Ray Tracing in Elastic and Viscoelastic Media

We consider several extensions of ray tracing (uniform asymptotics, complex rays, space-time rays) interrelated by the fact that they must be used jointly in order to deal with both focusing and attenuation. Two representative models of acoustic wave propagation are considered: elasticity and viscoelasticity. Basic ideas behind canonical functions and Maslov integrals for uniformly asymptotic evaluation of the wave field from ray field parameters are discussed. Complex space-time ray tracing algorithms for dispersive and attenuating media are presented. Two models of attenuation in a viscoelastic medium are compared: (1) complex space-time ray methods for general attenuation/dispersion, (2) real ray methods for weak attenuation.