A homotopy inversion method for Rayleigh wave dispersion data

Inverting Rayleigh-wave dispersion data may provide reliable velocity structure. A lot of linearized inversion methods are developed to handle this problem, however, which may be trapped by local extrema (minima or maxima) or no convergence of the solution without propriate initial models. Although several nonlinear approaches are also proposed, most of which face amount of computational consumption. In order to keep the balance, we introduce the homotopy method (HM), which can transform the nonlinear Rayleigh-wave dispersion equation into a linear equation system, and has global optimized property and less computational burden. We apply the HM to synthetic dispersion datasets, including noise-free and contaminated data. Through the comparison with the Competitive Particle Swarm Optimization (CPSO), a nonlinear approach, the HM is also less dependent on the initial model and may have higher computational efficiency. Real datasets from ambient noise in Weiyuan, Sichuan province, China, are further employed to study the effectiveness and applicability of the HM. Similar structure of more sufficient abnormal magnitude and boundary consistence is derived, which shows the uplift of the Weiyuan anticline with most less Root Mean Square Error (RMSE). It is concluded that, the HM is a potential candidate for most geophysical inversion problems with global optimization and efficiency balance.