Chapter 11 Poroelasticity: Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks — A review
Tobias M. Müller, Boris Gurevich, Maxim Lebedev, 2010. "Chapter 11 Poroelasticity: Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks — A review", Geophysics Today: A Survey of the Field as the Journal Celebrates its 75th Anniversary, Sergey Fomel
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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 centime-ter-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 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 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.
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“In celebration of the 75th year of publication, the Geophysics editorial team invited a collection of papers written by well-recognized experts in various areas of exploration geophysics. These invited papers not only form part of the present book, but they also appear in the September-October 2010 special section of the journal. Geophysics Today: A Survey of the Field as the Journal Celebrates its 75th Anniversary complements this special section with an additional group of papers, drawn from Geophysics during the recent past, that addresses areas the invited articles did not. The result is a snapshot of the state-ofthe- art in the field as Geophysics passes its three-quarter-century mark. This book is Geophysical References Series No. 16.”