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- W4243374901 abstract "PreviousNext No AccessElements of Seismic Dispersion: A Somewhat Practical Guide to Frequency-Dependent PhenomenaAppendix E: Biot Equations of MotionAuthors: Christopher L. LinerChristopher L. LinerAllied Geophysical Laboratories, , University of Houston, Houston, Texas, USSearch for more papers by this authorhttps://doi.org/10.1190/1.9781560802952.appe SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Abstract Poroelasticity theory is mathematically formidable, and only a brief overview is given here. The goal is to offer a glimpse of the components of the theory and how they relate to important rock properties. Detail sufficient to calculate results for the theory cannot be given here. For that level of study, the interested reader is referred to Geertsma and Smit (1961), Deresiewicz and Rice (1962), and especially Dutta and Ode (1983). The Biot theory of poroelastic media involves two coupled equations of motion (Deresiewicz and Rice, 1962), relating vector displacement of the solid matrix u (bold denotes a vector quantity) to pore-fluid vector displacement U N∇2 u+grad [ (D+N) div u+Q div U]= ∂2 ∂t2 ( ρ11 u+ ρ12 U) + ηϕ2 k0 ∂ ∂t (u−U) E-1 and grad [Q div u+R div U]= ∂2 ∂t2 ( ρ12 u+ ρ22 U) − ηϕ2 k0 ∂ ∂t (u−U), E-1 where grad and div are the gradient and divergence differential operators; D, N, R, Q are all nonnegative elastic moduli; ρ11 , ρ12 , ρ22 are dynamic coefficients; η is viscosity; ϕ is porosity; and k0 is permeability. The elastic modulus Q used here is not to be confused with the attenuation quality-factor Q introduced in Chapter 5. Permalink: https://doi.org/10.1190/1.9781560802952.appeFiguresReferencesRelatedDetails Elements of Seismic Dispersion: A Somewhat Practical Guide to Frequency-Dependent PhenomenaISBN (print):978-1-56080-291-4ISBN (online):978-1-56080-295-2Copyright: 2012 Pages: 193 publication data© 2012 All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means without written permission of the publisherPublisher:Society of Exploration Geophysicists HistoryPublished in print: 01 Jan 2012 CITATION INFORMATION Christopher L. Liner, (2012), Appendix E: Biot Equations of Motion, Distinguished Instructor Series : 153-154. https://doi.org/10.1190/1.9781560802952.appe Plain-Language Summary PDF DownloadLoading ..." @default.
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