Forward modelling of gravity data for unstructured grids using the finite‐volume method

Abstract

Forward modelling of gravity data in three dimensions by both closed‐form formulae and numerical methods is reflected in the recent literature. While the former methods give the exact response and are efficient for a small number of observation points, numerical methods are well‐suited for large numbers of points in terms of computation time and are preferred for certain inversion methods due to the sparsity of their resultant matrices. Using unstructured grids to discretize the space increases the capability for modelling underground structures. Methods like finite‐volume and finite‐element result in robust schemes for such domains. In this study, the Poisson's equation for gravitational potential is discretized by a finite‐volume scheme for tetrahedral grids and their dual Voronoi meshes and a system of equations solved for computing the potential at discrete points inside the grid. Gravity is then computed from the potential by a finite‐difference approximation. The accuracies of these schemes are analyzed and their time‐efficiency compared with a closed‐form formulae method.