Py_Admittance.Th_Admittance module

Compute theoretical transfer functions and gravity field given the input parameters. These can then be used to compute the localized/global admittance and correlation.

Py_Admittance.Th_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.Th_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.Th_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.Th_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.