harmonica.EQLHarmonic¶

class harmonica.EQLHarmonic(damping=None, points=None, relative_depth=500)[source]¶

Equivalent-layer for generic harmonic functions (gravity, magnetics, etc).

This equivalent layer can be used for:

Cartesian coordinates (geographic coordinates must be project before use)
Gravity and magnetic data (including derivatives)
Single data types
Interpolation
Upward continuation
Finite-difference based derivative calculations

It cannot be used for:

Joint inversion of multiple data types (e.g., gravity + gravity gradients)
Reduction to the pole of magnetic total field anomaly data
Analytical derivative calculations

Point sources are located beneath the observed potential-field measurement points by default [Cooper2000]. Custom source locations can be used by specifying the points argument. Coefficients associated with each point source are estimated through linear least-squares with damping (Tikhonov 0th order) regularization.

The Green’s function for point mass effects used is the inverse Cartesian distance between the grid coordinates and the point source:

\[\phi(\bar{x}, \bar{x}') = \frac{1}{||\bar{x} - \bar{x}'||}\]

where \(\bar{x}\) and \(\bar{x}'\) are the coordinate vectors of the observation point and the source, respectively.

Parameters

damping (None or float) – The positive damping regularization parameter. Controls how much smoothness is imposed on the estimated coefficients. If None, no regularization is used.
points (None or list of arrays (optional)) – List containing the coordinates of the point sources used as the equivalent layer. Coordinates are assumed to be in the following order: (easting, northing, upward). If None, will place one point source bellow each observation point at a fixed relative depth bellow the observation point [Cooper2000]. Defaults to None.
relative_depth (float) – Relative depth at which the point sources are placed beneath the observation points. Each source point will be set beneath each data point at a depth calculated as the elevation of the data point minus this constant relative_depth. Use positive numbers (negative numbers would mean point sources are above the data points). Ignored if points is specified.

Variables

points_ (2d-array) – Coordinates of the point sources used to build the equivalent layer.
coefs_ (array) – Estimated coefficients of every point source.
region_ (tuple) – The boundaries ([W, E, S, N]) of the data used to fit the interpolator. Used as the default region for the grid and scatter methods.

Methods Summary

`EQLHarmonic.filter`(coordinates, data[, weights])	Filter the data through the gridder and produce residuals.
`EQLHarmonic.fit`(coordinates, data[, weights])	Fit the coefficients of the equivalent layer.
`EQLHarmonic.get_params`([deep])	Get parameters for this estimator.
`EQLHarmonic.grid`([region, shape, spacing, …])	Interpolate the data onto a regular grid.
`EQLHarmonic.jacobian`(coordinates, points[, …])	Make the Jacobian matrix for the equivalent layer.
`EQLHarmonic.predict`(coordinates)	Evaluate the estimated equivalent layer on the given set of points.
`EQLHarmonic.profile`(point1, point2, size[, …])	Interpolate data along a profile between two points.
`EQLHarmonic.scatter`([region, size, …])	Interpolate values onto a random scatter of points.
`EQLHarmonic.score`(coordinates, data[, weights])	Score the gridder predictions against the given data.
`EQLHarmonic.set_params`(**params)	Set the parameters of this estimator.

EQLHarmonic.filter(coordinates, data, weights=None)¶

Filter the data through the gridder and produce residuals.

Calls fit on the data, evaluates the residuals (data - predicted data), and returns the coordinates, residuals, and weights.

No very useful by itself but this interface makes gridders compatible with other processing operations and is used by verde.Chain to join them together (for example, so you can fit a spline on the residuals of a trend).

Parameters

coordinates (tuple of arrays) – Arrays with the coordinates of each data point. Should be in the following order: (easting, northing, vertical, …).
data (array or tuple of arrays) – The data values of each data point. If the data has more than one component, data must be a tuple of arrays (one for each component).
weights (None or array or tuple of arrays) – If not None, then the weights assigned to each data point. If more than one data component is provided, you must provide a weights array for each data component (if not None).

Returns

coordinates, residuals, weights – The coordinates and weights are same as the input. Residuals are the input data minus the predicted data.

EQLHarmonic.fit(coordinates, data, weights=None)[source]¶

Fit the coefficients of the equivalent layer.

The data region is captured and used as default for the grid and scatter methods.

All input arrays must have the same shape.

Parameters

coordinates (tuple of arrays) – Arrays with the coordinates of each data point. Should be in the following order: (easting, northing, upward, …). Only easting, northing, and upward will be used, all subsequent coordinates will be ignored.
data (array) – The data values of each data point.
weights (None or array) – If not None, then the weights assigned to each data point. Typically, this should be 1 over the data uncertainty squared.

Returns

self – Returns this estimator instance for chaining operations.

EQLHarmonic.get_params(deep=True)¶

Get parameters for this estimator.

Parameters: deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns: params (mapping of string to any) – Parameter names mapped to their values.

EQLHarmonic.grid(region=None, shape=None, spacing=None, dims=None, data_names=None, projection=None, **kwargs)¶

Interpolate the data onto a regular grid.

The grid can be specified by either the number of points in each dimension (the shape) or by the grid node spacing. See verde.grid_coordinates for details. Other arguments for verde.grid_coordinates can be passed as extra keyword arguments (kwargs) to this method.

If the interpolator collected the input data region, then it will be used if region=None. Otherwise, you must specify the grid region.

Use the dims and data_names arguments to set custom names for the dimensions and the data field(s) in the output xarray.Dataset. Default names will be provided if none are given.

Parameters

region (list = [W, E, S, N]) – The boundaries of a given region in Cartesian or geographic coordinates.
shape (tuple = (n_north, n_east) or None) – The number of points in the South-North and West-East directions, respectively.
spacing (tuple = (s_north, s_east) or None) – The grid spacing in the South-North and West-East directions, respectively.
dims (list or None) – The names of the northing and easting data dimensions, respectively, in the output grid. Defaults to ['northing', 'easting']. NOTE: This is an exception to the “easting” then “northing” pattern but is required for compatibility with xarray.
data_names (list of None) – The name(s) of the data variables in the output grid. Defaults to ['scalars'] for scalar data, ['east_component', 'north_component'] for 2D vector data, and ['east_component', 'north_component', 'vertical_component'] for 3D vector data.
projection (callable or None) – If not None, then should be a callable object projection(easting, northing) -> (proj_easting, proj_northing) that takes in easting and northing coordinate arrays and returns projected northing and easting coordinate arrays. This function will be used to project the generated grid coordinates before passing them into predict. For example, you can use this to generate a geographic grid from a Cartesian gridder.

Returns

grid (xarray.Dataset) – The interpolated grid. Metadata about the interpolator is written to the attrs attribute.

Examples using `harmonica.EQLHarmonic`¶

Gridding and upward continuation¶

harmonica.EQLHarmonic¶

Examples using harmonica.EQLHarmonic¶

Examples using `harmonica.EQLHarmonic`¶