Three Integrating Methods for Gravity and Gravity Gradient 3-D Inversion and Their Comparison Based on a New Function of Discrete Stability

Integrated gravity and gravity gradient 3-D inversion can effectively improve the resolution of inversion results. This study aims to find a better way to extract geological information from gravity and gravity gradient data and to obtain the recovered model with a higher resolution. We present three different methods for integrating gravity and gravity gradient data in inversion: directly integrating gravity and gravity gradient data (DIGG), the sequential inversion of gravity and gravity gradient data (SIGG), and integrating gravity and gravity gradient components using a weighting matrix (IGGW). In addition, we propose a new discrete method for smooth inversion. We discretize the stabilizing functional into two parts. One is the square of the 2-norm of the model parameter, and the other one is the square of the Frobenius norm of the gradient of the model parameter. We adopt a conjugate gradient algorithm (CGA) to solve the objective function. We used the DIGG, SIGG, and IGGW inversion methods in a dip-slab model with multiple anomalous bodies. The inversion results show that by integrating gravity and gravity gradient in inversion, more reasonable results are obtained than by inverting a single data type. Among the presented methods, the IGGW method achieved the best performance in using information contained in gravity and gravity gradient data, followed by the SIGG method, and finally, by the DIGG method. We used the methods on actual data from Vinton salt dome, southwestern Louisiana, USA. The obtained results support the abovementioned conclusions.