A numerical study of solving the altimetry-gravimetry boundary value problem in coastal regions

Abstract

The paper presents numerical results for the solution of the altimetry-gravimetry boundary value problem with compatibility conditions along the coastline. The solution is based on the application of spherical Shannon wavelets based on the Abel- Poisson kernel and pseudo-diffferential operators. The orthogonality of Shannon wavelets can be used for the numerical solution overcoming some technical problems with generally non-orthogonal spherical wavelets. A numerical experiment has been conducted in eastern Canada and the results have been compared with the geoid heights computed from gravity anomalies by applying ID FFT spherical Stokes convolution with 50 km integration radius. The effect of compatibility conditions along the coastline on the solution are discussed and the following conclusions are drawn: spherical Shannon wavelets can be very successfully applied in the numerical solution of the AGBVP II and the smoothing effect of spherical wavelets is much more effective than the classical planar type of wavelets.