting prism layer
grav_data.inv.forward_gravity(model)

# calculate regional gravity
grav_data.inv.regional_separation(
    **regional_grav_kwargs,
)

grav_data.inv.plot_anomalies()

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 1.234691372574397e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 6.358838325841549e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 2.5717393541537776e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 9.25130121831585e-19.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 2.7707044442032168e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 1.861460664836524e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 6.751380185202175e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 6.692725127734375e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

# setup the inversion
optimal_inv = invert4geom.Inversion(
    grav_data,
    model,
    solver_damping=inv.solver_damping,
    # set stopping criteria
    l2_norm_tolerance=0.5,
    delta_l2_norm_tolerance=1.008,
)
optimal_inv.solver_damping, optimal_inv.model.zref, optimal_inv.model.density_contrast

(0.0041265208051870905, -6089.837118983269, 600)

# run the inversion
optimal_inv.invert(
    plot_dynamic_convergence=True,
    results_fname="../tmp/bishop_model_optimal",
)

_ = ptk.grid_compare(
    grid.basement_topo,
    optimal_inv.model.topography,
    region=inversion_region,
    grid1_name="True topography",
    grid2_name="Inverted topography",
    robust=True,
    hist=True,
    inset=False,
    verbose="q",
    title="difference",
    reverse_cpt=True,
    cmap="rain",
    points=constraint_points,
    points_style="x.3c",
)

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

# sample the inverted topography at the constraint points
constraint_points = ptk.sample_grids(
    constraint_points,
    optimal_inv.model.topography,
    "inverted_topography",
)

rmse = ptk.rmse(constraint_points.true_upward - constraint_points.inverted_topography)
print(f"RMSE: {rmse:.2f} m")

RMSE: 121.53 m

Absolute value of inversion error

inversion_error = np.abs(grid.basement_topo - optimal_inv.model.topography)
fig = ptk.plot_grid(
    inversion_error,
    hist=True,
    cmap="thermal",
    title="Absolute value of inversion error",
    robust=True,
    points=constraint_points,
    points_style="x.4c",
    # points_pen="1p",
    points_fill="white",
)
fig.show()

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

# plotting functions for uncertainty results
def uncert_plots(
    results,
    inversion_region,
    spacing,
    true_topography,
    constraints_df=None,
    weight_by=None,
):
    if (weight_by == "constraints") & (constraints_df is None):
        msg = "must provide constraints_df if weighting by constraints"
        raise ValueError(msg)

    stats_ds = invert4geom.merged_stats(
        results=results,
        plot=True,
        constraints_df=constraints_df,
        weight_by=weight_by,
        region=inversion_region,
    )

    try:
        mean = stats_ds.weighted_mean
        stdev = stats_ds.weighted_stdev
    except AttributeError:
        mean = stats_ds.z_mean
        stdev = stats_ds.z_stdev

    _ = ptk.grid_compare(
        true_topography,
        mean,
        region=vd.pad_region(inversion_region, -spacing),
        grid1_name="True topography",
        grid2_name="Inverted topography",
        robust=True,
        hist=True,
        inset=False,
        title="difference",
        reverse_cpt=True,
        cmap="rain",
        points=constraints_df,
        points_style="x.3c",
    )
    _ = ptk.grid_compare(
        np.abs(true_topography - mean),
        stdev,
        region=vd.pad_region(inversion_region, -spacing),
        grid1_name="True error",
        grid2_name="Stochastic uncertainty",
        cmap="thermal",
        robust=True,
        hist=True,
        inset=False,
        title="difference",
        points=constraints_df,
        points_style="x.3c",
        points_fill="white",
    )
    return stats_ds

Uncertainty analysis

# get mean spacing between nearest constraints
mean_constraint_spacing = np.mean(
    vd.median_distance(
        (constraint_points.easting, constraint_points.northing),
        k_nearest=1,
    )
)
mean_constraint_spacing

np.float64(58000.0)

# use optimal eq source parameters for regional separation in uncertainty analysis
# re-load the study from the saved pickle file
with pathlib.Path(f"{regional_grav_kwargs.get('cv_kwargs').get('fname')}.pickle").open(
    "rb"
) as f:
    study = pickle.load(f)
reg_eq_damping = min(study.best_trials, key=lambda t: t.values[0]).params["damping"]
reg_eq_depth = min(study.best_trials, key=lambda t: t.values[0]).params["depth"]

new_regional_grav_kwargs = dict(
    method="constraints",
    grid_method="eq_sources",
    constraints_df=constraint_points,
    damping=reg_eq_damping,
    depth=reg_eq_depth,
    block_size=None,
)

reg_eq_damping, reg_eq_depth

(4.184227553394269e-40, 110158.8963339568)

Damping component

# load study
with pathlib.Path("../tmp/bishop_model_damping_cv_study.pickle").open("rb") as f:
    study = pickle.load(f)

study_df = study.trials_dataframe()
study_df = study_df.sort_values("value")

# calculate zscores of values
study_df["value_zscore"] = sp.stats.zscore(study_df["value"])

# drop outliers (values with zscore > |2|)
study_df2 = study_df[(np.abs(study_df.value_zscore) < 2)]

# pick damping standard deviation based on optimization
stdev = np.log10(study_df2.params_damping).std()
print(f"calculated stdev: {stdev}")
# stdev = 0.4
print(f"using stdev: {stdev}")

calculated stdev: 0.6236538754220373
using stdev: 0.6236538754220373

fig = invert4geom.plot_scores(
    study_df.value,
    study_df.params_damping,
    param_name="Damping",
    logx=True,
    logy=True,
)
ax = fig.axes[0]

best = float(study_df2.params_damping.iloc[0])
upper = float(10 ** (np.log10(best) + stdev))
lower = float(10 ** (np.log10(best) - stdev))

y_lims = ax.get_ylim()
ax.vlines(best, ymin=y_lims[0], ymax=y_lims[1], color="r")
ax.vlines(upper, ymin=y_lims[0], ymax=y_lims[1], label="+/- std")
ax.vlines(lower, ymin=y_lims[0], ymax=y_lims[1])

x_lims = ax.get_xlim()
ax.set_xlim(
    min(x_lims[0], lower),
    max(x_lims[1], upper),
)
ax.legend()
print("best:", best, "\nstd:", stdev, "\n+1std:", upper, "\n-1std:", lower)

best: 0.0041265208051870905
std: 0.6236538754220373
+1std: 0.01734754067697559
-1std: 0.0009815900866133975

solver_dict = {
    "solver_damping": {
        "distribution": "normal",
        "loc": np.log10(optimal_inv.solver_damping),  # mean base 10 exponent
        "scale": stdev,  # standard deviation of base 10 exponent
        "log": True,
    },
}

fname = "../tmp/bishop_model_uncertainty_damping"

# delete files if already exist
for p in pathlib.Path().glob(f"{fname}*"):
    p.unlink(missing_ok=True)

uncert_damping_results = invert4geom.full_workflow_uncertainty_loop(
    optimal_inv,
    fname=fname,
    runs=10,
    parameter_dict=solver_dict,
    regional_grav_kwargs=new_regional_grav_kwargs,
    starting_topography_kwargs=starting_topography_kwargs,
)

stats_ds = uncert_plots(
    uncert_damping_results,
    optimal_inv.data.inner_region,
    optimal_inv.data.spacing,
    grid.basement_topo,
    constraints_df=constraint_points,
    weight_by="constraints",
)

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

Density component

# load study
with pathlib.Path("../tmp/bishop_model_density_optimization_study.pickle").open(
    "rb"
) as f:
    study = pickle.load(f)

study_df = study.trials_dataframe()
study_df = study_df.sort_values("value")

# calculate zscores of values
study_df["value_zscore"] = sp.stats.zscore(study_df["value"])

# drop outliers (values with zscore > |2|)
study_df2 = study_df[(np.abs(study_df.value_zscore) < 2)]

density_stdev = study_df2.params_density_contrast.std()
print(f"calculated stdev: {density_stdev}")

# manually pick a stdev
# density_stdev = 20
print(f"using stdev: {density_stdev}")

calculated stdev: 156.12076877995588
using stdev: 156.12076877995588

fig = invert4geom.plot_scores(
    study.trials_dataframe().value.values,
    study.trials_dataframe().params_density_contrast.values,
    param_name="Density",
    logx=False,
    logy=False,
)
ax = fig.axes[0]

best = study_df2.params_density_contrast.iloc[0]
upper = best + density_stdev
lower = best - density_stdev

y_lims = ax.get_ylim()
ax.vlines(best, ymin=y_lims[0], ymax=y_lims[1], color="r")
ax.vlines(upper, ymin=y_lims[0], ymax=y_lims[1], label="+/- std")
ax.vlines(lower, ymin=y_lims[0], ymax=y_lims[1])

x_lims = ax.get_xlim()
ax.set_xlim(
    min(x_lims[0], lower),
    max(x_lims[1], upper),
)
ax.legend()
print("best:", best, "\nstd:", density_stdev, "\n+1std:", upper, "\n-1std:", lower)

best: 600
std: 156.12076877995588
+1std: 756.1207687799558
-1std: 443.8792312200441

density_dict = {
    "density_contrast": {
        "distribution": "normal",
        "loc": optimal_inv.model.density_contrast,
        "scale": density_stdev,
    },
}

fname = "../tmp/bishop_model_uncertainty_density"

# delete files if already exist
for p in pathlib.Path().glob(f"{fname}*"):
    p.unlink(missing_ok=True)

uncert_density_results = invert4geom.full_workflow_uncertainty_loop(
    optimal_inv,
    fname=fname,
    runs=10,
    parameter_dict=density_dict,
    regional_grav_kwargs=new_regional_grav_kwargs,
    starting_topography_kwargs=starting_topography_kwargs,
)

uncert_plots(
    uncert_density_results,
    optimal_inv.data.inner_region,
    optimal_inv.data.spacing,
    grid.basement_topo,
    constraints_df=constraint_points,
    weight_by="constraints",
)

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

<xarray.Dataset> Size: 122kB
Dimensions:         (northing: 30, easting: 28, runs: 10)
Coordinates:
  * northing        (northing) float64 240B 1.959e+05 2.059e+05 ... 4.859e+05
  * easting         (easting) float64 224B 5.69e+04 6.69e+04 ... 3.269e+05
    top             (northing, easting) float64 7kB -5.893e+03 ... -6.09e+03
    bottom          (northing, easting) float64 7kB -6.09e+03 ... -6.727e+03
  * runs            (runs) <U5 200B 'run_0' 'run_1' 'run_2' ... 'run_8' 'run_9'
Data variables:
    run_num         (runs, northing, easting) float64 67kB -5.893e+03 ... -6....
    z_mean          (northing, easting) float64 7kB -5.899e+03 ... -6.729e+03
    z_stdev         (northing, easting) float64 7kB 15.6 30.93 ... 8.02 9.635
    weighted_mean   (northing, easting) float64 7kB -5.895e+03 ... -6.726e+03
    weighted_stdev  (northing, easting) float64 7kB 12.72 25.47 ... 7.148 7.922
    z_min           (northing, easting) float64 7kB -5.931e+03 ... -6.751e+03
    z_max           (northing, easting) float64 7kB -5.885e+03 ... -6.717e+03

xarray.Dataset

• Dimensions:
  • northing: 30
  • easting: 28
  • runs: 10
• Coordinates: (5)
  • northing
    (northing)
    float64
    1.959e+05 2.059e+05 ... 4.859e+05

    array([195900., 205900., 215900., 225900., 235900., 245900., 255900., 265900.,
           275900., 285900., 295900., 305900., 315900., 325900., 335900., 345900.,
           355900., 365900., 375900., 385900., 395900., 405900., 415900., 425900.,
           435900., 445900., 455900., 465900., 475900., 485900.])

  • easting
    (easting)
    float64
    5.69e+04 6.69e+04 ... 3.269e+05

    array([ 56900.,  66900.,  76900.,  86900.,  96900., 106900., 116900., 126900.,
           136900., 146900., 156900., 166900., 176900., 186900., 196900., 206900.,
           216900., 226900., 236900., 246900., 256900., 266900., 276900., 286900.,
           296900., 306900., 316900., 326900.])

  • top
    (northing, easting)
    float64
    -5.893e+03 -6.036e+03 ... -6.09e+03

    array([[-5893.05367353, -6035.9820001 , -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-5939.91544308, -5976.34724178, -6063.15387732, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-6028.03026961, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
    ...
            -3474.63275716, -3536.25568363, -3236.7158085 , -2919.34600776,
            -3429.9103342 , -4144.68634353, -4487.22707308, -4627.38360431,
            -5132.00411601, -5527.99051213, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-2887.88738922, -2912.82342525, -2866.82098419, -3163.35028307,
            -3364.14883139, -3194.84682407, -2772.06065164, -2897.62139059,
            -3457.0099333 , -3995.85976306, -4175.87254698, -4480.76073251,
            -5058.83022131, -5716.43841009, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-2678.01245034, -2435.99116397, -2704.3566568 , -3097.43506908,
            -3225.05963478, -2585.28220546, -2513.68971247, -2965.78135392,
            -3410.98541181, -3703.95845456, -3822.36211661, -4437.7048813 ,
            -5159.56210803, -5947.038794  , -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898]])

  • bottom
    (northing, easting)
    float64
    -6.09e+03 -6.09e+03 ... -6.727e+03

    array([[-6089.83711898, -6089.83711898, -6174.42248862, -6332.89001396,
            -6497.34858417, -6711.51537336, -6895.23021676, -7064.91323714,
            -7115.27162258, -7174.49840813, -7423.83652719, -7512.43998515,
            -7728.73043042, -7942.47286629, -8147.4163145 , -8396.1133918 ,
            -8503.13222874, -8744.20181638, -8815.58641273, -8886.6909276 ,
            -8920.20824634, -9008.20749321, -9071.60590708, -9121.86138543,
            -9017.41719492, -9173.31738745, -9231.53342531, -9148.5259148 ],
           [-6089.83711898, -6089.83711898, -6089.83711898, -6296.38543032,
            -6549.20215104, -6831.05573114, -6966.65974449, -7140.84690462,
            -7352.58142901, -7451.0085359 , -7683.84901278, -7789.63725722,
            -8018.39095023, -8253.59827852, -8328.7256799 , -8646.25414415,
            -8773.04856101, -8854.41298201, -8920.70545323, -8972.36292521,
            -9092.07452609, -9058.22558834, -9090.56414121, -9222.68231752,
            -9201.63537611, -9269.29246335, -9118.700171  , -9200.85136436],
           [-6089.83711898, -6167.93354442, -6279.55751309, -6434.25650535,
            -6691.93890519, -6921.9179114 , -7168.936825  , -7399.42883493,
            -7523.7842886 , -7725.05514792, -7992.23779661, -8175.65310827,
            -8351.76158765, -8576.48678615, -8585.91052873, -8769.53839481,
            -8878.35042543, -8922.31319734, -8976.88807459, -9088.72720365,
            -9168.44548165, -9100.12688316, -9151.70902392, -9237.568311  ,
    ...
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6184.65194872, -6779.83605882,
            -7261.48528135, -7608.12758247, -7852.52509354, -7896.18893113,
            -7944.64554715, -7914.542837  , -7528.43631642, -6529.97002772,
            -6601.57113546, -6735.62866856, -6566.37612401, -6608.48067501],
           [-6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6526.70598072, -7015.80530154,
            -7502.15684531, -7735.62191401, -7906.67324299, -7956.74141793,
            -7824.02337431, -7636.06935757, -7463.10693438, -6615.29889772,
            -6548.20455196, -6735.03575811, -6779.04025269, -6772.96493273],
           [-6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6833.93181796, -7273.42727586,
            -7702.86768764, -7875.10456676, -7961.90598124, -7965.72328897,
            -7764.50423777, -7335.8038841 , -7233.68709597, -6677.59418177,
            -6363.40780083, -6538.81620937, -6642.29892602, -6727.46228914]])

  • runs
    (runs)
    <U5
    'run_0' 'run_1' ... 'run_8' 'run_9'

    array(['run_0', 'run_1', 'run_2', 'run_3', 'run_4', 'run_5', 'run_6', 'run_7',
           'run_8', 'run_9'], dtype='<U5')

• Data variables: (7)
  • run_num
    (runs, northing, easting)
    float64
    -5.893e+03 -6.036e+03 ... -6.74e+03

    array([[[-5893.05367353, -6035.9820001 , -6174.42248862, ...,
             -9173.31738745, -9231.53342531, -9148.5259148 ],
            [-5939.91544308, -5976.34724178, -6063.15387732, ...,
             -9269.29246335, -9118.700171  , -9200.85136436],
            [-6028.03026961, -6167.93354442, -6279.55751309, ...,
             -9267.63859806, -9208.62584653, -9241.59690738],
            ...,
            [-2990.42857176, -3134.03163634, -3118.24720496, ...,
             -6735.62866856, -6566.37612401, -6608.48067501],
            [-2887.88738922, -2912.82342525, -2866.82098419, ...,
             -6735.03575811, -6779.04025269, -6772.96493273],
            [-2678.01245034, -2435.99116397, -2704.3566568 , ...,
             -6538.81620937, -6642.29892602, -6727.46228914]],
    
           [[-5885.22181973, -6049.62688652, -6182.38346217, ...,
             -9161.87833141, -9227.63723666, -9132.03131157],
            [-5888.91877603, -5949.70197333, -6044.11016091, ...,
             -9273.7557765 , -9072.47000007, -9189.05972222],
            [-5923.38402618, -6071.00280147, -6210.28408169, ...,
             -9260.82396886, -9193.98493905, -9238.42481053],
    ...
             -6774.16528607, -6605.04589111, -6643.96120854],
            [-2748.87576617, -2796.03024186, -2802.420896  , ...,
             -6742.16603667, -6784.81234451, -6771.32526475],
            [-2541.92419467, -2509.47638645, -2611.07560066, ...,
             -6578.21954198, -6634.39822868, -6720.23924075]],
    
           [[-5926.22391006, -5992.55371319, -6130.98293175, ...,
             -9206.97876483, -9256.53587986, -9191.04295986],
            [-6063.63143062, -6040.70065529, -6108.25561406, ...,
             -9282.2108371 , -9203.22570136, -9239.90782117],
            [-6302.18258336, -6393.25148032, -6457.5589169 , ...,
             -9288.05010001, -9251.44253927, -9263.50587722],
            ...,
            [-3018.98319873, -3182.79117383, -3148.46206005, ...,
             -6665.91280443, -6566.54091335, -6568.51112582],
            [-2916.0967437 , -2961.94484182, -2883.05381519, ...,
             -6675.69413928, -6764.46278933, -6748.93158193],
            [-2702.12255712, -2457.40425237, -2708.09880843, ...,
             -6480.07424394, -6656.45437059, -6739.58908848]]],
          shape=(10, 30, 28))

  • z_mean
    (northing, easting)
    float64
    -5.899e+03 ... -6.729e+03

    array([[-5898.62791249, -6031.05786837, -6165.91086856, -6329.91855376,
            -6497.47239171, -6711.27444831, -6896.71356893, -7066.8295966 ,
            -7112.63852614, -7176.65539101, -7421.4016992 , -7512.08214217,
            -7727.80727321, -7939.8472351 , -8148.96215429, -8398.34384397,
            -8500.19672309, -8745.1830741 , -8813.0629287 , -8887.49161405,
            -8920.06981502, -9005.55010072, -9071.30844817, -9125.41539608,
            -9015.65483732, -9177.9600941 , -9239.48401591, -9153.47394581],
           [-5951.46808106, -5983.0477925 , -6067.4571264 , -6297.8960467 ,
            -6549.03929707, -6833.48472306, -6969.52146319, -7139.11483578,
            -7354.58406553, -7450.86928058, -7681.83080267, -7788.85997081,
            -8016.75225207, -8253.28502129, -8327.19532159, -8646.28275607,
            -8771.54281461, -8851.50537692, -8921.58483348, -8967.37911813,
            -9090.37559688, -9058.31554068, -9089.14491983, -9223.76296121,
            -9204.69401301, -9277.47818289, -9116.75958045, -9207.9355623 ],
           [-6058.07132394, -6185.9063345 , -6297.54149703, -6450.9068141 ,
            -6703.68513241, -6933.93412971, -7180.04558082, -7405.90161506,
            -7524.47223044, -7725.4382504 , -7989.20590191, -8174.07777568,
            -8347.36450985, -8573.55799131, -8584.32984736, -8765.97438115,
            -8874.48199216, -8922.56612662, -8973.92875828, -9085.95088092,
            -9164.64370376, -9097.55995114, -9149.67488709, -9238.02214148,
    ...
            -3463.59924596, -3526.67712782, -3245.76862229, -2954.86090799,
            -3439.31201831, -4147.17201724, -4491.74038686, -4630.62941866,
            -5122.81223508, -5524.54075977, -6183.5836641 , -6785.45907883,
            -7265.06355266, -7613.19720256, -7859.7557974 , -7903.83587073,
            -7960.53474523, -7923.35681769, -7519.9718882 , -6530.32773663,
            -6584.00155316, -6725.68569987, -6571.25781088, -6605.035404  ],
           [-2868.99012518, -2907.81309173, -2862.31044294, -3142.81998107,
            -3338.61066339, -3178.15207695, -2793.97484475, -2925.18102283,
            -3458.18391912, -3995.86470505, -4175.0907359 , -4478.84845354,
            -5053.14090018, -5718.5664542 , -6526.15299395, -7021.03493789,
            -7505.3662226 , -7738.32507588, -7911.73923128, -7962.82876004,
            -7833.76486558, -7645.12854119, -7458.12964007, -6612.34111347,
            -6536.26455153, -6719.71914871, -6778.82749175, -6767.43615647],
           [-2661.43280553, -2458.68260383, -2692.30689235, -3050.93607614,
            -3182.5140138 , -2582.11476611, -2542.09385783, -2968.53050252,
            -3401.90275191, -3702.03653896, -3824.83162554, -4430.32174496,
            -5161.70357988, -5955.45421849, -6839.24156011, -7277.66609478,
            -7707.40834954, -7875.34289299, -7964.49127218, -7962.26285176,
            -7773.16089613, -7346.94043992, -7229.12008066, -6668.67915858,
            -6358.61700571, -6532.98750071, -6642.14146274, -6729.08518521]])

  • z_stdev
    (northing, easting)
    float64
    15.6 30.93 30.28 ... 8.02 9.635

    array([[ 15.6026113 ,  30.92880435,  30.27633584,  34.52505424,
             14.04753871,   6.20568593,   7.5647268 ,   5.96939738,
              3.05979684,   6.2495183 ,  13.48188451,  22.21459809,
             28.39516715,  11.26682337,   5.68018341,   5.73807953,
             15.29912443,  11.77651173,   3.85190378,  10.89186857,
              9.69349816,   6.36254506,   2.17566505,   7.37348176,
             47.5641012 ,  33.30437934,  33.54198715,  42.5442686 ],
           [113.81825713,  59.85147821,  35.67983121,  19.95815801,
             31.0817649 ,  28.45679172,  35.66582699,  32.01912539,
              6.83990796,   7.33002267,  11.93626005,   7.88595325,
              8.51049457,  13.26245944,   7.72487034,  13.97818963,
              3.59834309,   6.05387748,  18.73709383,   9.79966819,
             25.42657579,  18.07643386,   4.8370135 ,   4.79721202,
             17.46117875,  17.80157917,  65.5626989 ,  36.7966906 ],
           [252.9952737 , 217.74970709, 167.26829359, 135.18216928,
            119.41972187, 100.73223905,  71.91872304,  46.00520252,
             31.48172825,   8.23412174,   4.68044358,   6.99819939,
              4.43716983,  17.24509533,  13.05245387,  15.80637673,
              9.74647801,  18.94220505,  21.91906206,  28.15673044,
             30.39836617,  19.57668349,  14.59200731,   5.8186682 ,
    ...
            130.14118094, 124.33959737,   7.95539722, 120.68770096,
             49.03380594,  69.77463535,  68.74331455,   7.03097927,
             39.8366677 ,  39.27902991,   8.41880652,  17.43815272,
             38.08855456,  54.39720137,  58.45585103,  73.38118777,
             88.43153461, 116.51932031,  31.43231982, 118.71360423,
            139.24266008,  54.72608261,  31.22506209,  39.67668372],
           [ 92.54056931,  91.9994773 ,  72.63181032, 139.3385302 ,
            191.19996343, 108.21660882,  45.44670975,  60.65467464,
             28.16958871,  85.84072854,  13.41595196,  38.94897446,
             35.367419  ,  18.06347933,  17.49495377,  38.46500035,
             26.44516761,  35.78804185,  40.25568588,  49.31073691,
             63.88853337,  78.40872921,  14.27636289,  85.17032763,
            112.32947753,  33.69526   ,   7.50390866,   9.68593244],
           [ 87.13234487,  56.60653664,  90.32593832, 203.19891519,
            226.49456499,  20.67657789,  53.47389766,  27.87485395,
             74.33316671,  47.23173562,  40.01958024,  41.91178649,
             16.06100022,  43.45312262,  65.15717647,  63.51989012,
             11.21875701,   1.79894607,   8.7036536 ,  40.55595308,
             27.06917747,  42.61692441,   9.88321992,  49.43987289,
             87.97905255,  47.98598414,   8.02043276,   9.63491605]])

  • weighted_mean
    (northing, easting)
    float64
    -5.895e+03 -6.04e+03 ... -6.726e+03

    array([[-5894.51697946, -6039.65260797, -6174.09922762, -6339.62711304,
            -6501.18720247, -6709.52651546, -6894.69911647, -7068.05421263,
            -7113.09336535, -7177.11420876, -7425.22296936, -7518.31192894,
            -7735.93580015, -7942.9989493 , -8150.33593897, -8399.83214195,
            -8496.02957713, -8748.4098266 , -8813.96536367, -8890.37421764,
            -8922.50417142, -9007.27474183, -9070.78463984, -9123.68128425,
            -9002.28580352, -9168.79160389, -9230.61650635, -9141.7030926 ],
           [-5919.73394217, -5966.35798907, -6057.34837844, -6292.40847006,
            -6540.27210666, -6825.73017324, -6959.37708171, -7130.00282653,
            -7356.27488198, -7452.7971267 , -7685.15325089, -7790.31986793,
            -8018.91685298, -8256.98833633, -8326.02033138, -8650.1881072 ,
            -8772.28981905, -8853.09398248, -8926.66789954, -8969.65347617,
            -9097.5861488 , -9063.16423444, -9089.8368159 , -9224.68791887,
            -9199.83110629, -9273.25118948, -9098.37198891, -9197.77194887],
           [-5987.9274288 , -6125.32963244, -6251.18783524, -6413.38068326,
            -6670.54723631, -6906.02667486, -7160.38248741, -7393.38895153,
            -7515.70371323, -7723.14298001, -7989.901202  , -8175.94472158,
            -8346.88365519, -8578.12271335, -8587.80653876, -8770.37312777,
            -8877.06231458, -8927.73973862, -8980.06940392, -9093.83525443,
            -9173.23943013, -9102.76206949, -9153.67551345, -9239.60406699,
    ...
            -3426.04300599, -3489.55082103, -3244.82932285, -2992.44437296,
            -3453.81324345, -4126.76146888, -4472.15529029, -4632.44473406,
            -5133.82075005, -5535.38814286, -6185.87000772, -6780.75750078,
            -7254.54426857, -7597.94262669, -7843.60321347, -7883.4977338 ,
            -7936.23863941, -7890.61238776, -7511.83374087, -6562.69431785,
            -6623.07978921, -6740.58862999, -6579.25270847, -6616.10835585],
           [-2840.80178827, -2880.35041589, -2843.27576133, -3102.72370088,
            -3281.65176252, -3145.15331042, -2808.0842362 , -2943.9080117 ,
            -3449.59645943, -3970.72170674, -4171.53812349, -4489.93049395,
            -5062.91034062, -5723.55249066, -6521.65301628, -7010.15795916,
            -7498.19418508, -7728.19826013, -7900.48775565, -7949.09141301,
            -7816.13500438, -7623.03507407, -7456.9670293 , -6635.77356395,
            -6567.73524764, -6728.28235033, -6780.81772267, -6769.58348703],
           [-2634.57055027, -2458.31549316, -2668.26241533, -2990.28714371,
            -3112.72791858, -2580.61976968, -2557.54698379, -2960.0545961 ,
            -3379.28918651, -3688.33237577, -3836.55981578, -4442.04855441,
            -5166.29102789, -5943.39410308, -6821.19583097, -7259.68142084,
            -7704.92584405, -7875.74490215, -7962.04172326, -7951.01617713,
            -7766.05930402, -7335.29337227, -7227.65582775, -6682.21002849,
            -6383.00300268, -6546.38161454, -6639.90478335, -6726.43885772]])

