Approximate expressions for viscous attenuation in marine sediments: Relating Biot's "critical" and "peak" frequencies

Simple approximate relations are proposed for the viscous attenuation per c ycle of the fast compressional and shear waves in the low-to-intermediate f requency range. Corresponding closed-form formulas are derived for frequenc ies at which maximum viscous attenuation per cycle occurs according to the Biot-Stoll theory of elastic wave propagation in marine sediments. In the n ew formulas, Biot's approximation [M. A. Blot, J. Acoust. Sec. Am, 34, 1254 -1264 (1962)] for the frequency-dependent viscosity correction factor F(f) and the assumption of relatively low specific loss (Q(-1) < 0.2) [J. Geerts ma and D. C. Smith, Geophysics 26(2), 169-181 (1962)] are used to provide a n accurate representation of the fast compressional and shear wave attenuat ion from low frequencies through a transition region extending to two or th ree times Blot's critical frequency f(c). The approximate viscodynamic beha vior of marine sediments for the fast compressional and shear waves shows s imilarities to that of a ''homogeneous relaxation'' process for an anelasti c linear element [A. M, Freudenthal and H. Geiringer, Encyclopedia of Physi cs (Springer-Verlag, 1958), Vol. 6]. (C) 2000 Acoustical Society of America . [S0001-4966(00)03307-5].