Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks — A review Tobias M. Müller 1 , Boris Gurevich 2 , and Maxim Lebedev 3 ABSTRACT 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. INTRODUCTION Seismic waves in earth materials are subject to attenuation and dispersion in a broad range of frequencies and scales from free oscil- lations of the entire earth to ultrasound in small rock samples Aki and Richards, 1980. Attenuation refers to the exponential decay of wave amplitude with distance; dispersion is a variation of propaga- tion velocity with frequency. Attenuation and dispersion can be caused by a variety of physical phenomena that can be divided broadly into elastic processes, where the total energy of the wave- field is conserved scattering attenuation, geometric dispersion, and inelastic dissipation, where wave energy is converted into heat. Of particular interest to exploration geophysics is inelastic attenuation and dispersion of body waves P- and S-waves resulting from the presence of fluids in the pore space of rocks. It is believed that an un- derstanding of fluid-related dissipation in hydrocarbon reservoir rocks, combined with improved measurements of attenuation and/or dispersion from recorded seismic data, may be used in the future to estimate hydraulic properties of these rocks. Dissipation-related seismic attributes are already employed in seismic interpretation and reservoir characterization, but so far their use has been mostly em- pirical and qualitative. Theoretical models of frequency-dependent attenuation and dispersion may help develop quantitative attributes, which can be calibrated using well logs and laboratory measure- ments. It is commonly accepted that the presence of fluids in the pore Manuscript received by the Editor 20 January 2010; revised manuscript received 29 April 2010; published online 14 September 2010. 1 CSIRO Earth Science and Resource Engineering, Perth, Australia. E-mail: tobias.mueller@csiro.au. 2 CSIRO Earth Science and Resource Engineering and Curtin University of Technology, Perth,Australia. E-mail: b.gurevich@curtin.edu.au. 3 Curtin University of Technology, Perth,Australia. m.lebedev@curtin.edu.au. © 2010 Society of Exploration Geophysicists. All rights reserved. GEOPHYSICS, VOL. 75, NO. 5 SEPTEMBER-OCTOBER 2010; P. 75A147–75A164, 9 FIGS. 10.1190/1.3463417 75A147 Downloaded 08 Oct 2010 to 129.215.6.194. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/