粘弹性波动方程的系数反演

A Numerical Algorithm for Solving Coefficient Inverse Problems of Viscoelastic Wave Equation

波动方程的系数反演是一种用于识别地下介质物理力学参数的重要方法。过去这方面的研究一般都建立在弹性模型的基础上,本文则提出了粘弹性反演模型,这种模型更能真实地反映波在地下传播的实际情形。在粘弹性反演模型的基础上,我们还提出了一整套行之有效的数值反演方法,并在频域中完成了反演计算。最后的数值计算结果是令人满意的,证明了本文的模型和方法的合理性。

The inverse problems,with a bright future are in the forefront of both theoretical and applicational science researches within the international scope.Especially the studi- es in exploring the variations of physical parameters in closing objects by using acous- tic wave or seismic wave methods are paid great attention to,because of its relation with many domains such as mathematics,mechanics,physics and computer science and its wide applications in geological exploration,engineering and medicine.This sort of problems can be included in the category of determining coefficients terms in a partial differential eqations in mathematics.The previous researches are based on the elastic media model.A model of coefficient inverse problems of wave equation in visco- elastic media is proposed in this paper,which describes characteristics of geological media more truly.The finite element method and the least-squares inversion process are used to solve the inverse question of plane viscoelastic wave equation in the frequ- ency domain.A numerical perturbational algorithm has also been employed for obtaining the gradient matrix quickly and accurately.Singular Values Decomposition(SVD)produ- ces significant improvements in computational precision.Based on above-mentioned studies,the authors have compiled the computational programs.Some numerical examples, showing the validity and practicality of the model and the numerical algorithm,are also given.