LSQR based geopotential recovery

Abstract

In the context of present and forthcoming geoscientific satellite missions, numerical solution strategies for large and ill-conditioned linear systems of equations as occurring in geopotential recovery are of great interest. Due to the character of the inverse problem, i.e. to solve a highly over determined problem, least squares procedures are usually adopted. To meet the arising challenge from the computational point of view, an iterative algorithm based on bidiago-nalization and QR decomposition, referred to as LSQR, is presented. Moreover, in terms of LSQR tuning, an adoption and extension of the original algorithm for its use in satellite geodesy was realized. In particular, regularization and preconditioning is addressed. The LSQR algorithm is applied to a simulated GOCE (Gravity field and steady-state Ocean Circulation Explorer) data set. Its parallel implementation on a (shared memory) supercomputing platform results in a highly effective tool for solving least squares problems.