二维双相介质多参数反演的同伦法

从材料响应的理论合成应与实际测量数据相拟合这一出发点，双相介质波动方程参数的反演，可以转化为非线性算子方程的零点求解问题，然后用同伦方法求出非线性算子等于零的根作为反问题的解。本文将同伦方法应用于具有边界元数值解的二维双相介质波动方程的多参数反演，并将反演结果同非线性全局优化方法进化策略法进行了比较，数值计算结果表明了同伦方法的可行性和有效性。

HOMOTOPY METHOD IN MULTI-PARAMETER INVERSION OF 2D POROUS MEDIA

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.