  • weighted_stdev
    (northing, easting)
    float64
    12.72 25.47 23.97 ... 7.148 7.922

    array([[ 12.71925264,  25.46620323,  23.97298911,  28.89957491,
             11.89512238,   5.49461091,   6.06205859,   5.59234464,
              2.77982502,   5.78052749,  11.28354107,  18.86230189,
             24.22651489,   9.01783259,   5.12946093,   5.47288013,
             14.06984838,  10.53101126,   2.88817571,   9.48786813,
              8.10847801,   4.95428824,   1.86256211,   5.40006768,
             41.73843772,  27.14688604,  26.19905467,  34.91103929],
           [ 94.11970965,  49.28016471,  29.59270979,  16.47459492,
             26.48527145,  23.37601534,  30.00182841,  28.04634731,
              6.41381431,   6.04926825,   9.8123929 ,   6.37051075,
              6.71618153,  11.35957489,   7.05698046,  12.3243672 ,
              2.97292797,   4.63742705,  16.19692103,   7.13858307,
             21.58172799,  15.28040446,   3.72597842,   4.49469008,
             14.19781193,  13.06143773,  57.04365454,  29.52489328],
           [207.47839186, 180.58169478, 137.75422697, 111.03258962,
             98.78570733,  82.89776147,  58.39349578,  37.34189374,
             26.83504985,   7.02528018,   4.14914009,   5.81506418,
              4.38635282,  14.7255648 ,  10.63806993,  12.95587381,
              7.70567708,  16.21361215,  17.91888933,  23.58897101,
             25.50558721,  15.82245615,  11.78309259,   5.16952085,
    ...
            110.12381841, 106.24503076,   6.897337  , 110.45320117,
             42.52826109,  58.90828968,  57.07985465,   6.76611734,
             32.19818195,  32.34479295,   6.7785432 ,  13.65358951,
             31.5245188 ,  45.1646418 ,  47.88931674,  60.78008969,
             71.49292737,  97.22051669,  28.63327204, 100.43023174,
            115.18649369,  44.29299113,  27.15652403,  32.91603925],
           [ 81.21904995,  77.96594428,  60.17397339, 118.932841  ,
            163.9747438 ,  94.47326165,  45.27912984,  57.70804363,
             24.21385139,  72.62989876,  11.20774564,  32.51052929,
             28.57146959,  15.8108085 ,  14.79024215,  31.88839995,
             21.54629383,  30.08971241,  33.23093984,  40.50599015,
             52.30403662,  65.19658064,  13.04502892,  71.37469119,
             93.33640526,  25.84741755,   6.45863624,   7.78013902],
           [ 77.03496902,  56.91158761,  75.91344818, 177.33955625,
            200.25346412,  18.8209513 ,  56.46807927,  23.69508152,
             64.63487583,  40.11288277,  34.53104811,  33.98115603,
             14.36776766,  35.43933501,  53.93131556,  53.48548297,
              8.28844681,   1.80744061,   6.89181029,  35.37987331,
             20.86472982,  34.93231417,   9.276773  ,  39.87464347,
             73.62612284,  39.68780265,   7.14808263,   7.92168461]])

  • z_min
    (northing, easting)
    float64
    -5.931e+03 ... -6.751e+03

    array([[-5930.99409023, -6067.1716641 , -6195.62351903, -6373.67750914,
            -6519.67788679, -6721.82301884, -6915.05647733, -7073.62058423,
            -7116.01219555, -7188.09914185, -7433.46168398, -7542.9549737 ,
            -7763.71663424, -7950.46138125, -8159.57443044, -8408.85059337,
            -8527.30146803, -8761.81226593, -8816.34191753, -8906.26265349,
            -8935.72067592, -9010.63534847, -9075.98292304, -9146.19204394,
            -9102.69047647, -9257.08426476, -9326.44578718, -9253.2607112 ],
           [-6212.27232893, -6121.55108596, -6147.44042948, -6344.38566825,
            -6616.31693765, -6901.11650456, -7046.81060594, -7201.03104105,
            -7365.87148342, -7461.06949102, -7695.10444488, -7800.34561055,
            -8027.57508625, -8271.57252727, -8347.82956776, -8662.40829006,
            -8774.01580145, -8856.22478331, -8951.79680118, -8975.0454339 ,
            -9121.49979049, -9086.11047043, -9095.35166848, -9230.26173574,
            -9245.70551618, -9327.38891428, -9243.99362628, -9297.78973771],
           [-6648.58018597, -6684.26924948, -6685.06293227, -6764.48418081,
            -6977.36577632, -7166.38698837, -7350.93644773, -7516.44114459,
            -7590.62121476, -7742.21220708, -7994.22472341, -8180.17384197,
            -8353.7536094 , -8589.35492218, -8602.30029027, -8780.53314751,
            -8881.75210255, -8951.82212659, -8999.32997217, -9121.17726923,
            -9197.99572464, -9123.27355476, -9166.88853217, -9246.74428943,
    ...
            -3762.00817211, -3809.52603054, -3260.83705096, -3131.81250583,
            -3497.30829466, -4303.48943771, -4649.70283835, -4641.93798151,
            -5160.42065695, -5575.5962712 , -6193.97537747, -6828.70847382,
            -7352.26452714, -7736.78086175, -7997.21974322, -8070.31416464,
            -8171.28854686, -8186.5466245 , -7577.49097229, -6706.37119493,
            -6751.17616735, -6791.3226462 , -6622.93338501, -6655.98342575],
           [-3074.85267708, -3122.91624932, -3032.84070894, -3459.36584846,
            -3774.88322686, -3420.28295653, -2871.6178301 , -3018.43945864,
            -3520.8601392 , -4188.86916839, -4205.98620969, -4526.09908233,
            -5093.60364809, -5747.08890891, -6566.10684782, -7106.45982462,
            -7568.53807371, -7815.92434466, -8003.33415717, -8077.60502758,
            -7980.89176855, -7819.69667289, -7476.03871229, -6732.24058607,
            -6676.36253937, -6742.16603667, -6787.07746648, -6775.29088505],
           [-2855.24645534, -2532.76191208, -2899.66867233, -3503.66266076,
            -3681.38283064, -2615.42259749, -2640.35233844, -3032.6572198 ,
            -3566.32939154, -3807.9673867 , -3873.59971249, -4474.02191533,
            -5185.40605375, -6054.26356547, -6990.2659671 , -7415.72127048,
            -7738.79381336, -7878.57843521, -7986.22802913, -8045.25562181,
            -7843.30934558, -7437.60997699, -7242.1699889 , -6727.00851896,
            -6479.16948907, -6592.11800547, -6656.45437059, -6751.03244657]])

  • z_max
    (northing, easting)
    float64
    -5.885e+03 ... -6.717e+03

    array([[-5885.22181973, -5961.6864598 , -6092.55849976, -6253.78105358,
            -6465.90783563, -6703.64907342, -6887.17128025, -7052.41489334,
            -7106.98334819, -7168.65020657, -7393.48010513, -7463.74533429,
            -7668.16954706, -7912.51400657, -8138.17363548, -8390.49176999,
            -8478.42744713, -8725.04987726, -8802.85957707, -8865.17715513,
            -8897.49525324, -8989.62893792, -9068.76096142, -9119.60270676,
            -8950.45832255, -9136.84435672, -9204.19749268, -9099.89990432],
           [-5807.68874031, -5909.02082856, -6026.48388524, -6271.20332302,
            -6506.09975794, -6795.64622099, -6926.32567503, -7094.11208613,
            -7341.57016201, -7433.27468369, -7655.19791577, -7769.44815715,
            -7994.93683824, -8226.35569566, -8317.62183419, -8621.16751776,
            -8763.05297234, -8835.96972255, -8882.58915757, -8939.70318637,
            -9037.63265738, -9017.69983216, -9076.94031229, -9211.55107701,
            -9185.12051453, -9264.18280176, -9023.0944976 , -9167.82713871],
           [-5743.86977763, -5902.9243247 , -6084.74221959, -6283.56207716,
            -6549.6092477 , -6807.12950494, -7091.12678859, -7347.68840088,
            -7480.09388885, -7714.4794105 , -7978.69286266, -8160.31429564,
            -8339.34893945, -8538.5009837 , -8553.06940244, -8731.33772095,
            -8851.88371253, -8882.21148061, -8922.06710955, -9025.17946979,
            -9100.72234058, -9049.51693863, -9113.86592111, -9228.25660039,
    ...
            -3305.82445051, -3377.47295861, -3235.44089935, -2706.02272979,
            -3330.21460355, -4068.34740971, -4410.72089791, -4620.40269936,
            -5031.32989697, -5432.64035843, -6162.88282929, -6770.07281185,
            -7214.8392182 , -7544.89895467, -7786.54575325, -7809.00754592,
            -7857.25156321, -7774.22294739, -7462.6839968 , -6264.43844591,
            -6268.85094073, -6596.88278828, -6504.20304821, -6514.1079959 ],
           [-2748.87576617, -2796.03024186, -2753.65196844, -2972.52503672,
            -3110.3375593 , -3036.10199329, -2718.27925381, -2809.96318789,
            -3420.72642058, -3899.8404435 , -4154.1214316 , -4390.18540388,
            -4968.48597118, -5681.46648018, -6497.79862857, -6977.97413591,
            -7470.69832948, -7693.86017973, -7862.75851055, -7902.60111753,
            -7756.07734577, -7551.11693274, -7432.72258385, -6418.68198625,
            -6283.90982916, -6636.28244391, -6764.46278933, -6747.88076759],
           [-2541.92419467, -2319.83008541, -2561.20308963, -2801.54916073,
            -2874.1442064 , -2536.74458857, -2473.53699049, -2931.4459901 ,
            -3307.63519929, -3644.68561297, -3737.99979714, -4331.77196038,
            -5132.08814789, -5909.08565315, -6753.77627899, -7197.40003783,
            -7697.61263401, -7871.80318741, -7956.44035478, -7899.05553521,
            -7747.24987044, -7310.25772056, -7210.60888399, -6549.66889703,
            -6159.90656725, -6424.45559797, -6632.15267466, -6716.95823963]])

Zref component

# load study
with pathlib.Path("../tmp/bishop_model_zref_optimization_study.pickle").open("rb") as f:
    study = pickle.load(f)

study_df = study.trials_dataframe()
study_df = study_df.sort_values("value")

# calculate zscores of values
study_df["value_zscore"] = sp.stats.zscore(study_df["value"])

# drop outliers (values with zscore > |2|)
study_df2 = study_df[(np.abs(study_df.value_zscore) < 2)]

zref_stdev = study_df2.params_zref.std()
print(f"calculated stdev: {zref_stdev}")

# manually pick a stdev
# zref_stdev = 20
print(f"using stdev: {zref_stdev}")

calculated stdev: 1296.6547255564465
using stdev: 1296.6547255564465

fig = invert4geom.plot_scores(
    study.trials_dataframe().value.values,
    study.trials_dataframe().params_zref.values,
    param_name="Reference level",
    logx=False,
    logy=False,
)
ax = fig.axes[0]

best = study_df2.params_zref.iloc[0]
upper = best + zref_stdev
lower = best - zref_stdev

y_lims = ax.get_ylim()
ax.vlines(best, ymin=y_lims[0], ymax=y_lims[1], color="r")
ax.vlines(upper, ymin=y_lims[0], ymax=y_lims[1], label="+/- std")
ax.vlines(lower, ymin=y_lims[0], ymax=y_lims[1])

x_lims = ax.get_xlim()
ax.set_xlim(
    min(x_lims[0], lower),
    max(x_lims[1], upper),
)
ax.legend()
print("best:", best, "\nstd:", zref_stdev, "\n+1std:", upper, "\n-1std:", lower)

best: -6089.837118983269
std: 1296.6547255564465
+1std: -4793.182393426822
-1std: -7386.491844539715

zref_dict = {
    "zref": {
        "distribution": "normal",
        "loc": optimal_inv.model.zref,
        "scale": zref_stdev,
    },
}

fname = "../tmp/bishop_model_uncertainty_zref"

# delete files if already exist
for p in pathlib.Path().glob(f"{fname}*"):
    p.unlink(missing_ok=True)

uncert_zref_results = invert4geom.full_workflow_uncertainty_loop(
    optimal_inv,
    fname=fname,
    runs=10,
    parameter_dict=zref_dict,
    regional_grav_kwargs=new_regional_grav_kwargs,
    starting_topography_kwargs=starting_topography_kwargs,
)

uncert_plots(
    uncert_zref_results,
    optimal_inv.data.inner_region,
    optimal_inv.data.spacing,
    grid.basement_topo,
    constraints_df=constraint_points,
    weight_by="constraints",
)

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

<xarray.Dataset> Size: 122kB
Dimensions:         (northing: 30, easting: 28, runs: 10)
Coordinates:
  * northing        (northing) float64 240B 1.959e+05 2.059e+05 ... 4.859e+05
  * easting         (easting) float64 224B 5.69e+04 6.69e+04 ... 3.269e+05
    top             (northing, easting) float64 7kB -5.892e+03 ... -6.253e+03
    bottom          (northing, easting) float64 7kB -6.253e+03 ... -6.726e+03
  * runs            (runs) <U5 200B 'run_0' 'run_1' 'run_2' ... 'run_8' 'run_9'
Data variables:
    run_num         (runs, northing, easting) float64 67kB -5.892e+03 ... -6....
    z_mean          (northing, easting) float64 7kB -5.89e+03 ... -6.729e+03
    z_stdev         (northing, easting) float64 7kB 3.565 8.422 ... 1.722 2.357
    weighted_mean   (northing, easting) float64 7kB -5.89e+03 ... -6.729e+03
    weighted_stdev  (northing, easting) float64 7kB 3.564 8.347 ... 1.727 2.367
    z_min           (northing, easting) float64 7kB -5.896e+03 ... -6.733e+03
    z_max           (northing, easting) float64 7kB -5.884e+03 ... -6.726e+03

xarray.Dataset

• Dimensions:
  • northing: 30
  • easting: 28
  • runs: 10
• Coordinates: (5)
  • northing
    (northing)
    float64
    1.959e+05 2.059e+05 ... 4.859e+05

    array([195900., 205900., 215900., 225900., 235900., 245900., 255900., 265900.,
           275900., 285900., 295900., 305900., 315900., 325900., 335900., 345900.,
           355900., 365900., 375900., 385900., 395900., 405900., 415900., 425900.,
           435900., 445900., 455900., 465900., 475900., 485900.])

  • easting
    (easting)
    float64
    5.69e+04 6.69e+04 ... 3.269e+05

    array([ 56900.,  66900.,  76900.,  86900.,  96900., 106900., 116900., 126900.,
           136900., 146900., 156900., 166900., 176900., 186900., 196900., 206900.,
           216900., 226900., 236900., 246900., 256900., 266900., 276900., 286900.,
           296900., 306900., 316900., 326900.])

  • top
    (northing, easting)
    float64
    -5.892e+03 ... -6.253e+03

    array([[-5891.82953288, -6038.76818522, -6177.77868283, -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ],
           [-5926.17085755, -5968.39078703, -6058.11718921, -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ],
           [-5999.39938517, -6142.08743925, -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
    ...
            -3460.60673989, -3525.144402  , -3235.89560395, -2926.76639535,
            -3434.16447578, -4138.34043852, -4480.25989448, -4628.41080038,
            -5134.41489981, -5531.97186638, -6185.61617358, -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ],
           [-2879.91250644, -2902.53470604, -2856.29998001, -3147.5455163 ,
            -3347.98086694, -3185.50714745, -2772.7471106 , -2899.76905403,
            -3455.74990059, -3987.75036021, -4174.27802111, -4484.00823857,
            -5061.80391285, -5718.90501566, -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ],
           [-2670.34749999, -2425.86971631, -2691.39999247, -3080.59814376,
            -3207.86600666, -2581.72118804, -2512.4228843 , -2963.7054155 ,
            -3405.56356252, -3699.33900254, -3826.51978905, -4441.27567379,
            -5161.80769672, -5943.43952799, -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ]])

  • bottom
    (northing, easting)
    float64
    -6.253e+03 ... -6.726e+03

    array([[-6252.7764982 , -6252.7764982 , -6252.7764982 , -6335.49707329,
            -6499.64116522, -6712.1392358 , -6895.05558349, -7063.33794354,
            -7117.251905  , -7176.53090526, -7425.17934101, -7515.04436347,
            -7731.40774856, -7944.0430039 , -8148.59098262, -8395.64446092,
            -8504.78583106, -8743.9147327 , -8817.56393051, -8887.9793994 ,
            -8922.50072029, -9009.91433376, -9071.50505011, -9119.64965358,
            -9016.24821828, -9168.39127578, -9224.57041418, -9143.13160637],
           [-6252.7764982 , -6252.7764982 , -6252.7764982 , -6293.83655016,
            -6545.2566853 , -6826.04578836, -6963.5706126 , -7139.92257098,
            -7351.14350964, -7452.81207004, -7684.42578857, -7791.86762123,
            -8019.55787354, -8254.11112612, -8330.41313058, -8646.14992672,
            -8772.26919812, -8856.0660118 , -8922.01903907, -8975.52439071,
            -9093.98578558, -9060.7132078 , -9091.90933411, -9221.68840872,
            -9198.65949951, -9264.09431064, -9114.99965498, -9194.93111847],
           [-6252.7764982 , -6252.7764982 , -6259.7876956 , -6417.91425051,
            -6678.54364128, -6910.53391795, -7159.77641487, -7392.59647677,
            -7521.92039175, -7724.43977099, -7991.75721678, -8175.08310521,
            -8351.63365009, -8575.25521298, -8587.45798689, -8770.10013977,
            -8879.43090109, -8923.57108239, -8980.3102014 , -9090.80722621,
            -9170.89913859, -9103.02710548, -9154.15368052, -9236.68284458,
    ...
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6777.08145744,
            -7257.05526122, -7601.87546969, -7844.4676996 , -7889.03726112,
            -7933.53124937, -7900.73815587, -7523.97373335, -6547.0778874 ,
            -6615.96197249, -6740.17801321, -6571.64274368, -6613.32091576],
           [-6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6523.18512262, -7012.29082335,
            -7498.54272358, -7732.59040282, -7902.82905076, -7950.49667649,
            -7818.1078134 , -7628.57204197, -7458.08146815, -6627.04921421,
            -6559.10095585, -6737.43236614, -6777.00143395, -6772.01685186],
           [-6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6252.7764982 , -6252.7764982 ,
            -6252.7764982 , -6252.7764982 , -6825.24417219, -7268.10338241,
            -7699.6797601 , -7875.40321934, -7960.37847195, -7962.96942316,
            -7760.00284153, -7335.10522738, -7231.10117729, -6684.68498911,
            -6374.49562973, -6543.06150214, -6642.17064593, -6726.37031963]])

  • runs
    (runs)
    <U5
    'run_0' 'run_1' ... 'run_8' 'run_9'

    array(['run_0', 'run_1', 'run_2', 'run_3', 'run_4', 'run_5', 'run_6', 'run_7',
           'run_8', 'run_9'], dtype='<U5')

• Data variables: (7)
  • run_num
    (runs, northing, easting)
    float64
    -5.892e+03 ... -6.729e+03

    array([[[-5891.82953288, -6038.76818522, -6177.77868283, ...,
             -9168.39127578, -9224.57041418, -9143.13160637],
            [-5926.17085755, -5968.39078703, -6058.11718921, ...,
             -9264.09431064, -9114.99965498, -9194.93111847],
            [-5999.39938517, -6142.08743925, -6259.7876956 , ...,
             -9263.85041867, -9204.30117301, -9236.21812392],
            ...,
            [-2984.18554988, -3125.57683645, -3108.65906523, ...,
             -6740.17801321, -6571.64274368, -6613.32091576],
            [-2879.91250644, -2902.53470604, -2856.29998001, ...,
             -6737.43236614, -6777.00143395, -6772.01685186],
            [-2670.34749999, -2425.86971631, -2691.39999247, ...,
             -6543.06150214, -6642.17064593, -6726.37031963]],
    
           [[-5888.2117388 , -6043.04612972, -6176.83636617, ...,
             -9172.17029165, -9234.21944877, -9144.26969593],
            [-5929.20637409, -5971.97431309, -6060.00826889, ...,
             -9275.37108828, -9105.80128808, -9201.1903953 ],
            [-6002.51118087, -6145.20436496, -6264.74687717, ...,
             -9268.75969703, -9208.73461427, -9244.48975753],
    ...
             -6750.72479121, -6572.0914681 , -6616.18271313],
            [-2887.53859381, -2911.71177984, -2865.0572411 , ...,
             -6735.89305326, -6797.88574025, -6782.72771745],
            [-2675.825123  , -2433.2950019 , -2698.29838478, ...,
             -6554.12728371, -6640.91054128, -6728.98378367]],
    
           [[-5893.13973363, -6038.25960285, -6177.98207098, ...,
             -9164.38370492, -9212.22386675, -9143.78908142],
            [-5924.27701911, -5964.32120064, -6054.30815272, ...,
             -9246.94704991, -9134.56379157, -9188.64250973],
            [-5997.25595721, -6138.08106882, -6255.41012795, ...,
             -9256.46700606, -9200.60816681, -9225.0183543 ],
            ...,
            [-2980.74247965, -3121.28402981, -3104.24308011, ...,
             -6737.18285219, -6570.81793641, -6613.57060253],
            [-2876.92003384, -2898.52404086, -2852.32380214, ...,
             -6735.9129167 , -6769.61481819, -6769.85766783],
            [-2668.86199113, -2423.18207666, -2688.74982221, ...,
             -6541.25560615, -6644.03573695, -6729.13265251]]],
          shape=(10, 30, 28))

  • z_mean
    (northing, easting)
    float64
    -5.89e+03 -6.044e+03 ... -6.729e+03

    array([[-5890.06000801, -6044.11697969, -6177.60705823, -6340.16699046,
            -6500.11542965, -6711.86298641, -6894.99685297, -7068.70402545,
            -7114.03705961, -7178.36459066, -7425.04670583, -7517.46442139,
            -7732.54376378, -7945.33743354, -8149.71457322, -8399.16610917,
            -8503.34868098, -8747.55196966, -8815.6875975 , -8890.49162562,
            -8923.46554811, -9009.08504149, -9072.6750976 , -9123.16952155,
            -9015.9463952 , -9171.05079318, -9229.65376391, -9145.08579478],
           [-5928.87702847, -5971.32308142, -6059.66785453, -6295.70715393,
            -6546.26677186, -6828.80437336, -6963.52302977, -7136.04957709,
            -7355.69026888, -7452.25530708, -7686.38300676, -7792.15613321,
            -8021.67004785, -8255.56422824, -8332.46446306, -8646.58081595,
            -8775.79866215, -8854.15782701, -8926.15557886, -8973.87556977,
            -9095.17332283, -9062.0769549 , -9093.64033588, -9221.66616941,
            -9202.43613544, -9268.27849396, -9115.49661658, -9199.34090696],
           [-6003.85448823, -6143.9588895 , -6263.34094997, -6421.93425385,
            -6678.71336985, -6912.31397168, -7161.74481078, -7395.23890001,
            -7519.51735894, -7725.49069211, -7991.72143466, -8177.08726041,
            -8351.65347194, -8577.59353438, -8588.52447659, -8771.7394842 ,
            -8878.59882088, -8926.91310772, -8978.59084813, -9092.80187794,
            -9169.73679769, -9104.74797879, -9153.5154118 , -9240.07668867,
    ...
            -3461.84618055, -3525.98561482, -3236.4701375 , -2927.212217  ,
            -3434.64950089, -4138.93732338, -4480.94536468, -4628.870263  ,
            -5137.08608826, -5532.49768819, -6185.845536  , -6780.3999    ,
            -7257.76014255, -7602.28074329, -7846.5679152 , -7887.42416587,
            -7936.00255965, -7901.13949202, -7523.57903794, -6547.64605759,
            -6617.91402699, -6743.21075169, -6571.83771803, -6614.69012667],
           [-2881.93240278, -2904.79815927, -2858.39935192, -3149.25866715,
            -3349.21468444, -3186.35813387, -2773.33105406, -2900.22900135,
            -3456.23824551, -3988.32212154, -4175.00224447, -4485.44294893,
            -5062.22262051, -5721.24182407, -6526.00384591, -7012.70471653,
            -7500.04245574, -7733.7548065 , -7902.46852719, -7953.45966683,
            -7816.8544801 , -7629.14659305, -7460.81996401, -6627.58238043,
            -6563.29466279, -6736.54351955, -6782.47057679, -6775.51361548],
           [-2672.07191793, -2427.92845137, -2693.24885458, -3081.99460422,
            -3208.83701838, -2582.31965715, -2512.74831414, -2963.88362614,
            -3405.77071115, -3699.64945621, -3827.2336029 , -4442.00835581,
            -5164.94757424, -5942.64511459, -6828.82842567, -7266.96035852,
            -7703.45225563, -7875.10281904, -7963.60564533, -7959.65607122,
            -7764.51065145, -7333.74704048, -7233.43973404, -6683.64802023,
            -6375.92986047, -6546.76224059, -6642.60611734, -6728.51660814]])

  • z_stdev
    (northing, easting)
    float64
    3.565 8.422 0.8927 ... 1.722 2.357

    array([[ 3.56485571,  8.42202767,  0.89266679,  6.79197548,  1.96734935,
             5.14698784,  4.53634316,  9.26509645, 11.50358041,  6.09711227,
             2.27924076,  2.98326788,  3.39037118,  1.74586574,  2.42234003,
             7.70289725, 18.16754258,  8.610411  , 11.69634345,  2.76896622,
             6.79392868,  7.42882819,  3.25197262,  8.40405606, 19.17957675,
             6.78286826, 16.42274185,  2.52696935],
           [ 5.37095295,  7.24746369,  5.44795558,  5.0658046 ,  1.83022407,
             5.54577151,  3.30957325, 15.48296715, 10.90712276,  5.31580567,
             4.06513318,  6.44174559,  2.42766326,  5.07311858,  7.38283756,
             6.55878534,  6.42761651,  7.76588533,  7.77268063, 12.95532834,
             3.81160073,  1.82261207,  3.7104508 ,  4.83447585,  8.47068944,
            19.14939812, 16.50068604, 10.70108275],
           [ 8.63590093,  5.93756915,  8.29104117,  8.60504434,  2.01589478,
             2.86275577,  4.95842665,  8.66653554,  8.38178499,  1.33724931,
             1.1603625 ,  6.19287691,  3.54686976, 12.69335709,  1.18598718,
             6.15164796,  2.8563599 ,  7.90859577,  4.90310864,  5.68461051,
             2.02791345,  2.35818186,  3.14745776, 10.11300881,  3.18790696,
             9.02087147,  7.69685972, 14.48386779],
           [ 1.435639  ,  5.17808258,  7.72133622,  4.22834863, 11.66976271,
             4.92277695,  5.61375072,  1.00080875,  1.85814178,  8.63705172,
    ...
             1.19940834,  7.08858345, 16.24727159,  1.72111457,  8.17732933,
             2.3903678 ,  8.98742283,  5.33833789],
           [ 5.34808547,  6.27028953,  6.23846711,  5.07459116,  3.540208  ,
             1.93860209,  0.80673426,  0.54137255,  0.61562394,  0.71180365,
             1.05221207,  1.03677436,  5.82783797,  1.90060439,  1.76067248,
             7.22503094,  1.80509411,  0.69190656,  6.84437208,  5.82685447,
             9.12464684,  2.89595822,  3.37014461,  2.82332762,  8.07289672,
             6.79519495,  1.70019929,  1.99695099],
           [ 5.05688475,  6.20341843,  5.96580876,  4.71128642,  2.93542399,
             1.32522781,  0.77428224,  1.19773942,  1.22192794,  0.98245713,
             0.80908724,  2.44234344,  1.09607641,  4.2401679 ,  6.35300488,
             1.48659145,  3.42125995,  4.2793135 ,  4.92033526,  4.80750873,
             5.34752809,  5.69825116, 13.36716305,  2.41036401, 10.51795072,
             0.76760123, 12.88933306,  6.38065484],
           [ 3.49572722,  4.87684897,  4.56865439,  3.18982121,  1.54976813,
             0.972739  ,  2.0718151 ,  2.6340188 ,  2.62037569,  2.22363143,
             1.42410745,  1.09672401,  4.53369719,  3.11031997,  6.01165573,
            10.88115274, 10.29147138,  2.05315454,  3.91686008, 16.79686265,
            10.00850647, 14.17501344,  4.644418  ,  7.35732698,  2.1908701 ,
             6.35877239,  1.72201132,  2.35718844]])

