Wavelet evaluation of some singular geodetic integrals

Abstract

The paper presents a method of evaluating some singular geodetic integrals using wavelets. The wavelet transform is a powerful tool in evaluating some singular geodetic integrals. Due to its localization properties in both of the time (space) and frequency (scale) domains, and because the kernels of some geodetic integrals have singular points and decay smoothly and quickly away from the singularities, many numbers of wavelet transform coefficients of the kernels become zeros or negligible, and only small number of wavelet transform coefficients are significant. It is thus possible to significantly compress the kernels of these integrals in a wavelet basis by neglecting the zero coefficients and the small coefficients below a certain threshold. Therefore, wavelets provide a convenient way for efficiently evaluating these integrals in terms of fast computation and savings of computer memory. In this contribution, a modified algorithm for the wavelet evaluation of Stokes integrals is presented. And the same modified algorithm is applied to the evaluation of Vening Meinesz and terrain corrections integral, whose kernels have stronger singularities than of Stokes’ kernel. Numerical examples illustrate the efficiency and accuracy of the wavelet methods.