弹性波变阶数旋转交错网格数值模拟（英文）

Variable-order rotated staggered-grid method for elastic-wave forward modeling

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。

Numerical simulations of a seismic wavefield are important to analyze seismic wave propagation. Elastic-wave equations are used in data simulation for modeling migration and imaging. In elastic wavefield numerical modeling, the rotated staggered-grid method （RSM） is a modification of the standard staggered-grid method （SSM）. The variable-order method is based on the method of variable-length spatial operators and wavefield propagation, and it calculates the real dispersion error by adapting different finite-difference orders to different velocities. In this study, the variable-order rotated staggered-grid method （VRSM） is developed after applying the variable-order method to RSM to solve the numerical dispersion problem of RSM in low-velocity regions and reduce the computation cost. Moreover, based on theoretical dispersion and the real dispersion error of wave propagation calculated with the wave separation method, the application of the original method is extended from acoustic to shear waves, and the calculation is modified from theoretical to time-varying values. A layered model and an overthrust model are used to demonstrate the applicability of VRSM. We also evaluate the order distribution, wave propagation, and computation time. The results suggest that the VRSM order distribution is reasonable and VRSM produces high-precision results with a minimal computation cost.