Efficient large-scale 3D gravity modeling using a fast evaluate kernel matrix combined with compressed matrix techniques

Abstract

A fast calculated kernel matrix method is coupled with a compressed matrix technique to solve the large-scale gravity forward-modeling problem. This method accelerates the coefficient matrix computation by reducing the arctangent, logarithm, and multiplication functions in the prismatic gravity analytical expression. In addition, the use of the compressed matrix technique presents a significant advantage in that it does not require the storage of redundant kernel matrices, further reducing the memory requirements and computation time. Moreover, the discrete convolution of the compressed matrix with density is executed through the 2D fast Fourier transform (FFT). Two typical synthetic models are used to test the performance of the novel algorithm. The results demonstrate that the developed algorithm is approximately 15 times faster than the traditional algorithm. Concurrently, it demands almost 1/7th of the memory while ensuring equivalent computational accuracy. To further illustrate the capability of the algorithm, we apply our method to the terrain correction of an airborne gravity data set using a real digital elevation model. Our approach efficiently calculates 250,000 observation points across 25 million cells in only 5.42 s, compared with 234.81 s for the latest 2D Gauss-FFT method.