  • weighted_mean
    (northing, easting)
    float64
    -5.89e+03 -6.044e+03 ... -6.729e+03

    array([[-5890.15041588, -6043.9645336 , -6177.62387451, -6340.03637236,
            -6500.16306478, -6712.00231291, -6895.11771242, -7068.52025065,
            -7114.32489727, -7178.52539786, -7425.10326212, -7517.43377047,
            -7732.46324042, -7945.36439014, -8149.77450331, -8398.99624629,
            -8503.8324333 , -8747.35663835, -8815.99202209, -8890.51019728,
            -8923.64841699, -9009.28191889, -9072.75886668, -9122.97764893,
            -9016.46338639, -9170.89450763, -9229.25036332, -9145.05700122],
           [-5928.76810784, -5971.15851391, -6059.5455395 , -6295.59005988,
            -6546.23686144, -6828.67964984, -6963.61153546, -7136.44192967,
            -7355.4403428 , -7452.39505381, -7686.29732604, -7792.33062358,
            -8021.6739048 , -8255.43758125, -8332.65850439, -8646.40498551,
            -8775.67211023, -8854.35355992, -8925.99703389, -8974.21665114,
            -9095.08012296, -9062.10855987, -9093.72926707, -9221.53546567,
            -9202.24896156, -9267.78773933, -9115.94341786, -9199.09534523],
           [-6003.68949882, -6143.82371857, -6263.15055246, -6421.74546048,
            -6678.66468335, -6912.25530238, -7161.62613605, -7395.02998818,
            -7519.72810534, -7725.50650746, -7991.69037836, -8176.93733101,
            -8351.74904731, -8577.26553819, -8588.53058272, -8771.58802429,
            -8878.66994757, -8926.73453688, -8978.70858658, -9092.66692789,
            -9169.69140916, -9104.78771855, -9153.59664682, -9239.83437849,
    ...
            -3461.76234453, -3525.94265316, -3236.45914359, -2927.21833828,
            -3434.65631396, -4138.93429104, -4480.9266413 , -4628.84479456,
            -5136.98024521, -5532.44799235, -6185.81099576, -6780.23581831,
            -7257.7187977 , -7602.29157698, -7846.40123398, -7887.57082309,
            -7935.77545028, -7901.21740989, -7523.66621127, -6547.70697046,
            -6617.70890639, -6743.0604421 , -6571.81689595, -6614.66668133],
           [-2881.81681927, -2904.65268592, -2858.25821138, -3149.14811996,
            -3349.14880877, -3186.33615571, -2773.34336656, -2900.25915746,
            -3456.26860348, -3988.34366089, -4175.00528716, -4485.40850579,
            -5062.19631948, -5721.16902234, -6525.85332097, -7012.7352734 ,
            -7499.96661925, -7733.86769265, -7902.59889668, -7953.37457554,
            -7816.99008399, -7629.3008292 , -7460.47744903, -6627.64333204,
            -6563.04404346, -6736.53725312, -6782.16985957, -6775.38327667],
           [-2671.99898541, -2427.8191937 , -2693.14497254, -3081.92412916,
            -3208.81048636, -2582.33995862, -2512.8039751 , -2963.95470765,
            -3405.84144954, -3699.70927051, -3827.26634153, -4442.02871078,
            -5164.88867485, -5942.72659074, -6828.71197305, -7267.25082726,
            -7703.20772855, -7875.15634073, -7963.56655941, -7960.08963184,
            -7764.2903838 , -7334.12256742, -7233.34708627, -6683.84267189,
            -6375.91132354, -6546.63198839, -6642.6420903 , -6728.53347971]])

  • weighted_stdev
    (northing, easting)
    float64
    3.564 8.347 0.8916 ... 1.727 2.367

    array([[ 3.56385622,  8.3465085 ,  0.89162509,  6.73810423,  1.98598687,
             5.17507642,  4.56634283,  9.20370364, 11.49678524,  6.16127817,
             2.30001889,  2.95668662,  3.38205999,  1.7573582 ,  2.45961988,
             7.66132164, 18.25537856,  8.57106435, 11.72616616,  2.77960653,
             6.86464727,  7.45881385,  3.29821116,  8.3670094 , 19.30490133,
             6.75584189, 16.39764388,  2.50375295],
           [ 5.33216049,  7.21518107,  5.42620071,  5.04615192,  1.81245329,
             5.51905569,  3.32762392, 15.47759344, 10.8606721 ,  5.33366778,
             4.03994986,  6.48631859,  2.4215851 ,  5.0690567 ,  7.47780677,
             6.59135959,  6.37852079,  7.76816262,  7.717914  , 13.00205142,
             3.80477785,  1.85240244,  3.7661798 ,  4.8662871 ,  8.42580995,
            19.16745639, 16.63013059, 10.65554443],
           [ 8.56626493,  5.91507335,  8.25566077,  8.55809149,  2.01330676,
             2.84297598,  4.94462553,  8.64544102,  8.37511459,  1.34240786,
             1.16817852,  6.17959254,  3.57332079, 12.71649476,  1.19143045,
             6.14659955,  2.85405081,  7.87151148,  4.89078173,  5.66862275,
             2.05819315,  2.38322392,  3.15264996, 10.08829478,  3.21769767,
             9.01975449,  7.65212102, 14.47026436],
           [ 1.43269968,  5.15508521,  7.68312097,  4.19307526, 11.60954205,
             4.90994577,  5.63290963,  0.99804523,  1.84578448,  8.63127712,
    ...
             1.21267781,  7.10015104, 16.27574958,  1.70923279,  8.17460521,
             2.37792568,  8.96062909,  5.28964957],
           [ 5.32986084,  6.25344515,  6.22436917,  5.06299312,  3.52976734,
             1.92858175,  0.79904224,  0.54551735,  0.61919026,  0.70723666,
             1.04332293,  1.034787  ,  5.77658065,  1.90419509,  1.75028527,
             7.19095583,  1.79799865,  0.69215601,  6.83095837,  5.82448522,
             9.11526776,  2.91682876,  3.37899461,  2.82610958,  8.07163622,
             6.75987881,  1.68897961,  1.97610151],
           [ 5.03537619,  6.1826849 ,  5.94795575,  4.69566916,  2.92129386,
             1.31315117,  0.78353138,  1.21548751,  1.23972994,  0.99806242,
             0.81011547,  2.41639726,  1.09552291,  4.1995222 ,  6.33115728,
             1.48903493,  3.40502272,  4.32452751,  4.94508644,  4.76522492,
             5.35266047,  5.73864583, 13.37266559,  2.42371908, 10.48439473,
             0.77579499, 12.83891921,  6.33695229],
           [ 3.47276075,  4.85313569,  4.54849814,  3.17306176,  1.53592202,
             0.98750081,  2.09460796,  2.65732039,  2.64426715,  2.24724803,
             1.44413711,  1.11136728,  4.48493595,  3.11616552,  5.96649908,
            10.91926283, 10.25959095,  2.06245777,  3.8833205 , 16.81949148,
             9.95800452, 14.21960194,  4.61770759,  7.37555623,  2.16683618,
             6.31448609,  1.72668017,  2.36727029]])

  • z_min
    (northing, easting)
    float64
    -5.896e+03 ... -6.733e+03

    array([[-5895.73550378, -6065.15865186, -6179.09578467, -6356.3634018 ,
            -6504.39296841, -6721.22949242, -6904.08966377, -7089.16929479,
            -7130.63194865, -7191.0202251 , -7430.40003087, -7524.98621647,
            -7739.00248594, -7948.83266687, -8155.70982649, -8416.80437922,
            -8536.95581563, -8766.93062001, -8835.53188252, -8895.64435727,
            -8938.48344169, -9022.40073684, -9080.53988941, -9141.88891075,
            -9053.41119832, -9186.18987385, -9263.1027547 , -9151.54807838],
           [-5941.88956557, -5987.70730727, -6072.64060908, -6306.9569229 ,
            -6551.36671574, -6840.39788489, -6969.21762076, -7156.51174823,
            -7378.91785588, -7461.25056516, -7695.8228873 , -7804.3190403 ,
            -8027.09547106, -8265.54164077, -8349.76659922, -8656.42297736,
            -8791.51270811, -8866.17118287, -8944.68232804, -8996.86804685,
            -9102.96793322, -9066.80046542, -9102.86374336, -9228.19630377,
            -9221.8982613 , -9303.91593506, -9149.19350891, -9223.0007716 ],
           [-6026.02362508, -6157.76046461, -6281.6696852 , -6441.97356683,
            -6683.03610789, -6919.27722408, -7170.9458159 , -7412.38677882,
            -7530.53282193, -7728.03708999, -7993.43301068, -8190.03244147,
            -8358.8944124 , -8600.8111493 , -8590.78319527, -8784.50320199,
            -8882.68972241, -8944.81132719, -8984.89633266, -9105.11269949,
            -9171.52592316, -9110.08583397, -9158.66200561, -9261.70369578,
    ...
            -3469.5265093 , -3530.45592188, -3238.55086798, -2928.36194563,
            -3435.89540382, -4140.70019431, -4483.43804552, -4630.50287742,
            -5152.42802606, -5534.86848214, -6190.4986353 , -6796.2670174 ,
            -7261.86627578, -7603.35748579, -7860.62058052, -7895.81235105,
            -7953.79876034, -7906.36424666, -7528.91452974, -6551.2639258 ,
            -6632.5365851 , -6758.99918525, -6576.33633598, -6620.06486152],
           [-2893.29363346, -2918.39793623, -2871.35314002, -3159.58415906,
            -3355.91780805, -3189.72469802, -2775.15779057, -2903.19528556,
            -3459.24712974, -3990.8249355 , -4176.6485776 , -4492.18271262,
            -5063.87572109, -5732.38254214, -6538.80442122, -7015.0038711 ,
            -7507.35237119, -7742.71717031, -7911.75774551, -7965.54878937,
            -7825.51866701, -7639.52030336, -7483.41662274, -6631.21549854,
            -6584.72299655, -6737.69306977, -6809.58020275, -6790.3080777 ],
           [-2680.41960897, -2439.07727087, -2703.56896621, -3089.36235208,
            -3212.75658236, -2584.7672241 , -2517.41920204, -2969.4762681 ,
            -3411.3740771 , -3704.61514438, -3830.70419557, -4444.69049126,
            -5176.9250948 , -5947.92495849, -6842.72740859, -7284.76382083,
            -7724.47338406, -7879.10889047, -7973.3689055 , -7985.86333693,
            -7786.17613896, -7356.29982876, -7243.544645  , -6695.12724279,
            -6381.90637159, -6561.45751371, -6645.54319621, -6732.97619897]])

  • z_max
    (northing, easting)
    float64
    -5.884e+03 ... -6.726e+03

    array([[-5884.37431145, -6038.2380292 , -6176.24341169, -6334.5489708 ,
            -6497.82233827, -6705.54923349, -6887.97568016, -7058.44392982,
            -7091.46453684, -7172.3321457 , -7421.17482818, -7514.90423551,
            -7727.92728982, -7943.60101752, -8147.74470572, -8391.83800785,
            -8474.48201806, -8738.34286234, -8794.79936797, -8887.97493726,
            -8915.87767887, -8996.94460206, -9069.91928633, -9114.18714838,
            -8988.96961567, -9163.37484678, -9207.55061089, -9142.96555469],
           [-5924.27701911, -5963.43741122, -6053.29344896, -6289.95654537,
            -6545.02224506, -6823.14164249, -6959.48793539, -7107.82865139,
            -7343.57132106, -7443.17852415, -7682.25038864, -7783.95840714,
            -8019.55787354, -8248.48973372, -8325.52438632, -8634.65904945,
            -8770.39027282, -8838.93472794, -8919.23226295, -8951.88321778,
            -9090.24963186, -9060.60389195, -9090.37935467, -9212.39863813,
            -9194.27730103, -9238.6458656 , -9094.63914413, -9187.91828937],
           [-5997.25595721, -6136.94794389, -6254.04476182, -6413.09661219,
            -6675.93509758, -6909.85967804, -7156.20889885, -7384.78346257,
            -7503.81087615, -7724.19942539, -7989.52830116, -8169.13644098,
            -8346.78388261, -8556.87801019, -8587.45798689, -8762.79651656,
            -8872.92907365, -8918.60628867, -8968.23648153, -9085.5762887 ,
            -9164.72769735, -9102.5542663 , -9147.77111121, -9226.9874192 ,
    ...
            -3457.4896307 , -3524.07173668, -3235.82451466, -2926.73115242,
            -3434.10941297, -4138.34043852, -4480.01096212, -4627.62293049,
            -5132.82988063, -5529.85883334, -6183.8898443 , -6773.11084344,
            -7255.77991784, -7601.494995  , -7838.02027209, -7876.20464125,
            -7924.24353121, -7897.95803284, -7517.56805566, -6543.81482404,
            -6607.18481146, -6735.97047971, -6569.87930356, -6613.32091576],
           [-2876.42762677, -2897.42356594, -2851.08933801, -3143.63871312,
            -3346.19448202, -3185.26850828, -2772.65841117, -2899.19343519,
            -3455.1456146 , -3987.50167856, -4174.27802111, -4483.83202332,
            -5060.78566284, -5718.46764523, -6519.31706708, -7010.72289633,
            -7496.18988249, -7729.43721474, -7894.41719569, -7949.63792871,
            -7806.51163389, -7622.72011493, -7443.06979208, -6624.72848743,
            -6551.74623307, -6735.03310482, -6768.9461874 , -6769.59016376],
           [-2668.86199113, -2422.95270825, -2688.34408023, -3078.88630758,
            -3207.5569524 , -2581.48750759, -2510.60367956, -2960.56351107,
            -3402.55697748, -3697.22372723, -3825.94178483, -4441.147041  ,
            -5161.73928485, -5937.8106514 , -6823.18069401, -7250.85011066,
            -7691.42986735, -7871.57314664, -7960.17096556, -7929.16639419,
            -7753.18331514, -7311.39456326, -7228.1688583 , -6672.34894105,
            -6374.30165328, -6541.2020508 , -6640.33565726, -6726.37031963]])

Constraints component

fname = "../tmp/bishop_model_uncertainty_constraints"

# delete files if already exist
for p in pathlib.Path().glob(f"{fname}*"):
    p.unlink(missing_ok=True)

uncert_constraints_results = invert4geom.full_workflow_uncertainty_loop(
    optimal_inv,
    fname=fname,
    runs=10,
    sample_constraints=True,
    constraints_df=constraint_points,
    regional_grav_kwargs=new_regional_grav_kwargs,
    starting_topography_kwargs=starting_topography_kwargs,
)

uncert_plots(
    uncert_constraints_results,
    optimal_inv.data.inner_region,
    optimal_inv.data.spacing,
    grid.basement_topo,
    constraints_df=constraint_points,
    weight_by="constraints",
)

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

<xarray.Dataset> Size: 122kB
Dimensions:         (northing: 30, easting: 28, runs: 10)
Coordinates:
  * northing        (northing) float64 240B 1.959e+05 2.059e+05 ... 4.859e+05
  * easting         (easting) float64 224B 5.69e+04 6.69e+04 ... 3.269e+05
    top             (northing, easting) float64 7kB -5.85e+03 ... -6.09e+03
    bottom          (northing, easting) float64 7kB -6.09e+03 ... -6.694e+03
  * runs            (runs) <U5 200B 'run_0' 'run_1' 'run_2' ... 'run_8' 'run_9'
Data variables:
    run_num         (runs, northing, easting) float64 67kB -5.85e+03 ... -6.7...
    z_mean          (northing, easting) float64 7kB -5.897e+03 ... -6.705e+03
    z_stdev         (northing, easting) float64 7kB 99.45 107.2 ... 54.95 61.82
    weighted_mean   (northing, easting) float64 7kB -5.897e+03 ... -6.713e+03
    weighted_stdev  (northing, easting) float64 7kB 90.02 97.62 ... 53.79 59.04
    z_min           (northing, easting) float64 7kB -6.071e+03 ... -6.804e+03
    z_max           (northing, easting) float64 7kB -5.7e+03 ... -6.586e+03

xarray.Dataset

• Dimensions:
  • northing: 30
  • easting: 28
  • runs: 10
• Coordinates: (5)
  • northing
    (northing)
    float64
    1.959e+05 2.059e+05 ... 4.859e+05

    array([195900., 205900., 215900., 225900., 235900., 245900., 255900., 265900.,
           275900., 285900., 295900., 305900., 315900., 325900., 335900., 345900.,
           355900., 365900., 375900., 385900., 395900., 405900., 415900., 425900.,
           435900., 445900., 455900., 465900., 475900., 485900.])

  • easting
    (easting)
    float64
    5.69e+04 6.69e+04 ... 3.269e+05

    array([ 56900.,  66900.,  76900.,  86900.,  96900., 106900., 116900., 126900.,
           136900., 146900., 156900., 166900., 176900., 186900., 196900., 206900.,
           216900., 226900., 236900., 246900., 256900., 266900., 276900., 286900.,
           296900., 306900., 316900., 326900.])

  • top
    (northing, easting)
    float64
    -5.85e+03 -6.005e+03 ... -6.09e+03

    array([[-5850.25377309, -6004.70932235, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-5850.0647763 , -5898.96142511, -5995.63439427, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-5893.43571938, -6036.86705879, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
    ...
            -3475.48576386, -3547.1021114 , -3265.75667054, -2963.93330079,
            -3479.42399391, -4193.20167702, -4541.7962652 , -4693.48722251,
            -5205.15527981, -5605.97861532, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-2897.78670058, -2917.86592784, -2869.79366132, -3161.13383604,
            -3363.59794891, -3205.62945177, -2798.44411315, -2932.34525714,
            -3494.57950021, -4033.81267346, -4222.82889484, -4533.46950328,
            -5111.705554  , -5765.01512097, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-2698.48682459, -2448.68442529, -2708.95582907, -3094.73144157,
            -3221.69813391, -2597.04666368, -2531.93980725, -2987.89155692,
            -3434.89408205, -3732.35249267, -3858.91912412, -4472.04763823,
            -5186.4256986 , -5957.85161711, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898]])

  • bottom
    (northing, easting)
    float64
    -6.09e+03 -6.09e+03 ... -6.694e+03

    array([[-6089.83711898, -6089.83711898, -6150.16470535, -6315.90298504,
            -6481.65545577, -6692.15909793, -6869.75288866, -7030.2828565 ,
            -7069.83060946, -7118.98050487, -7359.67595298, -7447.39801004,
            -7666.89933508, -7888.3006012 , -8109.05346058, -8379.01022213,
            -8510.12850433, -8779.87783369, -8876.67222386, -8970.40215606,
            -9019.22230578, -9113.28281267, -9172.10951543, -9207.93636666,
            -9077.23566953, -9203.73323926, -9228.08710833, -9111.24729123],
           [-6089.83711898, -6089.83711898, -6089.83711898, -6237.4583404 ,
            -6494.0653252 , -6779.9663734 , -6917.91688318, -7092.63880431,
            -7307.26526178, -7406.76694828, -7641.07449468, -7752.57194472,
            -7990.64367951, -8240.12019554, -8332.9178279 , -8672.165631  ,
            -8820.89174293, -8925.46802715, -9013.30666018, -9080.19214863,
            -9210.72584021, -9177.36599676, -9200.49733628, -9315.53204463,
            -9267.94368721, -9305.08575379, -9117.88200927, -9168.98728815],
           [-6089.83711898, -6089.83711898, -6160.66644345, -6326.89410448,
            -6594.25962912, -6836.37033357, -7096.80200179, -7340.5757718 ,
            -7478.87070329, -7694.78890058, -7975.59107747, -8174.75980255,
            -8366.9482453 , -8611.41814216, -8640.82753868, -8844.01124464,
            -8971.02860009, -9032.58253401, -9100.84762865, -9221.64142467,
            -9304.02980759, -9229.9362722 , -9268.84872912, -9334.18018933,
    ...
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6262.04554619, -6855.16059478,
            -7332.56977809, -7672.78953175, -7909.73019754, -7943.93296691,
            -7982.02208221, -7939.02375065, -7553.16340155, -6564.84335065,
            -6628.98119708, -6744.07683424, -6564.53490891, -6595.82845933],
           [-6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6566.62711032, -7047.13309705,
            -7527.40571566, -7754.15332142, -7920.29044019, -7966.38316841,
            -7831.1896823 , -7639.87597272, -7470.86010918, -6632.99265355,
            -6562.7967393 , -6732.14533287, -6765.04044965, -6748.63093815],
           [-6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6826.99567104, -7253.36862481,
            -7677.1151252 , -7844.58808897, -7929.08886842, -7932.45371389,
            -7739.97845997, -7318.26775284, -7221.76638398, -6675.40032289,
            -6365.230511  , -6529.70908278, -6619.54664441, -6694.47060771]])

  • runs
    (runs)
    <U5
    'run_0' 'run_1' ... 'run_8' 'run_9'

    array(['run_0', 'run_1', 'run_2', 'run_3', 'run_4', 'run_5', 'run_6', 'run_7',
           'run_8', 'run_9'], dtype='<U5')

• Data variables: (7)
  • run_num
    (runs, northing, easting)
    float64
    -5.85e+03 -6.005e+03 ... -6.75e+03

    array([[[-5850.25377309, -6004.70932235, -6150.16470535, ...,
             -9203.73323926, -9228.08710833, -9111.24729123],
            [-5850.0647763 , -5898.96142511, -5995.63439427, ...,
             -9305.08575379, -9117.88200927, -9168.98728815],
            [-5893.43571938, -6036.86705879, -6160.66644345, ...,
             -9306.09168573, -9214.86534738, -9217.14677596],
            ...,
            [-2988.13265939, -3129.65012767, -3114.7345709 , ...,
             -6744.07683424, -6564.53490891, -6595.82845933],
            [-2897.78670058, -2917.86592784, -2869.79366132, ...,
             -6732.14533287, -6765.04044965, -6748.63093815],
            [-2698.48682459, -2448.68442529, -2708.95582907, ...,
             -6529.70908278, -6619.54664441, -6694.47060771]],
    
           [[-5849.62723253, -5985.27376155, -6109.64619287, ...,
             -8984.35022932, -9060.03359549, -9005.67493221],
            [-5894.52050391, -5922.80427167, -5996.92191858, ...,
             -9092.70745731, -8950.46102044, -9053.43632724],
            [-5979.12394041, -6104.62051323, -6204.00903368, ...,
             -9111.13622603, -9053.97894638, -9096.05645362],
    ...
             -6789.24598205, -6529.39122249, -6474.89685245],
            [-2903.57314997, -2934.09990553, -2896.47181078, ...,
             -6769.16176071, -6727.61181111, -6629.89776588],
            [-2705.72612699, -2470.70281104, -2745.82923435, ...,
             -6558.83748179, -6584.30217718, -6585.83938447]],
    
           [[-5925.97676056, -6038.43681158, -6150.77306272, ...,
             -9148.93984145, -9226.43758699, -9155.0884432 ],
            [-5942.67598099, -5957.87491553, -6028.16912743, ...,
             -9281.21528864, -9113.97399973, -9178.62346487],
            [-5997.74584835, -6119.55051005, -6224.46012876, ...,
             -9313.91160521, -9206.1112171 , -9187.34984598],
            ...,
            [-2983.55181271, -3138.37466509, -3134.38016802, ...,
             -6795.6279028 , -6645.31936973, -6704.29107974],
            [-2871.85425667, -2905.58606567, -2870.91542808, ...,
             -6812.98038631, -6848.77027725, -6833.4322589 ],
            [-2656.02654768, -2419.90090528, -2695.99071373, ...,
             -6632.47424156, -6699.38877026, -6749.94203428]]],
          shape=(10, 30, 28))

  • z_mean
    (northing, easting)
    float64
    -5.897e+03 ... -6.705e+03

    array([[-5896.63872274, -6044.91536798, -6186.13592754, -6349.37589489,
            -6516.3395287 , -6732.93270886, -6920.72791883, -7095.02823502,
            -7149.17149508, -7212.07415181, -7465.38963068, -7558.26505992,
            -7777.73132685, -7991.55607398, -8196.42223507, -8443.10448789,
            -8544.33517173, -8780.1696577 , -8841.75320582, -8903.03162295,
            -8925.93220946, -9003.66674813, -9058.00236289, -9101.66439238,
            -8990.56659278, -9143.62247231, -9199.69244017, -9115.56009847],
           [-5928.54264805, -5968.00180525, -6056.09379715, -6291.41585811,
            -6544.94921035, -6830.84409502, -6971.88866107, -7153.03199277,
            -7374.97414377, -7480.15543925, -7717.88569828, -7826.38435178,
            -8055.74121434, -8289.34899173, -8359.71908778, -8672.1108557 ,
            -8790.84951534, -8865.29867731, -8925.41189492, -8969.24982175,
            -9084.2070237 , -9046.09477855, -9073.86033184, -9202.67251391,
            -9178.57884786, -9244.48034468, -9089.22214132, -9171.38526247],
           [-5999.69534032, -6134.23771478, -6245.49394362, -6400.45527629,
            -6659.19870021, -6895.21280457, -7152.26802265, -7394.71367005,
            -7531.61122317, -7744.49648297, -8018.71221914, -8205.10933387,
            -8378.39043398, -8598.24596101, -8599.61625251, -8772.94321133,
            -8871.38385189, -8908.84623457, -8958.559528  , -9067.60330199,
            -9147.02872756, -9080.42758229, -9133.62629102, -9219.80521149,
    ...
            -3491.43490431, -3555.60004487, -3263.85357275, -2950.59811866,
            -3454.38743017, -4155.2682694 , -4493.65977396, -4639.38888487,
            -5145.44895718, -5544.94708507, -6201.77996717, -6798.6074261 ,
            -7282.01517013, -7629.62012472, -7874.60733983, -7916.98190115,
            -7962.4261798 , -7926.09328453, -7546.65083193, -6564.07022344,
            -6633.07620175, -6753.7965216 , -6579.769081  , -6616.98105107],
           [-2895.33275083, -2921.40048373, -2877.82536454, -3172.01593523,
            -3374.35409918, -3213.21028925, -2800.19896749, -2926.57310035,
            -3480.39789154, -4010.02038657, -4191.58617905, -4496.4035    ,
            -5069.53140926, -5721.45847525, -6522.66158586, -7007.21365803,
            -7493.26438332, -7727.18648046, -7900.70708582, -7953.90609151,
            -7825.1284896 , -7639.14866006, -7474.27934908, -6638.96700624,
            -6571.06687409, -6743.14771147, -6778.50822175, -6764.8460662 ],
           [-2682.74464483, -2440.45572875, -2708.07718799, -3099.5763031 ,
            -3230.20585667, -2605.71560094, -2539.35987753, -2991.69197999,
            -3433.37764718, -3724.72833425, -3845.87346759, -4453.81122567,
            -5165.07474844, -5934.78230067, -6804.7975975 , -7235.31898901,
            -7664.40382062, -7838.00212887, -7928.44045818, -7937.09169844,
            -7748.67172686, -7329.53205499, -7234.61411297, -6687.99507741,
            -6376.9420427 , -6541.09339395, -6630.43765673, -6705.35440274]])

