Abstract Three‐dimensional gravity forward modeling with conventional numerical methods requires solving large‐scale linear system using direct matrix inversion or iterative solvers, incurring substantial computational costs that critically limit large‐scale three‐dimensional inversions. To address this issue, we introduce a novel computational framework that leverages the fast Fourier transform (FFT) to accelerate three‐dimensional gravity finite‐difference (FD) forward modeling. Our methodology first discretizes the gravitational potential Poisson equation using central differences on a three‐dimensional regular mesh of right rectangular prisms aligned with the coordinate axes. We then accelerate the forward algorithm by implementing a three‐dimensional FFT. Crucially, this FFT‐accelerated FD approach converts the spatial‐domain FD linear system into a wavenumber‐domain algebraic equation. Despite the computational overhead of an inverse FFT step for spatial‐domain reconstruction, this acceleration strategy effectively resolves bottlenecks associated with large‐scale matrix inversion. We validate numerical precision and computational efficiency of our FFT‐accelerated FD forward algorithm through benchmark testing on two synthetic models and a real‐world geological basement study. While maintaining the required computational accuracy, the FFT‐accelerated FD approach delivers substantial reductions in runtime and memory requirements.
Tong et al. (Sun,) studied this question.