Optimization of computations in global geopotential field applications

Abstract

Most boundary value problems of the geopotential field have integral and series solutions in terms of Green's convolution kernels. These solutions are advantageously evaluated using fast Spherical Harmonic Transforms (SHTs) for regular arrays of simulated or observed global data. However, the computational complexity and numerical conditioning of SHTs for relatively dense data are quite challenging and recent algorithmic developments warrant further investigations for geodetic and geophysical applications. Global multiresolution applications for scalar, vector and tensor fields on the Earth and its neighborhood require spherical harmonic analysis and synthesis using convolution filters with data decimation and dilation. For global spherical grid applications, efficient and reliable SHTs are needed just as Fast Fourier Transforms (FFTs) are used in regional planar applications. With the availability of enormous quantities of space, surface and subsurface data, extensive data structuring and management are unavoidable for most array computations. Different methodologies imply very different strategies and conflicting claims often appear in the literature. Discussions of the implicit and other assumptions with simulated results would undoubtedly help to clarify the situation and help decide on appropriate data structuring strategies for different computational applications. © Springer-Verlag Berlin Heidelberg 2003.