  • z_stdev
    (northing, easting)
    float64
    99.45 107.2 124.7 ... 54.95 61.82

    array([[ 99.44663088, 107.16258928, 124.69100818, 139.44134501,
            146.24415478, 141.76962358, 126.17282158, 107.59109619,
             98.49783025, 106.24817004, 123.78478231, 135.31427898,
            141.93938822, 144.16910858, 145.15866624, 146.66379449,
            142.72444657, 132.34814625, 117.00521875, 110.98358407,
            125.3491567 , 153.49046193, 179.18391162, 192.41665721,
            188.30111908, 172.07359105, 144.87373687, 114.24844369],
           [ 92.69989505, 103.61581419, 118.85210325, 132.28235963,
            139.6094416 , 136.16627927, 121.36097123, 102.98141949,
             89.1679544 ,  87.22402325,  97.20886899, 108.97456141,
            121.71139678, 134.30946698, 145.17156148, 155.34898839,
            154.87587516, 142.18671114, 120.91042584, 102.8428362 ,
            103.47774067, 121.90040761, 144.38995159, 159.05517018,
            158.21292556, 144.77316462, 120.50608854,  95.59506861],
           [ 87.79552554, 101.88582302, 114.76651292, 125.21852753,
            130.39197748, 127.23159348, 116.73927   , 101.85841987,
             86.43230735,  77.31425267,  78.63746538,  89.51792317,
            109.12675177, 133.79417857, 155.5546111 , 173.27273824,
            178.30397989, 167.93953306, 146.63318816, 122.45701989,
            107.3536302 , 108.81166261, 121.50005619, 131.92945422,
    ...
             55.27356193,  56.94703222,  60.61853974,  67.28093793,
             77.48252256,  89.53352227,  94.59368545,  91.85154324,
             89.96288056,  84.89144923,  82.81812613,  83.09081589,
             83.32067052,  80.82481423,  78.26118903,  81.60177105,
             94.44109579, 111.45080139, 118.62599775, 104.48731956,
             98.77928665,  89.36068792,  80.01782345,  88.51776919],
           [ 23.15182044,  27.498703  ,  31.98229816,  36.46196953,
             39.74160194,  44.40868948,  50.73418465,  60.36090194,
             69.15759591,  79.59253146,  81.91682862,  82.36518993,
             83.93172841,  84.55027195,  92.08680932,  96.8780135 ,
             99.2704913 ,  94.84007338,  87.4356717 ,  84.10861114,
             89.39805826, 100.69138367, 108.91387482,  98.63635671,
             90.03934792,  78.9240158 ,  67.76252275,  73.38408247],
           [ 25.43824325,  23.25139644,  22.77173493,  24.57326965,
             29.72742076,  35.07996278,  44.91907404,  54.43201889,
             64.53051218,  72.71024683,  74.07866748,  78.51318809,
             80.62252825,  89.45065931, 102.49590039, 112.03589909,
            116.3284697 , 111.71296451, 101.76481955,  94.17851722,
             93.1889543 ,  97.68539579, 104.32450285,  96.84410178,
             82.5109729 ,  67.82266268,  54.94969852,  61.82120467]])

  • weighted_mean
    (northing, easting)
    float64
    -5.897e+03 ... -6.713e+03

    array([[-5896.5657654 , -6043.44472061, -6183.04502343, -6344.50659402,
            -6509.67005815, -6724.46421543, -6910.71788599, -7083.84562875,
            -7137.41912797, -7200.33052834, -7454.05021779, -7548.20483225,
            -7769.35506119, -7985.24449613, -8192.34447626, -8441.14513918,
            -8544.11082908, -8781.16135811, -8843.39191481, -8904.77876754,
            -8927.44599648, -9004.79806057, -9058.8832509 , -9102.63424158,
            -8992.05949045, -9146.12610109, -9203.55639332, -9120.91083726],
           [-5925.32801718, -5964.1479324 , -6051.43131496, -6285.82127921,
            -6538.21795075, -6823.03301247, -6963.21234977, -7143.71396176,
            -7365.50444503, -7471.22257292, -7710.0904297 , -7820.59870066,
            -8052.55876935, -8289.21656382, -8362.67385868, -8677.88467645,
            -8798.69808286, -8874.23014745, -8934.42339981, -8977.46810986,
            -9090.96773893, -9050.99708229, -9076.98824969, -9204.37654686,
            -9179.35882684, -9244.96205808, -9089.98364342, -9172.89223522],
           [-5993.52470735, -6127.97188404, -6239.27668787, -6394.15628685,
            -6652.67488195, -6888.34165357, -7145.08526156, -7387.40829976,
            -7524.67224459, -7738.58347661, -8014.64924128, -8203.87920209,
            -8380.77884716, -8604.70853794, -8609.96491267, -8786.73772594,
            -8887.54335487, -8925.90808301, -8975.15982032, -9082.5261765 ,
            -9159.26928992, -9089.34505048, -9139.25377751, -9222.48873862,
    ...
            -3487.15692916, -3553.84262782, -3265.61066149, -2956.21290084,
            -3464.09979656, -4169.39514358, -4511.00135786, -4658.15830668,
            -5165.21555262, -5563.92304274, -6218.8572134 , -6812.58587178,
            -7292.15736798, -7635.74043405, -7877.04446372, -7916.50749915,
            -7960.02169141, -7922.80166434, -7543.68019569, -6562.45904809,
            -6633.06267425, -6755.89540157, -6584.08367796, -6623.45742045],
           [-2894.00056425, -2918.59687876, -2874.17415684, -3168.14685292,
            -3371.2414896 , -3211.79343003, -2801.21878349, -2930.63838483,
            -3487.74869655, -4021.08326306, -4205.25356026, -4512.04948823,
            -5086.77467245, -5738.74372101, -6539.56130035, -7021.8564823 ,
            -7504.88824278, -7735.22689574, -7905.14203614, -7955.156216  ,
            -7823.98006784, -7636.63315612, -7471.56277867, -6637.28400294,
            -6570.98354706, -6745.35337632, -6783.36563033, -6772.28767745],
           [-2683.60924657, -2439.88704657, -2706.43692678, -3097.42557241,
            -3228.17927176, -2604.67385476, -2539.78302287, -2994.22747835,
            -3438.52693115, -3732.68120946, -3856.02168904, -4466.48593362,
            -5179.36159141, -5950.53518094, -6820.99724515, -7250.23932168,
            -7677.0729516 , -7847.60201533, -7934.61516429, -7939.95455277,
            -7748.77167513, -7327.90647919, -7232.41020325, -6686.46467036,
            -6376.93705499, -6543.35042521, -6635.48390541, -6713.26378179]])

  • weighted_stdev
    (northing, easting)
    float64
    90.02 97.62 113.6 ... 53.79 59.04

    array([[ 90.02038114,  97.62310518, 113.57878229, 126.79186605,
            132.9815941 , 129.49403343, 116.6844438 , 101.97950801,
             95.5632816 , 102.71302408, 117.8186721 , 127.42661541,
            133.17585656, 135.55286732, 137.23635217, 139.59042221,
            137.05033519, 128.94347439, 116.41486729, 111.41018419,
            122.84492223, 146.00650936, 167.21800121, 177.53261978,
            172.50307454, 157.11013734, 132.80683709, 107.17689383],
           [ 86.01709436,  96.12575208, 109.96814929, 122.22832067,
            129.15290619, 126.51980902, 113.92463239,  98.55322264,
             87.30876135,  85.82745247,  94.27628996, 104.16232039,
            115.40867538, 127.05174776, 137.47385115, 147.69807839,
            148.46352052, 138.49852663, 121.17733342, 106.52463538,
            106.30621722, 119.77849161, 137.01643327, 147.80347859,
            145.02931594, 131.49584985, 109.24959758,  88.49074857],
           [ 84.06726308,  96.77479709, 108.58884676, 118.42215908,
            123.52777851, 120.9396019 , 111.45925643,  97.85078283,
             83.76872804,  75.72140676,  77.49371479,  87.94243172,
            106.21683895, 128.99364968, 149.01594438, 165.6342777 ,
            170.95767959, 162.63829556, 144.95716078, 125.06470761,
            112.25604784, 111.47715116, 119.41051818, 125.39539527,
    ...
             54.41252254,  54.93984863,  56.77463693,  61.87047914,
             71.33006271,  83.61627113,  90.22841228,  89.80388276,
             90.17964748,  86.68310137,  84.62803498,  83.41555458,
             81.88364319,  78.50140823,  75.89602957,  78.9187406 ,
             90.32717835, 105.29456525, 111.09703769,  97.32293312,
             91.65096851,  82.45549356,  72.92686219,  79.63620154],
           [ 21.07007227,  25.3979308 ,  30.46123953,  35.50990898,
             38.91976787,  42.82726577,  47.6581817 ,  55.51439635,
             63.12581822,  73.0829658 ,  76.52828776,  79.02086034,
             83.16769984,  85.9395884 ,  94.26110435,  98.32452351,
             99.51073329,  94.34187094,  86.89779049,  83.63256906,
             88.24860403,  98.24777271, 105.29090492,  94.79570986,
             86.16313146,  75.09924992,  63.35230303,  67.08648564],
           [ 25.16695367,  21.71281554,  20.63120523,  22.62869079,
             27.97562895,  33.08601363,  41.93061051,  50.14319639,
             59.00044607,  66.57047992,  68.64259492,  74.55617094,
             79.17775891,  90.54261027, 105.01616307, 114.52811504,
            118.12752272, 112.89081661, 102.77410081,  95.36371731,
             94.30086722,  98.26648047, 104.23075169,  96.33068372,
             81.85935069,  67.17714898,  53.79426379,  59.03690789]])

  • z_min
    (northing, easting)
    float64
    -6.071e+03 ... -6.804e+03

    array([[-6071.21419157, -6200.52183399, -6336.82492508, -6545.06849536,
            -6766.83027156, -7005.02187955, -7175.42741277, -7297.23162889,
            -7273.7238312 , -7361.46039714, -7688.72605976, -7820.36015294,
            -8041.69025639, -8219.68656664, -8451.6697075 , -8751.8423702 ,
            -8865.19958709, -9067.43847497, -9046.76418888, -9025.20781039,
            -9129.25139228, -9279.53125381, -9383.98526745, -9447.03294061,
            -9320.75191432, -9434.67268886, -9429.26928404, -9271.1266675 ],
           [-6086.36507683, -6105.98048229, -6212.90884327, -6475.0360471 ,
            -6775.04513768, -7081.52852434, -7210.85912185, -7353.75026338,
            -7515.22180181, -7632.45750156, -7894.85552073, -8034.99768214,
            -8271.60921069, -8479.62360532, -8597.50648083, -8963.56235993,
            -9094.36070453, -9134.06664182, -9115.70845767, -9080.19214863,
            -9210.72584021, -9234.40879945, -9309.1089809 , -9463.81308048,
            -9437.96122587, -9480.69542101, -9282.17502457, -9311.91495713],
           [-6137.16336507, -6270.5015814 , -6411.22421523, -6587.24721582,
            -6859.0001823 , -7112.29863218, -7368.47543232, -7591.04095577,
            -7687.38393498, -7889.36594945, -8182.43504163, -8372.06891953,
            -8534.86637107, -8745.08464433, -8813.78541689, -9035.25214573,
            -9144.87364341, -9149.60910941, -9127.99921851, -9221.64142467,
            -9304.02980759, -9229.9362722 , -9271.64413602, -9384.43193039,
    ...
            -3584.52573769, -3653.63808758, -3361.95966352, -3043.31077451,
            -3539.40381629, -4262.65723215, -4630.39077144, -4792.68339302,
            -5312.53419477, -5710.93773283, -6355.70845347, -6926.90352001,
            -7373.3829562 , -7722.93776555, -7998.45795696, -8057.94285738,
            -8111.71117668, -8079.12628928, -7702.53051285, -6697.03658654,
            -6763.40820533, -6887.94533126, -6710.34479194, -6748.68508258],
           [-2941.41577007, -2980.8537011 , -2943.11749465, -3235.98852796,
            -3440.52751647, -3291.24344472, -2884.69542018, -3014.30565972,
            -3562.0798074 , -4085.05492906, -4292.39710103, -4621.61904502,
            -5219.27787135, -5884.10531423, -6694.5945035 , -7166.63891577,
            -7625.09733961, -7827.06679748, -8003.21090752, -8072.23196168,
            -7957.92384953, -7784.58245887, -7626.99434471, -6777.81591657,
            -6703.50388184, -6867.27277215, -6882.93952436, -6858.17388127],
           [-2708.97761115, -2470.70281104, -2745.82923435, -3146.25238082,
            -3288.53353174, -2669.63934589, -2610.0228855 , -3066.75237294,
            -3506.45417092, -3805.90270436, -3933.98787654, -4555.61009114,
            -5296.02546077, -6098.59888813, -6993.2105654 , -7425.11082818,
            -7834.61951976, -7970.8803495 , -8068.61574946, -8085.53285133,
            -7900.02681512, -7477.80861703, -7387.23311173, -6831.30182986,
            -6509.23456396, -6667.37488121, -6744.38828567, -6803.80262507]])

  • z_max
    (northing, easting)
    float64
    -5.7e+03 -5.797e+03 ... -6.586e+03

    array([[-5700.00134164, -5796.86016242, -5895.93607204, -6043.28393101,
            -6222.65504845, -6484.53071304, -6750.52165186, -6933.72246043,
            -6989.28539188, -7065.22861098, -7281.66596625, -7349.058813  ,
            -7550.75358462, -7760.23513711, -7977.69834192, -8253.82546892,
            -8368.90923082, -8590.90765898, -8643.40040539, -8699.85612345,
            -8723.49131638, -8807.81009876, -8786.90619081, -8763.92624882,
            -8629.71121764, -8793.25803962, -8893.78624926, -8878.05248029],
           [-5739.93487783, -5734.15685021, -5788.0932399 , -6006.87457502,
            -6266.62721239, -6588.79215166, -6797.57864015, -7005.56541707,
            -7223.77931841, -7337.92787582, -7596.30014718, -7705.34203264,
            -7909.55754692, -8097.45610015, -8142.72520777, -8444.42722363,
            -8571.31135316, -8640.53353502, -8701.55540627, -8751.13521488,
            -8877.48456134, -8859.21302931, -8817.3110731 , -8883.38618458,
            -8839.47377323, -8921.55562774, -8816.50772047, -8966.74472649],
           [-5824.47762257, -5915.93643617, -5999.91382   , -6141.7900133 ,
            -6405.67762575, -6671.63248241, -6980.0577948 , -7264.90413533,
            -7394.80734017, -7610.64919713, -7899.52429404, -8093.41879085,
            -8217.28784404, -8387.25455176, -8329.08131957, -8459.84813887,
            -8543.80322411, -8597.9595411 , -8689.51454118, -8842.70407006,
            -8944.69086117, -8908.84108893, -8897.84239899, -8930.00012587,
    ...
            -3398.18509498, -3474.12993487, -3156.03704088, -2818.81222421,
            -3301.73137324, -3985.28088022, -4324.17520037, -4487.79606598,
            -5007.98576816, -5430.16727041, -6079.43651549, -6650.87122592,
            -7132.64206984, -7476.4946118 , -7726.11136298, -7785.89376479,
            -7826.23238769, -7732.11375658, -7318.6864709 , -6349.37595142,
            -6420.29577954, -6562.81761111, -6440.56560356, -6474.89685245],
           [-2851.32661116, -2881.69887512, -2826.9162626 , -3108.70588246,
            -3307.43892508, -3150.41747852, -2714.93855828, -2817.14851947,
            -3352.89094147, -3864.83659691, -4046.39513296, -4358.99827467,
            -4946.88663987, -5619.88584474, -6391.11724155, -6853.07710112,
            -7313.41528971, -7538.06835017, -7718.74114715, -7793.4653481 ,
            -7695.90442544, -7468.97648296, -7268.38436662, -6440.69005661,
            -6383.41539105, -6581.69214236, -6669.66799402, -6629.89776588],
           [-2640.98854523, -2402.9224633 , -2669.02896397, -3064.3697465 ,
            -3189.44032551, -2559.60744008, -2474.05424145, -2907.90420012,
            -3330.51887839, -3606.55052597, -3725.04720183, -4330.05608672,
            -5051.31106483, -5835.09281489, -6665.49751976, -7053.25312382,
            -7452.804008  , -7617.12564648, -7716.77282375, -7749.43159888,
            -7598.2653914 , -7190.85203631, -7062.30268835, -6516.5290326 ,
            -6226.32799799, -6422.48818133, -6564.55864424, -6585.83938447]])

Gravity component

fname = "../tmp/bishop_model_uncertainty_grav"

# delete files if already exist
for p in pathlib.Path().glob(f"{fname}*"):
    p.unlink(missing_ok=True)

uncert_grav_results = invert4geom.full_workflow_uncertainty_loop(
    optimal_inv,
    fname=fname,
    runs=10,
    sample_gravity=True,
    regional_grav_kwargs=new_regional_grav_kwargs,
    starting_topography_kwargs=starting_topography_kwargs,
)

uncert_plots(
    uncert_grav_results,
    optimal_inv.data.inner_region,
    optimal_inv.data.spacing,
    grid.basement_topo,
    constraints_df=constraint_points,
    weight_by="constraints",
)

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

<xarray.Dataset> Size: 122kB
Dimensions:         (northing: 30, easting: 28, runs: 10)
Coordinates:
  * northing        (northing) float64 240B 1.959e+05 2.059e+05 ... 4.859e+05
  * easting         (easting) float64 224B 5.69e+04 6.69e+04 ... 3.269e+05
    top             (northing, easting) float64 7kB -5.915e+03 ... -6.09e+03
    bottom          (northing, easting) float64 7kB -6.09e+03 ... -6.727e+03
  * runs            (runs) <U5 200B 'run_0' 'run_1' 'run_2' ... 'run_8' 'run_9'
Data variables:
    run_num         (runs, northing, easting) float64 67kB -5.915e+03 ... -6....
    z_mean          (northing, easting) float64 7kB -5.899e+03 ... -6.722e+03
    z_stdev         (northing, easting) float64 7kB 22.88 26.58 ... 24.27 23.4
    weighted_mean   (northing, easting) float64 7kB -5.899e+03 ... -6.723e+03
    weighted_stdev  (northing, easting) float64 7kB 22.86 26.47 ... 23.6 23.3
    z_min           (northing, easting) float64 7kB -5.941e+03 ... -6.757e+03
    z_max           (northing, easting) float64 7kB -5.867e+03 ... -6.667e+03

xarray.Dataset

• Dimensions:
  • northing: 30
  • easting: 28
  • runs: 10
• Coordinates: (5)
  • northing
    (northing)
    float64
    1.959e+05 2.059e+05 ... 4.859e+05

    array([195900., 205900., 215900., 225900., 235900., 245900., 255900., 265900.,
           275900., 285900., 295900., 305900., 315900., 325900., 335900., 345900.,
           355900., 365900., 375900., 385900., 395900., 405900., 415900., 425900.,
           435900., 445900., 455900., 465900., 475900., 485900.])

  • easting
    (easting)
    float64
    5.69e+04 6.69e+04 ... 3.269e+05

    array([ 56900.,  66900.,  76900.,  86900.,  96900., 106900., 116900., 126900.,
           136900., 146900., 156900., 166900., 176900., 186900., 196900., 206900.,
           216900., 226900., 236900., 246900., 256900., 266900., 276900., 286900.,
           296900., 306900., 316900., 326900.])

  • top
    (northing, easting)
    float64
    -5.915e+03 -6.014e+03 ... -6.09e+03

    array([[-5914.82520219, -6013.66312409, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-5945.9810908 , -5949.02107028, -6078.04936227, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-6004.87663754, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
    ...
            -3439.03669375, -3515.18564557, -3236.61575819, -2918.59052269,
            -3412.49897885, -4112.49803485, -4517.07586036, -4602.81604736,
            -5144.24369029, -5514.0594749 , -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-2888.82393525, -2942.14888443, -2835.85116016, -3131.54784831,
            -3367.52171304, -3156.35966453, -2756.06933439, -2879.08102735,
            -3423.01246048, -3995.90183964, -4149.91349157, -4464.5734618 ,
            -5039.07548559, -5657.34099533, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-2684.96706261, -2446.03870484, -2693.26564568, -3057.82804034,
            -3175.22835951, -2553.81887924, -2483.17792043, -2964.18176426,
            -3414.49815132, -3679.57094255, -3789.47211011, -4441.56513843,
            -5182.7568628 , -5978.75539132, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898]])

  • bottom
    (northing, easting)
    float64
    -6.09e+03 -6.09e+03 ... -6.727e+03

    array([[-6089.83711898, -6089.83711898, -6193.28958821, -6354.44422957,
            -6534.10615287, -6734.28649206, -6898.14936258, -7112.47547659,
            -7104.23517273, -7174.24937137, -7460.21647883, -7571.05085918,
            -7695.37166374, -7925.56911891, -8153.54683621, -8378.40067762,
            -8425.49669123, -8711.96142947, -8806.33464999, -8932.54708907,
            -8880.11554409, -8977.20027865, -9034.78948754, -9119.68167814,
            -8999.95625841, -9149.56699107, -9231.66615784, -9141.59739808],
           [-6089.83711898, -6089.83711898, -6089.83711898, -6256.147928  ,
            -6545.61212713, -6846.60017783, -7024.95768203, -7182.83541735,
            -7300.72782259, -7445.8978701 , -7660.77477332, -7722.78685663,
            -8039.24234461, -8266.76986654, -8334.01090861, -8611.88189834,
            -8769.64350423, -8850.53649351, -8949.85153513, -8937.86919904,
            -9048.21858067, -9100.34623787, -9076.04141175, -9297.55048092,
            -9217.96193647, -9231.49727692, -9113.36941208, -9106.69619011],
           [-6089.83711898, -6196.50450467, -6291.66319432, -6403.71534696,
            -6713.95888035, -6859.68092478, -7115.28520839, -7390.23489327,
            -7534.73247798, -7754.60521532, -8020.77809753, -8190.11125945,
            -8302.69296041, -8510.07028736, -8621.95363064, -8811.9171991 ,
            -8928.70071651, -8926.60416358, -9076.23153324, -9107.85069553,
            -9111.7324877 , -9100.09072834, -9114.94228578, -9237.18125409,
    ...
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6202.96865921, -6765.94640452,
            -7274.8661901 , -7603.59523776, -7841.12695399, -7901.84957892,
            -7964.3753444 , -7921.66006525, -7606.48951944, -6538.08060547,
            -6604.02375734, -6771.22435438, -6630.24679398, -6641.68183611],
           [-6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6512.26351757, -7018.54095304,
            -7440.84671815, -7750.34576398, -7913.02905334, -7987.46349048,
            -7825.98209342, -7588.27886547, -7433.59413151, -6620.45537822,
            -6598.1710991 , -6768.71872823, -6794.23261747, -6743.32539071],
           [-6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6833.64753729, -7219.37479324,
            -7699.01056194, -7912.68042676, -7979.20165021, -7976.42299785,
            -7771.07664483, -7380.50864144, -7273.11851143, -6720.19809189,
            -6372.4062479 , -6523.80305366, -6632.09803551, -6726.90295385]])

  • runs
    (runs)
    <U5
    'run_0' 'run_1' ... 'run_8' 'run_9'

    array(['run_0', 'run_1', 'run_2', 'run_3', 'run_4', 'run_5', 'run_6', 'run_7',
           'run_8', 'run_9'], dtype='<U5')

• Data variables: (7)
  • run_num
    (runs, northing, easting)
    float64
    -5.915e+03 -6.014e+03 ... -6.72e+03

    array([[[-5914.82520219, -6013.66312409, -6193.28958821, ...,
             -9149.56699107, -9231.66615784, -9141.59739808],
            [-5945.9810908 , -5949.02107028, -6078.04936227, ...,
             -9231.49727692, -9113.36941208, -9106.69619011],
            [-6004.87663754, -6196.50450467, -6291.66319432, ...,
             -9255.13936536, -9233.65858735, -9114.80063179],
            ...,
            [-2997.23029967, -3101.90114879, -3106.12186224, ...,
             -6771.22435438, -6630.24679398, -6641.68183611],
            [-2888.82393525, -2942.14888443, -2835.85116016, ...,
             -6768.71872823, -6794.23261747, -6743.32539071],
            [-2684.96706261, -2446.03870484, -2693.26564568, ...,
             -6523.80305366, -6632.09803551, -6726.90295385]],
    
           [[-5897.63251241, -6069.024601  , -6152.59386835, ...,
             -9157.92160582, -9257.26879087, -9102.33949531],
            [-5899.89912292, -6007.26227106, -6073.08489161, ...,
             -9267.7177296 , -9094.11998155, -9187.60118799],
            [-6008.74156929, -6111.69215983, -6262.98455889, ...,
             -9282.39871122, -9251.40349303, -9216.6709523 ],
    ...
             -6757.62760776, -6553.28447914, -6634.6153505 ],
            [-2888.89396088, -2921.86700668, -2864.99171349, ...,
             -6706.35146046, -6789.20400923, -6784.56659938],
            [-2662.56290692, -2413.33171681, -2694.49155936, ...,
             -6604.94513679, -6630.53006666, -6728.57753233]],
    
           [[-5872.68029523, -6024.19358026, -6207.18823352, ...,
             -9234.15338072, -9183.09131425, -9127.9775758 ],
            [-5955.17750157, -5958.3199068 , -6083.79410997, ...,
             -9255.07242242, -9077.23624564, -9160.63803675],
            [-6033.65756624, -6127.20043011, -6238.82915944, ...,
             -9300.73454878, -9235.75561238, -9217.69629773],
            ...,
            [-2977.15671616, -3135.82776883, -3086.82886484, ...,
             -6723.13551894, -6573.96515097, -6643.74654849],
            [-2885.84663869, -2902.79742476, -2856.4382124 , ...,
             -6779.03347165, -6780.81186954, -6794.86361382],
            [-2675.76727094, -2422.92673636, -2714.80793811, ...,
             -6518.67814301, -6697.11963935, -6720.21446483]]],
          shape=(10, 30, 28))

  • z_mean
    (northing, easting)
    float64
    -5.899e+03 ... -6.722e+03

    array([[-5898.83774812, -6020.63093124, -6185.41580958, -6344.85762483,
            -6498.15691499, -6725.52073538, -6891.77239031, -7057.18401287,
            -7127.69151861, -7184.03520578, -7436.91286968, -7529.49240483,
            -7728.87197325, -7949.73287632, -8145.03335978, -8393.22519631,
            -8485.13163537, -8736.5296863 , -8833.92277265, -8895.17307366,
            -8921.9989804 , -8992.99251957, -9059.06916642, -9127.14263109,
            -9004.48577595, -9167.42405031, -9242.07020335, -9144.70399149],
           [-5945.04293509, -5944.09117341, -6066.92169806, -6282.11366966,
            -6540.517932  , -6825.16471778, -6977.33469211, -7111.88653769,
            -7332.89673652, -7453.34098882, -7679.28894285, -7776.67544346,
            -8002.89452947, -8253.4798122 , -8324.71325695, -8636.87713157,
            -8769.24193307, -8846.86279179, -8919.79251838, -8969.25912083,
            -9093.21794757, -9079.08938374, -9128.635815  , -9249.49655381,
            -9201.00187052, -9256.18353243, -9099.79374734, -9168.90783679],
           [-6000.08204967, -6135.08000863, -6269.8453298 , -6412.15193469,
            -6679.41587015, -6916.47303931, -7180.53555428, -7400.71401278,
            -7534.05323678, -7742.26189194, -7988.499529  , -8191.4419978 ,
            -8358.04753163, -8564.30106933, -8579.1293759 , -8786.26425662,
            -8906.61614329, -8916.14679726, -9002.4212165 , -9122.83882332,
            -9170.48287012, -9092.70020019, -9127.17657294, -9228.49449099,
    ...
            -3463.62424572, -3514.43955443, -3236.96958576, -2926.38937764,
            -3430.94258855, -4135.57705   , -4484.06731517, -4624.3572225 ,
            -5135.752703  , -5541.85815162, -6175.26649619, -6791.23299483,
            -7252.30839227, -7578.61973018, -7836.29781342, -7882.86227273,
            -7944.53599335, -7906.91669478, -7517.33689462, -6543.51864763,
            -6592.17628926, -6747.17227447, -6570.15012528, -6624.72675296],
           [-2876.33779094, -2915.30183246, -2865.17791419, -3146.53424289,
            -3348.05456097, -3178.74213991, -2770.24155437, -2903.47394818,
            -3447.42032452, -3979.77121131, -4160.98464872, -4479.05199017,
            -5049.97928266, -5711.3423412 , -6529.12199804, -7006.5032182 ,
            -7496.17052836, -7751.83001905, -7914.97128196, -7951.40092462,
            -7807.14011148, -7631.05249813, -7466.45641417, -6637.84884125,
            -6545.00079789, -6757.15289808, -6779.81022409, -6783.18367379],
           [-2675.01958331, -2423.13053263, -2692.80306743, -3069.42382454,
            -3207.05550111, -2580.28705291, -2509.63505545, -2956.21522671,
            -3409.08778091, -3698.40435525, -3821.50866476, -4435.42748472,
            -5171.36672232, -5951.66982941, -6821.07064899, -7265.21061262,
            -7693.49506654, -7855.88709541, -7961.27066865, -7976.12242385,
            -7745.8631337 , -7336.75608243, -7241.83588569, -6680.39236035,
            -6363.97853436, -6549.65780787, -6641.28932387, -6722.30038557]])

