Inversing physical parameter of two-phase viscoelastic media by homotopy method

In this paper, we inverse the physical parameters of saturated porous viscoelastic media from observed dynamic responses of displacement, velocity, or acceleration in time domain. This inverse problem is ill-posed due to the measurement error and the high insufficient measured data. In this paper, the ill-posed parameter inverse problem in the two-phase viscoelastic media is solved by computing a minimization problem of nonlinear functional by homotopy method, which has good convergent property for given initial values. Numerical results show our algorithm convergences well even with measurement noises or errors. We also observe that the inversed results based on observed response of displacement are better than the results based on responses of velocity and acceleration.