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<p>We propose an efficient and high-precision holographic approach for three-dimensional (3D) magnetotelluric modeling. The core is to accurately obtain the space-wavenumber spectrum of the electromagnetic field based on a realistic magnetotelluric model using an appropriate approach, and then transform all wavenumber spectral information back into the spatial domain to obtain the true distribution of the electromagnetic field. Specifically, the approach converts the 3D partial diff erential equation governing the secondary vector potential in the spatial domain into a set of 1D ordinary diff erential equations at diff erent wavenumbers through a 2D Fourier transform in the horizontal direction. A holographic Fourier transform is applied in the horizontal direction to ensure the completeness of both spatial and wavenumber domain information. In the vertical direction, plane wave decomposition is introduced to mitigate the boundary eff ects caused by the upper and lower boundaries. Additionally, the grid size can be freely adjusted in both the horizontal and vertical directions. Leveraging the high parallelism of the algorithm, CPU parallel computation is used to solve the 1D ordinary differential equations, while GPU parallel computation is applied to the holographic Fourier transform, thereby implementing a CPU-GPU parallel architecture. An abnormal prism model is designed to analyze the wavenumber spectrum characteristics of its anomalous vector potential. The results are compared with the integral equation method to verify the accuracy of the algorithm and the validity of the wavenumber domain logarithmic sampling rule. A combined model is designed to compare the computational accuracy and efficiency of the proposed algorithm, grid expansion FFT, and Gauss-FFT. The results demonstrate that the proposed algorithm balances both computational efficiency and accuracy. Parallel experimental results demonstrate that the CPU-GPU parallel architecture is well-suited for the proposed algorithm. When applied to the Dublin model, the results show that, while meeting accuracy requirements, the forward calculation for model with millions of nodes model takes only 16.6 seconds. This is significant for achieving fine inversion imaging and interpretation of magnetotelluric under large-scale complex conditions.</p>

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Holographic approach for three-dimensional magnetotelluric modeling and CPU-GPU Parallel Architecture

  • 期刊论文

  • 发表日期：

    2025年6月20日

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  • De-Xiang Zhu,
  • Shi-Kun Dai,
  • Hong-Jun Tian,
  • Qing-Rui Chen,
  • Wen-Xue Zhao

摘要

We propose an efficient and high-precision holographic approach for three-dimensional (3D) magnetotelluric modeling. The core is to accurately obtain the space-wavenumber spectrum of the electromagnetic field based on a realistic magnetotelluric model using an appropriate approach, and then transform all wavenumber spectral information back into the spatial domain to obtain the true distribution of the electromagnetic field. Specifically, the approach converts the 3D partial diff erential equation governing the secondary vector potential in the spatial domain into a set of 1D ordinary diff erential equations at diff erent wavenumbers through a 2D Fourier transform in the horizontal direction. A holographic Fourier transform is applied in the horizontal direction to ensure the completeness of both spatial and wavenumber domain information. In the vertical direction, plane wave decomposition is introduced to mitigate the boundary eff ects caused by the upper and lower boundaries. Additionally, the grid size can be freely adjusted in both the horizontal and vertical directions. Leveraging the high parallelism of the algorithm, CPU parallel computation is used to solve the 1D ordinary differential equations, while GPU parallel computation is applied to the holographic Fourier transform, thereby implementing a CPU-GPU parallel architecture. An abnormal prism model is designed to analyze the wavenumber spectrum characteristics of its anomalous vector potential. The results are compared with the integral equation method to verify the accuracy of the algorithm and the validity of the wavenumber domain logarithmic sampling rule. A combined model is designed to compare the computational accuracy and efficiency of the proposed algorithm, grid expansion FFT, and Gauss-FFT. The results demonstrate that the proposed algorithm balances both computational efficiency and accuracy. Parallel experimental results demonstrate that the CPU-GPU parallel architecture is well-suited for the proposed algorithm. When applied to the Dublin model, the results show that, while meeting accuracy requirements, the forward calculation for model with millions of nodes model takes only 16.6 seconds. This is significant for achieving fine inversion imaging and interpretation of magnetotelluric under large-scale complex conditions.