  • z_stdev
    (northing, easting)
    float64
    22.88 26.58 20.58 ... 24.27 23.4

    array([[22.87814122, 26.58009726, 20.57776424, 17.18286167, 36.2943426 ,
            19.72100224, 25.29676654, 35.84549919, 25.33055057, 25.0550877 ,
            37.46001398, 24.51859638, 42.79277725, 37.34725279, 22.68017146,
            36.53553986, 36.32200676, 19.08507494, 56.61053508, 30.84057977,
            46.49784059, 31.43671127, 38.90220186, 25.81653948, 27.42285357,
            38.31852781, 57.95573248, 28.73431243],
           [30.13517878, 28.95129428, 25.08639605, 21.54506156, 24.83862107,
            30.75373406, 29.63784255, 28.62063301, 28.17201584, 30.61180148,
            17.12062775, 42.6890381 , 23.13775817, 31.49497014, 28.3520819 ,
            39.47274367, 37.89882194, 34.89478001, 32.73954134, 32.95090797,
            47.7484829 , 48.02108529, 32.0018612 , 52.08783995, 31.70953679,
            38.19413367, 27.14002648, 35.17141366],
           [47.45272352, 31.91133607, 21.86393957, 30.12207117, 22.19194411,
            33.6183497 , 38.84024803, 31.67239025, 34.51574578, 30.86466153,
            36.61376812, 53.45359943, 40.54036881, 37.97571149, 26.98887209,
            32.19019429, 40.54992665, 32.0570284 , 34.36378368, 32.51349089,
            30.5896924 , 21.16355411, 21.77064599, 29.81359307, 47.43694207,
            31.40502112, 33.23001495, 61.45464246],
           [26.27845626, 18.33420043, 30.42994009, 26.7961688 , 20.33293263,
            27.96022822, 29.31840004, 33.22680764, 27.50707   , 29.75659329,
    ...
            33.60127287, 27.80856507, 37.30286905, 36.28957714,  9.65716437,
            23.45178988, 31.69550743, 24.21881986],
           [ 8.13307693, 12.41820029, 23.61665937, 14.16732835, 20.94186632,
            14.69219538, 14.93289961, 11.103673  , 16.1137694 , 23.8841732 ,
            22.63175695, 24.89824326, 22.00400656, 34.59849561, 21.78327799,
            26.51199498, 24.49288375, 25.93803973, 43.98172193, 38.66578029,
            26.18014727, 39.65825258, 38.0719609 , 19.23442174, 21.43923389,
            32.97385403, 34.54553688, 28.89733142],
           [20.96400769, 13.63282789, 13.95231528, 16.12805783, 20.6504222 ,
            20.63783355, 13.49719208, 19.07479639, 16.34526123, 22.84894437,
            20.68295514, 19.50704865, 18.55479258, 24.69721318, 28.90885358,
            18.9542477 , 36.97999487, 26.29616834, 36.69953084, 36.27524259,
            38.68871066, 40.96075783, 28.06216767, 22.36114271, 31.71973123,
            28.01841325, 25.3309417 , 33.10864148],
           [11.99958566, 12.54961216, 19.3261188 , 11.95903362, 18.70870411,
            19.1430272 , 21.09762803, 21.12545208, 20.006015  , 19.03214526,
            18.82094965, 20.85298984, 19.64958135, 31.04736241, 25.94220147,
            28.73768665, 21.06845311, 31.12044311, 36.96954314, 16.77503577,
            23.21210043, 33.10543141, 35.59072675, 38.79185806, 26.20909993,
            37.29930529, 24.26885238, 23.39613728]])

  • weighted_mean
    (northing, easting)
    float64
    -5.899e+03 ... -6.723e+03

    array([[-5899.05511521, -6021.22070478, -6185.03278472, -6344.72655593,
            -6498.30738584, -6725.86619079, -6892.86216057, -7057.53107429,
            -7128.70994663, -7183.33824527, -7437.02909176, -7529.4716568 ,
            -7727.86826567, -7949.51151229, -8145.44581335, -8392.65660945,
            -8484.68757321, -8736.8726836 , -8833.73337702, -8895.38953287,
            -8920.56314399, -8992.76896228, -9059.17786061, -9126.23893405,
            -9004.92829407, -9166.87819694, -9243.52416338, -9144.67882624],
           [-5944.49830998, -5944.71720402, -6066.50625211, -6282.20722187,
            -6540.80343545, -6825.50375848, -6977.19124719, -7111.62361885,
            -7332.34430362, -7453.47115989, -7679.29902812, -7777.30841106,
            -8003.41219909, -8253.30865104, -8324.31920543, -8636.85995206,
            -8768.14141929, -8846.4208461 , -8919.38999222, -8969.52508006,
            -9093.17199702, -9078.89784445, -9128.81506356, -9250.74496867,
            -9201.20246568, -9255.56195578, -9100.90711226, -9169.21703586],
           [-6000.55806175, -6135.3835315 , -6270.46445392, -6412.06860463,
            -6679.48159503, -6916.18549959, -7179.90226177, -7400.52263424,
            -7534.07051413, -7742.57907341, -7987.78877973, -8191.14546381,
            -8357.72327023, -8563.87344204, -8578.80297937, -8787.2505054 ,
            -8907.17498731, -8915.82829142, -9002.29326762, -9122.66863321,
            -9170.37761882, -9092.00036758, -9127.62205611, -9229.81466991,
    ...
            -3462.96375131, -3514.34680943, -3236.8868261 , -2926.28912688,
            -3431.55956299, -4135.30861447, -4483.66721249, -4624.55264669,
            -5136.19764101, -5542.40176417, -6176.09797501, -6791.15533405,
            -7252.7261502 , -7578.56266954, -7837.06846895, -7882.99405435,
            -7944.19182511, -7906.75715069, -7517.48827166, -6543.63715516,
            -6592.85862684, -6747.25522236, -6569.6717629 , -6624.57694209],
           [-2876.38861219, -2915.80295184, -2864.96835803, -3146.39922648,
            -3348.75737282, -3177.87037141, -2770.54919677, -2903.60006378,
            -3447.16066807, -3979.32441539, -4161.5329778 , -4478.37612076,
            -5050.04300784, -5710.89467847, -6528.92699952, -7006.09438318,
            -7496.67937299, -7751.90321575, -7914.72702087, -7951.26560254,
            -7807.66722887, -7631.63077601, -7467.13606623, -6637.64802222,
            -6545.52300756, -6756.81352871, -6780.15702967, -6783.33088735],
           [-2675.04255892, -2423.09520657, -2692.60573928, -3069.03751013,
            -3206.90295102, -2580.2354005 , -2509.82466601, -2956.39925086,
            -3409.28820319, -3697.92824411, -3821.43514361, -4436.00474798,
            -5171.59444202, -5951.35049848, -6822.1773374 , -7263.98619944,
            -7693.93881273, -7856.55259356, -7961.06797113, -7976.60434815,
            -7745.45822898, -7336.52986529, -7242.09304836, -6679.73335525,
            -6364.91676321, -6550.4461977 , -6641.00481226, -6722.75977244]])

  • weighted_stdev
    (northing, easting)
    float64
    22.86 26.47 20.6 ... 23.6 23.3

    array([[22.85849576, 26.47186553, 20.602695  , 16.90058099, 36.1978509 ,
            19.23592884, 24.90705528, 35.46203749, 25.42799258, 24.99301401,
            38.03707354, 24.50656216, 43.31351629, 36.91350933, 23.16279586,
            37.15793717, 36.23373909, 19.59963001, 56.36984229, 31.23978801,
            45.72246145, 31.72923254, 38.78745319, 25.35003786, 27.26917645,
            37.82063743, 58.2155524 , 28.79271712],
           [29.93657011, 28.92975488, 25.10438872, 21.38445918, 24.65609867,
            30.8571968 , 29.6750996 , 29.07910865, 28.07693531, 31.0027838 ,
            17.09654846, 42.83603058, 23.2385736 , 31.0395365 , 28.21648867,
            39.39316094, 37.83213138, 34.68804982, 32.80255499, 33.04439046,
            48.34259095, 48.30604246, 32.08121257, 52.71033508, 31.04053188,
            38.53367723, 27.37735222, 35.15356238],
           [47.2135485 , 32.09849933, 21.71588646, 30.23114956, 22.1711067 ,
            33.70216182, 38.65581988, 31.85487106, 34.03955384, 30.18104663,
            37.04871133, 53.23870269, 40.95735488, 38.4986454 , 27.29550895,
            32.02300776, 40.65214696, 31.45568488, 35.12878488, 32.8363743 ,
            30.75923848, 21.42414809, 21.69099242, 30.03721897, 47.80097396,
            31.52651973, 33.02408355, 62.19902433],
           [26.40207307, 18.1824139 , 30.09628447, 26.86098513, 20.87380547,
            27.84842992, 29.31047447, 32.89520955, 27.48640533, 29.38581713,
    ...
            34.05873464, 28.15906231, 36.79075111, 36.03791618,  9.59916626,
            23.73784693, 31.65139342, 24.32596513],
           [ 7.99050587, 12.28273352, 23.36593179, 14.28227472, 20.54383951,
            14.63269728, 14.9247944 , 11.08335405, 16.23001493, 23.43161932,
            23.37038239, 25.11493279, 21.87278583, 34.04261018, 21.34669193,
            26.91934901, 24.59845451, 26.00572156, 43.61870822, 38.46139947,
            26.67590867, 39.37310978, 38.34378558, 19.29660823, 21.48091981,
            33.16870165, 34.77233374, 28.63767656],
           [21.06521524, 13.52638313, 13.93104618, 16.48218903, 20.43294095,
            20.8017908 , 13.55728029, 18.88444265, 16.67649025, 23.14499267,
            20.64503166, 19.47107247, 18.38838013, 24.61833242, 28.98044191,
            19.08219265, 37.2220263 , 26.36586287, 36.98678911, 36.18526235,
            37.87888336, 41.10130706, 28.13367582, 22.5756587 , 31.85179359,
            28.36756572, 25.29954602, 33.36201231],
           [11.96507495, 12.56434172, 19.23640974, 12.12369568, 18.66589905,
            19.06131085, 20.8724799 , 21.07894142, 19.83279935, 18.86692031,
            18.8965058 , 20.68640118, 19.67261218, 31.05416685, 26.52014635,
            28.95265867, 21.35624678, 31.20106669, 36.92189741, 16.90129692,
            23.08090875, 33.01108772, 35.15018709, 39.2483689 , 26.21856212,
            37.4648135 , 23.60223721, 23.29516756]])

  • z_min
    (northing, easting)
    float64
    -5.941e+03 ... -6.757e+03

    array([[-5941.00508853, -6069.024601  , -6214.8237847 , -6385.35644961,
            -6534.22524491, -6749.15659463, -6923.62250165, -7112.47547659,
            -7174.6879634 , -7243.16746405, -7492.66216731, -7571.05085918,
            -7789.78923062, -8016.78441903, -8190.07122442, -8459.94110177,
            -8537.08387773, -8781.81385945, -8942.29131719, -8942.06923157,
            -9001.16904014, -9035.80084616, -9103.52354804, -9180.96478502,
            -9035.70045467, -9234.15338072, -9347.70948659, -9193.02913341],
           [-6018.07463336, -6007.26227106, -6090.84219455, -6314.79296457,
            -6573.06463973, -6901.86505555, -7024.95768203, -7182.83541735,
            -7373.19536861, -7502.20176198, -7714.79739334, -7828.72809708,
            -8039.24234461, -8308.237397  , -8366.66450012, -8700.34916288,
            -8825.98698501, -8927.02334558, -8963.12965632, -9036.95053824,
            -9165.2094575 , -9157.09887773, -9176.20685696, -9319.80094058,
            -9250.77891235, -9334.42502833, -9158.14252572, -9230.14965626],
           [-6063.90579487, -6196.50450467, -6304.14735762, -6483.76114313,
            -6713.95888035, -6966.00171154, -7247.57758671, -7464.91934303,
            -7593.20880708, -7814.8218862 , -8047.42553854, -8251.60790579,
            -8410.63664438, -8653.57913725, -8621.95363064, -8830.02040439,
            -8956.68022383, -8966.01785046, -9076.23153324, -9178.42075798,
            -9222.84064747, -9116.57116182, -9162.32434092, -9280.40069239,
    ...
            -3510.23887743, -3545.0404494 , -3265.90522905, -2941.87741036,
            -3463.97673979, -4189.08952898, -4517.07586036, -4667.15429994,
            -5169.48900831, -5587.99777516, -6202.96865921, -6836.64396105,
            -7283.19828369, -7612.63515069, -7908.37086088, -7945.36991398,
            -7970.03839418, -7971.92421847, -7606.48951944, -6580.06433917,
            -6627.30492386, -6805.25039023, -6630.24679398, -6692.00276405],
           [-2910.02366021, -2942.14888443, -2889.08775867, -3174.99821161,
            -3377.23718382, -3205.91253912, -2789.88236237, -2935.36277945,
            -3475.8754792 , -4010.09494522, -4196.54322245, -4513.2118873 ,
            -5071.60384767, -5749.72032921, -6579.80097937, -7041.31679785,
            -7539.81637727, -7814.79497504, -7966.09830854, -8003.07994659,
            -7855.67564809, -7701.51979272, -7526.78984913, -6682.00132688,
            -6598.1710991 , -6802.13064627, -6835.84850462, -6859.64248102],
           [-2696.537989  , -2446.03870484, -2728.52739384, -3092.09956486,
            -3248.37966231, -2607.76781047, -2535.90371906, -2989.66345888,
            -3435.85195469, -3741.35563657, -3855.88496256, -4473.34387094,
            -5195.50199953, -6011.80164232, -6882.37025916, -7302.0611283 ,
            -7738.49268965, -7912.68042676, -8023.22363154, -8002.95102795,
            -7783.15409779, -7381.090596  , -7276.82287534, -6732.34841896,
            -6405.65371078, -6614.55758388, -6697.11963935, -6757.02652903]])

  • z_max
    (northing, easting)
    float64
    -5.867e+03 ... -6.667e+03

    array([[-5866.81318295, -5964.54923396, -6152.59386835, -6321.53184911,
            -6416.81166366, -6679.43464916, -6845.31190311, -6991.39767273,
            -7081.34143274, -7155.81264668, -7352.44506161, -7488.12029611,
            -7659.49510258, -7883.72114266, -8109.53504182, -8316.67033259,
            -8425.49669123, -8711.96142947, -8757.34075578, -8855.74948711,
            -8848.15176604, -8941.85085011, -8965.11854564, -9093.54895197,
            -8933.02621629, -9112.22985787, -9164.30964322, -9102.33949531],
           [-5899.89912292, -5903.1176061 , -6021.31603792, -6255.17743393,
            -6479.53053033, -6788.2214716 , -6933.15472308, -7075.50388663,
            -7300.72782259, -7398.99395772, -7660.77477332, -7722.77656498,
            -7970.97163439, -8220.66647977, -8267.78163259, -8581.50746776,
            -8706.6627257 , -8786.33809191, -8858.01256836, -8934.01523649,
            -9026.09754929, -8987.87173669, -9076.04141175, -9163.0108226 ,
            -9145.58640566, -9194.9067228 , -9055.82047402, -9106.69619011],
           [-5925.70333676, -6082.27949963, -6238.82915944, -6378.9910634 ,
            -6644.87042976, -6859.68092478, -7115.28520839, -7360.60368542,
            -7480.8999691 , -7706.56207079, -7925.52172119, -8073.34532229,
            -8270.86915626, -8510.07028736, -8524.02338773, -8731.90169371,
            -8856.48557242, -8853.3161954 , -8941.49580985, -9066.02432962,
            -9111.7324877 , -9050.41345632, -9091.8174297 , -9187.88509405,
    ...
            -3436.8815399 , -3494.51255159, -3211.44820431, -2911.19214883,
            -3402.78902838, -4105.46833641, -4427.26289765, -4585.78831823,
            -5089.83772863, -5479.51282075, -6128.12431362, -6756.80621707,
            -7198.60571658, -7535.11372634, -7734.31303357, -7810.61731576,
            -7883.26932827, -7848.99611119, -7476.97803319, -6506.47315182,
            -6560.1113777 , -6677.80421298, -6524.7349839 , -6581.01085087],
           [-2839.07325929, -2886.93959146, -2835.85116016, -3114.3249672 ,
            -3308.58631409, -3141.84766265, -2752.28618375, -2871.06736401,
            -3422.00324478, -3941.94065669, -4131.99503949, -4454.61316382,
            -5006.76919133, -5657.34099533, -6489.43981592, -6975.25148806,
            -7430.17266887, -7714.93151038, -7845.23506884, -7904.41519886,
            -7724.55053815, -7541.72191422, -7433.59413151, -6593.08230192,
            -6489.20855462, -6706.35146046, -6733.33847512, -6743.32539071],
           [-2649.91119309, -2403.96900429, -2663.63948067, -3046.43919135,
            -3175.22835951, -2549.7002597 , -2478.51634004, -2920.6739565 ,
            -3373.53363685, -3675.7714643 , -3789.44074612, -4407.09901156,
            -5138.86057349, -5902.51326063, -6798.76893115, -7219.37479324,
            -7669.10594037, -7797.32277   , -7880.28364221, -7938.15684657,
            -7711.69170499, -7285.80188013, -7180.33955024, -6621.17470597,
            -6317.42635582, -6505.34944204, -6608.45207928, -6667.2428696 ]])

Regional field estimation uncertainty

We will do the same thing for the regional estimation procedure. First we will re-separate the regional to see what equivalent source gridding parameter values were determined optimal. We then estimate an uncertainty distribution for these parameter values, and create an ensemble of regional models which each randomly sample both the parameter values and the gravity data.

mean_constraint_spacing, reg_eq_depth, reg_eq_damping

(np.float64(58000.0), 110158.8963339568, 4.184227553394269e-40)

np.abs(np.log10(reg_eq_damping))

np.float64(39.37838470499734)

regional_misfit_parameter_dict = {
    "depth": {
        "distribution": "uniform",
        "loc": 2 * mean_constraint_spacing,  # lower bound
        "scale": 5 * mean_constraint_spacing,  # range, 2+5=7
    },
    # "depth": {
    #     "distribution": "normal",
    #     "loc": reg_eq_depth,  # mean base 10 exponent
    #     "scale": reg_eq_depth / 5,  # standard deviation of exponent
    # },
    "damping": {
        "distribution": "uniform",
        "loc": np.log10(reg_eq_damping),
        "scale": np.abs(np.log10(reg_eq_damping)),
        # "scale": 2,
        "log": True,
    },
}

regional_misfit_stats, _ = invert4geom.regional_misfit_uncertainty(
    runs=100,
    parameter_dict=regional_misfit_parameter_dict,
    grav_ds=optimal_inv.data,
    region=optimal_inv.data.inner_region,
    **new_regional_grav_kwargs,
)

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 3.3448368022655944e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 2.430972225114141e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 2.478559371295503e-19.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 2.443996774166576e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 9.485053714965411e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 9.097875879951273e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 2.1480456216951407e-18.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 1.898693387017394e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 1.9572992172738425e-16.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 3.5134788506555314e-19.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 5.23087412579779e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 3.126140843907381e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 1.5059180507423272e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 4.5069152346119606e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 1.6020989853685096e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 1.0362926780019026e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 6.861710612325211e-17.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 1.3636302844467475e-16.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

# update grav dataset
optimal_inv.data["reg_uncert"] = regional_misfit_stats.z_stdev

Regional gravity component

fname = "../tmp/bishop_model_uncertainty_regional"

# delete files if already exist
for p in pathlib.Path().glob(f"{fname}*"):
    p.unlink(missing_ok=True)

uncert_regional_results = invert4geom.full_workflow_uncertainty_loop(
    optimal_inv,
    fname=fname,
    runs=10,
    regional_misfit_parameter_dict=regional_misfit_parameter_dict,
    regional_grav_kwargs=new_regional_grav_kwargs,
    starting_topography_kwargs=starting_topography_kwargs,
)

uncert_plots(
    uncert_regional_results,
    optimal_inv.data.inner_region,
    optimal_inv.data.spacing,
    grid.basement_topo,
    constraints_df=constraint_points,
    weight_by="constraints",
)

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/sklearn/linear_model/_ridge.py:227: LinAlgWarning: An ill-conditioned matrix detected: slice 0 has rcond = 2.12370216650492e-16.
  return linalg.solve(A, Xy, assume_a="pos", overwrite_a=True).T

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

<xarray.Dataset> Size: 122kB
Dimensions:         (northing: 30, easting: 28, runs: 10)
Coordinates:
  * northing        (northing) float64 240B 1.959e+05 2.059e+05 ... 4.859e+05
  * easting         (easting) float64 224B 5.69e+04 6.69e+04 ... 3.269e+05
    top             (northing, easting) float64 7kB -5.878e+03 ... -6.09e+03
    bottom          (northing, easting) float64 7kB -6.09e+03 ... -6.46e+03
  * runs            (runs) <U5 200B 'run_0' 'run_1' 'run_2' ... 'run_8' 'run_9'
Data variables:
    run_num         (runs, northing, easting) float64 67kB -5.878e+03 ... -6....
    z_mean          (northing, easting) float64 7kB -5.868e+03 ... -6.558e+03
    z_stdev         (northing, easting) float64 7kB 100.1 107.4 ... 275.3 269.7
    weighted_mean   (northing, easting) float64 7kB -5.907e+03 ... -6.481e+03
    weighted_stdev  (northing, easting) float64 7kB 44.81 52.78 ... 184.6 172.2
    z_min           (northing, easting) float64 7kB -5.961e+03 ... -7.189e+03
    z_max           (northing, easting) float64 7kB -5.608e+03 ... -6.171e+03

xarray.Dataset

• Dimensions:
  • northing: 30
  • easting: 28
  • runs: 10
• Coordinates: (5)
  • northing
    (northing)
    float64
    1.959e+05 2.059e+05 ... 4.859e+05

    array([195900., 205900., 215900., 225900., 235900., 245900., 255900., 265900.,
           275900., 285900., 295900., 305900., 315900., 325900., 335900., 345900.,
           355900., 365900., 375900., 385900., 395900., 405900., 415900., 425900.,
           435900., 445900., 455900., 465900., 475900., 485900.])

  • easting
    (easting)
    float64
    5.69e+04 6.69e+04 ... 3.269e+05

    array([ 56900.,  66900.,  76900.,  86900.,  96900., 106900., 116900., 126900.,
           136900., 146900., 156900., 166900., 176900., 186900., 196900., 206900.,
           216900., 226900., 236900., 246900., 256900., 266900., 276900., 286900.,
           296900., 306900., 316900., 326900.])

  • top
    (northing, easting)
    float64
    -5.878e+03 -5.968e+03 ... -6.09e+03

    array([[-5877.82187116, -5968.23413248, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-5954.43909728, -5880.94903164, -5985.64976365, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-6089.83711898, -6030.31881147, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
    ...
            -3518.84255656, -3557.52230508, -3246.3030474 , -2924.2387636 ,
            -3438.46786222, -4145.07951214, -4479.20177654, -4612.22049576,
            -5096.32650127, -5456.41978172, -6075.2726978 , -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-3038.8838536 , -3043.30979352, -2981.22372827, -3252.55178778,
            -3416.05848589, -3211.88698055, -2767.39216792, -2893.26900635,
            -3457.85884111, -3992.96193161, -4177.69810302, -4473.62363492,
            -5012.57119856, -5635.74134447, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898],
           [-2812.24675762, -2570.6510817 , -2860.99472492, -3239.68478477,
            -3285.67436355, -2587.83371703, -2476.18369495, -2938.76676818,
            -3381.64590035, -3673.73706787, -3823.95899799, -4473.76249716,
            -5257.04841179, -6058.52984295, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898]])

  • bottom
    (northing, easting)
    float64
    -6.09e+03 -6.09e+03 ... -6.46e+03

    array([[-6089.83711898, -6089.83711898, -6098.42513559, -6281.12016302,
            -6444.81021943, -6665.76580116, -6852.73895863, -7053.77146666,
            -7114.90272649, -7234.62998262, -7493.4197448 , -7584.91258709,
            -7771.06579831, -7977.7046937 , -8166.56952813, -8425.41025729,
            -8501.03970462, -8773.43126128, -8859.37308513, -8949.09824932,
            -8995.34994969, -9034.9152163 , -9078.75516451, -9074.65522978,
            -8863.7494514 , -8980.06598179, -8985.49131549, -8874.98247145],
           [-6089.83711898, -6089.83711898, -6089.83711898, -6225.07372772,
            -6491.76593293, -6812.20725137, -6978.44539586, -7189.61149424,
            -7470.22356342, -7603.75633148, -7873.34485155, -7979.47341946,
            -8210.19525311, -8441.02544575, -8485.5846996 , -8789.03865041,
            -8893.81666255, -8957.11528902, -9021.06331796, -9056.19032456,
            -9166.30842784, -9110.66041   , -9086.97939138, -9168.23009809,
            -9079.92080075, -9083.10515489, -8850.68890429, -8874.80786923],
           [-6104.45572483, -6089.83711898, -6185.21296961, -6356.70455831,
            -6626.2226054 , -6890.5614477 , -7185.43603306, -7465.64595134,
            -7626.30554486, -7867.05752908, -8164.3851614 , -8364.97427464,
            -8537.49043001, -8758.27812615, -8739.79545172, -8904.46163951,
            -8992.42384524, -9024.71904819, -9064.73334944, -9169.95176421,
            -9235.84193351, -9135.75366112, -9149.70619395, -9186.3599086 ,
    ...
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6655.90136925,
            -7141.33284346, -7516.59342941, -7808.21820628, -7898.27481147,
            -8001.06320583, -7994.2939053 , -7609.10253901, -6590.56401631,
            -6617.22681118, -6679.62816848, -6458.8112573 , -6442.31502134],
           [-6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6407.88566853, -6872.35491768,
            -7357.87368111, -7621.42786555, -7856.27486322, -7983.05133081,
            -7897.68792329, -7725.71499968, -7563.37446157, -6679.93398247,
            -6537.60387313, -6637.84527213, -6621.24461756, -6578.42698392],
           [-6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6089.83711898, -6089.83711898,
            -6089.83711898, -6089.83711898, -6904.5592322 , -7249.00296561,
            -7635.24861317, -7805.7967088 , -7990.57225493, -8084.94080755,
            -7964.70289244, -7495.50935767, -7323.233612  , -6616.18343519,
            -6189.55091411, -6238.2002255 , -6317.35887027, -6459.92000196]])

  • runs
    (runs)
    <U5
    'run_0' 'run_1' ... 'run_8' 'run_9'

    array(['run_0', 'run_1', 'run_2', 'run_3', 'run_4', 'run_5', 'run_6', 'run_7',
           'run_8', 'run_9'], dtype='<U5')

• Data variables: (7)
  • run_num
    (runs, northing, easting)
    float64
    -5.878e+03 -5.968e+03 ... -6.62e+03

    array([[[-5877.82187116, -5968.23413248, -6098.42513559, ...,
             -8980.06598179, -8985.49131549, -8874.98247145],
            [-5954.43909728, -5880.94903164, -5985.64976365, ...,
             -9083.10515489, -8850.68890429, -8874.80786923],
            [-6104.45572483, -6030.31881147, -6185.21296961, ...,
             -9093.9104962 , -8985.61356607, -8942.08517394],
            ...,
            [-3130.00808769, -3261.63542632, -3223.73807491, ...,
             -6679.62816848, -6458.8112573 , -6442.31502134],
            [-3038.8838536 , -3043.30979352, -2981.22372827, ...,
             -6637.84527213, -6621.24461756, -6578.42698392],
            [-2812.24675762, -2570.6510817 , -2860.99472492, ...,
             -6238.2002255 , -6317.35887027, -6459.92000196]],
    
