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<p>Gravity anomalies arising from heterogeneous density distributions are governed by the three-dimensional (3-D) Poisson equation. General integral approaches suffer from complex formulations and lack flexibility when sources exhibit varying physical properties. In contrast, conventional numerical methods entail solving a large sparse linear system via matrix inversion. To overcome these challenges, we introduce a Fourier pseudospectral scheme for the 3-D Poisson equation for the gravitational potential, subject to homogeneous Dirichlet boundary conditions. First, applying the Fourier transform along the Cartesian directions converts the spatial Poisson equation into an algebraic system in Fourier space, enabling direct computation of the gravitational potential in 3-D Fourier space. Furthermore, accurate evaluation of vector and tensor gravitational fields within the domain is achieved by exploiting the differentiation properties of the discrete Fourier transform for spatial derivatives, thereby enhancing model accuracy. Finally, the computational accuracy and efficiency of the Fourier pseudospectral forward-modeling algorithm are assessed using density models of varying complexity.</p>

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3-D Fourier pseudospectral forward modeling of vector and tensor gravitational fields due to variable density model

  • 期刊论文

  • 发表日期：

    2026年7月28日

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  • Yu Su,
  • Xiao-zhong Tong,
  • Chun-ming Liu,
  • Hai-fei Liu,
  • Hong-jun Tian,
  • Jie-yu Su

摘要

Gravity anomalies arising from heterogeneous density distributions are governed by the three-dimensional (3-D) Poisson equation. General integral approaches suffer from complex formulations and lack flexibility when sources exhibit varying physical properties. In contrast, conventional numerical methods entail solving a large sparse linear system via matrix inversion. To overcome these challenges, we introduce a Fourier pseudospectral scheme for the 3-D Poisson equation for the gravitational potential, subject to homogeneous Dirichlet boundary conditions. First, applying the Fourier transform along the Cartesian directions converts the spatial Poisson equation into an algebraic system in Fourier space, enabling direct computation of the gravitational potential in 3-D Fourier space. Furthermore, accurate evaluation of vector and tensor gravitational fields within the domain is achieved by exploiting the differentiation properties of the discrete Fourier transform for spatial derivatives, thereby enhancing model accuracy. Finally, the computational accuracy and efficiency of the Fourier pseudospectral forward-modeling algorithm are assessed using density models of varying complexity.