The Study On Dynamic Response And Material Parameters Inversion Of Layered Two-phase Viscoelastic Medium

Based on the theory of porous media and viscoelasticity, this thesis studies the seismic response of the visoelastic two-phase media by finite-element method. Furthermore, some of the material parameters are inversed using the numerical homotopy method.An explicit finite-element expression is deduced for wave equation of viscoelastic two-phase media. Combined with the boundary continuity condition between two kinds of two-phase medium, this finite-element method is facilitated to compute the seismic response of layered model. Then the dynamic response of media in one-layer, two-layer and three-layer semi-space geological model is investigated respectively. Additionally, the influence of media parameter variation on the displacement,velocity and acceleration is analyzed numerically.The dynamic response of displacement,velocity and acceleration is used to inverse media parameters. According to the principle that the computed dynamic response should fit the measured one, the parameter inversion problem of media is reduced to a problem of nonlinear operator equation's zero solution or minimization problem of a nonlinear functional, and then the homoptohy method is used to find the solution of inversion problem. The numerical results show that the functional minimization homoptohy method is more effective for material parameter inversion in time domain, with larger convergence range, less iteration step number and better convergence efficiency. In addition, the noise resistance analysis is introduced in the inversion problems to verify the stability of the homotopy inversion method, which shows that when the measured seismic data contains 5% random noise, the inversion result is satisfying.The results in this thesis enrich the application range of media wave theory and the homotopy method's application in inversion problems, which are of great theoretical and practical significance.