Stokes integration versus wavelet techniques for regional geoid modelling

Abstract

For the computation of high resolution regional geoid models, gravity and terrain data in connection with a global geopotential model play a very important role. The data sets are usually combined in a remove-restore procedure. In many cases, the transformation from gravity anomalies to geoid undulations is done using Stokes’s integration kernel or a modified integration kernel, e.g., based on the spectral combination technique. Least squares collocation may be used for this task as well, but for continental-scale computations the integration techniques are often preferred due to their high computational efficiency. Besides the classical integration techniques, the wavelet technique is investigated in this contribution. The wavelet technique also uses residual gravity field quantities in a remove-restore procedure. However, the computations are carried out in two steps. The first step consists of a convolution of the residual gravity data with several wavelet functions, being contracted or dilated variants of one prototype (“mother”) wavelet function. This leads to a decomposition of the whole spectrum of the original data into a set of filtered detail signals with unique spatial resolution. This type of space and frequency analysis is called multi-scale analysis (MSA). The second step then convolves the residual gravity details with an integration kernel (e.g., Stokes) and leads to corresponding geoid undulations. The second step, applied to every decomposed detail (scale) of the original data, corresponds to the classical integration techniques. In this contribution, both the classical integration and spherical wavelet techniques are applied using Europe as a test area. The differences in methodology and numerical performance of both techniques are investigated. Finally, the results are evaluated by independent GPS and levelling control points.