An efficient accelerating algorithm for 3D gravity anomalies forward modeling using discrete sine transform

• Published in: Journal of applied geophysics Vol. 241; p. 105831
• Main Authors: Tong, Chenxi, Tong, Xiaozhong, Wei, Kanggui
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2025
• Subjects: 3D Poisson equation; Discrete sine transform (DST); Forward modeling; Gravity anomalies; Vertex-centered finite-difference algorithm; Gravity anomalies; Vertex-centered finite-difference algorithm; 3D Poisson equation; Forward modeling; Discrete sine transform (DST)
• ISSN: 0926-9851
• DOI: 10.1016/j.jappgeo.2025.105831

Conventional numerical techniques for forward modeling of gravity anomalies need to solve a large sparse system of linear equations through matrix inversion. In such cases, the computational expense of the forward algorithm can bring a significant limitation for large-scale 3D gravity inversion. To address this challenge, we propose an acceleration scheme utilizing discrete sine transform (DST) for 3D finite-difference forward modeling of gravity anomalies. Firstly, a 7-point vertex-centered central difference scheme is employed to discretize the 3D Poisson equation using hexahedral meshes along the x-axis, y-axis, and z-axis. Subsequently, the forward algorithm is accelerated by applying the 3D DST technique. The DST-accelerated finite-difference approach, compared to the traditional finite-difference, incorporates the DST technique to convert the 3D finite-difference problem in the spatial domain to an algebraic problem in the wavenumber domain. The proposed accelerating approach can effectively overcome the challenges of large-scale matrix inversion, despite the need for an additional inverse DST during the reduction of the research problem's dimensionality. The numerical accuracy and computational efficiency of our method are validated through the utilization of two synthetic density models and a real basement instance. The minimal disparity between the DST-accelerated finite-difference approximations and the exact integral solutions for the three-component gravity field and its corresponding six-component gravity gradient demonstrates the high accuracy of our proposed forward approach. The DST-accelerated finite-difference technique not only maintains high accuracy but also significantly reduces computational time, showcasing its superiority over conventional numerical methods in terms of both precision and efficiency. •A DST-accelerating finite-difference algorithm for the 3D gravity forward modeling.•The proposed accelerating approach can effectively avoid the large-scale matrix inversion in traditional finite-difference methods.•The DST-accelerated technique not only maintains high accuracy but also significantly reduces computational time.