Py_Admittance package

Submodules

Module contents

Py_Admittance

Py_Admittance provides functions and an example scripts for calculating global/localized admittances of gravity and topography. These can be used to invert for parameters such as the elastic thickness of the lithosphere and density of the crust and surface.

ForwardGravity

Compute the theoretical gravity field given a set of input parameters.

TransferTGz

Compute theoretical transfer functions for calculating the admittance and correlation given a set of input parameters.

LocalAdmitCorr

Compute the localized admittance of two functions.

GlobalAdmitCorr

Compute the global admittance of two functions.

Py_Admittance.ForwardGravity(topo, G, mass, g0, Tc, Te, rhoc, rhom, lmax, ratio_L=0, alpha_L=1, depth_L=50000.0, E=100000000000.0, v=0.25, nmax=5, R_ref=None, rhol=None, lmaxgrid=None, option_deg1=None, option_deg2=None, return_corr=False)

Compute the theoretical gravity field given the input parameters. For more information, see Broquet & Wieczorek (2019).

Returns:

  • grav_Th (array, dimension (2, lmax+1, lmax+1)) – Theoretical global gravity field in mGal.

  • Corr_Th (array, dimension (lmax+1)) – If return_corr is True, returns the theoretical correlation for surface/internal loads that are out of phase (alpha_L != 1).

Parameters:

  • topo (array, dimension (2,lmax+1,lmax+1)) – Array with the spherical harmonic coefficients of the surface topography.

  • G (float) – Gravitational constant.

  • mass (float) – Mass of the planet.

  • g0 (float) – Gravitational attraction at the surface.

  • Tc (float) – Average crustal thickness.

  • Te (float) – Elastic thickness of the lithosphere.

  • rhoc (float) – Density of the crust.

  • rhom (float) – Density of the mantle.

  • lmax (int) – Maximum spherical harmonic degree for calculations.

  • ratio_L (float, optional, default = 0) – Ratio of the internal / surface load.

  • alpha_L (float, optional, default = 1) – Phase relationship for the internal / surface load. This parameter is experimental.

  • depth_L (float, optional, default = 50e3) – Depth of the internal load.

  • E (float, optional, default = 100e9) – Young’s modulus.

  • v (float, optional, default = 0.25) – Poisson’s ratio.

  • nmax (int, optional, default = 5) – Order of the finite-amplitude correction.

  • R_ref (float, optional, default = None) – Reference radius for gravity field calculations. If None, this parameter is set to the mean radius of the topography file.

  • rhol (float, optional, default = None) – Density of the surface topography. If None, this parameter is set to rhoc.

  • lmaxgrid (int, optional, default = None) – Resolution of the input grid for the finite-amplitude correction routines. If None, this parameter is set to 3*lmax. For accurate results, this parameter should be about 3 times lmax, though this should be verified for each application. Lowering this parameter significantly increases speed.

  • option_deg1 (string, optional, default = None) – How to treat degree-1 displacement. If set to “Zero”, the degree-1 displacement is zeroed out. If set to “Airy”, the degree-1 topography is assumed to be Airy compensated. If anything else, no special treatment is applied to degree-1.

  • option_deg2 (string/float, optional, default = None) – How to treat degree-2 topography. If set to “Zero”, the C20 topography is zeroed out. If set to “Flat”, the C20 topography is not considered as a load, but is added back for finite-amplitude calculations. If set to a float, only option_deg2 * topography is used as a load. If anything else, no special treatment is applied to degree-2.

  • return_corr (string, optional, default = False) – If set to True, return the theoretical global correlation.

Py_Admittance.GlobalAdmitCorr(topo, grav, lmax=None)

Compute the global admittance and correlation functions from the input gravity and topography. For more information, see Broquet & Wieczorek (2019).

Returns:

  • Admittance (array, dimension (lmax+1)) – Global admittance function in mGal/km.

  • Correlation (array, dimension (lmax+1)) – Global correlation function.

  • Admit_error (array, dimension (lmax+1)) – Global admittance uncertainty in mGal/km.

Parameters:

  • topo (dimension (2, lmax+1, lmax+1)) – Spherical harmonic coefficients of the topography (km).

  • grav (dimension (2, lmax+1, lmax+1)) – Spherical harmonic coefficients of the gravity field (mGal).

  • lmax (int, optional, default = None) – Maximum degree at which the admittance and correlation are computed. If None, lmax = min(lmax_topo, lmax_grav). lmax must be <= min(lmax_topo, lmax_grav).

Py_Admittance.LocalAdmitCorr(topo, grav, lat, lon, theta, lwin, lmax=None, quiet=True)

Compute the localized admittance and correlation functions from the input gravity and topography. For more information, see Broquet & Wieczorek (2019).

Returns:

  • Admittance (array, dimension (lmax-lwin+1)) – Localized admittance function in mGal/km.

  • Correlation (array, dimension (lmax-lwin+1)) – Localized correlation function.

  • Admit_error (array, dimension (lmax-lwin+1)) – Localized admittance uncertainty in mGal/km.

Parameters:

  • topo (dimension (2, lmax+1, lmax+1)) – Spherical harmonic coefficients of the topography (km).

  • grav (dimension (2, lmax+1, lmax+1)) – Spherical harmonic coefficients of the gravity field (mGal).

  • lat (float) – Central latitude (°) of the localization window.

  • lon (float) – Central longitude (°) of the localization window.

  • theta (float) – Angular radius (°) of the localization window.

  • lwin (int) – Bandwidth of the localization window.

  • lmax (int, optional, default = None) – Maximum degree at which the admittance and correlation are computed. If None, lmax = min(lmax_topo, lmax_grav). lmax must be <= min(lmax_topo, lmax_grav).

  • quiet (string, optional, default = True) – If False, the function will provide information regarding the spatio-spectral concentration of the localization window.

Py_Admittance.TransferTGz(g0, R, Tc, Te, rhol, rhoc, rhom, rhobar, lmax, ratio_L=0, alpha_L=1, depth_L=50000.0, E=100000000000.0, v=0.25)

Compute theoretical transfer function given the input parameters, including the admittance and correlation. For more information, see Broquet & Wieczorek (2019).

Returns:

  • T_s (array, dimension (lmax+1)) – Transfer function for flexure due to surface loads.

  • Qw_l (array, dimension (lmax+1)) – Transfer function for flexure due to surface/internal loads.

  • Qw_lz (array, dimension (lmax+1)) – Transfer function for flexure du to internal load.

  • Trsf_s (array, dimension (lmax+1)) – Transfer function for gravity from surface load.

  • Trsf_L (array, dimension (lmax+1)) – Transfer for gravity from internal load.

  • Correlation (array, dimension (lmax+1)) – Theoretical global correlation for out of phase surface/internal loads (alpha_L != 1).

Parameters:

  • g0 (float) – Gravitational attraction at the surface.

  • R (float) – Mean radius of the planet.

  • Tc (float) – Average crustal thickness.

  • Te (float) – Elastic thickness of the lithosphere.

  • rhol (float) – Density of the surface topography.

  • rhoc (float) – Density of the crust.

  • rhom (float) – Density of the mantle.

  • lmax (int) – Maximum spherical harmonic degree for calculations.

  • ratio_L (float, optional, default = 0) – Ratio of the internal / surface load.

  • alpha_L (float, optional, default = 1) – Phase relationship for the internal / surface load. This parameter is experimental.

  • depth_L (float, optional, default = 50e3) – Depth of the internal load.

  • E (float, optional, default = 100e9) – Young’s modulus.

  • v (float, optional, default = 0.25) – Poisson’s ratio.