Topography effects (pygeoid.reduction.topography)

Topographic reduction in gravity and geoid modelling

pygeoid.reduction.topography.bouguer_plate(height, density=<Quantity 2670. kg / m3>)

Return an attraction of an infinite Bouguer plate.

Parameters:

• height (Quantity) – Height above sea level.

• density (Quantity) – Density of the prism. Default is 2670 kg/m**3.

Return type:

Unit(“mGal”)

Notes

\[F_B = 2\pi G\delta H,\]

where \(G\) – gravitational constant, \(\delta\) – density, \(H\) – height above sea level.

pygeoid.reduction.topography.spherical_bouguer_cap(height, density=<Quantity 2670. kg / m3>)

Return spherical Bouguer correction.

Parameters:

• height (Quantity) – Height above sea level.

• density (Quantity) – Density of the prism. Default is 2670 kg/m**3.

Return type:

Unit(“mGal”)

Notes

The corected (spherical) Bouguer attraction accounts the curvature of the Earth. It is calclated by the closed-form formula for a spherical cap of radius 166.7 km [1]:

\[F_{SB} = 2\pi G ((1 + \mu) H - \lambda R),\]

where \(G\) – gravitational constant, \(\delta\) – density, \(H\) – height above sea level, \(\lambda\) and \(\mu\) – dimensionless coefficients, \(R = R_e + H\) – sum of the mean radius of the Earth and the height.

References

[1]

LaFehr, T.R., 1991. An exact solution for the gravity

curvature (Bullard B) correction. Geophysics, 56(8), pp.1179-1184.