A wavelet adaptive-homotopy method for inverse problem in the fluid-saturated porous media

In this paper, we consider a parameter identification problem for the elastic wave equations in the fluid-saturated porous media. A wavelet adaptive-homotopy method is proposed for the recovery of porosity. This algorithm combines the wavelet multiscale inversion idea with the adaptive-homotopy method. And the adaptive-homotopy method provides a simple way to adapt computational refinement to the choice of the homotopy parameter. Numerical results illustrate that the wavelet adaptive-homotopy method is globally convergent and highly effective for solving the inverse problem.