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invert4geom.synthetic

invert4geom.synthetic#

Module Contents#

Functions#

gaussian2d(x, y, sigma_x, sigma_y[, x0, y0, angle])

Non-normalized 2D Gaussian function for creating synthetic topography.

synthetic_topography_simple(spacing, region[, ...])

Create a synthetic topography dataset with a few features.

synthetic_topography_regional(spacing, region[, ...])

Create a synthetic topography dataset with a few features which represent the

contaminate(data, stddev[, percent, ...])

Add pseudorandom gaussian noise to an array.
gaussian2d(x, y, sigma_x, sigma_y, x0=0, y0=0, angle=0.0)[source]#

Non-normalized 2D Gaussian function for creating synthetic topography.

Parameters:

  • x (NDArray) – Coordinates at which to calculate the Gaussian function

  • y (NDArray) – Coordinates at which to calculate the Gaussian function

  • sigma_x (float) – Standard deviation in the x and y directions

  • sigma_y (float) – Standard deviation in the x and y directions

  • x0 (float, optional) – Coordinates of the center of the distribution, by default 0

  • y0 (float, optional) – Coordinates of the center of the distribution, by default 0

  • angle (float, optional) – Rotation angle of the gaussian measure from the x axis (north) growing positive to the east (positive y axis), by default 0.0

Returns:

Gaussian function evaluated at x, y

Return type:

NDArray

Notes

This function was adapted from the Fatiando-Legacy function gaussian2d: https://legacy.fatiando.org/api/utils.html?highlight=gaussian#fatiando.utils.gaussian2d

synthetic_topography_simple(spacing, region, registration='g', scale=1, yoffset=0)[source]#

Create a synthetic topography dataset with a few features.

Parameters:

  • spacing (float) – grid spacing in meters

  • region (tuple[float, float, float, float]) – bounding edges of the grid in meters in format (xmin, xmax, ymin, ymax)

  • registration (str, optional) – grid registration type, either “g” for gridline or “p” for pixel, by default “g”

  • scale (float, optional) – value to scale the topography by, by default 1

  • yoffset (float, optional) – value to offset the topography by, by default 0

Returns:

synthetic topography dataset

Return type:

xr.Dataset

synthetic_topography_regional(spacing, region, registration='g', scale=1, yoffset=0)[source]#

Create a synthetic topography dataset with a few features which represent the surface responsible for the regional component of gravity.

Parameters:

  • spacing (float) – grid spacing in meters

  • region (tuple[float, float, float, float]) – bounding edges of the grid in meters in format (xmin, xmax, ymin, ymax)

  • registration (str, optional) – grid registration type, either “g” for gridline or “p” for pixel, by default “g”

  • scale (float, optional) – value to scale the topography by, by default 1

  • yoffset (float, optional) – value to offset the topography by, by default 0

Returns:

synthetic topography dataset

Return type:

xr.Dataset

contaminate(data, stddev, percent=False, percent_as_max_abs=True, seed=0)[source]#

Add pseudorandom gaussian noise to an array. Noise added is normally distributed with zero mean and a standard deviation from stddev.

Parameters:

  • data (NDArray | list[NDArray]) – data to contaminate, can be a single array, or a list of arrays.

  • stddev (float | list[float]) – standard deviation of the Gaussian noise that will be added to data. Length must be the same as data if data is a list.

  • percent (bool, optional) – If True, will consider stddev as a decimal percentage of the data and the standard deviation of the Gaussian noise will be calculated with this, by default False

  • percent_as_max_abs (bool, optional) – If True, and percent is True, the stddev used as the standard deviation of the Gaussian noise will be the max absolute value of the data. If False, and percent is True, the stddev will be calculated on a point-by-point basis, so each data points’ noise will be the same percentage, by default True

  • seed (float, optional) – seed to use for the random number generator, by default 0

Returns:

a tuple of (contaminated data, standard deviations).

Return type:

tuple[NDArray | list[NDArray], float | list[float]]

Notes

This function was adapted from the Fatiando-Legacy function gaussian2d: https://legacy.fatiando.org/api/utils.html?highlight=gaussian#fatiando.utils.contaminate

Examples

>>> import numpy as np
>>> data = np.ones(5)
>>> noisy, std = contaminate(data, 0.05, seed=0, percent=True)
>>> print(std)
0.05
>>> print(noisy)
array([1.00425372, 0.99136197, 1.02998834, 1.00321222, 0.97118374])
>>> data = [np.zeros(5), np.ones(3)]
>>> noisy = contaminate(data, [0.1, 0.2], seed=0)
>>> print(noisy[0])
array([ 0.00850745, -0.01727606,  0.05997669,  0.00642444, -0.05763251])
>>> print(noisy[1])
array([0.89814061, 1.0866216 , 1.01523779])
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