Ray Tracing with Adaptive Step Size Control in Inhomogeneous Anisotropic Media

Abstract

Summary We present a new ray tracing software with adaptive step size control as an efficient tool for modeling wave propagation in inhomogeneous anisotropic media. After a short review of the theoretical and numerical basics of ray tracing algorithms, we apply initial-value and two-point ray tracing to two strongly anisotropic velocity models. We compare the efficiency and accuracy of integrating ray tracing systems numerically with three different Runge-Kutta methods. These are the classical Runge-Kutta method with constant step size and two embedded Runge-Kutta methods, the Cash-Karp method and the Dormand-Prince method, with adaptive step size control. The results show that ray tracing with adaptive step size control is significantly more efficient than standard ray tracing algorithms with constant step size. Additionally, our software is more user-friendly because adaptive step size control provides relief from the necessity of having a priori knowledge about the spatial and temporal behavior of ray propagation and the maximum allowed step size in a given medium.