Models for attenuation in marine sediments that incorporate structural relaxation processes

Abstract

Biot’s model leads to an attenuation coefficient at low frequencies that is proportional to ω2, and such is consistent with physical models of viscous attenuation of fluid flows through narrow constrictions driven by pressure differences between larger fluid pockets within the granular configuration. Much data suggests, however, that the attenuation coefficient is linear in ω for some sediments and over a wide range of frequencies. A common model that predicts such a dependence stems from theoretical work by Stoll and Bryan [J. Acoust. Soc. Am. 47, 1440 (1970)], in which the elastic constants of the solid frame are taken to be complex numbers, with small constant imaginary parts. Such invariably leads to a linear ω dependence at sufficiently low frequencies and this conflicts with common intuitive notions. The present paper incorporates structural relaxation, with a generalization of the formulations of Hall [Phys. Rev. 73, 775 (1948)] and Nachman, Smith, and Waag [J. Acoust. Soc. Am. 88, 1584 (1990)]. The mathematical form and plausibility of such is established, and it is shown that the dependence is as ω2 at low frequencies, and that a likely realization is one where the dependence is linear in ω at intermediate frequency ranges.