Abstract：According to the principle that the computed response and measured response should be fitted， the parameter inversion problem is reduced to a problem of solving nonlinear equations of point zero in this paper. Then the homotopy method is used to solve nonlinear equation and get solution of the point zero which is the parameter，porosity，to be inversed. The essence of traditional optimal methods，such as gradient method，perturbation method or time-convolution regularization iterative method，is based on Newton iterative method with local convergence. The homotopy method is a newly developed powerful device for solving nonlinear problems. It is introduced to improve the convergent state of Newton iterative method. The basic idea of the homotopy method is to construct a homotopy map with the homotopy parameter，then to track the homotopy path with the homotopy parameter as the variable numerically，and at last，yield the solution. The homotopy method is widely convergent by avoiding the local convergence of Newton iterative method. In this paper，the homotopy method is used to find the solution of inversion problem. For the 2D wave equation in porous media with boundary element solutions，the inversion results obtained by homotopy method are compared with those by the nonlinear optimum method and evolution strategy algorithm. The numerical results show that the parameter inversion by using homotopy method is feasible and effective.
