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Optimizing staggered-grid finite-difference method based on the least-squares combination of the square window function

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Abstract

The staggered-grid finite-difference method (SGFDM) has been extensively employed in numerical modeling, seismic imaging, and waveform inversion because of its high efficiency, accuracy, and practicality. Numerical modeling accuracy is crucial for imaging and inversion. Truncating the spatial convolution sequence of the pseudospectral method by window functions can derive the finite-difference method. However, truncation error is inevitable; it can create illusions in numerical modeling, leading to misjudgments. To reduce the truncation error and improve numerical modeling accuracy, enhancing the performance of the truncated window function is imperative. In this study, a new optimal window function was investigated based on the least-squares combination of square windows. Then, the new optimized window function was used to truncate the spatial convolution sequence of the pseudospectral method and obtain an optimized SGFDM. Dispersion analysis showed that the optimized SGFDM has wider spectrum coverage than the conventional SGFDM at the same order. In addition, at low orders, the error range of the new optimized SGFDM could be strictly controlled within 1‱, whereas, at high orders, while ensuring accuracy, the spectrum coverage significantly improved. Finally, numerical modeling for elastic waves demonstrated that the optimized SGFDM could superiorly suppress numerical dispersion and improve calculation efficiency.

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Authors and Affiliations

  1. College of Information Science and Technology, Beijing University of Chemical Technology, Beijing, 100029, China

    Chao-pu Chen, Zhi-yang Wang, Wen-lei Bai, Cheng-fang Zhang & Zi-rui Meng

  2. Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China

    Hong Liu

  3. University of Chinese Academy of Sciences, Beijing, 100049, China

    Hong Liu

Authors
  1. Chao-pu Chen
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  2. Hong Liu
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  3. Zhi-yang Wang
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  4. Wen-lei Bai
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  5. Cheng-fang Zhang
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  6. Zi-rui Meng
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Corresponding author

Correspondence to Zhi-yang Wang.

Additional information

This work was supported by the Joint Funds of the National Natural Science Foundation of China (grant number U20B2014), the State Key Program of National Natural Science Foundation of China (grant number 41630319), and the National Science and Technology Major Project of China (grant number 2016ZX05024-001-001).

Chen Chao-pu, a postgraduate student at Beijing University of Chemical Technology, specializes in High-Speed Rail Seismology, Asymmetric Elastic Wave Equations, modelling and imaging of complex structures.

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Chen, Cp., Liu, H., Wang, Zy. et al. Optimizing staggered-grid finite-difference method based on the least-squares combination of the square window function. Appl. Geophys. (2021). https://doi.org/10.1007/s11770-021-0884-4

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  • DOI: https://doi.org/10.1007/s11770-021-0884-4

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