Conventional inversion and forward modeling of large-scale potential field data from gravity and magnetic exploration, demanding high computer performance, exhibit low efficiency. Hence, this study defined a footprint determination method for potential fields, analyzed the influencing factors, and innovatively proposed a footprint-FFT strategy for forward modeling of potential fields. The footprint-FFT algorithm improved the forward modeling process from three aspects: (1) Kernel matrices were calculated based on the potential field-derived properties, significantly reducing their size; (2) A footprint concept for potential fields was introduced and defined, decoupling data scales from kernel matrix sizes, thus improving the kernel matrix computing efficiency and reducing the hardware cost; (3) Based on the above, the computing area was divided into subspaces, and the footprint-FFT strategy was first proposed for the batch computing of potential fields in subspaces, accelerating the forward modeling process. By reducing the computational complexity and storage of the kernel matrix, the method proposed in this study significantly improved the operational speed while ensuring computational accuracy. This method enabled the fast forward modeling of potential fields with more than 1 billion grids on a laptop computer within a few minutes. Theoretical examples demonstrate that this method has high efficiency and moderate requirements for computer configuration, manifesting considerable potential in the forward modeling and inversion of large-scale potential field data.
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