The computation of the gravity field of the earth by boundary element method and wavelet algorithm
by
Andreas Rathsfeld
Weierstrass Institute for Applied Analysis and Stochastics

To compute the gravity field of the earth, a harmonic potential is to be determined in the exterior of the earth. Depending on the measured data, there exist several interesting boundary value problems. We suppose that the geometry of the earth is given and that the modulus of the gradient of the gravity potential is measured on the surface of the earth or over a rectangular part of it. Then, introducing a simple approximation of the gravity field and linearising the nonlinear boundary condition, it remains to solve the problem of oblique derivative. A single layer representation for the gravity field leads to a strongly singular integral equation over the surface of the earth which can be solved by piecewise linear collocation.

Note that the corresponding boundary integral equation is given over a manifold which has a finite degree of smoothness only. On the other hand, the manifold can be represented by parametrizations over a small number of simple parameter domains. Therefore, the collocation method turns out to be a good candidate for the application of fast wavelet algorithms.

A different ``boundary value problem'' arises if the measurements on the surface of the earth are replaced by second order derivatives along the orbit of a satellite mission. In this case the integral equation turns into an improperly posed first kind integral equation. The numerical solution of this equation is much more involved.

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Date received: July 27, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadk-54.