The Integral-Equation-Based Approaches for Modelling the Local Gravity Field in the Remove–Restore Scheme

Abstract

We study the accuracy of local gravity field modelling using four different types of the integral-equation-based approaches, namely the Poisson integral, Green integral, point-mass, and radial multipole approaches. We investigate how these four discretised integral equations perform when the gravity data are corrected for the residual terrain model (RTM-correction) and for the reference gravity field (remove-restore scheme). All integral equations are discretised below data points at the chosen constant depth relative to the Bjerhammar sphere. The choice of the optimal depth of discretization is done based on minimising the RMS fit between the observed and predicted gravity data. In all four approaches the number of unknown parameters is identical to the number of input gravity data and the systems of discretised integral equations are solved using Jacobi iteration. The regularisation is not applied. The study area in New Zealand comprises a rough part of the Southern Alps in the South Island with flat coastal regions including offshore areas. The results of numerical experiments are presented and discussed. We demonstrate that the application of the RTM-correction to gravity data significantly improves the accuracy of the gravity field approximation when using the Green integral approach.