流固边界耦合介质高阶有限差分地震正演模拟方法

摘要

本文针对流固边界耦合介质提出了一种高效、稳定的正演数值模拟方法.首先,从一阶位移-应力弹性波方程出发,基于海底流固边界的位移和应力的连续性条件,采用三次样条海底界面定量表征方法,推导出不规则海底界面下流固边界耦合介质中的地震波波动方程;其次,通过空间微分的高阶差分格式提高数值模拟的空间精度,并结合已推导的地震波波动方程,将四阶时间微分转换至高阶空间微分,进一步提高了数值模拟的时间精度;最后,在与标量波波动方程数值模拟结果对比分析的基础上,分别利用简单的水平层状模型和复杂海底模型,验证和讨论了本文提出的流固边界耦合介质高阶有限差分地震波正演模拟方法的有效性和准确性.%This paper proposes a novel and stable forward modeling method,which can describe the wave propagation through fluid-solid coupled media.Firstly,we deduce the seismic wave equations of fluid-solid coupled media with irregular interface of seabed utilizing the cubicspline quantitative method based on the continuity of stress and displacement of the interface.And then,the high-order differential scheme for spatial differentiation is introduced into the method above,which can improve the spatial accuracy of numerical simulation.Furthermore,we also suppress the time discretization that reduces the numerical dispersion by transforming the fourth-order time differential into higher-order spatial differential method.Finally,comparing with results of the scalar wave equation and numerical simulation,we analyze the numericalresults of the method proposed in this paper for a simple horizontal layered model and a complexone.The numerical simulation of wave propagation in the fluid-solid coupled media indicatesthat the method proposed in this paper is convenient and accurate.