Regularized collocation for Spherical harmonics Gravitational Field Modeling

Motivated by the problem of satellite gravity gradiometry, which is the reconstruction of the Earth gravity potential from the satellite data provided in the form of the second-order partial derivatives of the gravity potential at a satellite altitude, we discuss a special regularization technique for solving this severely ill-posed problem in a spherical framework. We are especially interested in the regularized collocation method. As a core ingredient we present an a posteriori parameter choice rule, namely the weighted discrepancy principle, and proves its order optimality. Finally, we illustrate our theoretical findings by numerical results for the computation of the Fourier coefficients of the gravitational potential directly from the noisy synthetic data.