           [[-5607.71558987, -5712.17049188, -5861.74007328, ...,
             -9252.67618447, -9287.02157999, -9209.02024711],
            [-6034.29707058, -5901.05167965, -5967.99222463, ...,
             -9096.17065398, -8913.91258904, -9029.33222882],
            [-6392.9235631 , -6171.84380967, -6275.21900953, ...,
             -9028.354317  , -8978.50039948, -9002.62178182],
    ...
             -6624.40045654, -6347.98214564, -6257.79624706],
            [-3139.82698624, -3127.7197926 , -3045.49210011, ...,
             -6545.64602646, -6460.10838761, -6344.44156271],
            [-2904.08943712, -2654.50450596, -2925.57261144, ...,
             -6037.61376827, -6043.60985488, -6170.79174319]],
    
           [[-5928.96276368, -5961.67982453, -6068.94355874, ...,
             -9046.24907378, -9048.92662156, -8978.06904091],
            [-6030.76178885, -5971.7436058 , -6029.84125604, ...,
             -9127.78466861, -8998.98720695, -9008.62045012],
            [-6258.25875663, -6222.65511569, -6275.65910892, ...,
             -9145.1931653 , -9074.15405281, -9054.15864237],
            ...,
            [-3102.01071853, -3281.93418092, -3214.41634336, ...,
             -6663.97715452, -6554.98643432, -6539.54042146],
            [-3058.04163705, -3043.75292262, -2986.41647156, ...,
             -6601.69742746, -6654.47931542, -6661.63386892],
            [-2835.968832  , -2478.7871206 , -2925.44736057, ...,
             -6372.18827461, -6500.82192542, -6620.06970391]]],
          shape=(10, 30, 28))

  • z_mean
    (northing, easting)
    float64
    -5.868e+03 ... -6.558e+03

    array([[-5868.44857588, -5937.05408304, -6057.97408578, -6242.29906405,
            -6416.33511728, -6646.49710003, -6847.35682246, -7060.12253302,
            -7140.61877187, -7275.09093507, -7535.96544779, -7640.92658837,
            -7830.70220925, -8035.39893875, -8219.09196352, -8462.74856839,
            -8532.40944658, -8781.00510992, -8856.71991756, -8938.08142737,
            -8983.00126188, -9025.17268405, -9076.05914456, -9084.50181667,
            -8902.27048321, -9019.70723313, -9028.53741397, -8934.08920915],
           [-6007.28670938, -5914.29496837, -6000.17776744, -6228.34015465,
            -6485.94008186, -6792.05538203, -6953.9667151 , -7154.52212266,
            -7418.23679944, -7549.30439018, -7807.70736151, -7917.78291918,
            -8143.81229583, -8371.24359084, -8428.25793585, -8722.19556399,
            -8831.82304859, -8901.26102575, -8969.56647725, -9010.53383847,
            -9121.09034606, -9080.38206497, -9071.05134171, -9159.67432794,
            -9093.55172822, -9109.3636061 , -8902.78050671, -8949.59381093],
           [-6203.32612235, -6102.44424813, -6227.41012125, -6384.52636226,
            -6634.86514854, -6879.52935107, -7150.36950441, -7406.71579992,
            -7554.6454726 , -7779.19901277, -8059.098791  , -8254.15340879,
            -8426.18298533, -8643.9255178 , -8644.11208675, -8811.9629023 ,
            -8909.07801761, -8953.10270601, -9001.51752736, -9108.79427759,
            -9179.51383516, -9098.41179029, -9123.23476247, -9170.46560339,
    ...
            -3538.03018214, -3595.64418169, -3275.83942152, -2938.11751312,
            -3476.66871209, -4216.45464015, -4550.20720525, -4666.00315742,
            -5124.53524126, -5482.80631334, -6089.56164912, -6652.09765457,
            -7112.41939034, -7462.86191382, -7730.56696785, -7811.4989376 ,
            -7905.98215745, -7897.36901267, -7525.38934858, -6563.19840312,
            -6588.23724091, -6678.56171919, -6493.5127484 , -6491.33273444],
           [-3011.50462286, -3012.83938808, -2956.57006842, -3260.46936553,
            -3458.69706529, -3260.80428786, -2803.05320258, -2935.47856728,
            -3531.31386827, -4082.93106441, -4247.76022249, -4526.82542313,
            -5059.68284135, -5675.98334505, -6422.33604098, -6868.51837881,
            -7321.46193806, -7566.14671883, -7781.21428754, -7896.22146086,
            -7818.79460712, -7661.5221878 , -7500.50163829, -6665.96681534,
            -6534.75260691, -6656.873374  , -6662.65956593, -6631.9669471 ],
           [-2783.96103141, -2526.62038432, -2843.35667395, -3274.85314379,
            -3357.01946479, -2631.28219738, -2537.36513989, -3033.52449765,
            -3498.27689446, -3786.04438537, -3912.20330545, -4547.34025082,
            -5312.23860272, -6078.29266845, -6868.50912066, -7184.76040065,
            -7537.29768934, -7693.44482342, -7865.74159408, -7962.17814636,
            -7872.01132461, -7465.16963645, -7320.68760493, -6669.07200316,
            -6283.82820912, -6353.08871451, -6439.7084336 , -6557.64366235]])

  • z_stdev
    (northing, easting)
    float64
    100.1 107.4 106.6 ... 275.3 269.7

    array([[100.10853637, 107.44999979, 106.601866  ,  98.97426296,
             82.59741639,  56.95418312,  29.47849003,  29.15012989,
             53.75926208,  82.46837169, 119.14481443, 123.79678988,
            126.97111342, 120.02540573, 103.07011919,  88.13051891,
             54.39512706,  51.23113648,  40.37574723,  44.30680943,
             50.58091949,  55.70689969,  60.10228349,  65.606905  ,
             91.16668483,  94.76791857, 108.18880986, 137.2458387 ],
           [ 48.55687522,  39.07967624,  27.44128559,  33.88761011,
             45.89108687,  56.25733641,  75.47262717,  93.24003201,
            113.15047317, 129.65618553, 147.63299359, 153.37839853,
            159.96591861, 162.42075735, 150.85959589, 149.54605078,
            137.28181245, 123.24334608, 110.37429951,  97.47601087,
             85.12157888,  67.84631725,  52.51523789,  35.06422909,
             41.88166202,  61.06448618,  98.54717732, 178.80653848],
           [109.58494816,  81.14395471,  43.08735534,  37.37539635,
             42.1719782 ,  65.239739  ,  94.93265476, 129.298048  ,
            162.22635123, 189.48084672, 212.34337508, 224.72129526,
            228.37025718, 225.79475035, 209.15550331, 194.9392576 ,
            177.03098957, 157.31160866, 139.83493997, 124.23388918,
            109.12584385,  93.38605582,  77.31731552,  60.15513456,
    ...
             75.15599876,  74.17254239,  78.34513921, 145.62822853,
            124.98663269, 114.91129301, 115.93894293, 108.90255327,
            112.52497922,  93.97605224, 103.12913112, 128.82186937,
            159.95105899, 191.1173757 , 214.4824727 , 228.63655215,
            227.76437245, 213.98141391, 177.45688431, 122.07701401,
             79.64217953,  61.908575  ,  91.95103863, 142.13295411],
           [100.29968729,  90.2502094 ,  82.46403221, 109.8081983 ,
            131.42120692,  96.49235537, 121.76634165, 154.38655822,
            141.75345766, 149.15275431, 144.21248274, 127.91317767,
            101.53951492,  90.3400422 , 102.90912393, 139.7665609 ,
            169.12118045, 199.85931904, 217.2125923 , 219.90326883,
            207.53107626, 178.41614655, 144.44920921,  83.60345432,
             74.32972355,  99.3847494 , 135.14800272, 174.70292348],
           [100.96194405,  92.51508506, 126.12256721, 193.58638999,
            197.91908907, 131.18542367, 180.58415995, 198.68248406,
            216.36926728, 221.11220878, 199.15045724, 168.13019503,
            109.21154356,  56.99127261,  96.00090609, 184.3195793 ,
            249.98447881, 290.57333458, 292.24304033, 265.51893832,
            213.19239563, 140.44212456, 116.27085602, 125.53060723,
            180.27171733, 242.03145272, 275.29010265, 269.68303226]])

  • weighted_mean
    (northing, easting)
    float64
    -5.907e+03 ... -6.481e+03

    array([[-5906.92169327, -5978.48103673, -6098.8542226 , -6281.80556418,
            -6450.08759983, -6668.75172832, -6855.38489855, -7050.15400976,
            -7117.69813871, -7238.94722699, -7484.32805352, -7586.68449883,
            -7775.13714541, -7982.94492224, -8174.04257697, -8424.69023715,
            -8509.80296258, -8762.23845441, -8847.85700545, -8934.41894192,
            -8983.04332704, -9024.31373494, -9071.63357267, -9075.29486862,
            -8895.64252255, -9001.97273765, -9005.20455688, -8898.83539736],
           [-5996.26076215, -5919.51916604, -6008.31601139, -6241.59760757,
            -6504.96390506, -6814.05885123, -6983.2668493 , -7187.73672618,
            -7449.94710479, -7586.45943427, -7843.96481347, -7958.21029695,
            -8182.55310564, -8407.97890474, -8469.43598318, -8756.31768522,
            -8866.03623354, -8935.11851422, -9001.56696986, -9041.51208357,
            -9145.50338921, -9103.12533849, -9089.95482686, -9168.02799099,
            -9095.75428179, -9101.23185752, -8895.52075148, -8909.26642043],
           [-6168.28574203, -6095.57502975, -6220.37909828, -6388.87309662,
            -6649.68763461, -6905.87935986, -7187.14896328, -7453.69572386,
            -7614.32677029, -7846.29538644, -8129.76068677, -8327.75321431,
            -8500.3955559 , -8712.32092662, -8712.39080377, -8872.63540307,
            -8964.50638727, -9003.76028445, -9047.69892689, -9148.20915821,
            -9213.31131954, -9132.14479083, -9150.73150716, -9189.1919241 ,
    ...
            -3550.48528464, -3593.82526522, -3244.01049518, -2879.1803718 ,
            -3421.98363838, -4167.87912242, -4502.57666747, -4622.87884643,
            -5085.26424888, -5464.45799886, -6092.00332032, -6676.88643433,
            -7158.42826713, -7527.35890829, -7806.75051327, -7895.62273739,
            -7987.66870424, -7970.24027353, -7579.59938675, -6604.75591649,
            -6599.81501526, -6672.70809966, -6478.38801231, -6454.32455943],
           [-3047.86568492, -3043.61146317, -2980.50882534, -3287.02671566,
            -3477.97418717, -3249.42798296, -2752.34513576, -2869.33871017,
            -3470.89121499, -4020.33819395, -4184.70719966, -4472.31500041,
            -5023.04427634, -5663.71160128, -6431.5847816 , -6904.66778714,
            -7375.26352279, -7637.28767405, -7860.80428369, -7975.16847272,
            -7891.39714096, -7719.74035057, -7527.91554646, -6679.73659477,
            -6521.77188049, -6625.35692514, -6621.89738146, -6581.48146892],
           [-2821.09568316, -2546.49741605, -2874.73505948, -3313.61447156,
            -3374.5643844 , -2598.61907677, -2465.22528359, -2956.77037795,
            -3414.19366646, -3694.09706391, -3825.9477825 , -4473.94603086,
            -5267.18044908, -6070.52133228, -6896.3428872 , -7257.53971184,
            -7638.6655229 , -7812.12722464, -7980.74780152, -8056.85304245,
            -7933.98306923, -7497.68994407, -7303.60390654, -6625.48029893,
            -6220.61989184, -6271.07842839, -6354.8108961 , -6480.91107758]])

  • weighted_stdev
    (northing, easting)
    float64
    44.81 52.78 53.61 ... 184.6 172.2

    array([[ 44.8082099 ,  52.77916464,  53.61450384,  46.15960443,
             37.90256685,  26.97660598,  15.02072915,  16.07706525,
             25.16880416,  40.84352246,  70.07722188,  67.83015456,
             69.96697188,  66.58263819,  56.53896159,  52.59887832,
             30.58156781,  39.24572331,  31.79373362,  33.07834912,
             30.65230923,  28.40637927,  23.48908847,  21.25555302,
             66.09251537,  62.66797813,  74.25054743, 102.52448318],
           [ 42.83596996,  43.71905853,  25.09414782,  22.0218122 ,
             23.43421788,  24.60699169,  33.85378092,  47.42080977,
             75.19550357,  84.07637508, 106.87501055, 104.17545258,
            113.24682308, 117.78937149,  93.67160121, 103.75555078,
             88.00573198,  71.05258215,  58.8852459 ,  46.05195929,
             45.90947176,  25.99315668,  16.92346192,  10.9235453 ,
             35.3679658 ,  50.66966916,  99.10762781, 134.93742514],
           [ 79.85726767,  87.66608985,  43.45466791,  42.38361148,
             33.23965499,  30.33500868,  37.22535296,  58.36818854,
             72.67108078,  90.79591219, 112.43501034, 120.02322921,
            121.21629885, 128.25206723, 102.32115415,  98.49986468,
             85.08124281,  68.28914337,  55.80784165,  52.70363575,
             47.82846324,  28.39048531,  22.14928312,  17.11011251,
    ...
             58.87747184,  59.20735718,  29.04604855, 101.91121   ,
             63.35000004,  49.16799721,  53.17003002,  49.50741307,
             59.408788  ,  47.17780311,  53.85610154,  62.48911854,
             63.52842197,  62.44239631,  59.2464461 ,  64.01119983,
             68.78603354,  77.37291383,  76.81632627,  42.85808161,
             35.15606871,  33.03201808,  78.72879625, 108.46833768],
           [ 55.37745529,  54.07988836,  48.05840645,  75.35097404,
            110.81867113,  61.93601199,  54.15781522,  76.73671563,
             49.02714864,  59.57070853,  57.6048604 ,  56.65132077,
             49.34847471,  62.82834106,  64.86720999,  83.06624266,
             70.88560428,  72.2505039 ,  63.58882911,  61.37525058,
             63.19952473,  61.08194464,  83.6933645 ,  29.97372925,
             40.23904362,  57.01675393,  90.72500203, 124.63907121],
           [ 56.48404335,  72.18644616,  67.95527039, 146.41140085,
            160.61719414,  37.39058336,  62.35301268,  59.28223534,
             72.62892494,  73.25182382,  71.79295566,  64.57107402,
             47.63582458,  40.95392369,  39.63244416,  73.67042534,
             85.85419437,  95.61394767,  88.0972026 ,  92.92408803,
             94.32189217,  57.66879411,  73.19151381,  59.70947889,
            104.49706411, 149.02945429, 184.60378772, 172.19390029]])

  • z_min
    (northing, easting)
    float64
    -5.961e+03 ... -7.189e+03

    array([[-5960.65833211, -6065.60905428, -6179.90317292, -6336.91447127,
            -6475.99861499, -6685.09953918, -6864.93888007, -7137.75961418,
            -7274.14230668, -7458.90438719, -7766.45131871, -7883.35585485,
            -8073.04066933, -8262.76942082, -8418.61378257, -8631.68630165,
            -8657.98081909, -8887.02388977, -8940.55117104, -9015.49509932,
            -9066.45178582, -9130.92973839, -9215.73199334, -9260.46040597,
            -9098.81304122, -9252.67618447, -9287.02157999, -9209.02024711],
           [-6100.62702707, -6001.94273392, -6056.26413816, -6279.91663172,
            -6537.11774545, -6850.59528548, -7032.86934317, -7266.34976794,
            -7572.03910486, -7728.80485714, -8018.73381095, -8136.10289003,
            -8371.56008193, -8598.81762527, -8629.93610802, -8917.49744029,
            -9001.4456489 , -9043.0943867 , -9087.36484261, -9105.97974129,
            -9202.67180754, -9134.79418517, -9102.5243933 , -9194.20985279,
            -9164.07856498, -9241.75995052, -9067.67247905, -9356.92713969],
           [-6392.9235631 , -6249.58675892, -6299.86848015, -6468.2808375 ,
            -6709.04022254, -6942.89462161, -7236.72518103, -7538.29799036,
            -7720.30696738, -7980.94564622, -8295.11944177, -8505.0508941 ,
            -8680.15248912, -8896.73188028, -8865.10481551, -9014.60985954,
            -9084.04784794, -9096.71497084, -9119.01199505, -9209.64672007,
            -9264.17231065, -9154.91945877, -9160.99261919, -9208.10991766,
    ...
            -3642.92322902, -3731.39392512, -3492.79326148, -3209.99060354,
            -3744.46457365, -4455.51022273, -4808.43937702, -4949.79917445,
            -5440.84561815, -5756.15519973, -6322.77037955, -6827.90060312,
            -7243.66513202, -7597.71675744, -7838.18389748, -7912.87902015,
            -8042.96971886, -8057.03541085, -7672.86975955, -6645.20187573,
            -6697.09922609, -6842.51303151, -6675.8604115 , -6753.50916574],
           [-3139.82698624, -3127.7197926 , -3045.49210011, -3393.68339489,
            -3655.37506346, -3489.00187784, -3121.25561398, -3303.32645767,
            -3893.52761626, -4433.3076688 , -4542.61815284, -4821.46109358,
            -5336.06895889, -5905.01097353, -6613.34776193, -7035.20727738,
            -7472.92547466, -7729.18254128, -7910.44145509, -8002.84747786,
            -7949.7447386 , -7795.90429684, -7628.63405751, -6777.61852106,
            -6741.25911235, -6921.32038262, -6952.45051822, -6935.02562728],
           [-2904.08943712, -2654.50450596, -2925.57261144, -3535.6564978 ,
            -3627.99564234, -3016.60300996, -3044.64763232, -3601.15514228,
            -4099.64633377, -4371.35656542, -4403.79734321, -4928.04427806,
            -5544.43731681, -6219.05206435, -6943.33659976, -7344.48173266,
            -7718.12087054, -7889.56541997, -8015.07983738, -8153.48423624,
            -8059.84218259, -7585.11485003, -7611.02063899, -7027.49759999,
            -6679.99848778, -6788.72323195, -6971.47587235, -7188.70739423]])

  • z_max
    (northing, easting)
    float64
    -5.608e+03 ... -6.171e+03

    array([[-5607.71558987, -5712.17049188, -5848.62575294, -6025.47785667,
            -6217.79114514, -6496.00640212, -6760.61704279, -7028.94435981,
            -7092.89722908, -7202.13601793, -7395.66063581, -7518.06378453,
            -7708.82136358, -7922.95094233, -8126.84028304, -8369.46968947,
            -8471.4243176 , -8704.08942671, -8798.66056403, -8861.25756556,
            -8867.41753624, -8896.88234138, -8951.3883609 , -8979.61049561,
            -8789.54943785, -8912.15806077, -8886.9181083 , -8725.21522955],
           [-5954.43909728, -5880.94903164, -5962.44379902, -6167.76009817,
            -6389.17769517, -6658.10534117, -6772.77000692, -6930.92925269,
            -7160.41979395, -7251.32553542, -7483.71088424, -7567.26999949,
            -7781.85796505, -8005.11760994, -8058.84571589, -8369.59084156,
            -8493.08444618, -8583.37522461, -8677.25576675, -8746.18410028,
            -8894.96828021, -8888.09439144, -8918.40203566, -9058.16795922,
            -9034.99174986, -9028.31550468, -8763.47662085, -8696.23914837],
           [-6102.85348369, -6030.31881147, -6185.21296961, -6356.70455831,
            -6551.11374354, -6716.15615626, -6902.85918324, -7075.42524188,
            -7142.05211543, -7299.37533153, -7527.81781345, -7688.78139622,
            -7846.50548938, -8072.42266035, -8091.41209254, -8293.59389032,
            -8429.61062693, -8516.40682755, -8607.30993757, -8759.67908272,
            -8873.36567859, -8827.41740268, -8895.41441114, -8990.96934206,
    ...
            -3364.05465384, -3483.38431843, -3214.03385706, -2722.11947013,
            -3341.71682609, -4136.82770437, -4476.39766443, -4606.65331864,
            -5026.92297613, -5416.69131247, -5892.57140627, -6320.25943775,
            -6655.00326019, -6899.48903589, -7094.00168372, -7140.90678008,
            -7243.65922223, -7285.75547875, -7026.02458019, -6207.8493773 ,
            -6377.22602846, -6598.10970826, -6347.98214564, -6257.79624706],
           [-2796.64434951, -2811.36963125, -2732.90275164, -2971.1569557 ,
            -3182.77617626, -3138.31639268, -2681.37756027, -2766.59688837,
            -3448.69522804, -3985.51511444, -4166.46927791, -4437.67844657,
            -4985.64714263, -5589.8825224 , -6215.86081907, -6510.90012501,
            -6838.66168788, -6985.55713968, -7142.14290542, -7249.00227004,
            -7212.38903248, -7142.88690334, -7124.22525136, -6436.3037739 ,
            -6457.6942559 , -6545.64602646, -6460.10838761, -6344.44156271],
           [-2567.43045506, -2321.73420452, -2478.31020221, -2804.43391138,
            -2965.4095444 , -2517.62518966, -2403.67097625, -2936.28566553,
            -3378.58632417, -3670.0519089 , -3788.66028631, -4441.18440114,
            -5229.65880199, -6009.86892943, -6595.99100972, -6671.25303279,
            -6839.18948019, -6887.20207542, -7041.43829112, -7208.62663906,
            -7272.30970987, -7067.46494321, -7173.84093969, -6594.72525529,
            -6082.53753687, -6037.61376827, -6043.60985488, -6170.79174319]])

Total Uncertainty

fname = "../tmp/bishop_model_uncertainty_full"

# delete files if already exist
for p in pathlib.Path().glob(f"{fname}*"):
    p.unlink(missing_ok=True)

uncert_results = invert4geom.full_workflow_uncertainty_loop(
    optimal_inv,
    fname=fname,
    runs=20,
    sample_gravity=True,
    sample_constraints=True,
    constraints_df=constraint_points,
    parameter_dict=density_dict | zref_dict | solver_dict,
    regional_grav_kwargs=new_regional_grav_kwargs,
    starting_topography_kwargs=starting_topography_kwargs,
)

uncert_plots(
    uncert_results,
    optimal_inv.data.inner_region,
    optimal_inv.data.spacing,
    grid.basement_topo,
    constraints_df=constraint_points,
    weight_by="constraints",
)

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

<xarray.Dataset> Size: 189kB
Dimensions:         (northing: 30, easting: 28, runs: 20)
Coordinates:
  * northing        (northing) float64 240B 1.959e+05 2.059e+05 ... 4.859e+05
  * easting         (easting) float64 224B 5.69e+04 6.69e+04 ... 3.269e+05
    top             (northing, easting) float64 7kB -4.093e+03 ... -5.735e+03
    bottom          (northing, easting) float64 7kB -5.845e+03 ... -5.845e+03
  * runs            (runs) <U6 480B 'run_0' 'run_1' ... 'run_18' 'run_19'
Data variables:
    run_num         (runs, northing, easting) float64 134kB -4.093e+03 ... -7...
    z_mean          (northing, easting) float64 7kB -4.572e+03 ... -6.145e+03
    z_stdev         (northing, easting) float64 7kB 602.4 450.5 ... 608.9 628.5
    weighted_mean   (northing, easting) float64 7kB -4.578e+03 ... -6.155e+03
    weighted_stdev  (northing, easting) float64 7kB 572.7 432.4 ... 538.2 571.3
    z_min           (northing, easting) float64 7kB -5.573e+03 ... -7.522e+03
    z_max           (northing, easting) float64 7kB -3.294e+03 ... -4.94e+03

xarray.Dataset

• Dimensions:
  • northing: 30
  • easting: 28
  • runs: 20
• Coordinates: (5)
  • northing
    (northing)
    float64
    1.959e+05 2.059e+05 ... 4.859e+05

    array([195900., 205900., 215900., 225900., 235900., 245900., 255900., 265900.,
           275900., 285900., 295900., 305900., 315900., 325900., 335900., 345900.,
           355900., 365900., 375900., 385900., 395900., 405900., 415900., 425900.,
           435900., 445900., 455900., 465900., 475900., 485900.])

  • easting
    (easting)
    float64
    5.69e+04 6.69e+04 ... 3.269e+05

    array([ 56900.,  66900.,  76900.,  86900.,  96900., 106900., 116900., 126900.,
           136900., 146900., 156900., 166900., 176900., 186900., 196900., 206900.,
           216900., 226900., 236900., 246900., 256900., 266900., 276900., 286900.,
           296900., 306900., 316900., 326900.])

