基于Navier方程的非均匀介质弹性波反演结果的误差及其修正方法

项目名称： 基于Navier方程的非均匀介质弹性波反演结果的误差及其修正方法

项目编号： No.11272168

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 向志海

作者单位： 清华大学

项目金额： 65万元

中文摘要： 弹性波反演技术在地震工程和复合材料无损探伤等领域应用非常广泛。对于这类非均匀介质的弹性波动问题，目前普遍采用Navier方程进行描述，并在此基础上建立反演方法。但是最近人们在用Navier方程进行弹性波绕波器件设计时遇到了难以克服的困难，并认为应该采用Willis方程来精确描述非均匀介质中的弹性波动问题。不过，由于Willis方程非常复杂，目前还很难在工程界得到应用。为解决这个问题，本研究试图首先证明Willis方程的普适性，并通过弹性波绕波器件的设计来进一步验证这个结论。若该结论成立，就可以推导Navier方程相对于Willis方程的误差估计。在此基础上再探讨这种控制方程的模型误差对弹性波反演结果所造成的影响。最后，试图建立一些误差修正算法，来保证非均匀介质中基于Navier方程的弹性波反演结果的可靠性。本研究既探讨了一个基础理论问题，其预期结果又会对实际工程应用有很大帮助。

中文关键词： 非均匀介质；Willis方程；初应力；超材料；反问题

英文摘要： Elastic wave inversion is widely used in seismology and the non-destructive evaluation of composites, etc. The Navier equation is commonly used to describe this kind of elastic wave propagation problem in inhomogeneous media and accordingly, one can establish the inverse method. However,recently insurmountable difficulties occurred when people tried to use the Navier equation to design elastic wave steering devices. It conceives that the Willis equation is a proper choice to precisely describe the elastic wave propagation in inhomogeneous media. Unfortuenately, owing to its complexity, the Willis equation can hardly find the application in engineering at present. To solve this problem, this study firstly tries to prove the universality of the Willis equation via the coordinate transformation approach and the design of elastic wave steering devices. If this can be proved, the error estimation between the Navier equation and the Willis equation will be obtained. Based on this, it is possible to discuss the influence of model errors on the elastic wave inversion. Finally, correction algorithms will be established to ensure the reliability of inverse elastic wave results, based on the Navier equation. This study investigates a basic theoretic problem. The expected results would be very helpful for engineering appli

英文关键词： Inhomogeneous media；Willis equations；initial stresses；metamaterials；inverse problems