Regional gravity field modeling using free-positioned point masses

A two-step free-positioned point mass method is used for regional gravity field modeling together with the remove-compute-restore (RCR) technique. The Quasi-Newton algorithm (L-BFGS-B) is implemented to solve the nonlinear problem with bound constraints in the first step, while in the second step the magnitudes of the point masses are re-adjusted with known positions in the least-squares sense. In order to reach a good representation of the gravity field, a number of parameter sets have to be defined carefully before the computations. The effects of four important parameter sets (depth limits, number of point masses, original/reduced basis functions and optimization directions) are investigated for regional gravity field modeling based on two numerical test cases with synthetic and real data. The results show that the selection of the initial depth and depth limits is of most importance. The number of point masses for obtaining a good fit is affected by the data distribution, while a dependency on the data variability (signal variation) is negligible. Long-wavelength errors in the predicted height anomalies can be reduced significantly by using reduced basis functions, and the radial-direction optimization proves to be stable and reliable for regular and irregular data scenarios. If the parameter sets are defined properly, the solutions are similar to the ones computed by least-squares collocation (LSC), but require fewer unknowns than LSC.