Abstract:Most of geophysical inversion are non-linear problems,the homotopy method based on path tracking is effective method for solving this kind of problems.The path skip is often appealed in common homotopy,which can't effectively solve the accurate path tracking issue.The paper presented tomotopy path tracking algorithm that can stably solve the non-linear equations set.The method uses the local curvature of homotopy zero curve to control prediced step-length,uses improved Newton iteration in reference [19] to end judgment,which further improved the stability and reliability,realized accurate path tracking and avoided the path skip in a process of tracking.The numerical calculation showed that the method has good stability and wide practicality,without strict limitation in selection of first value,the solution can be fast convergence,even though random selected first value deviates far from the solution of objective function,so it is large-scope convergent method that is suitable for solving geophysical non-linear inversion.