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针对有限差分数值模拟的频散问题,本文将交错网格技术和紧致差分格式相结合,推导了横向各向同性介质一阶速度-应力波动方程的紧致交错网格差分格式;对比分析了紧致交错网格差分格式、交错网格差分格式以及紧致差分格式的截断误差主项,并利用Fourier误差分析方法分析了上述三种差分格式的近似精度;在此基础上,分别采用上述三种差分格式进行了波场数值模拟。结果表明,当差分方程阶数相同时,紧致交错网格差分格式截断误差最小,数值频散最弱,差分精度最高,证实了该方法的有效性。
In order to solve the dispersion problem of finite difference numerical simulation, the paper proposes a compactly staggered grid finite difference scheme for the first-order velocity-stress wave equation of transversely isotropic media by combining the staggered grid technique with the compact difference scheme. Compactness staggered grid difference scheme, staggered grid difference scheme, and compactness difference scheme, and analyzed the approximate accuracy of the above three schemes using Fourier error analysis method. On this basis, The difference scheme is used to simulate the wave field. The results show that the compact truncated grid scheme has the smallest truncation error, the lowest dispersion value and the highest differential accuracy when the order of the difference equations is the same. It proves the effectiveness of the proposed method.