A direct method and its numerical interpretation in the determination of the Earth's gravity field from terrestrial data

Abstract

In the determination of the gravity field of the Earth the present accuracy requiremerits represent an important driving impulse for the use of direct and numerical methods in the solution of boundary value problems for partial differential equations. The aim of this paper is to discuss the numerical solution of the linear gravimetric boundary value problem. The approach used follows the principles of Galerkin's approximations. It is formulated directly for the surface of the Earth as the boundary of the domain of harmonicity. Thus, the accuracy of the gravity field model is only limited by the accuracy of gravimetric data and the data coverage, and by the capability of the computer hardware. The approach offers a certain freedom in the choice of a function basis suitable for representing the gravity potential of the Earth. Extensive numerical simulations have been done using simulated gravity data derived from the EGM96. Solutions for spherical and more general boundaries have been computed. The solutions also show the oblique derivative effect, usually neglected in geodesy. Moreover, different function bases (such as point masses, reproducing kernels, and Poisson multi-pole wavelets) were used to represent the disturbing potential. The computed global gravity field models are compared with the EGM96 input data in terms of potential values and gravity disturbances at points on the boundary surface. © Springer-Verlag Berlin Heidelberg 2007.