Linear and nonlinear seismic Rayleigh waves with damping: a heuristic direct method

Abstract

In this study, nonlinearity in earthquake is investigated for the propagating seismic waves instead of linear waves. Assuming the presence of nonlinear effects in this earthquake modeling, the Rayleigh waves are formed by incorporating the nonlinear sine-Gordon equation into the linear asymptotic governing equations for finding similarity reduction. The existence of reduction to the modified asymptotic governing equations is demonstrated and is consequently shown to give both the linear and nonlinear Rayleigh waves solutions. The related velocity and amplitude dependent Rayleigh waves are obtained and also the nonlinear form of Rayleigh waves. Multiple nonlinear surface displacements are identified. These nonlinear waves are shown to leave the trails of crucial surface displacements.