A numerically efficient technique of regional gravity field modeling using Radial Basis Functions

Abstract

Radial Basis Functions (RBFs) have been extensively used in regional gravity and (quasi)geoid modeling. Reliable models require the choice of an optimal number of RBFs and of their parameters. The RBF parameters are typically optimized using a regularization algorithm. Therefore, the determination of the number of RBFs is the most challenging task in the modeling procedure. For this purpose, we design a data processing scheme to optimize the number of RBFs and their parameters simultaneously. Using this scheme, the gravimetric quasi-geoid model can be validated without requiring additional information on the quasi-geoidal geometry obtained from GPS/leveling data. Furthermore, the Levenberg–Marquardt algorithm, used for regularization, is modified to enhance its numerical performance. We demonstrate that these modifications guarantee the convergence of the solution to the global minimum while substantially decreasing the number of iterations. The proposed methodology is evaluated using synthetic gravity data and compared with existing methods for validating the RBF parameterization of the gravity field.