Global Gravity Field Model (pygeoid.sharm.ggm.GlobalGravityFieldModel)

class pygeoid.sharm.ggm.GlobalGravityFieldModel(coeffs, gm, r0, errors=None, ell=None, omega=None)[source]

Class for working with the global gravity field models.

The theory and formulas used by this class as in the ICGEM calculation service and described in the Scientific Technical Report STR09/02 [1].

Parameters:

  • coeffs (Quantity) – Dimensionless fully-normalized spherical harmonics coefficients with the sahpe (2, lmax+1, lmax+1). Where lmax is the maximum degree of the coefficients.

  • gm (Quantity) – Gravitational parameter that is associated with the gravitational potential coefficients.

  • r0 (Quantity) – Reference radius of the gravitational potential coefficients.

  • coeffs – Uncertainties of the spherical harmonic coefficients. It should have the same shape as coeffs.

  • ell (instance of the pygeoid.reduction.ellipsoid.LevelEllipsoid) – Reference ellipsoid to which noramal gravity field is referenced to. Default is None (default ellipsoid will be used).

  • omega (Quantity) – Angular rotation rate of the body.

  • errors (bool)

References

and Their Calculation from Spherical Harmonic Models’. Deutsches GeoForschungsZentrum (GFZ), 2013. https://doi.org/10.2312/GFZ.b103-0902-26.

property resolution

Return half-wavelength of the model.

property gravitational_potential

Return SHGravPotential class instance for the gravitational potential.

property gravity_potential

Return SHGravPotential class instance for the gravity potential.

property anomalous_potential

Return SHGravPotential class instance for anomalous potential.

property normal_potential

Return normal potential class instance.

gravitation(lat, lon, r, lmax=None)[source]

Return gradient vector.

The magnitude and the components of the gradient of the potential calculated on or above the ellipsoid without the centrifugal potential (eqs. 7 and 122 of STR09/02).

Parameters:

  • lat (Quantity) – Spherical latitude.

  • lon (Quantity) – Spherical longitude.

  • r (Quantity) – Radial distance.

  • lmax (int, optional) – Maximum degree of the coefficients. Default is None (use all the coefficients).

Returns:

Gravitation.

Return type:

Quantity

gravity(lat, lon, r, lmax=None)[source]

Return gravity value.

The magnitude of the gradient of the potential calculated on or above the ellipsoid including the centrifugal potential (eqs. 7 and 121 − 124 of STR09/02).

Parameters:

  • lat (Quantity) – Spherical latitude.

  • lon (Quantity) – Spherical longitude.

  • r (Quantity) – Radial distance.

  • lmax (int, optional) – Maximum degree of the coefficients. Default is None (use all the coefficients).

Returns:

Gravity.

Return type:

Quantity

gravity_disturbance(lat, lon, r, lmax=None)[source]

Return gravity disturbance.

The gravity disturbance is defined as the magnitude of the gradient of the potential at a given point minus the magnitude of the gradient of the normal potential at the same point (eqs. 87 and 121 − 124 of STR09/02).

Parameters:

  • lat (Quantity) – Spherical latitude.

  • lon (Quantity) – Spherical longitude.

  • r (Quantity) – Radial distance.

  • lmax (int, optional) – Maximum degree of the coefficients. Default is None (use all the coefficients).

Returns:

Gravity disturbance.

Return type:

Quantity

gravity_disturbance_sa(lat, lon, r, lmax=None)[source]

Return gravity disturbance in spherical approximation.

The gravity disturbance calculated by spherical approximation (eqs. 92 and 125 of STR09/02) on (h=0) or above (h>0) the ellipsoid.

Parameters:

  • lat (Quantity) – Spherical latitude.

  • lon (Quantity) – Spherical longitude.

  • r (Quantity) – Radial distance.

  • lmax (int, optional) – Maximum degree of the coefficients. Default is None (use all the coefficients).

Returns:

Gravity disturbance.

Return type:

Quantity

gravity_anomaly_sa(lat, lon, r, lmax=None)[source]

Return (Molodensky) gravity anomaly in spherical approximation.

The gravity anomaly calculated by spherical approximation (eqs. 100 or 104 and 126 of STR09/02). Unlike the classical gravity anomaly, the Molodensky gravity anomaly and the spherical approximation can be generalised to 3-d space, hence here it can be calculated on (h=0) or above (h>0) the ellipsoid.

Parameters:

  • lat (Quantity) – Spherical latitude.

  • lon (Quantity) – Spherical longitude.

  • r (Quantity) – Radial distance.

  • lmax (int, optional) – Maximum degree of the coefficients. Default is None (use all the coefficients).

Returns:

Gravity anomaly.

Return type:

Quantity

height_anomaly_ell(lat, lon, r, ref_pot=None, lmax=None)[source]

Return height anomaly above the ellispoid.

The height anomaly can be generalised to a 3-d function, (sometimes called “generalised pseudo-height-anomaly”). Here it can be calculated on (h=0) or above (h>0) the ellipsoid, approximated by Bruns’ formula (eqs. 78 and 118 of STR09/02)

Parameters:

  • lat (Quantity) – Spherical latitude.

  • lon (Quantity) – Spherical longitude.

  • r (Quantity) – Radial distance.

  • ref_pot (Quantity) – Reference potential value W0 for the zero degree term. Defaut is None (zero degree term is not considered).

  • lmax (int, optional) – Maximum degree of the coefficients. Default is None (use all the coefficients).

Returns:

Anomaly height.

Return type:

Quantity