On fast multigrid iteration techniques for the solution of normal equations in satellite gravity recovery

Dedicated satellite-to-satellite tracking (SST) or gradiometry missions like GRACE and GOCE will provide gravity field information with unprecedented resolution and precision. It has been recognized that better gravity field models and estimates of the geoid are useful for a wide range of research and application, including ocean circulation and climate change studies, physics of the Earthʹs interior and height datum connection and unification. The computation of these models will require the solution of large and non-sparse normal equation systems, especially if "brute force" approaches are applied. Evidently, there is a need for fast solvers. The multigrid approach is not only an extremely fast iterative solution technique, it yields, en passant, a welldefined sequence of coarser approximations as a byproduct to the final gravity field solution. We investigate the implementation of multigrid methods to satellite data analysis using space-domain representations of the anomalous gravity field. Multigrid algorithms are considered as stand-alone solvers as well as for the construction of preconditioners in the conjugate gradient technique. Our numerical results, concerning two regional gravity inversions from simulated GRACE and GOCE data, show that multigrid solvers run much faster than conjugate gradient solvers with conventional preconditioners.