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.

Wavefi elds in porous media saturated by two immiscible fl uids are simulated in this paper. Based on the sealed system theory, the medium model considers both the relative motion between the fl uids and the solid skeleton and the relaxation mechanisms of porosity and saturation (capillary pressure). So it accurately simulates the numerical attenuation property of the wavefi elds and is much closer to actual earth media in exploration than the equivalent liquid model and the unsaturated porous medium model on the basis of open system theory. The velocity and attenuation for different wave modes in this medium have been discussed in previous literature but studies of the complete wave-fi eld have not been reported. In our work, wave equations with the relaxation mechanisms of capillary pressure and the porosity are derived. Furthermore, the wavefi eld and its characteristics are studied using the numerical fi nite element method. The results show that the slow P3-wave in the non-wetting phase can be observed clearly in the seismic band. The relaxation of capillary pressure and the porosity greatly affect the displacement of the non-wetting phase. More specifi cally, the displacement decreases with increasing relaxation coeffi cient.