Low-frequency shear wave propagation in periodic systems of alternating solid and viscous fluid layers

Waves in periodic layered systems at low frequencies can be studied using a n asymptotic analysis of the Rytov's exact dispersion equations. Since the wavelength of the shear wave in the fluid (viscous skin depth) is much smal ler than the wavelength of the shear wave in the solid, the presence of vis cous fluid layers requires a consideration of higher terms in the asymptoti c expansions. For a shear wave with the directions of propagation and of pa rticle motion in the bedding plane, the attenuation (inverse Q) obtained by this procedure is Q(-1)= omega eta phi/mu(s)(1 - phi) + omega phi rho(f)(2 )h(f)(2)/12 rho eta +o(omega), where omega is frequency, rho is weighted av erage density of the solid/fluid system, h(f) is the thickness of fluid lay ers, is fluid volume fraction, i.e., the "porosity," mu(s) is solid shear m odulus, and rho(f) and eta are the density and viscosity of the fluid, resp ectively. The term proportional to eta is responsible for the viscous shear relaxation, while the term proportional to eta(-1) accounts for the visco- inertial (poroelastic) attenuation of Blot's type. This result shows that t he characteristic frequencies of visco-elastic omega(VE), poroelastic omega (B), and scattering omega(R) attenuation mechanisms obey the relation omega (VE)omega(B)=omega(R)(2), which explains why the visco-elastic and poroelas tic mechanisms are usually treated separately in the context of macroscopic theories that imply omega much less than omega(R). The poroelastic mechani sm dominates over the visco-elastic one when the frequency-independent para meter B =omega(B)/omega(VE)= 12 eta(2)/mu(s)rho(f)h(f)(2)much less than 1, and vice versa. (C) 1999 Acoustical Society of America.