Application of Sparse Regularization in Spherical Radial Basis Functions-Based Regional Geoid Modeling in Colorado

Abstract

Spherical radial basis function (SRBF) is an effective method for calculating regional gravity field models. Calculating gravity field models with high accuracy and resolution requires dense basis functions, resulting in complex models. This study investigated the application of sparse regularization in SRBFs-based regional gravity field modeling. L1-norm regularization, also known as the least absolute shrinkage selection operator (LASSO), was employed in the parameter estimation procedure. LASSO differs from L2-norm regularization in that the solution obtained by LASSO is sparse, specifically with a portion of the parameters being zero. A sparse model would be advantageous for improving the numerical efficiency by reducing the number of SRBFs. The optimization problem of the LASSO was solved using the fast iterative shrinkage threshold algorithm, which is known for its high efficiency. The regularization parameter was selected using the Akaike information criterion. It was specifically tailored to the L1-norm regularization problem. An approximate covariance matrix of the estimated parameters in the sparse solution was analytically constructed from a Bayesian viewpoint. Based on the remove–compute–restore technique, a regional geoid model of Colorado (USA) was calculated. The numerical results suggest that the LASSO adopted in this study provided competitive results compared to Tikhonov regularization; however, the number of basis functions in the final model was less than 25% of the Tikhonov regularization. Without significantly reducing model accuracy, the LASSO solution provides a very simple model. This is the first study to apply the LASSO to SRBFs-based modeling of the regional gravity field in real gravity observation data.