  • top
    (northing, easting)
    float64
    -4.093e+03 ... -5.735e+03

    array([[-4092.5467965 , -4415.15348114, -4528.11843267, -4798.08933905,
            -5059.71279706, -5475.57236934, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5650.68522665],
           [-4954.71484118, -5009.61733613, -5147.22990984, -5335.56104055,
            -5686.40081189, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787],
           [-5498.71895658, -5511.83802358, -5561.662859  , -5815.66773905,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
    ...
            -3709.33743929, -3715.35517775, -3469.40405962, -3174.78472691,
            -3640.40169256, -4406.54486914, -4768.43028177, -4775.25348996,
            -5280.30192028, -5491.51273712, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787],
           [-3346.48077648, -3309.2200238 , -3197.68349365, -3429.17014126,
            -3661.1579879 , -3506.21261246, -3050.62933661, -3238.27920522,
            -3764.84077718, -4376.70648006, -4445.25585377, -4622.935259  ,
            -5159.33619843, -5618.74901221, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787],
           [-3221.46942379, -2872.6628699 , -3100.91911269, -3556.40068479,
            -3665.51740131, -2865.7161934 , -2873.20348322, -3382.93078748,
            -3858.67882191, -4085.07561974, -4125.39512497, -4662.50222086,
            -5346.28982867, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5734.9022586 ]])

  • bottom
    (northing, easting)
    float64
    -5.845e+03 ... -5.845e+03

    array([[-5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5888.57546185, -6331.48547932,
            -6566.51404034, -6791.77684627, -7310.23349322, -7468.58227511,
            -7754.77336863, -7795.53244797, -8029.47040709, -8116.77563349,
            -7948.30241143, -8241.75863512, -8155.82462408, -8069.07793479,
            -8092.90577378, -8066.76976407, -7931.53278897, -7818.28044574,
            -7272.33427602, -7181.26418017, -7006.99096948, -5844.61581787],
           [-5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -6162.956998  , -6455.10599648, -6608.07886476,
            -7224.84167423, -7326.09603892, -7690.25202616, -7921.60965612,
            -7952.87798234, -8348.7845    , -8174.89559603, -8592.97956945,
            -8555.02755453, -8660.72179148, -8735.59091057, -8724.35298512,
            -8986.05654539, -8763.96167533, -8582.92834842, -8845.47069867,
            -8405.10587274, -8169.27107884, -7919.40336924, -6725.72972221],
           [-5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -6101.0529305 , -6438.32368743, -6775.36868319, -7214.14828396,
            -7318.02507862, -7684.11877019, -7992.86933384, -8242.52075237,
            -8375.05531495, -8760.77662566, -8511.68971189, -8725.19384438,
            -8855.59616379, -8911.35491633, -8772.72728108, -8963.51358078,
            -9148.487129  , -8861.27695722, -8718.45035251, -8935.54559913,
    ...
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -6086.15858743, -6657.59174036,
            -7015.35601151, -7407.92246549, -7647.59696938, -7847.50715668,
            -7988.36162413, -7998.09118294, -7542.39966405, -6318.35429635,
            -6549.41328908, -6500.96973323, -6226.22005163, -5933.1231146 ],
           [-5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -6358.13073197, -6926.54558388,
            -7116.17526358, -7408.30830008, -7496.71209926, -7791.54470284,
            -7640.14400376, -7553.86958681, -7497.97940618, -6446.09147046,
            -6376.98631136, -6574.47106321, -6558.09438642, -6092.22631671],
           [-5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -6003.55165218, -6686.73101142, -6704.30521388,
            -6981.59900135, -7094.86616168, -7189.19505516, -7357.19310682,
            -7389.89565849, -6987.71031352, -7073.05655197, -6383.83856417,
            -6034.89991253, -6003.12386338, -6081.31168053, -5844.61581787]])

  • runs
    (runs)
    <U6
    'run_0' 'run_1' ... 'run_19'

    array(['run_0', 'run_1', 'run_2', 'run_3', 'run_4', 'run_5', 'run_6', 'run_7',
           'run_8', 'run_9', 'run_10', 'run_11', 'run_12', 'run_13', 'run_14',
           'run_15', 'run_16', 'run_17', 'run_18', 'run_19'], dtype='<U6')

• Data variables: (7)
  • run_num
    (runs, northing, easting)
    float64
    -4.093e+03 ... -7.522e+03

    array([[[-4092.5467965 , -4415.15348114, -4528.11843267, ...,
             -7181.26418017, -7006.99096948, -5650.68522665],
            [-4954.71484118, -5009.61733613, -5147.22990984, ...,
             -8169.27107884, -7919.40336924, -6725.72972221],
            [-5498.71895658, -5511.83802358, -5561.662859  , ...,
             -8223.78572104, -8110.63875552, -6908.88477988],
            ...,
            [-3434.78997653, -3438.46558514, -3380.90964832, ...,
             -6500.96973323, -6226.22005163, -5933.1231146 ],
            [-3346.48077648, -3309.2200238 , -3197.68349365, ...,
             -6574.47106321, -6558.09438642, -6092.22631671],
            [-3221.46942379, -2872.6628699 , -3100.91911269, ...,
             -6003.12386338, -6081.31168053, -5734.9022586 ]],
    
           [[-4617.07728056, -4903.40260904, -5138.08237997, ...,
             -7867.8472589 , -7591.52788863, -6504.06502501],
            [-5185.32487583, -5362.157477  , -5462.37424039, ...,
             -8478.8699923 , -8158.28969539, -7295.24908223],
            [-5460.09390411, -5523.24315743, -5705.97141535, ...,
             -8519.46291389, -8373.77937304, -7468.04305798],
    ...
             -6142.93220392, -5841.04662991, -5433.1767471 ],
            [-2872.64366717, -2865.19283756, -2723.5986785 , ...,
             -5999.30144525, -5844.61686952, -5375.60854805],
            [-2522.18667776, -2284.31476792, -2568.91840561, ...,
             -5410.2642175 , -5327.18369732, -4939.94464913]],
    
           [[-5308.85832114, -5245.33241045, -5966.94272083, ...,
             -8304.083819  , -8351.69790379, -7196.53122   ],
            [-5892.40307954, -6071.58590339, -5980.06723307, ...,
             -9090.95786007, -8019.69265925, -8080.86634146],
            [-6551.70801291, -6037.87750055, -5199.05409887, ...,
             -8651.57040186, -8802.04932149, -8261.64998887],
            ...,
            [-4563.63657034, -3818.55926096, -4064.96502622, ...,
             -8672.99417617, -6666.6660689 , -7015.47247069],
            [-4270.84186715, -4006.51721491, -3326.3632774 , ...,
             -6574.24472636, -7882.89232269, -7561.31177533],
            [-5385.01455477, -3851.41146969, -4709.61086644, ...,
             -7198.15649571, -7787.59002022, -7522.38516959]]],
          shape=(20, 30, 28))

  • z_mean
    (northing, easting)
    float64
    -4.572e+03 ... -6.145e+03

    array([[-4571.99388116, -4760.8130382 , -4994.41908485, -5170.09226328,
            -5537.1903122 , -5876.1432114 , -6322.88723952, -6659.77641559,
            -6993.45155396, -7190.847452  , -7677.89187756, -7680.64869183,
            -7974.18409371, -7975.76564256, -8139.12425237, -8188.34902092,
            -8148.31226291, -8248.6180952 , -8269.99251832, -8186.4514216 ,
            -8246.78378722, -8156.4068633 , -8132.8124988 , -7978.17548131,
            -7611.61140152, -7514.21830167, -7162.82394196, -6232.9623963 ],
           [-5247.61210744, -5316.49528258, -5362.58029804, -5630.63670601,
            -6041.74496395, -6299.83684414, -6694.19969147, -6876.75649929,
            -7361.39470943, -7506.26516022, -7780.49152631, -7990.20617715,
            -8075.17082941, -8388.20590331, -8230.09247169, -8543.22101476,
            -8561.17907208, -8575.50043505, -8612.70412689, -8671.67255991,
            -8726.36125083, -8722.92084124, -8579.10437302, -8601.81476129,
            -8403.84088745, -8208.50235972, -7735.1535319 , -6944.86454567],
           [-5744.12365016, -5697.18250159, -5807.1134496 , -6111.77086143,
            -6134.27760826, -6747.60212823, -6836.26319805, -7375.57811887,
            -7451.64568649, -7826.47635251, -8170.12977811, -8320.26130401,
            -8488.85615716, -8567.14680915, -8648.91473714, -8630.13873209,
            -8709.59064209, -8758.47521257, -8793.01394737, -8872.87013697,
            -8997.41947674, -8831.01980284, -8902.7016368 , -8800.78944379,
    ...
            -3839.16013279, -3738.54399895, -3622.42638763, -3157.48776617,
            -3698.0045756 , -4385.41092821, -4715.6794888 , -4737.40516543,
            -5136.3881364 , -5450.50322142, -5926.70739023, -6529.9921575 ,
            -6812.23744684, -7211.85156869, -7540.77104778, -7551.51578833,
            -7860.57552999, -7853.0627322 , -7464.92146863, -6693.65971656,
            -6570.18158294, -6766.85263415, -6431.74068617, -6205.64062122],
           [-3590.94661966, -3577.99412485, -3240.05561048, -3636.93674421,
            -3667.7992147 , -3710.68803082, -3040.48351693, -3368.86916196,
            -3828.20371667, -4303.45783704, -4431.65113086, -4620.60863038,
            -5078.68379232, -5526.38315874, -6198.72992507, -6531.53948484,
            -6903.79922879, -7204.14966787, -7250.13353731, -7653.03403392,
            -7461.72094666, -7515.96998707, -7451.14874713, -6598.91962432,
            -6615.77227037, -6637.67287555, -6635.03602634, -6301.64876159],
           [-3708.49847868, -3057.70512048, -3501.11285879, -3781.67795388,
            -3946.87756141, -3017.81074445, -3194.5846958 , -3542.98070867,
            -3948.03730893, -4198.33644144, -4158.41769995, -4687.31397426,
            -5222.13419526, -5789.69357209, -6359.12395629, -6467.71642652,
            -6731.70928407, -6780.3584782 , -7055.50237421, -7185.15490398,
            -7298.0987577 , -7096.6147169 , -7108.62607772, -6611.53172099,
            -6316.14091644, -6372.42714052, -6366.24361107, -6145.0958704 ]])

  • z_stdev
    (northing, easting)
    float64
    602.4 450.5 522.3 ... 608.9 628.5

    array([[ 602.39945982,  450.47587727,  522.25206816,  430.96899102,
             476.47996851,  426.6470692 ,  519.23048014,  467.59629372,
             578.93850882,  544.07788402,  750.0628945 ,  611.87202561,
             733.53297475,  594.29056259,  645.83755598,  584.13566756,
             591.15870328,  525.87069176,  599.55623769,  463.95319704,
             520.32114178,  411.03217424,  483.67458841,  448.94804908,
             460.50691306,  521.50194941,  619.27089827,  662.85555743],
           [ 371.02305468,  381.48454802,  337.23141326,  336.34345551,
             508.277347  ,  344.34737369,  421.60360637,  320.22349013,
             393.90744004,  369.45917768,  385.41729711,  442.4922373 ,
             406.0877521 ,  520.03278871,  452.0331109 ,  461.8763098 ,
             408.11443435,  419.43828078,  380.9015145 ,  411.26283461,
             324.82239094,  392.60531125,  305.88194571,  369.86567772,
             372.07588363,  438.41394537,  526.72013878,  578.3488574 ],
           [ 327.24624037,  203.48596998,  268.4228491 ,  616.11811623,
             713.10491443,  695.73777961,  427.90878785,  390.09972847,
             216.76323836,  244.34495575,  335.7440405 ,  327.13133275,
             382.33633986,  385.29442222,  519.4657026 ,  362.06508457,
             305.04702437,  311.99249384,  336.59901307,  248.32297136,
             303.40610019,  289.23542354,  365.85348621,  259.42033886,
    ...
             307.47270201,  313.43964519,  587.38296839,  678.34342211,
             372.96396979,  184.91029543,  466.79660115,  632.92733182,
             968.62204446,  742.53837463,  472.21097679,  222.74711599,
             206.5461336 ,  169.4037173 ,  255.54077685,  281.86049605,
             339.87465726,  126.53088331,  229.68225846,  574.16948559,
             424.07282167,  578.26588201,  400.46863337,  464.32942981],
           [ 511.35782332,  472.01124351,  631.73436153,  364.17776223,
             521.34052085,  640.24345106,  824.11882802,  422.14283804,
             254.89288552,  264.89781442,  257.02696342,  463.1020756 ,
             554.71644523,  599.20534394,  324.04563904,  250.8569049 ,
             139.35628855,  355.78706719,  360.91392556,  458.11030688,
             267.05293893,  243.3191765 ,  390.092908  ,  397.37805242,
             601.2318627 ,  436.37074366,  537.03114116,  571.59526824],
           [ 743.73061143,  887.43973217,  626.68355603,  427.59092709,
             609.67214223,  763.96827508,  585.725305  ,  464.64363239,
             407.49312518,  384.59427651,  390.00883837,  304.26369971,
             350.0252161 ,  205.68121832,  300.91326118,  216.34233702,
             358.08158625,  276.65267766,  342.16414408,  202.22023491,
             231.18281259,  332.43647816,  389.83253494,  489.0516328 ,
             566.79721424,  546.9077105 ,  608.8953635 ,  628.51195461]])

  • weighted_mean
    (northing, easting)
    float64
    -4.578e+03 ... -6.155e+03

    array([[-4577.65448429, -4774.31904339, -4976.16788612, -5190.90159264,
            -5524.74569725, -5892.88731025, -6299.62451033, -6669.45080486,
            -6957.39676939, -7213.26649759, -7600.43681987, -7704.78926644,
            -7912.93515684, -7991.83564724, -8109.79491224, -8191.71177856,
            -8139.87561423, -8264.73804986, -8242.66838507, -8214.7022839 ,
            -8220.70992659, -8171.07167259, -8111.3270235 , -7973.91740816,
            -7617.62876243, -7507.05822354, -7131.72774039, -6267.94947506],
           [-5233.63799165, -5290.32749407, -5361.74268261, -5643.27769633,
            -5981.83320775, -6334.53661543, -6648.86890793, -6908.15709183,
            -7321.38352098, -7499.85361741, -7798.47918876, -7965.92453635,
            -8101.08975023, -8340.202684  , -8275.66669247, -8515.01748903,
            -8557.7150222 , -8564.48016684, -8635.72930174, -8643.30362376,
            -8738.96875574, -8687.80576979, -8595.37608409, -8578.33954652,
            -8380.08192395, -8173.18159977, -7722.98138787, -6931.24634207],
           [-5713.00207951, -5698.44622966, -5826.3578879 , -6028.52759504,
            -6249.76986817, -6644.7541592 , -6905.06268721, -7317.12830284,
            -7478.31461024, -7821.82435366, -8132.70625821, -8321.8006134 ,
            -8452.5290128 , -8598.83802589, -8593.23183655, -8654.29220888,
            -8713.80273368, -8763.99887457, -8779.9589766 , -8896.08073619,
            -8973.154267  , -8876.47379746, -8868.38152033, -8806.76105856,
    ...
            -3804.83815665, -3730.51092759, -3591.13087305, -3167.66037781,
            -3678.79664312, -4392.17708097, -4669.6519139 , -4789.95652851,
            -5071.18852523, -5486.78607229, -5914.96733506, -6497.3985503 ,
            -6844.40586895, -7203.52784759, -7506.20068564, -7604.75490238,
            -7819.27834269, -7858.15691687, -7505.15386609, -6666.05467038,
            -6630.87707276, -6733.07824227, -6461.21480454, -6224.35580997],
           [-3554.76144774, -3542.84758795, -3241.15597829, -3602.30994838,
            -3665.28900896, -3672.14117608, -3056.56322496, -3348.06468261,
            -3826.75008225, -4290.25876896, -4445.24926836, -4594.30997471,
            -5105.96471825, -5505.76578666, -6203.79492244, -6519.02574957,
            -6906.0591785 , -7153.44493948, -7311.72832447, -7585.31889602,
            -7516.67251975, -7509.28799319, -7419.93519603, -6658.22482068,
            -6583.18231916, -6668.36029695, -6616.89347703, -6306.68332973],
           [-3623.26243929, -3032.4757292 , -3444.46583491, -3736.24901417,
            -3884.39036967, -3002.91517661, -3151.66534682, -3517.80736391,
            -3922.79160371, -4170.74355857, -4150.17566991, -4670.64270157,
            -5203.80528813, -5788.68832857, -6328.18642824, -6488.74387849,
            -6709.07152776, -6822.41288441, -7035.72968525, -7200.87092323,
            -7293.19799393, -7095.3929496 , -7101.53545223, -6609.81228254,
            -6321.42634062, -6387.61436868, -6360.18279552, -6155.20748012]])

  • weighted_stdev
    (northing, easting)
    float64
    572.7 432.4 467.7 ... 538.2 571.3

    array([[572.7290907 , 432.41813634, 467.69965545, 421.45442955,
            428.25783353, 414.08279435, 456.89969853, 447.12516778,
            503.93500221, 518.03300624, 618.65919266, 573.98820541,
            622.54815902, 566.91096847, 582.22132074, 556.16461254,
            545.1034904 , 507.0455772 , 518.97242964, 452.42683344,
            451.22581765, 408.82898024, 437.17576368, 439.18889191,
            446.95858182, 501.33325475, 573.14071115, 673.64903308],
           [336.75976128, 332.50994387, 303.29124235, 313.07408181,
            362.87843509, 297.11210741, 326.5355485 , 293.81018705,
            344.62602148, 345.86587189, 367.99911917, 384.38815472,
            384.17232266, 439.12298557, 418.80247619, 411.43856995,
            389.09960105, 380.78802392, 355.053805  , 348.55096274,
            313.98591407, 333.85152737, 302.26618332, 355.84667116,
            368.01583162, 418.97628027, 528.34515195, 537.79822862],
           [282.99981469, 187.41802647, 228.60331675, 367.80212968,
            418.45154585, 405.14090797, 266.26350607, 266.57145943,
            197.46641732, 232.49877743, 285.54290125, 303.69404189,
            314.30740754, 326.75733802, 390.49271732, 337.02457452,
            293.43578781, 298.33032883, 293.32003809, 233.97072153,
            251.55969115, 250.81600132, 278.41244304, 269.12767667,
    ...
            274.83243163, 293.79370489, 527.97272747, 631.15390846,
            309.39407797, 176.74623482, 312.71882565, 450.7950407 ,
            692.68135615, 564.29116291, 360.20990431, 180.09683016,
            165.38497894, 166.73874007, 191.87714977, 210.76915557,
            223.93902339, 125.46221875, 211.6946127 , 429.6605958 ,
            392.25747814, 444.25393449, 395.14804554, 442.71345345],
           [471.3657904 , 444.69321376, 590.08136476, 323.64329476,
            476.39927279, 585.62332947, 772.01654954, 388.42898749,
            248.52211955, 237.26697267, 232.17237805, 328.34235728,
            429.30972767, 443.78538146, 263.91578957, 212.51572651,
            151.93514471, 248.81559536, 248.4544569 , 286.45951004,
            207.11224929, 201.52910188, 312.05277882, 385.31075416,
            482.24038721, 429.20650984, 475.64217021, 515.11553981],
           [642.99953188, 840.77308339, 545.5201619 , 387.55344769,
            537.87594763, 724.68998984, 526.96046267, 412.195386  ,
            379.38912432, 345.5783978 , 357.07215546, 281.71363491,
            272.63639656, 188.23951511, 234.94551686, 223.45728888,
            313.43640471, 296.61907228, 298.70290303, 228.16141547,
            221.44453695, 290.64969393, 354.20334094, 442.60682996,
            516.37422093, 518.22163   , 538.17205339, 571.30869469]])

  • z_min
    (northing, easting)
    float64
    -5.573e+03 ... -7.522e+03

    array([[ -5573.42839321,  -5498.65129683,  -5966.94272083,
             -5877.46399605,  -6504.29062158,  -6482.78784314,
             -7466.03373418,  -7261.86645279,  -8284.81509996,
             -7873.15176319,  -9688.36170867,  -8527.79470013,
             -9745.92908846,  -8738.18961258,  -9290.51955181,
             -8962.28114669,  -9118.90982565,  -8916.98757357,
             -9701.44493391,  -8911.96806317,  -9559.45399102,
             -8893.32292337,  -9218.8877178 ,  -8770.93912309,
             -8400.62117336,  -8332.35989663,  -8351.69790379,
             -7278.60106395],
           [ -5892.40307954,  -6085.40793883,  -5980.06723307,
             -6288.12533047,  -7886.44207179,  -6852.720786  ,
             -8037.44244414,  -7250.59550994,  -8238.96814792,
             -7939.05870287,  -8248.99306219,  -9005.78249185,
             -8513.69800703,  -9698.28323226,  -8757.82873827,
             -9452.45715471,  -9049.34014304,  -9359.9811239 ,
             -9035.955085  ,  -9752.73348874,  -9279.81430806,
             -9824.02975016,  -9145.96963332,  -9302.90572498,
             -8897.82045088,  -9090.95786007,  -8496.48270257,
             -8080.86634146],
    ...
           [ -4533.79383347,  -4706.95760221,  -4429.0070529 ,
             -4731.64826263,  -4818.67079243,  -5475.90566447,
             -4413.89362563,  -4324.26002156,  -4123.10248061,
             -4926.31636949,  -5090.46790901,  -6228.71396163,
             -7009.08785902,  -7258.0225072 ,  -7433.04254032,
             -7172.52155013,  -7136.93668924,  -8596.03278731,
             -7691.53423738,  -9562.14901364,  -7909.82620523,
             -8276.44680949,  -8657.29346038,  -7141.85913762,
             -8444.0723021 ,  -7287.45379768,  -7882.89232269,
             -7561.31177533],
           [ -5385.01455477,  -4272.29225647,  -4983.44087003,
             -4590.15288672,  -5168.99815781,  -4038.31929149,
             -4376.66281475,  -4569.86630651,  -4676.07422275,
             -4973.72317751,  -4798.67292862,  -5187.67675431,
             -6273.99203627,  -6449.61930984,  -7287.28864607,
             -6885.05688394,  -7820.67965424,  -7509.15837611,
             -8181.32649825,  -7745.40852834,  -7876.45545513,
             -8035.39422643,  -7913.8752162 ,  -7636.63767324,
             -7481.13303916,  -7198.15649571,  -7787.59002022,
             -7522.38516959]])

  • z_max
    (northing, easting)
    float64
    -3.294e+03 -3.847e+03 ... -4.94e+03

    array([[-3293.92474617, -3847.08960543, -4046.28787823, -4297.9285758 ,
            -4599.39881669, -4952.80251119, -5258.61696785, -5556.16914512,
            -5746.59181567, -5931.81898598, -6152.31279899, -6294.0748936 ,
            -6481.52594722, -6628.13572664, -6690.27606635, -6756.43377025,
            -6858.11166791, -7026.11317831, -7077.45382211, -7174.33677941,
            -7384.14696182, -7411.15173087, -7367.14807444, -7127.93608877,
            -6738.68204251, -6438.11139254, -5923.1965927 , -4613.95094947],
           [-4635.34587394, -4614.96046264, -4690.1662378 , -4885.25257729,
            -5207.72437519, -5419.38956322, -5805.88954064, -6064.79207965,
            -6270.9965305 , -6439.39462574, -6672.71990054, -6858.2163248 ,
            -7035.0157891 , -7199.44491512, -7328.62230009, -7546.08870712,
            -7701.81196794, -7683.90702207, -7855.09898622, -7958.56393495,
            -8039.45375172, -7966.73617231, -7879.82804128, -7756.4322959 ,
            -7466.56892577, -7004.03965188, -6181.29081   , -5823.86777644],
           [-5062.53194822, -5290.62487974, -5199.05409887, -5507.08885366,
            -3112.20891535, -6329.38899981, -5077.43131797, -6858.06918671,
            -7018.11449697, -7192.73007951, -7371.15083278, -7554.22220641,
            -7721.30303646, -7628.333565  , -7799.19937058, -7916.31160566,
            -8039.5246846 , -8068.10093806, -8202.68520213, -8361.20436615,
            -8562.64719196, -8015.81420733, -8529.65602522, -8420.45422528,
    ...
            -3465.97425924, -2748.70242189, -2926.68616362, -1181.57863851,
            -3124.31873522, -4014.17360488, -3872.46114941, -2713.29239329,
            -2142.63985657, -3530.73775479, -4290.80966302, -6293.63183615,
            -6120.26334832, -6924.02582119, -7235.68743313, -6492.96158367,
            -7548.8355945 , -7584.99963658, -6890.67401912, -5790.95093951,
            -5492.60728017, -5561.16010501, -5296.41731928, -5132.27609041],
           [-2431.09927035, -2707.45173728, -1372.86684137, -3031.17170686,
            -2297.85899567, -2691.02067778,  -506.51101827, -2404.7664553 ,
            -3165.44052692, -3823.38068068, -3958.97115447, -3726.48065042,
            -3689.7104347 , -3541.00639628, -5570.7936126 , -5918.99516892,
            -6643.61906069, -6839.25704418, -5806.08479876, -7346.01524355,
            -6481.19368174, -7029.78828981, -6461.66178568, -5567.7609514 ,
            -5215.92826484, -5253.59762239, -5121.55666146, -4980.88898004],
           [-2314.47128491,    73.91331833, -2362.22377146, -2896.58149287,
            -2911.23812578,  -403.22871245, -1885.52036878, -2462.66259772,
            -3032.46389701, -3330.8441464 , -3431.69802479, -4024.77786988,
            -4476.6459499 , -5483.7061751 , -5802.92990636, -6078.51203865,
            -6129.35248541, -6274.01577841, -6620.11287384, -6887.15178122,
            -6923.33612986, -6574.38868655, -6116.60281955, -5434.32997279,
            -5017.72470673, -4997.19309992, -4955.72021905, -4939.94464913]])

Comparing results

results = [
    uncert_results,
    uncert_regional_results,
    uncert_grav_results,
    uncert_constraints_results,
    uncert_density_results,
    uncert_zref_results,
    uncert_damping_results,
]
names = [
    "full",
    "regional",
    "grav",
    "constraints",
    "density",
    "zref",
    "damping",
]
# get cell-wise stats for each ensemble
stats = []
for r in results:
    ds = invert4geom.merged_stats(
        results=r,
        plot=False,
        constraints_df=constraint_points,
        weight_by="constraints",
        region=optimal_inv.data.inner_region,
    )
    stats.append(ds)

# get the standard deviation of the ensemble of ensembles
stdevs = []
for i, s in enumerate(stats):
    stdevs.append(s.weighted_stdev.rename(f"{names[i]}_stdev"))

merged = xr.merge(stdevs, compat="override")
merged

<xarray.Dataset> Size: 61kB
Dimensions:            (northing: 30, easting: 28)
Coordinates:
  * northing           (northing) float64 240B 1.959e+05 2.059e+05 ... 4.859e+05
  * easting            (easting) float64 224B 5.69e+04 6.69e+04 ... 3.269e+05
    top                (northing, easting) float64 7kB -4.093e+03 ... -5.735e+03
    bottom             (northing, easting) float64 7kB -5.845e+03 ... -5.845e+03
Data variables:
    full_stdev         (northing, easting) float64 7kB 572.7 432.4 ... 571.3
    regional_stdev     (northing, easting) float64 7kB 44.81 52.78 ... 172.2
    grav_stdev         (northing, easting) float64 7kB 22.86 26.47 ... 23.6 23.3
    constraints_stdev  (northing, easting) float64 7kB 90.02 97.62 ... 59.04
    density_stdev      (northing, easting) float64 7kB 12.72 25.47 ... 7.922
    zref_stdev         (northing, easting) float64 7kB 3.564 8.347 ... 2.367
    damping_stdev      (northing, easting) float64 7kB 29.26 32.49 ... 20.56

xarray.Dataset

• Dimensions:
  • northing: 30
  • easting: 28
• Coordinates: (4)
  • northing
    (northing)
    float64
    1.959e+05 2.059e+05 ... 4.859e+05

    array([195900., 205900., 215900., 225900., 235900., 245900., 255900., 265900.,
           275900., 285900., 295900., 305900., 315900., 325900., 335900., 345900.,
           355900., 365900., 375900., 385900., 395900., 405900., 415900., 425900.,
           435900., 445900., 455900., 465900., 475900., 485900.])

  • easting
    (easting)
    float64
    5.69e+04 6.69e+04 ... 3.269e+05

    array([ 56900.,  66900.,  76900.,  86900.,  96900., 106900., 116900., 126900.,
           136900., 146900., 156900., 166900., 176900., 186900., 196900., 206900.,
           216900., 226900., 236900., 246900., 256900., 266900., 276900., 286900.,
           296900., 306900., 316900., 326900.])

