Sparse Spherical Harmonic Component Selection for Gravity Field Modeling

Gravity field modeling with spherical harmonics is a fundamental task in physical geodesy. In conventional solutions, all spherical harmonic (SH) components below a prescribed maximum degree and order are typically retained, even though some components may contribute little to the final model. This study investigates SH component selection in gravity field modeling using sparse regularization, specifically the Lasso and adaptive Lasso. A statistical strategy is introduced for incorporating a reference global gravity model by accounting for its variance-covariance information. The resulting L1-norm-regularized estimation problem is solved with an efficient gradient-based algorithm, and the regularization parameter is selected using tailored criteria, including generalized cross-validation and the corrected Akaike information criterion. In addition, an approximate variance-covariance matrix of the estimated parameters is derived analytically from a Bayesian perspective, showing that only the non-zero coefficients contribute to the non-zero covariance structure. Closed-loop simulations based on EGM2008 show that the proposed method achieves modeling accuracy comparable to that of conventional Tikhonov regularization while retaining less than 10% of the SH components. The results demonstrate the feasibility of sparse SH modeling for obtaining compact gravity field representations without substantial loss of accuracy.