An approximate Biot model for marine sediments with nonuniform pore sizes

Abstract

The issue of attenuation and dispersion in marine sediments has been investigated by Hamilton [Geophysics (1972)] in detail. In his paper, Hamilton stated that an adequate model for marine sediments must be anelastic in which viscous damping and velocity dispersion should be considered if the pore water moves significantly relative to mineral structure. He introduced an attenuation parameter k which is empirically related to mean grain size and porosity. Based on the experimental measurements in frequencies within 14–100 kHz, he suggested a nearly elastic model with linear frequency dependency of attenuation and negligible velocity dispersion. Then, he explained the peak value of k for fine sands under the context of frictional energy losses between grains. In this study, an approximate Biot model is proposed. The new model includes both frame anelasticity and viscous damping in marine sediments with nonuniform pore sizes. For most marine sediments, the approximate model predicts similar frequency dependency of attenuation and velocity dispersion of compressional and shear waves to those of predicted by the Biot model. It has been shown that mean grain size and porosity dependency of parameter k can be also predicted by the new model without introducing an empirical relation. [Work supported by ONR.]