Approximate analytical models for cylindrical shear wave propagation in viscoelastic media

Abstract

Improved approximate frequency domain expressions are derived for cylindrical shear wave propagation in viscoelastic media. These expressions extend prior results that describe cylindrical wave propagation in lossless media. Previously, an analytical expression for a cylindrical wave was obtained in terms of a Hankel function and a large argument approximation was applied to the result. A leading frequency-dependent term was then treated as a constant with respect to frequency. In the improved expression, the frequency-dependence of the leading term is retained. For lossless media, the leading term is a fractional integrator, and for viscoelastic media, the leading term is either a fractional integrator or an integer-order integrator, depending on the frequency range. The lossless and the viscoelastic models are evaluated in the frequency domain for simplified source geometries and compared to numerical results. The comparison shows that the agreement between the analytical and the numerical models is excellent. Implications for time-domain calculations in viscous media will also be discussed. [This work was supported in part by NIH Grant Nos. R01 EB012079 and R01 DK092255.]