弹性波传播的低数值频散波场模拟方法  

A wave-field simulation method of elastic wave propagation using low numerical dispersion

作　　者：张朝元[1] 

机构地区：[1]大理学院数学与计算机学院,云南大理671003

出　　处：《成都理工大学学报（自然科学版）》2015年第2期236-243,共8页Journal of Chengdu University of Technology: Science & Technology Edition

基　　金：国家自然科学基金资助项目(41464004);Statoil Company资助项目(4502502663);云南省教育厅科学研究基金重点项目(2013Z152)

摘　　要：压制数值频散以提高计算精度是检验地震波数值模拟方法的一个重要标准。基于弹性波传播方程,建立了低数值频散波场模拟的八阶FNRK方法。该方法以Runge-Kutta方法对时间导数进行三阶离散,以近似解析离散算子替代差分算子对空间偏导数进行八阶离散,结合通量校正传输技术消除离散后的数值频散。弹性波场模拟结果表明,与高阶有限差分方法相比,该方法能在压制数值频散方面具有明显的优势,计算精度提高,且适应于地震波在大规模复杂介质中传播的波场模拟。Suppressing the numerical dispersion to enhance the computational accuracy is an important standard to check a numerical simulation method of seismic wave. Based on the elastic wave equations,the eighth-order FNRK method is established using the low numerical dispersion.The new method employs a third-order Runge-Kutta method to discretize the temporal derivatives,uses the eighth-order nearly-analytic discrete operator instead of the finite-difference operator to discretize the high-order spatial derivatives, and uses the flux-corrected transport technique to eliminate the discretized numerical dispersion.The results of the elastic wave-field simulation show that this method enhances the computational accuracy and has an obvious superiority in eliminating the numerical dispersion,compared with the traditional high-order finite-difference method.At the same time,this new method has a strong adaptability for simulating the seismic wave propagation in the large-scale complex media.

关 键 词：弹性波方程 RUNGE-KUTTA 方法 近似解析离散化算子 通量校正传输技术 数值频散 波场模拟 

分 类 号：P631.4[天文地球—地质矿产勘探] O241[天文地球—地质学]