A Fast Fourier Finite Element Approach for 3D CSEM Modeling Using Different Fourier Transform Methods

A novel Fourier finite element algorithm for 3D controlled-source electromagnetic (CSEM) problems using different 2D Fourier transform methods is presented. As an important and effective tool, the 2D Fourier transform method simplifies the 3D CSEM problem into multiple 1D problems solved by 1D finite element method, which can be used to significantly accelerate the 3D frequency-domain electromagnetic (EM) forward modeling algorithms. For this proposed Fourier finite element method, two different transformation techniques, including a standard FFT algorithm with different grid expansion coefficient, and a Gauss-FFT algorithm with different Gaussian quadrature nodes, are investigated and compared in terms of balancing modeling accuracy and efficiency. All the different Fourier transform algorithms are numerically checked by integral equation (IE) reference solutions. The comparison results of numerical tests show that the present 3D CSEM modeling method with standard FFT or Gauss-FFT not only can guarantee the accuracy, but can also reduce the computing cost for any EM problem in general. Additionally, the standard FFT algorithm has high simulation efficiency and relatively low accuracy, while the Gauss-FFT algorithm has high simulation accuracy and relatively low efficiency. Because of its faster numerical solution, we infer that the standard FFT with grid expansion is more applicable for solving large-scale CSEM forward problems.