An acoustic wave equation based on viscoelasticity

Abstract

An acoustic wave equation for pressure accounting for viscoelastic attenuation is derived from viscoelastic equations of motion. It is assumed that the relaxation moduli are completely monotonic. The acoustic equation differs significantly from the equations proposed by Szabo (1994) and in several other papers. Integral representations of dispersion and attenuation are derived. General properties and asymptotic behavior of attenuation and dispersion in the low and high frequency range are studied. The results are compatible with experiments. The relation between the asymptotic properties of attenuation and wavefront singularities is examined. The theory is applied to some classes of viscoelastic models and to the quasi-linear attenuation reported in seismology.