Source code for harmonica.gravity_corrections

# Copyright (c) 2018 The Harmonica Developers.
#
# This code is part of the Fatiando a Terra project (https://www.fatiando.org)
#
"""
Gravity corrections like Normal Gravity and Bouguer corrections.
"""
import numpy as np

from .constants import GRAVITATIONAL_CONST

[docs]def bouguer_correction(topography, density_crust=2670, density_water=1040):
r"""
Gravitational effect of topography using a Bouguer plate approximation

Used to remove the gravitational attraction of topography above the
ellipsoid from the gravity disturbance. The infinite plate approximation is
adequate for regions with flat topography and observation points close to
the surface of the Earth.

This function calculates the classic Bouguer correction:

.. math::

g_{bg} = 2 \pi G \rho h

in which :math:G is the gravitational constant and :math:g_{bg} is the
gravitational effect of an infinite plate of thickness :math:h and
density :math:\rho.

In the oceans, subtracting normal gravity from the observed gravity results
in over correction because the normal Earth has crust where there was water
in the real Earth. The Bouguer correction for the oceans aims to remove
this residual effect due to the over correction:

.. math::

g_{bg} = 2 \pi G (\rho_w - \rho_c) |h|

in which :math:\rho_w is the density of water and :math:\rho_c is the
density of the crust of the normal Earth. We need to take the absolute
value of the bathymetry :math:h because it is negative and the equation
requires a thickness value (positive).

Parameters
----------
topography : array or :class:xarray.DataArray
Topography height and bathymetry depth in meters.
Should be referenced to the ellipsoid (ie, geometric heights).
density_crust : float
Density of the crust in :math:kg/m^3.
Used as the density of topography on land and the density of the normal
Earth's crust in the oceans.
density_water : float
Density of water in :math:kg/m^3.

Returns
-------
grav_bouguer : array or :class:xarray.DataArray
The gravitational effect of topography and residual bathymetry in mGal.

"""
# Need to cast to array to make sure numpy indexing works as expected for
# 1D DataArray topography
oceans = np.array(topography < 0)
continent = np.logical_not(oceans)
density = np.full(topography.shape, np.nan, dtype="float")
density[continent] = density_crust
# The minus sign is used to negate the bathymetry (which is negative and
# the equation calls for "thickness", not height). This is more practical
# than taking the absolute value of the topography.
density[oceans] = -1 * (density_water - density_crust)
bouguer = 1e5 * 2 * np.pi * GRAVITATIONAL_CONST * density * topography
return bouguer