Application of the ray-series method to linear viscoelastic wave propagation

Summary

The classical ray-series method for electromagnetic wave propagation in inhomogeneous media is applied to the problem of wave propagation in isotropic, homogeneous, linear viscoelastic media characterized by virtually arbitrary time-dependent relaxation or creep functions. The full three-dimensional treatment is presented, followed by the specialization to the one-dimensional propagating pulse problem. In this last case, the ray-series is evaluated numerically for the creep function

$$\psi (t) = \frac{1}{\mu }\left\{ {1 + \frac{q}{\alpha }\left. {\left[ {\left. {\left( {1 + \frac{1}{\tau }} \right)^\alpha - 1} \right]} \right.} \right\}} \right.H(t)$$

for various model parameter ranges and for various initial source functions.