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地震波场数值模拟方法对理解和分析地震波的传播规律具有着重要的意义。弹性波动方程能够模拟地下介质的实际情况,为偏移和成像提供有效的依据。在弹性波波场数值模拟中,旋转交错网格数值模拟(RSM)修改了标准交错网格数值模拟(SSM)方法,将同类的参数定义在同样的节点上,拓宽了稳定性条件的约束,但在低速区会出现较严重的频散。变阶数差分方法是自适应空间算子长度方法的一种变化和推广。它以理论频散误差研究为基础,结合实际波场传播的情况进行误差计算,对不同速度匹配不同的差分阶数。本文研究了变阶数旋转交错网格数值模拟(VRSM),即是将变阶数方法应用到RSM中,它可以很好地解决RSM在低速区域的数值频散问题,以及减少不必要的时间损耗;同时讨论了旋转交错网格的理论频散特性,并基于波场分离的方法分析了实际波场传播的频散误差,将原方法的应用范围由声波推广到剪切波,由理论值推广到时变值。在数值模拟试验中,VRSM将被应用于水平层模型和Overthrust模型。通过阶数分配以及相应波场传播效果和计算时间的分析,验证了该方法应用于复杂介质波场模拟中的实用性和有效性。实验的结果表明VRSM能够合理分配不同速度所对应的差分阶数,能保证计算的精确性,并合理控制计算的时间。
Seismic wave field numerical simulation method is of great significance for understanding and analyzing the propagation law of seismic waves. Elastic wave equation can simulate the actual situation of underground medium, providing an effective basis for migration and imaging. In the numerical simulation of the elastic wave field, the staggered-grid numerical simulation (RSM) modifies the standard staggered-grid numerical simulation (SSM) method and defines the same parameters on the same nodes, broadening the constraints of the stability conditions, But in the low-speed zone will appear more serious dispersion. Variable-order difference method is a kind of change and promotion of adaptive space operator length method. Based on the theoretical dispersion error study, it calculates the error based on the actual wave field propagation and matches different differential orders for different velocities. In this paper, the variable-order rotation staggered-grid numerical simulation (VRSM) is studied. That is to say, the variable-order method is applied to RSM. It can solve the problem of numerical dispersion of RSM in low speed region and reduce the unnecessary time At the same time, the theoretical dispersion characteristics of the staggered grid are discussed, and the dispersion error of the actual wave field is analyzed based on the wave field separation method. The range of the original method is extended from the sonic wave to the shear wave, and the theoretical value Promote to time-varying value. In numerical simulations, VRSM will be applied to both horizontal and Overthrust models. Through the analysis of order assignment, wave propagation and computation time, the practicability and validity of this method in wavefield simulation of complex media are verified. The experimental results show that the VRSM can reasonably allocate the different orders of different velocities to ensure the accuracy of the calculation and control the calculation time reasonably.