Sparse Regional Gravity Field Modeling by Greedy SRBF

Abstract

Spherical Radial Basis Function (SRBF) is one of the mainstream methods for regional gravity field modeling. Its traditional solution relies on Tikhonov regularization, which requires inverting a high-dimensional square matrix whose dimension equals the number of SRBF. Additionally, constructing a large-scale design matrix during the prediction phase incurs significant computational and storage costs, making it difficult to handle large-scale datasets. To address this bottleneck, this paper treats SRBF as an overcomplete dictionary and reformulates the gravity field modeling problem as a sparse coefficient recovery problem. Two classic greedy algorithms—Matching Pursuit (MP) and Orthogonal Matching Pursuit (OMP)—are introduced to solve for the sparse combination coefficients, thereby fundamentally avoiding the inversion of high-dimensional matrices and the construction of large-scale design matrices. Using the complex mountainous area of Colorado, USA, as the study area, we conduct experiments that fuse ground and airborne gravity data with 37,351 SRBF nodes generated based on the Reuter grid. The results show that when the OMP algorithm reaches a sparsity of approximately 3000 non-zero coefficients, the external validation standard deviation relative to the GSVS17 benchmark points is 2.19 cm, which is comparable to the accuracy achieved by Tikhonov regularization. Under a similar sparsity level, the MP algorithm achieves an accuracy of 2.37 cm. Both algorithms produce a highly sparse model—only about 8% of the total SRBF coefficients are non-zero-yielding substantial reductions in storage and prediction cost while maintaining geoid-level accuracy. Additional experiments conducted in the Auvergne region (presented in the Appendix) further validate the general applicability of the proposed Greedy SRBF method across different geographical areas and SRBF densities.