优化的时空域等效交错网格有限差分正演模拟

Forward modeling by optimized equivalent staggered-grid finite-difference method for time-space domain

地震波有限差分数值模拟中,使用优化的差分系数可以有效地减少数值频散(相速度误差)。为了同时压制空间频散与时间频散,提出一种时空优化的等效交错网格有效差分正演模拟方法。采用以减少给定波数范围内所有传播方向的相对频散误差为目标函数,并借助牛顿法快速获取优化的差分系数。频散分析表明等效交错网格正演在低速介质中容易出现空间频散,在高速介质中高波数分量容易出现时间频散,数值模拟显示该方法既能有效地压制空间频散,也可以减少时间频散。Marmousi模型测试表明该方法适用于复杂地质模型的地震波场正演模拟。相比传统差分方法,该时空优化差分方法在不增加计算量的前提下,可以有效地提高数值模拟精度。

Optimized finite-difference(FD)coefficients can effectively suppress numerical dispersion errors(phase velocityerrors)in seismic wave modeling.Most optimized FD schemes used to solve seismic wave equation suppress only spatial butnot temporal dispersion errors.In this paper,we develop an optimized FD scheme with high spatial and temporal accuracy fornumerical scalar-wave modeling based on equivalent staggered grids.The final aim of optimized FD coefficients is to reducephase velocity errors.We design an objective function for minimizing relative temporal and spatial dispersion errors of wavespropagating in all directions.In addition,Newton method is applied to quickly solve this nonlinear problem.Dispersion anal-ysis has demonstrated that space dispersion easily appear in the low-velocity media,while time dispersion has more probabili-ty to occur in the high-velocity media.Modeling tests indicate that the proposed method ensures high accuracy not only in thetime domain but also in the space domain.Compared with the traditional methods,the proposed method can improve numeri-cal accuracy without sacrificing computation efficiency.