二维弹性介质中瑞利波高阶有限差分模拟分析

HIGH-ORDER FINITE DIFFERENCE MODELING OF RAYLEIGH WAVE IN TWO-DIMENSIONAL ELASTIC MEDIA

为探讨瑞利波在复杂介质中的形成机理和传播规律,正确认识瑞利波实测结果,提高反演结果的精度,从弹性波方程出发,采用4×10阶高阶交错网格有限差分方法对弹性半空间介质进行全波场模拟。通过对均匀半空间介质、正常地层顺序地基模型和含有低速夹层地基模型的正演模拟,获得了它们各自的地震记录和瞬时快照。由模拟结果可知:以往常规的低阶有限差分方法存在严重的数值频散,不适合用来研究介质中瑞利波的频散特性;而高阶交错网格有限差分法可有效地压制模拟中的数值频散影响,其层状介质的模拟结果与以往频散方程的计算结果吻合;今后可采用此方法模拟非层状的复杂介质模型,从而进一步根据频散曲线研究复杂介质的频散规律,指导实际勘探工作。

In order to study the generation mechanism and propagation rule of Rayleigh waves in complex media,and to understand the collected results correctly and improve the inversion precision,it was used the 4×10 high-order finite difference method with staggered grids to simulate full-wave-fields in elastic media.Synthetic single-shot records and snaps of a homogeneous half-space,a layered media in which shear wave velocity increasing with depth and a layered media with a low velocity interlayer were got by the above simulation.According to the results of model simulation,the past low-order finite difference method is not suitable to study the dispersion characteristics of Rayleigh waves because it may cause serious numerical dispersion.The high-order finite difference method with staggered grids can suppress numerical dispersion effectively,and its modeling results of layered media are consistent with calculation results of dispersion equation.Therefore,this method can be used to study complex non-layered media,and to discuss their dispersion characteristics and instruct practical prospecting works.