Extinction of elastic wave energy due to scattering in a viscoelastic medium

Forward scattering theorem for elastic longitudinal and shear wave scatterings by an arbitrary-shaped three-dimensional object embedded in a viscoelastic medium is derived. It is shown that the formulae for extinction cross-sections of an object in an energy-absorbing medium are formally the same with those of the object in the lossless elastic medium. Numerical calculations are executed for the longitudinal wave scattering in an epoxy matrix by a spherical inclusion with different material properties. The condition of negative extinction is examined with the causality constraint on the viscoelastic medium taken into account. It is found that the negative extinction occurs in the Rayleigh limit when the attenuation of the medium is sufficiently high and, more restrictedly, the wave speed in the object is larger than that in the medium, while it occurs less likely in the high frequency range considered in this paper (0