Three dimensional fast forward modeling of gravity anomalies under arbitrary undulating terrain

In order to improve the applicability and computational efficiency of the space-wavenumber domain 3D gravity anomaly forward algorithm, we propose the three-dimensional forward modeling of gravity anomalies in space-wavenumber mixed domain based on arbitrary Fourier transform, and perform CPU-GPU parallel acceleration based on NVIDIA CUDA platform. The arbitrary Fourier transform method first converts the two-dimensional Fourier transform into one-dimensional Fourier transform in two directions, and then discretizes the one-dimensional Fourier transform, the function in the discrete unit is fitted by a quadratic interpolation shape function, and finally the analytical expression of the unit integral is obtained. This method has the advantages in terms of flexible element division, high integration accuracy, fast calculation speed, and small truncation effect of Fourier transform. By using the CPU to solve differential equations in parallel, and the GPU to calculate the arbitrary Fourier transform in parallel, we implement the CPU-GPU parallel acceleration scheme, and further improve the efficiency of the algorithm. A gravity model with constant density is used to verify the accuracy of algorithm by comparing the analytical solution, we compare the accuracy and efficiency between arbitrary Fourier transform and Gauss-FFT. In general, the algorithm selects a few wavenumbers and has highly efficiency. Compared with the CPU serial alogrithm, the efficiency of the CPU-GPU parallel algorithm is greatly improved, and the forward modeling of 10 million nodes only takes a few seconds. Finally, the numerical simulation of three-dimensional gravity anomaly is carried out by using actual terrain data, which proves the efficiency and practicability of the method, which is of great significance for inversion and comprehensive interpretation.