  • top
    (northing, easting)
    float64
    -4.093e+03 ... -5.735e+03

    array([[-4092.5467965 , -4415.15348114, -4528.11843267, -4798.08933905,
            -5059.71279706, -5475.57236934, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5650.68522665],
           [-4954.71484118, -5009.61733613, -5147.22990984, -5335.56104055,
            -5686.40081189, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787],
           [-5498.71895658, -5511.83802358, -5561.662859  , -5815.66773905,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
    ...
            -3709.33743929, -3715.35517775, -3469.40405962, -3174.78472691,
            -3640.40169256, -4406.54486914, -4768.43028177, -4775.25348996,
            -5280.30192028, -5491.51273712, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787],
           [-3346.48077648, -3309.2200238 , -3197.68349365, -3429.17014126,
            -3661.1579879 , -3506.21261246, -3050.62933661, -3238.27920522,
            -3764.84077718, -4376.70648006, -4445.25585377, -4622.935259  ,
            -5159.33619843, -5618.74901221, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787],
           [-3221.46942379, -2872.6628699 , -3100.91911269, -3556.40068479,
            -3665.51740131, -2865.7161934 , -2873.20348322, -3382.93078748,
            -3858.67882191, -4085.07561974, -4125.39512497, -4662.50222086,
            -5346.28982867, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5734.9022586 ]])

  • bottom
    (northing, easting)
    float64
    -5.845e+03 ... -5.845e+03

    array([[-5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5888.57546185, -6331.48547932,
            -6566.51404034, -6791.77684627, -7310.23349322, -7468.58227511,
            -7754.77336863, -7795.53244797, -8029.47040709, -8116.77563349,
            -7948.30241143, -8241.75863512, -8155.82462408, -8069.07793479,
            -8092.90577378, -8066.76976407, -7931.53278897, -7818.28044574,
            -7272.33427602, -7181.26418017, -7006.99096948, -5844.61581787],
           [-5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -6162.956998  , -6455.10599648, -6608.07886476,
            -7224.84167423, -7326.09603892, -7690.25202616, -7921.60965612,
            -7952.87798234, -8348.7845    , -8174.89559603, -8592.97956945,
            -8555.02755453, -8660.72179148, -8735.59091057, -8724.35298512,
            -8986.05654539, -8763.96167533, -8582.92834842, -8845.47069867,
            -8405.10587274, -8169.27107884, -7919.40336924, -6725.72972221],
           [-5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -6101.0529305 , -6438.32368743, -6775.36868319, -7214.14828396,
            -7318.02507862, -7684.11877019, -7992.86933384, -8242.52075237,
            -8375.05531495, -8760.77662566, -8511.68971189, -8725.19384438,
            -8855.59616379, -8911.35491633, -8772.72728108, -8963.51358078,
            -9148.487129  , -8861.27695722, -8718.45035251, -8935.54559913,
    ...
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -6086.15858743, -6657.59174036,
            -7015.35601151, -7407.92246549, -7647.59696938, -7847.50715668,
            -7988.36162413, -7998.09118294, -7542.39966405, -6318.35429635,
            -6549.41328908, -6500.96973323, -6226.22005163, -5933.1231146 ],
           [-5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -6358.13073197, -6926.54558388,
            -7116.17526358, -7408.30830008, -7496.71209926, -7791.54470284,
            -7640.14400376, -7553.86958681, -7497.97940618, -6446.09147046,
            -6376.98631136, -6574.47106321, -6558.09438642, -6092.22631671],
           [-5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -5844.61581787, -5844.61581787, -5844.61581787,
            -5844.61581787, -6003.55165218, -6686.73101142, -6704.30521388,
            -6981.59900135, -7094.86616168, -7189.19505516, -7357.19310682,
            -7389.89565849, -6987.71031352, -7073.05655197, -6383.83856417,
            -6034.89991253, -6003.12386338, -6081.31168053, -5844.61581787]])

• Data variables: (7)
  • full_stdev
    (northing, easting)
    float64
    572.7 432.4 467.7 ... 538.2 571.3

    array([[572.7290907 , 432.41813634, 467.69965545, 421.45442955,
            428.25783353, 414.08279435, 456.89969853, 447.12516778,
            503.93500221, 518.03300624, 618.65919266, 573.98820541,
            622.54815902, 566.91096847, 582.22132074, 556.16461254,
            545.1034904 , 507.0455772 , 518.97242964, 452.42683344,
            451.22581765, 408.82898024, 437.17576368, 439.18889191,
            446.95858182, 501.33325475, 573.14071115, 673.64903308],
           [336.75976128, 332.50994387, 303.29124235, 313.07408181,
            362.87843509, 297.11210741, 326.5355485 , 293.81018705,
            344.62602148, 345.86587189, 367.99911917, 384.38815472,
            384.17232266, 439.12298557, 418.80247619, 411.43856995,
            389.09960105, 380.78802392, 355.053805  , 348.55096274,
            313.98591407, 333.85152737, 302.26618332, 355.84667116,
            368.01583162, 418.97628027, 528.34515195, 537.79822862],
           [282.99981469, 187.41802647, 228.60331675, 367.80212968,
            418.45154585, 405.14090797, 266.26350607, 266.57145943,
            197.46641732, 232.49877743, 285.54290125, 303.69404189,
            314.30740754, 326.75733802, 390.49271732, 337.02457452,
            293.43578781, 298.33032883, 293.32003809, 233.97072153,
            251.55969115, 250.81600132, 278.41244304, 269.12767667,
    ...
            274.83243163, 293.79370489, 527.97272747, 631.15390846,
            309.39407797, 176.74623482, 312.71882565, 450.7950407 ,
            692.68135615, 564.29116291, 360.20990431, 180.09683016,
            165.38497894, 166.73874007, 191.87714977, 210.76915557,
            223.93902339, 125.46221875, 211.6946127 , 429.6605958 ,
            392.25747814, 444.25393449, 395.14804554, 442.71345345],
           [471.3657904 , 444.69321376, 590.08136476, 323.64329476,
            476.39927279, 585.62332947, 772.01654954, 388.42898749,
            248.52211955, 237.26697267, 232.17237805, 328.34235728,
            429.30972767, 443.78538146, 263.91578957, 212.51572651,
            151.93514471, 248.81559536, 248.4544569 , 286.45951004,
            207.11224929, 201.52910188, 312.05277882, 385.31075416,
            482.24038721, 429.20650984, 475.64217021, 515.11553981],
           [642.99953188, 840.77308339, 545.5201619 , 387.55344769,
            537.87594763, 724.68998984, 526.96046267, 412.195386  ,
            379.38912432, 345.5783978 , 357.07215546, 281.71363491,
            272.63639656, 188.23951511, 234.94551686, 223.45728888,
            313.43640471, 296.61907228, 298.70290303, 228.16141547,
            221.44453695, 290.64969393, 354.20334094, 442.60682996,
            516.37422093, 518.22163   , 538.17205339, 571.30869469]])

  • regional_stdev
    (northing, easting)
    float64
    44.81 52.78 53.61 ... 184.6 172.2

    array([[ 44.8082099 ,  52.77916464,  53.61450384,  46.15960443,
             37.90256685,  26.97660598,  15.02072915,  16.07706525,
             25.16880416,  40.84352246,  70.07722188,  67.83015456,
             69.96697188,  66.58263819,  56.53896159,  52.59887832,
             30.58156781,  39.24572331,  31.79373362,  33.07834912,
             30.65230923,  28.40637927,  23.48908847,  21.25555302,
             66.09251537,  62.66797813,  74.25054743, 102.52448318],
           [ 42.83596996,  43.71905853,  25.09414782,  22.0218122 ,
             23.43421788,  24.60699169,  33.85378092,  47.42080977,
             75.19550357,  84.07637508, 106.87501055, 104.17545258,
            113.24682308, 117.78937149,  93.67160121, 103.75555078,
             88.00573198,  71.05258215,  58.8852459 ,  46.05195929,
             45.90947176,  25.99315668,  16.92346192,  10.9235453 ,
             35.3679658 ,  50.66966916,  99.10762781, 134.93742514],
           [ 79.85726767,  87.66608985,  43.45466791,  42.38361148,
             33.23965499,  30.33500868,  37.22535296,  58.36818854,
             72.67108078,  90.79591219, 112.43501034, 120.02322921,
            121.21629885, 128.25206723, 102.32115415,  98.49986468,
             85.08124281,  68.28914337,  55.80784165,  52.70363575,
             47.82846324,  28.39048531,  22.14928312,  17.11011251,
    ...
             58.87747184,  59.20735718,  29.04604855, 101.91121   ,
             63.35000004,  49.16799721,  53.17003002,  49.50741307,
             59.408788  ,  47.17780311,  53.85610154,  62.48911854,
             63.52842197,  62.44239631,  59.2464461 ,  64.01119983,
             68.78603354,  77.37291383,  76.81632627,  42.85808161,
             35.15606871,  33.03201808,  78.72879625, 108.46833768],
           [ 55.37745529,  54.07988836,  48.05840645,  75.35097404,
            110.81867113,  61.93601199,  54.15781522,  76.73671563,
             49.02714864,  59.57070853,  57.6048604 ,  56.65132077,
             49.34847471,  62.82834106,  64.86720999,  83.06624266,
             70.88560428,  72.2505039 ,  63.58882911,  61.37525058,
             63.19952473,  61.08194464,  83.6933645 ,  29.97372925,
             40.23904362,  57.01675393,  90.72500203, 124.63907121],
           [ 56.48404335,  72.18644616,  67.95527039, 146.41140085,
            160.61719414,  37.39058336,  62.35301268,  59.28223534,
             72.62892494,  73.25182382,  71.79295566,  64.57107402,
             47.63582458,  40.95392369,  39.63244416,  73.67042534,
             85.85419437,  95.61394767,  88.0972026 ,  92.92408803,
             94.32189217,  57.66879411,  73.19151381,  59.70947889,
            104.49706411, 149.02945429, 184.60378772, 172.19390029]])

  • grav_stdev
    (northing, easting)
    float64
    22.86 26.47 20.6 ... 23.6 23.3

    array([[22.85849576, 26.47186553, 20.602695  , 16.90058099, 36.1978509 ,
            19.23592884, 24.90705528, 35.46203749, 25.42799258, 24.99301401,
            38.03707354, 24.50656216, 43.31351629, 36.91350933, 23.16279586,
            37.15793717, 36.23373909, 19.59963001, 56.36984229, 31.23978801,
            45.72246145, 31.72923254, 38.78745319, 25.35003786, 27.26917645,
            37.82063743, 58.2155524 , 28.79271712],
           [29.93657011, 28.92975488, 25.10438872, 21.38445918, 24.65609867,
            30.8571968 , 29.6750996 , 29.07910865, 28.07693531, 31.0027838 ,
            17.09654846, 42.83603058, 23.2385736 , 31.0395365 , 28.21648867,
            39.39316094, 37.83213138, 34.68804982, 32.80255499, 33.04439046,
            48.34259095, 48.30604246, 32.08121257, 52.71033508, 31.04053188,
            38.53367723, 27.37735222, 35.15356238],
           [47.2135485 , 32.09849933, 21.71588646, 30.23114956, 22.1711067 ,
            33.70216182, 38.65581988, 31.85487106, 34.03955384, 30.18104663,
            37.04871133, 53.23870269, 40.95735488, 38.4986454 , 27.29550895,
            32.02300776, 40.65214696, 31.45568488, 35.12878488, 32.8363743 ,
            30.75923848, 21.42414809, 21.69099242, 30.03721897, 47.80097396,
            31.52651973, 33.02408355, 62.19902433],
           [26.40207307, 18.1824139 , 30.09628447, 26.86098513, 20.87380547,
            27.84842992, 29.31047447, 32.89520955, 27.48640533, 29.38581713,
    ...
            34.05873464, 28.15906231, 36.79075111, 36.03791618,  9.59916626,
            23.73784693, 31.65139342, 24.32596513],
           [ 7.99050587, 12.28273352, 23.36593179, 14.28227472, 20.54383951,
            14.63269728, 14.9247944 , 11.08335405, 16.23001493, 23.43161932,
            23.37038239, 25.11493279, 21.87278583, 34.04261018, 21.34669193,
            26.91934901, 24.59845451, 26.00572156, 43.61870822, 38.46139947,
            26.67590867, 39.37310978, 38.34378558, 19.29660823, 21.48091981,
            33.16870165, 34.77233374, 28.63767656],
           [21.06521524, 13.52638313, 13.93104618, 16.48218903, 20.43294095,
            20.8017908 , 13.55728029, 18.88444265, 16.67649025, 23.14499267,
            20.64503166, 19.47107247, 18.38838013, 24.61833242, 28.98044191,
            19.08219265, 37.2220263 , 26.36586287, 36.98678911, 36.18526235,
            37.87888336, 41.10130706, 28.13367582, 22.5756587 , 31.85179359,
            28.36756572, 25.29954602, 33.36201231],
           [11.96507495, 12.56434172, 19.23640974, 12.12369568, 18.66589905,
            19.06131085, 20.8724799 , 21.07894142, 19.83279935, 18.86692031,
            18.8965058 , 20.68640118, 19.67261218, 31.05416685, 26.52014635,
            28.95265867, 21.35624678, 31.20106669, 36.92189741, 16.90129692,
            23.08090875, 33.01108772, 35.15018709, 39.2483689 , 26.21856212,
            37.4648135 , 23.60223721, 23.29516756]])

  • constraints_stdev
    (northing, easting)
    float64
    90.02 97.62 113.6 ... 53.79 59.04

    array([[ 90.02038114,  97.62310518, 113.57878229, 126.79186605,
            132.9815941 , 129.49403343, 116.6844438 , 101.97950801,
             95.5632816 , 102.71302408, 117.8186721 , 127.42661541,
            133.17585656, 135.55286732, 137.23635217, 139.59042221,
            137.05033519, 128.94347439, 116.41486729, 111.41018419,
            122.84492223, 146.00650936, 167.21800121, 177.53261978,
            172.50307454, 157.11013734, 132.80683709, 107.17689383],
           [ 86.01709436,  96.12575208, 109.96814929, 122.22832067,
            129.15290619, 126.51980902, 113.92463239,  98.55322264,
             87.30876135,  85.82745247,  94.27628996, 104.16232039,
            115.40867538, 127.05174776, 137.47385115, 147.69807839,
            148.46352052, 138.49852663, 121.17733342, 106.52463538,
            106.30621722, 119.77849161, 137.01643327, 147.80347859,
            145.02931594, 131.49584985, 109.24959758,  88.49074857],
           [ 84.06726308,  96.77479709, 108.58884676, 118.42215908,
            123.52777851, 120.9396019 , 111.45925643,  97.85078283,
             83.76872804,  75.72140676,  77.49371479,  87.94243172,
            106.21683895, 128.99364968, 149.01594438, 165.6342777 ,
            170.95767959, 162.63829556, 144.95716078, 125.06470761,
            112.25604784, 111.47715116, 119.41051818, 125.39539527,
    ...
             54.41252254,  54.93984863,  56.77463693,  61.87047914,
             71.33006271,  83.61627113,  90.22841228,  89.80388276,
             90.17964748,  86.68310137,  84.62803498,  83.41555458,
             81.88364319,  78.50140823,  75.89602957,  78.9187406 ,
             90.32717835, 105.29456525, 111.09703769,  97.32293312,
             91.65096851,  82.45549356,  72.92686219,  79.63620154],
           [ 21.07007227,  25.3979308 ,  30.46123953,  35.50990898,
             38.91976787,  42.82726577,  47.6581817 ,  55.51439635,
             63.12581822,  73.0829658 ,  76.52828776,  79.02086034,
             83.16769984,  85.9395884 ,  94.26110435,  98.32452351,
             99.51073329,  94.34187094,  86.89779049,  83.63256906,
             88.24860403,  98.24777271, 105.29090492,  94.79570986,
             86.16313146,  75.09924992,  63.35230303,  67.08648564],
           [ 25.16695367,  21.71281554,  20.63120523,  22.62869079,
             27.97562895,  33.08601363,  41.93061051,  50.14319639,
             59.00044607,  66.57047992,  68.64259492,  74.55617094,
             79.17775891,  90.54261027, 105.01616307, 114.52811504,
            118.12752272, 112.89081661, 102.77410081,  95.36371731,
             94.30086722,  98.26648047, 104.23075169,  96.33068372,
             81.85935069,  67.17714898,  53.79426379,  59.03690789]])

  • density_stdev
    (northing, easting)
    float64
    12.72 25.47 23.97 ... 7.148 7.922

    array([[ 12.71925264,  25.46620323,  23.97298911,  28.89957491,
             11.89512238,   5.49461091,   6.06205859,   5.59234464,
              2.77982502,   5.78052749,  11.28354107,  18.86230189,
             24.22651489,   9.01783259,   5.12946093,   5.47288013,
             14.06984838,  10.53101126,   2.88817571,   9.48786813,
              8.10847801,   4.95428824,   1.86256211,   5.40006768,
             41.73843772,  27.14688604,  26.19905467,  34.91103929],
           [ 94.11970965,  49.28016471,  29.59270979,  16.47459492,
             26.48527145,  23.37601534,  30.00182841,  28.04634731,
              6.41381431,   6.04926825,   9.8123929 ,   6.37051075,
              6.71618153,  11.35957489,   7.05698046,  12.3243672 ,
              2.97292797,   4.63742705,  16.19692103,   7.13858307,
             21.58172799,  15.28040446,   3.72597842,   4.49469008,
             14.19781193,  13.06143773,  57.04365454,  29.52489328],
           [207.47839186, 180.58169478, 137.75422697, 111.03258962,
             98.78570733,  82.89776147,  58.39349578,  37.34189374,
             26.83504985,   7.02528018,   4.14914009,   5.81506418,
              4.38635282,  14.7255648 ,  10.63806993,  12.95587381,
              7.70567708,  16.21361215,  17.91888933,  23.58897101,
             25.50558721,  15.82245615,  11.78309259,   5.16952085,
    ...
            110.12381841, 106.24503076,   6.897337  , 110.45320117,
             42.52826109,  58.90828968,  57.07985465,   6.76611734,
             32.19818195,  32.34479295,   6.7785432 ,  13.65358951,
             31.5245188 ,  45.1646418 ,  47.88931674,  60.78008969,
             71.49292737,  97.22051669,  28.63327204, 100.43023174,
            115.18649369,  44.29299113,  27.15652403,  32.91603925],
           [ 81.21904995,  77.96594428,  60.17397339, 118.932841  ,
            163.9747438 ,  94.47326165,  45.27912984,  57.70804363,
             24.21385139,  72.62989876,  11.20774564,  32.51052929,
             28.57146959,  15.8108085 ,  14.79024215,  31.88839995,
             21.54629383,  30.08971241,  33.23093984,  40.50599015,
             52.30403662,  65.19658064,  13.04502892,  71.37469119,
             93.33640526,  25.84741755,   6.45863624,   7.78013902],
           [ 77.03496902,  56.91158761,  75.91344818, 177.33955625,
            200.25346412,  18.8209513 ,  56.46807927,  23.69508152,
             64.63487583,  40.11288277,  34.53104811,  33.98115603,
             14.36776766,  35.43933501,  53.93131556,  53.48548297,
              8.28844681,   1.80744061,   6.89181029,  35.37987331,
             20.86472982,  34.93231417,   9.276773  ,  39.87464347,
             73.62612284,  39.68780265,   7.14808263,   7.92168461]])

  • zref_stdev
    (northing, easting)
    float64
    3.564 8.347 0.8916 ... 1.727 2.367

    array([[ 3.56385622,  8.3465085 ,  0.89162509,  6.73810423,  1.98598687,
             5.17507642,  4.56634283,  9.20370364, 11.49678524,  6.16127817,
             2.30001889,  2.95668662,  3.38205999,  1.7573582 ,  2.45961988,
             7.66132164, 18.25537856,  8.57106435, 11.72616616,  2.77960653,
             6.86464727,  7.45881385,  3.29821116,  8.3670094 , 19.30490133,
             6.75584189, 16.39764388,  2.50375295],
           [ 5.33216049,  7.21518107,  5.42620071,  5.04615192,  1.81245329,
             5.51905569,  3.32762392, 15.47759344, 10.8606721 ,  5.33366778,
             4.03994986,  6.48631859,  2.4215851 ,  5.0690567 ,  7.47780677,
             6.59135959,  6.37852079,  7.76816262,  7.717914  , 13.00205142,
             3.80477785,  1.85240244,  3.7661798 ,  4.8662871 ,  8.42580995,
            19.16745639, 16.63013059, 10.65554443],
           [ 8.56626493,  5.91507335,  8.25566077,  8.55809149,  2.01330676,
             2.84297598,  4.94462553,  8.64544102,  8.37511459,  1.34240786,
             1.16817852,  6.17959254,  3.57332079, 12.71649476,  1.19143045,
             6.14659955,  2.85405081,  7.87151148,  4.89078173,  5.66862275,
             2.05819315,  2.38322392,  3.15264996, 10.08829478,  3.21769767,
             9.01975449,  7.65212102, 14.47026436],
           [ 1.43269968,  5.15508521,  7.68312097,  4.19307526, 11.60954205,
             4.90994577,  5.63290963,  0.99804523,  1.84578448,  8.63127712,
    ...
             1.21267781,  7.10015104, 16.27574958,  1.70923279,  8.17460521,
             2.37792568,  8.96062909,  5.28964957],
           [ 5.32986084,  6.25344515,  6.22436917,  5.06299312,  3.52976734,
             1.92858175,  0.79904224,  0.54551735,  0.61919026,  0.70723666,
             1.04332293,  1.034787  ,  5.77658065,  1.90419509,  1.75028527,
             7.19095583,  1.79799865,  0.69215601,  6.83095837,  5.82448522,
             9.11526776,  2.91682876,  3.37899461,  2.82610958,  8.07163622,
             6.75987881,  1.68897961,  1.97610151],
           [ 5.03537619,  6.1826849 ,  5.94795575,  4.69566916,  2.92129386,
             1.31315117,  0.78353138,  1.21548751,  1.23972994,  0.99806242,
             0.81011547,  2.41639726,  1.09552291,  4.1995222 ,  6.33115728,
             1.48903493,  3.40502272,  4.32452751,  4.94508644,  4.76522492,
             5.35266047,  5.73864583, 13.37266559,  2.42371908, 10.48439473,
             0.77579499, 12.83891921,  6.33695229],
           [ 3.47276075,  4.85313569,  4.54849814,  3.17306176,  1.53592202,
             0.98750081,  2.09460796,  2.65732039,  2.64426715,  2.24724803,
             1.44413711,  1.11136728,  4.48493595,  3.11616552,  5.96649908,
            10.91926283, 10.25959095,  2.06245777,  3.8833205 , 16.81949148,
             9.95800452, 14.21960194,  4.61770759,  7.37555623,  2.16683618,
             6.31448609,  1.72668017,  2.36727029]])

  • damping_stdev
    (northing, easting)
    float64
    29.26 32.49 31.03 ... 40.9 20.56

    array([[ 29.2638008 ,  32.49446486,  31.02768017,  21.14369402,
             12.30313937,  18.81051248,  26.70470399,  29.65910604,
             20.74085377,  18.45251498,  27.81856616,  16.9128906 ,
             12.31327934,  10.18554549,  11.28221124,  18.97036776,
             15.59778707,  22.18636642,  12.30238281,   8.07611213,
              2.06418594,   4.16244599,  12.19907594,  24.90539711,
             28.63588635,  48.40362102,  62.02752702,  49.84577874],
           [113.1598316 ,  69.79101523,  48.35510135,  45.50338652,
             54.38103004,  66.99448446,  63.12321238,  56.85551367,
             51.71160637,  39.86055614,  41.60459049,  31.59419396,
             29.81746992,  30.19194484,  20.71694922,  31.51859622,
             29.22820011,  20.44125362,  14.73585709,   9.3608767 ,
             10.35401784,   3.3427099 ,   8.73282536,  26.5706702 ,
             36.00165477,  53.21672183,  46.23475128,  49.50665017],
           [254.57753137, 213.6573974 , 174.76473411, 148.76911613,
            140.34720021, 131.2718525 , 121.47446983, 106.56866544,
             80.84601969,  64.83806052,  58.91922356,  51.00259175,
             45.04242331,  47.18000851,  28.09654569,  29.10225508,
             24.5921778 ,  16.44652778,   8.60018148,  10.1267515 ,
              8.86511145,   4.14604076,   7.44264964,  22.18566273,
    ...
            151.63148968, 129.80154277,  12.25825188, 154.96150844,
             76.17441696,  46.30372867,  42.81095216,  33.82606445,
             65.17554289,  82.32282438,  50.43525875,  15.00958918,
             14.64310993,  43.51427513,  75.53294832,  97.50472629,
            122.74811834, 122.06552361,  46.44436913, 115.90340025,
            119.14766357,  74.5822996 ,  63.43033649,  52.71946152],
           [ 86.65300856,  86.86665948,  87.55521429, 174.10276196,
            221.68822524, 127.70092453,  54.06844221,  85.87844786,
             10.29681128,  59.49909213,   3.59842113,  59.2347797 ,
             61.72704256,  44.50895665,  10.27367666,   6.64509258,
              8.11909025,  18.92915284,  45.09433982,  75.12515191,
             89.36145602,  83.9776536 ,  49.48915233,  84.1218611 ,
            106.57377331,  66.37922865,  37.74570814,  29.69681944],
           [ 78.08461313,  42.30699138, 115.18435337, 246.12521105,
            265.27869069,  49.25211567,  53.34159074,  12.186506  ,
             51.83283642,  30.01105716,  53.28500692,  43.39384346,
             15.41724495,  27.39955611,  51.5445143 ,  22.94622187,
              6.91764195,  10.49689623,  19.99015235,  51.83747117,
             67.11468596,  48.74894299,  32.69705977,  56.98296521,
            108.99197374,  76.91731268,  40.90167733,  20.56166194]])

titles = [
    "True error",
    "Total uncertainty",
    "Uncertainty from regional estimation",
    "Uncertainty from gravity",
    "Uncertainty from constraints",
    "Uncertainty from density",
    "Uncertainty from reference level",
    "Uncertainty from damping",
]
grids = list(merged.data_vars.values())

# grids.insert(0, np.abs(stats[0].weighted_mean - grid.basement_topo))
grids.insert(0, inversion_error)

grids = [
    g.sel(
        easting=slice(
            optimal_inv.data.inner_region[0], optimal_inv.data.inner_region[1]
        ),
        northing=slice(
            optimal_inv.data.inner_region[2], optimal_inv.data.inner_region[3]
        ),
    )
    for g in grids
]
cpt_lims = ptk.get_min_max(
    grids[0],
    robust=True,
)

fig_height = 9
for i, g in enumerate(grids):
    xshift_amount = 1
    if i == 0:
        fig = None
        origin_shift = "initialize"
        # cpt_lims = ptk.get_min_max(
        #     g,
        #     robust=True,
        # )
    elif i == 4:
        origin_shift = "both"
        xshift_amount = -3
    else:
        origin_shift = "x"

    fig = ptk.plot_grid(
        grid=g,
        fig_height=fig_height,
        title=titles[i],
        title_font="16p,Helvetica,black",
        # cmap="thermal",
        cpt_lims=cpt_lims,
        robust=True,
        cbar_label=f"standard deviation (m), mean: {int(np.nanmean(g))}",
        hist=True,
        fig=fig,
        origin_shift=origin_shift,
        xshift_amount=xshift_amount,
        yshift_amount=-1.25,
        points=constraint_points,
        points_style="x.2c",
        points_pen="1.5p",
        points_fill="white",
    )
    fig.text(
        position="TL",
        text=f"{string.ascii_lowercase[i]}",
        fill="white",
        pen=True,
        font="16p,Helvetica,black",
        offset="j.6/.2",
        clearance="+tO",
        no_clip=True,
    )
    if i == 0:
        # plot profile location, and endpoints on map
        start = [optimal_inv.data.inner_region[1], optimal_inv.data.inner_region[3]]
        stop = [optimal_inv.data.inner_region[0], optimal_inv.data.inner_region[2]]
        fig.plot(
            vd.line_coordinates(start, stop, size=100),
            pen="2p,black",
        )
        fig.text(
            x=start[0],
            y=start[1],
            text="A",
            fill="white",
            font="12p,Helvetica,black",
            justify="CM",
            clearance="+tO",
            no_clip=True,
        )
        fig.text(
            x=stop[0],
            y=stop[1],
            text="A' ",
            fill="white",
            font="12p,Helvetica,black",
            justify="CM",
            clearance="+tO",
            no_clip=True,
        )
fig.show()

/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:3414: UserWarning: origin_shift 'initialize' is deprecated, use None instead.
  fig.shift_figure(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1424: UserWarning: Since limits were passed to `cpt_lims`, parameter `robust` is unused.
  cmap, colorbar, cpt_lims = set_cmap(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1424: UserWarning: Since limits were passed to `cpt_lims`, parameter `robust` is unused.
  cmap, colorbar, cpt_lims = set_cmap(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1424: UserWarning: Since limits were passed to `cpt_lims`, parameter `robust` is unused.
  cmap, colorbar, cpt_lims = set_cmap(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1424: UserWarning: Since limits were passed to `cpt_lims`, parameter `robust` is unused.
  cmap, colorbar, cpt_lims = set_cmap(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1424: UserWarning: Since limits were passed to `cpt_lims`, parameter `robust` is unused.
  cmap, colorbar, cpt_lims = set_cmap(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1424: UserWarning: Since limits were passed to `cpt_lims`, parameter `robust` is unused.
  cmap, colorbar, cpt_lims = set_cmap(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1424: UserWarning: Since limits were passed to `cpt_lims`, parameter `robust` is unused.
  cmap, colorbar, cpt_lims = set_cmap(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1424: UserWarning: Since limits were passed to `cpt_lims`, parameter `robust` is unused.
  cmap, colorbar, cpt_lims = set_cmap(
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/polartoolkit/maps.py:1820: FutureWarning: The 'barwidth' parameter has been deprecated since v0.18.0 and will be removed in v0.20.0. Please use 'bar_width' instead.
  self.histogram(

data_dict = ptk.make_data_dict(
    names=titles,
    grids=grids,
    colors=[
        "red",
        "black",
        "blue",
        "magenta",
        "cyan",
        "green",
        "purple",
        "orange",
    ],
)

fig, df_data = ptk.plot_data(
    "points",
    start=[optimal_inv.data.inner_region[1], optimal_inv.data.inner_region[3]],
    stop=[optimal_inv.data.inner_region[0], optimal_inv.data.inner_region[2]],
    num=10000,
    fig_height=4,
    fig_width=15,
    data_dict=data_dict,
    data_legend_loc="jTR+jTL",
    data_legend_box="+gwhite",
    data_buffer=0.01,
    data_frame=["neSW", "xafg+lDistance (m)", "yag+luncertainty (m)"],
    # data_pen_style=[None,None,"4_2:2p"],
    # data_pen_thickness=[1, 1.5, 1],
    share_yaxis=True,
    start_label="A",
    end_label="A' ",
)
fig.show()

grdtrack [WARNING]: Some input points were outside the grid domain(s).
grdtrack [WARNING]: Some input points were outside the grid domain(s).
grdtrack [WARNING]: Some input points were outside the grid domain(s).
grdtrack [WARNING]: Some input points were outside the grid domain(s).
grdtrack [WARNING]: Some input points were outside the grid domain(s).
grdtrack [WARNING]: Some input points were outside the grid domain(s).
grdtrack [WARNING]: Some input points were outside the grid domain(s).
grdtrack [WARNING]: Some input points were outside the grid domain(s).
/home/mdtanker/invert4geom/.pixi/envs/default/lib/python3.13/site-packages/pygmt/src/legend.py:160: SyntaxWarning: Short-form parameter 'S' is not recommended. Use long-form parameter 'scale' instead.
  aliasdict.merge(kwargs)