A mathematical model of the bathymetry- generated external gravitational field - TENZER, Robert; VAJDA, Peter; HAMAYUN, K. (Contributions to Geophysics and Geodesy, 2010)
The currently available global geopotential models and the global elevationand bathymetry data allow modelling the topography-corrected and bathymetry strippedreference gravity field to a very high spectral resolution (up to degree 2160 of sphericalharmonics) using methods for a spherical harmonic analysis and synthesis of the gravityfield. When modelling the topography-corrected and crust-density-contrast stripped referencegravity field, additional stripping corrections are applied due to the ice, sedimentand other major known density contrasts within the Earth’s crust. The currently availabledata 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 limitedto a low spectral resolution, typically up to degree 180 of spherical harmonics. In thisstudy we derive the expressions used in forward modelling of the bathymetry-generatedgravitational field quantities and the corresponding bathymetric stripping corrections togravity field quantities by means of the spherical bathymetric (ocean bottom depth) functions.The expressions for the potential and its radial derivative are formulated for theadopted constant (average) ocean saltwater density contrast and for the spherical approximationof the geoid surface. These newly derived expressions are utilized in numericalexamples to compute the gravitational potential and attraction generated by the oceandensity contrast. The computation is realized globally on a 1 × 1 arc-deg geographicalgrid at the Earth’s surface.