Regularization for the Gravity Field Recovery from GOCE Observations

Abstract

The determination of the Earth’s gravitational potential from gravity gradients measured at satellite altitude along a non-polar orbit is an ill-posed problem, which lacks stability due to the polar gaps and the downward continuation from satellite altitude to the Earth’s surface. Even in the discrete world of observations the problem is still ill-conditioned, and some kind of regularization is indispensable to provide physically meaningful solutions up to high-degree and order. However, for large-scale problems the determination of the optimal regularization parameter is very expensive in terms of CPU-time, and strategies have to be developed to find this parameter with a minimum number of arithmetic operations. For the pair Tikhonov-Phillips/Morozov discrepancy principle the performance is analyzed for the gravity field recovery from GOCE SGG observations of two methods for accelerating the standard CG-algorithm recently proposed by Frommer & Maass. Moreover, the choice of a number of method-dependent parameters is investigated based on the analysis of several simulations up to degree and order 200 for white noise and colored noise observations and GOCE-like orbits.