General P, type-I S, and type-II S waves in anelastic solids; inhomogeneous wave fields in low-loss solids

Abstract

Abstract The physical characteristics for general plane-wave radiation fields in an arbitrary linear viscoelastic solid are derived. Expressions for the characteristics of inhomogeneous wave fields, derived in terms of those for homogeneous fields, are utilized to specify the characteristics and a set of reference curves for general P and S wave fields in arbitrary viscoelastic solids as a function of wave inhomogeneity and intrinsic material absorption. The expressions show that an increase in inhomogeneity of the wave fields causes the velocity to decrease, the fractional-energy loss (Q−1) to increase, the deviation of maximum energy flow with respect to phase propagation to increase, and the elliptical particle motions for P and type-I S waves to approach circularity. Q−1 for inhomogeneous type-I S waves is shown to be greater than that for type-II S waves, with the deviation first increasing then decreasing with inhomogeneity. The mean energy densities (kinetic, potential, and total), the mean rate of energy dissipation, the mean energy flux, and Q−1 for inhomogeneous waves are shown to be greater than corresponding characteristics for homogeneous waves, with the deviations increasing as the inhomogeneity is increased for waves of fixed maximum displacement amplitude. For inhomogeneous wave fields in low-loss solids, only the tilt of the particle motion ellipse for P and type-I S waves is independent to first order of the degree of inhomogeneity. Quantitative estimates for the characteristics of inhomogeneous plane body waves in layered low-loss solids are derived and guidelines established for estimating the effect of inhomogeneity on seismic body waves and a Rayleigh-type surface wave in low-loss media.