A Fast Forward and Inversion Strategy for Three-Dimensional Gravity Field

Obtaining a three-dimensional (3D) density distribution within a reasonable time is one of the most critical problems in gravity exploration. In this paper, we present an efficient 3D forward modeling and inversion method for gravity data. In forward modeling, the 3D model is discretized into multiple horizontal layers, with the gravity field at a point on the surface being the sum of the gravity fields from all layers. To calculate the gravity field from each horizontal layer, we use the fast Fourier transform (FFT) method and the Block Toeplitz with Toeplitz Blocks (BTTB) matrix, which dramatically reduces both the computation time and storage requirement. In the inversion, the observed gravity data are separated into multiple gravity components of different depths using the cutting separation method. An iterative method is used to adjust the model to fit the above gravity component for each cutting radius. The initial model is constructed from the transformation of gravity components. These methods were applied to both synthetic data and field data. The numerical simulation validated the proposed methods, and the inversion results of field data were consistent with information obtained from well logging. The computational time and memory usage were also reasonable.