Optimal regularization for geopotential model GOCO02S by Monte Carlo methods and multi-scale representation of density anomalies

GOCO02S is a combined satellite-only geopotential model, regularized from degrees 180 to 250 of the expansion into spherical harmonics. To investigate the start of the regularization, the normal equations of GOCO02S have been used to compute additional geopotential models by regularizations beginning at degrees 160, 200, 220 and with no regularization. Three different methods are applied to determine where to start the regularization. The simplest one considers the decrease of the degree variances of the not regularized solution. The second one tests for the same solution the hypothesis that the square root of the degree variance is equal to the value computed by the estimated harmonic coefficients. If the hypothesis has to be rejected for a certain degree, the error degree variance is so large that the estimated harmonic coefficients cannot be trusted anymore so that the regularization has to start at that degree. The third method uses the density anomalies by which the disturbing potential is caused resulting from the geopotential model. The density anomalies are well suited to visualize the effects of the higher degree harmonics. In contrast to the base functions of the harmonic coefficients with global support, the density anomalies are expressed by a B-spline surface with local support. Multi-scale representations were applied and the hypotheses tested that the wavelet coefficients are equal to zero. Accepting the hypotheses means that nonsignificant wavelet coefficients were determined which lead to nonsignificant density anomalies. By comparing these anomalies for different regularizations, the degree where to start the regularization is determined. It turns out that beginning the regularization at degree 180, as was done for GOCO02S, is a correct choice.