Adaptive Mesh-Free Approach for Gravity Inversion Using Modified Radial Basis Function

This article proposes a method of gravity inversion based on an adaptive mesh-free approach by using a modified radial basis function (RBF). We parametrize the density distribution by using a mesh-free approach. Scattered points are introduced in most mesh-free methods to discretize the given equations. The subsurface space is generally discretized into regular grid cells, while mesh-free methods can avoid the expensive mesh generation and manipulation required in traditional approaches. To deal with the problem of unstructured nodal discretization, we use a mesh-free discretization strategy to establish a mapping of subsurface grid cells to a cloud of discrete points. The nodes are adaptively refined during the inversion process to better recover abnormal bodies. In addition, the hybrid basis function and the modified RBF are used to improve the accuracy and stability of the solution. We verify the effectiveness of the proposed method by using several synthetic and real tests.