One major cause of elastic wave attenuation in heterogeneous porous media is wave-induced flow of the pore fluid between heterogeneities of various scales. It is believed that for frequencies below 1 kHz, the most important cause is the wave-induced flow between mesoscopic inhomogeneities, which are large compared with the typical individual pore size but small compared to the wavelength. Various laboratory experiments in some natural porous materials provide evidence for the presence of centimeter-scale mesoscopic heterogeneities. Laboratory and field measurements of seismic attenuation in fluid-saturated rocks provide indications of the role of the wave-induced flow. Signatures of wave-induced flow include the frequency and saturation dependence of P-wave attenuation and its associated velocity dispersion, frequency-dependent shear-wave splitting, and attenuation anisotropy. During the last four decades, numerous models for attenuation and velocity dispersion from wave-induced flow have been developed with varying degrees of rigor and complexity. These models can be categorized roughly into three groups according to their underlying theoretical framework. The first group of models is based on Biot's theory of poroelasticity. The second group is based on elastodynamic theory where local fluid flow is incorporated through an additional hydrodynamic equation. Another group of models is derived using the theory of viscoelasticity. Though all models predict attenuation and velocity dispersion typical for a relaxation process, there exist differences that can be related to the type of disorder ͑periodic, random, space dimension͒ and to the way the local flow is incorporated. The differences manifest themselves in different asymptotic scaling laws for attenuation and in different expressions for characteristic frequencies. In recent years, some theoretical models of wave-induced fluid flow have been validated numerically, using finite-difference, finite-element, and reflectivity algorithms applied to Biot's equations of poroelasticity. Application of theoretical models to real seismic data requires further studies using broadband laboratory and field measurements of attenuation and dispersion for different rocks as well as development of more robust methods for estimating dissipation attributes from field data.

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-scale͒ 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 soft͒ 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.