Three-dimensional numerical modeling of gravitational anomalies using the finite-difference ghost-point scheme

Abstract

Gravitational potential in continuous density media is described by the three-dimensional boundary value problem (BVP). Traditional forward-modeling approaches for gravitational anomalies are mainly based on integral solutions, which can compute full three-dimensional gravitational anomaly information including gravitational potential and vector gravitational fields but inevitably suffer from integral singularities. To resolve this technical bottleneck, a new numerical framework for three-dimensional gravitational modeling is established, with Robin boundary conditions effectively integrated into the finite-difference ghost-point scheme. The corresponding non-symmetrical linear system is then solved efficiently using a BiCGSTAB iterative solver coupled with incomplete LU (ILU) preconditioning. In addition, to achieve high accuracy in the vector gravitational fields, we employ the fourth-order compact difference approach to calculate the gravitational potential. Through numerical experiments conducted on the cubic and dipping dike models, comparisons between simulated results and analytical benchmarks confirm the accuracy of the developed forward-modeling method, demonstrating its reliability and superiority for three-dimensional gravitational forward problems. Furthermore, numerical simulations of the vector gravitational fields based on real terrain data verify the efficiency of the developed forward-modeling scheme, underscoring its promising application in refined inversion interpretation and comprehensive analysis of gravitational anomalies.