求解弹性波方程的高精度ONAD方法及其波场模拟  

A high-accuracy ONAD method and its wave-field simulation for solving elastic wave equation

作　　者：张朝元 ZHANG Chao-yuan(College of Mathematics and Computer, Dali University, Dali 671003, China)

机构地区：[1]大理大学数学与计算机学院,云南大理671003

出　　处：《成都理工大学学报（自然科学版）》2016年第5期623-629,共7页Journal of Chengdu University of Technology: Science & Technology Edition

基　　金：国家自然科学基金资助项目(41230210;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：基于弹性波传播方程,发展了一种高精度低数值频散的八阶ONAD(optimal nearlyanalytic discrete)方法,该方法利用八阶精度的近似解析离散算子对空间高阶偏导数进行离散,采用四阶精度的截断泰勒展开式离散时间高阶导数。八阶ONAD方法被用于模拟地震波在VTI介质模型和2个复杂层状介质模型中的传播。计算效率结果表明,该方法在运算速度和存储量上明显优越于八阶LWC方法。波场模拟结果显示,八阶ONAD方法在粗网格条件下可有效消除由速度强间断所造成的数值频散,有利于在强间断介质中使用粗网格进行波场模拟,是一种在地震勘探领域有着巨大应用潜力的数值方法。Based on the elastic wave equation, this paper develops an eighth-order UINAD t.optlmal nearly-analytic discrete） method with high accuracy and low numerical dispersion. This new method uses the nearly analytic discrete operators with eighth-accuracy to approximate the high-order derivatives in space and the truncated Taylor series expansion with fourth-order accuracy to discretize the temporal high-order derivatives. The eighth-order ONAD method is used to model the elastic wave propagations through the VTI medium and two complex layered media. The results of the computational efficiency show that this method is obviously superior to the eighth-order Lax-Wendroff Correction （LWC） method in the computation speed and the storage capacity. The wave-fields modeling results show that the eighth-order ONAD method can effectively eliminate the numerical dispersion caused by the speed of strong discontinuity in the coarse grid, and is conducive to the wave- field simulation in the discontinuous medium using a coarse grid. Therefore, the eighth-order ONAD method has great application potentiality in seismic exploration.

关 键 词：弹性波方程 ONAD方法 数值频散 波场模拟 高精度 

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