A mathematical model of the bathymetry- generated external gravitational field

Abstract

The currently available global geopotential models and the global elevation
and bathymetry data allow modelling the topography-corrected and bathymetry stripped
reference gravity field to a very high spectral resolution (up to degree 2160 of spherical
harmonics) using methods for a spherical harmonic analysis and synthesis of the gravity
field. When modelling the topography-corrected and crust-density-contrast stripped reference
gravity field, additional stripping corrections are applied due to the ice, sediment
and other major known density contrasts within the Earth’s crust. The currently available
data of global crustal density structures have, however, a very low resolution and accuracy.
The compilation of the global crust density contrast stripped gravity field is thus limited
to a low spectral resolution, typically up to degree 180 of spherical harmonics. In this
study we derive the expressions used in forward modelling of the bathymetry-generated
gravitational field quantities and the corresponding bathymetric stripping corrections to
gravity field quantities by means of the spherical bathymetric (ocean bottom depth) functions.
The expressions for the potential and its radial derivative are formulated for the
adopted constant (average) ocean saltwater density contrast and for the spherical approximation
of the geoid surface. These newly derived expressions are utilized in numerical
examples to compute the gravitational potential and attraction generated by the ocean
density contrast. The computation is realized globally on a 1 × 1 arc-deg geographical
grid at the Earth’s surface.