Abstract: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.