Adaptive Mesh-free Approach for Gravity Inversion

We proposes a method of gravity inversion based on an adaptive mesh-free approach by using a modified radial basis function . It can parametrize the density distribution by using a mesh-free approach. 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. Scattered points are introduced in most mesh-free methods to discretize the given equations. 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 radial basis function are used to improve the accuracy and stability of the solution. We verify the effectiveness of the proposed method by using several synthetic and empirical tests.