Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks — A review

摘要

One major cause of elastic wave attenuation in heterogeneous porous media is wave-induced flow of the pore fluid between het-erogeneities 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 com-pared 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 centime-ter-scale mesoscopic heterogeneities. Laboratory and field mea-surements 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 depen-dence of P-wave attenuation and its associated velocity disper-sion, frequency-dependent shear-wave splitting, and attenuation anisotropy. During the last four decades, numerous models for at-tenuation 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 ac-cording 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 equa-tion. Another group of models is derived using the theory of vis-coelasticity. 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 dimension) 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 char-acteristic frequencies. In recent years, some theoretical models of wave-induced fluid flow have been validated numerically, us-ing finite-difference, finite-element, and reflectivity algorithms applied to Biot's equations of poroelasticity. Application of theo-retical 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 ro-bust methods for estimating dissipation attributes from field data.