Local Gravity Field Modelling in Rugged Terrain Using Spherical Radial Basis Functions: Case Study for the Canadian Rocky Mountains

Abstract

We analyze the performance of a least-squares approximation of the gravity field using Spherical Radial Basis Functions (SRBFs) in rugged mountains. The numerical experiment is conducted for the gravity disturbances and for the topographically corrected gravity disturbances, both provided on a 5 ×5 arc-min grid located at the Earth’s surface. The target area is a rough part of the Canadian Rocky Mountains with adjacent planes. The data area and the parameterization area extend the target area in all directions by 3 arc-deg. The accuracy of the gravity field approximation is investigated using a SRBF parameterization (Poisson wavelet of order 3) on different spherical equal-angular grids with step sizes varying between 6 and 12 arc-min. For every choice of grid, the optimal depth of SRBFs bellow the Bjerhammar sphere is found using the minimization of the RMS differences between predicted and observed values. The results of the numerical experiment reveal that the application of the topographical correction to the observed gravity data reduces the number of SRBFs by more than 56%, and improves the fit to the data by 12%. Unfortunately, it also introduces a systematic bias in the adjusted gravity disturbances.