Gravity modeling and analyzing based on 3D Delaunay triangulation algorithm

Gravity modeling of three-dimensional geological body is one of the key problems for interpreting and applying gravity data. Aiming at three-dimensional geological body with irregular structure and varying density, we presented the gravity modeling approach based on 3D Delaunay triangulation algorithm in the paper. With 3D Delaunay triangulation, the geological body was divided into various tetrahedral vexels in optimal way, and then the gravity forward calculation formula for a tetrahedral vexel was derived, as well as the linear equations between the residual densities and the gravity anomalies. Taking a cuboid with varying density and a hybrid geological body with inclined step and varying density as examples, we compared and analyzed the validity for the forward computation of gravity anomalies using traditional cuboid vexel and 3D Delaunay triangulation algorithm respectively. Moreover, the density distribution of the hybrid geological body with inclined step and varying density was recovered by inversion using conjugate gradient algorithm with constrained density, and the inversion results were very consistent with the real geological body. Simulation results verified the correctness and validity of the gravity modeling method given in the paper. The gravity modeling based on 3D Delaunay triangulation algorithm could be applied to the gravity forward and inversion computation for the complicated and heterogeneous geological body with folds, cracks, faults and etc.