黏弹性介质参数反演的同伦方法

以介质的动态时域位移响应作为参数反演的依据，对黏弹性介质的材料参数进行反分析研究。动态时域位移响应比拟静态和频域位移响应含有更丰富的信息，且在实际工程中所测得的信息也多为动态时域信号，因此将时间全过程的位移信息用于黏弹性介质参数反分析，将使黏弹性介质参数反演的结果更为合理、更接近实际。根据位移响应的理论合成值应与实际测量数据相拟合的原则，将黏弹性介质参数反演问题转化为非线性算予方程的零点求解问题；然后，应用大范围收敛的同伦方法求出非线性算予等于0的根作为反问题的解。以黏弹性半空间介质为例进行数值模拟。模拟结果表明，反演结果不依赖于初始值的选取，且反算过程稳定收敛，说明同伦反演方法对于黏弹性参数的动态反演是适用、有效的。

PARAMETRIC INVERSION OF VISCOELASTIC MEDIA WITH HOMOTOPY METHOD

The physical parameters of viscoelastic media from their dynamic responses in time domain are inversed, which include more information than the quasi-static movement or response in frequency domain. Moreover, the movement in time domain is easy to measure, and the inversed results are reasonable and practicable. According to principle that the computed and measured dynamic responses should be fitted, the parametric inversion problem in viscoelastic media is deduced to solve a problem of nonlinear zero-equation by the homotopy method with wide convergence. It is a newly developed powerful device for solving nonlinear problem. This method is used to inverse material parameters of 3D halfspace viscoelastic media. Numerical results show that the homotopy method is nearly independent of the original value; and the method has high accuracy and validity for the dynamical identification problems of viscoelastic parameters.