各向同性和TI弹性波方程高精度有限差分数值解法新方法研究

项目名称： 各向同性和TI弹性波方程高精度有限差分数值解法新方法研究

项目编号： No.41474110

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 天文学、地球科学

项目作者： 刘洋

作者单位： 中国石油大学（北京）

项目金额： 90万元

中文摘要： 随着地震勘探由纵波向弹性波勘探发展，基于弹性波方程的正演和逆时偏移逐渐受到关注，其关键问题之一是弹性波方程数值求解。有限差分法是波动方程求解中常用的一种方法，高阶差分是提高精度的有效方法之一。目前的基于时空域频散关系的高阶差分方法应用于声波方程求解中能获得高精度数值解，但应用于弹性波方程求解中无法同时满足纵波和横波传播精度要求，精度不高。本项目针对二维、三维各向同性和TI(Transverse Isotropy，横向各向同性)弹性波方程，研究高精度高阶差分新方法，通过设计几个差分算子求解波动方程，来同时满足纵波和横波传播精度要求，并压制频散各向异性。经过研究，形成各个传播方向均具有2M阶精度的二维和三维各向同性弹性波方程有限差分数值解法、压制频散各向异性的二维和三维TI弹性波方程有限差分数值解法、针对性的吸收边界条件以及提高计算效率的差分算子优化方法，并对简单和复杂模型进行数值模拟与分析。

中文关键词： 弹性波方程；横向各向同性；有限差分；数值解法；频散关系

英文摘要： With the development of seismic exploration from P-wave exploration to elastic wave exploration, more attentions have been gradually paid to forward modeling and reverse-time migration, one of whose key issues is numerically solving wave equations. Finite-difference (FD) methods have been widely applied in solving wave equations and high-order FD methods are commonly used to improve the accuracy of numerical solutions. Present high-order FD methods based on time-space domain dispersion relations can obtain high-accuracy numerical solutions when applying to the acoustic wave equation, but not high when applying to the elastic wave equations because the methods can not simultaneously meet accuracy requirements of P-wave and S-wave propagations. This project will study new high-accuracy high-order FD methods to numerically solve 2D and 3D isotropic elastic wave equations and transversely isotropic (TI) elastic wave equations respectively. The new methods will be implemented through designing several FD operators to meet the accuracy requirements of P-wave and S-wave propagations and thus suppress anisotropic dispersions. This project plans to develop new FD methods with (2M)th-order accuracy along all propagation directions for 2D and 3D isotropic elastic wave equations, new FD methods significantly suppressing anisotropic dispersions for 2D and 3D TI elastic wave equations, absorption boundary conditions and optimized FD methods improving the computational efficiency. Numerical modeling and analysis will be performed for simple and complex isotropic and TI elastic models to demonstrate validities and advantages of the proposed methods.

英文关键词： Elastic wave equations;transverse isotropy;finite difference;numerical solution;dispersion relation