Numerical Computation of Spherical Waves in Two Viscoelastic Media

Abstract

By applying the correspondence principle, the Laplace transform solutions of spherical waves in viscoelastic model are derived in this study. The numerical inversion of Laplace transform developed by Bellman is introduced to invert the transform solution of spherical waves into time domain. A modification of the numerical inversion is particularly shown to enable one to obtain the viscoelastic waves adequately. The accuracy of the numerical inversion is proven by comparing the results calculated from series solution and Papoulis’ method. The efficiency of the numerical inversion is demonstrated by studying the wave parameters in 6-element and 5-element models. By examining the behavior of wave responses in time domain, it is found that the 5-element model behaves as a viscous liquid and the 6-element model as a solid.