Finite-difference numerical simulation method for two-dimensional scalar waves in a 25-point Laplace-Fourier domain

ChaoQun WANG, GuoChen WU, LingYun YANG

Prog Geophy ›› 2025, Vol. 40 ›› Issue (6) : 2698-2710.

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Prog Geophy ›› 2025, Vol. 40 ›› Issue (6) : 2698-2710. DOI: 10.6038/pg2025HH0496

Finite-difference numerical simulation method for two-dimensional scalar waves in a 25-point Laplace-Fourier domain

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Abstract

The computational accuracy and efficiency of the finite-difference forward modeling in the frequency domain determines the quality of the waveform inversion, and choosing a suitable difference format is the basis of the frequency domain forward modeling. At present, the optimization differential format of the rotating coordinate system is widely used in actual production, but the optimization differential format of the rotating coordinate system is limited by the condition of the equal spacing sampling. For the optimized differential format of the average guide method, it can not only be applied to different sampling intervals, but also improve the sampling accuracy. Therefore, this paper based on the traditional 9-point finite difference, it used the Average-Derivative Method (ADM) for the two-dimensional scalar wave equation to develop a 25-point finite difference optimized difference scheme and applied to Laplace-Fourier domain performance simulation. After optimization, the ADM-25 finite difference optimized difference scheme only needs about 5 points per minimum pseudo-wavelength to achieve a normalized error of less than 1%. At the same time, it adds a complete matching layer at the border to absorb boundary(Perfect Matched Layer, PML). According to the above condition. The rectangular grid test can be seen that the 25-point format of the average guidance method derived in this article can not only be applied to a square grid with equal spacing sampling, but also the complex model of a rectangular grid with different sampling spacing. The 25-point optimized difference coefficients are calculated and obtained under different spatial sampling interval ratios, it can accomplish the non-uniform numerical simulation in both the longitudinal and transverse directions and draw figures to convenient in this paper. Numerical example results show that the 25-point difference scheme based on the average derivative method has higher simulation accuracy than the classical 9-point difference scheme and proves the accuracy and stability of the ADM-25 point method.

Key words

Two-dimensional scalar wave equation / Laplace-Fourier domain / Finite difference / Optimization coefficient

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ChaoQun WANG , GuoChen WU , LingYun YANG. Finite-difference numerical simulation method for two-dimensional scalar waves in a 25-point Laplace-Fourier domain[J]. Progress in Geophysics. 2025, 40(6): 2698-2710 https://doi.org/10.6038/pg2025HH0496

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