A simple model for squirt-flow dispersion and attenuation in fluid-saturated granular rocks

TLDR

Seismic attenuation in fluid‑saturated rocks is largely caused by pore‑fluid flow, especially at sonic and ultrasonic frequencies where local flow between pores of varying shapes and orientations dominates. The authors develop a simple squirt‑flow model whose parameters can be independently measured or estimated from laboratory data. The model represents the rock as stiff porosity with compliant pores at grain contacts, modeling isotropic compliant pores through pressure relaxation in a disk‑shaped gap between adjacent grains. It predicts complex, frequency‑dependent bulk and shear moduli that agree with Gassmann’s and Mavko–Jizba equations at low and high frequencies, and shows that attenuation and dispersion are mainly governed by dry bulk modulus variation with pressure and are largely independent of fluid properties.

Abstract

A major cause of seismic attenuation in fluid-saturated rocks is the flow of the pore fluid induced by the passing wave. At sonic and ultrasonic frequencies, attenuation appears to be dominated by the local (pore-scale) flow between pores of different shapes and orientations. A simple squirt flow model is developed in which all of the parameters can be independently measured or estimated from measurements. The pore space of the rock is assumed to consist of stiff porosity and compliant (or soft) pores present at grain contacts. The effect of isotropically distributed compliant pores is modeled by considering pressure relaxation in a disk-shaped gap between adjacent grains. This derivation gives the complex and frequency-dependent effective bulk and shear moduli of a rock, in which the compliant pores are liquid saturated and stiff pores are dry. The resulting squirt model is consistent with Gassmann’s and Mavko–Jizba equations at low and high frequencies, respectively. The magnitude of attenuation and dispersion given by the model is directly related to the variation of dry bulk modulus with pressure and is relatively independent of fluid properties.