Asymptotic ray theory in heterogeneous viscoelastic solids

The propagation of time-harmonic waves in heterogeneous, prestressed, viscoelastic solids is investigated by following the ray description. Solutions are found which may be viewed as longitudinal and transverse waves. The eikonal equations are affected by the prestress and then rays are not parallel to the gradient of the phase function. The asymptotic properties of the Fourier transform of the relaxation functions are inspected in connection with thermodynamics and shown to affect the evolution of the amplitude coefficients along the rays. Then the amplitude coefficients of any order are determined in terms of quantities evaluated at each ray. Emphasis is given to the behaviour of the leading-order terms and the dissipative properties are shown to result in a damping of the amplitude. As an application, rays and phase function are obtained for stratified solids when the prestress is isotropic.