弹性波紧致有限差分数值模拟及逆时偏移
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    摘要:

    为提高地震波数值模拟及弹性波逆时偏移(Elastic Reverse Time Migration, ERTM)的精度,本文构造了求解二维各向同性介质一阶应力-速度弹性波方程的交错网格紧致有限差分(Compact Finite Difference, CFD)格式。通过理论推导,明确了该格式的差分系数、频散特性及稳定性条件,并与同阶常规有限差分(Finite Difference, FD)格式进行对比分析。研究表明,在高波数范围内,CFD格式精度显著高于同阶FD格式,能有效压制数值频散,甚至低阶CFD格式精度可超越高阶FD格式;尽管同阶CFD格式稳定性条件更严格(允许的最大时间步长较小),但在包含低速海水层的海上地震模型中,其对数值频散的压制效果尤为突出,显著提升了反射波等关键波场的模拟精度。正演模拟与Marmousi模型ERTM实验验证了CFD格式的有效性:基于该格式的模拟地震记录频散效应明显减弱,成像结果更接近参考标准。这证明该格式适用于高精度地震波数值模拟及ERTM,可为海上复杂场景高精度地震数据处理提供有效解决方案。

    Abstract:

    To enhance the accuracy of seismic wave numerical simulation and elastic reverse time migration (ERTM), this paper constructs a staggered-grid compact finite difference (CFD) scheme for solving the first-order stress-velocity elastic wave equations in two-dimensional isotropic media. Through theoretical derivation, the difference coefficients, dispersion characteristics, and stability conditions of this scheme are determined, and a comparative analysis is conducted with conventional finite difference (FD) schemes of the same order. The study demonstrates that within the high-wavenumber range, the CFD scheme exhibits significantly higher accuracy than same-order FD schemes, effectively suppressing numerical dispersion. Remarkably, even low-order CFD schemes can surpass the accuracy of high-order FD schemes. Although the stability condition for same-order CFD schemes is more stringent (permitting a slightly smaller maximum time step), their suppression effect on numerical dispersion is particularly prominent in marine seismic models containing low-velocity seawater layers, substantially improving the simulation accuracy of key wavefield information such as reflected waves. The effectiveness of the CFD scheme is verified by forward modeling and ERTM experiments using the Marmousi model: seismic records simulated with this scheme exhibit markedly reduced dispersion effects, and the imaging results align more closely with the reference standard. This proves the scheme"s applicability for high-precision seismic wave numerical simulation and ERTM, providing an effective solution for high-accuracy seismic data processing in complex marine scenarios.

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  • 收稿日期:2025-09-14
  • 最后修改日期:2025-10-29
  • 录用日期:2025-10-30
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