Three-dimensional magnetic field forward modeling using quadratic finite element continuous Fourier transform and parallel CPU/GPU acceleration

Abstract Efficient and high-precision methods for magnetic field modeling were crucial for the accurate inversion and interpretation of magnetic survey data. In response, an efficient magnetic field forward modeling algorithm using quadratic finite element continuous Fourier transform (QFE-CFT), leveraging central processing unit/graphics processing unit (CPU/GPU) parallel computing, was proposed to meet these demands. By applying a 2D Fourier transform in the horizontal directions, the 3D partial differential equation was reduced to a set of independent 1D ordinary differential equations in the vertical direction, significantly improving computational efficiency and enabling parallel acceleration. The finite element method was then used to form a five-diagonal linear system, which was efficiently solved using the chasing method. Finally, the magnetic field in the spatial domain was obtained using the quadratic finite element continuous inverse Fourier transform (QFE-CIFT). A model with anomalous spheres near the boundary of the considered computational area was designed to validate the accuracy and effectiveness of the algorithm. Comparisons with the standard-fast Fourier transform (FFT), Gauss-FFT, and nonuniform FFT algorithms demonstrated that the proposed method was unaffected by boundary effects. By using OpenMP for equation solving and GPU acceleration for the QFE-CFT, the computational efficiency of the CPU/GPU parallel algorithm was significantly enhanced compared to the CPU serial algorithm, achieving an acceleration ratio of up to 86 times under the given hardware conditions. This approach provided a powerful tool for high-precision magnetic data inversion and geological interpretation.