1、HANDBOOK OF GEOPHYSICAL EXPLORATION SEISMIC EXPLORATION VOLUME 31 WAVE FIELDS IN REAL MEDIA:WAVE PROPAGATION IN ANISOTROPIC,ANELASTIC AND POROUS MEDIA HANDBOOK OF GEOPHYSICAL EXPLORATION SEISMIC EXPLORATION Editors:Klaus Helbig and Sven Treitel Volume 1.Basic Theory in Reflection e i s m o l o 2.Sei
2、smic Instrumentation,2nd dition 3.Seismic Field Techniques2 4A.Seismic Inversion and Deconvolution:Classical Methods 4B.Seismic Inversion and Deconvolution:Dual-Sensor Technology 5.Seismic Migration(Theory and Practice)6.Seismic Velocity nalsis 7.Seismic Noise Attenuation 8.Structural 1nterpretation
3、2 9.Seismic Stratigraphy 10.Production Seismology 1 1.3-D Seismic xloration 12.Seismic Resolution 13.Refraction Seismics 14.Vertical Seismic Profiling:Principles 3rd Updated and Revised Edition 15A.Seismic Shear Waves:Theory 15B.Seismic Shear Waves:Applications 16A.Seismic Coal Exploration:Surface e
4、 t h o d s 16B.Seismic Coal Exploration:In-Seam Seismics 17.Mathematical Aspects of Seismology 18.Physical Properties of Rocks 19.Shallow High-Resolution Reflection Seismics 20.Pattern Recognition and Image Processing 2 1.Supercomputers in Seismic Exploration 22.Foundations of Anisotropy for Explora
5、tion Seismics 23.Seismic TomographyZ 24.Borehole coustics 25.High Frequency Crosswell Seismic profiling2 26.Applications of Anisotropy in Vertical Seismic profiling1 27.Seismic Multiple Elimination Techniques1 28.Wavelet Transforms and Their Applications to Seismic Data Acquisition,Compression,Proce
6、ssing and interpretationi 29.Seismic Signatures and Analysis of Reflection Data in Anisotropic Media 30.Computational Neural Networks for Geophysical Data Processing 3 1.Wave Fields in Real Media:Wave Propagation in Anisotropic,Anelastic and Porous Media 1n preparation.2lanned.SEISMIC EXPLORATION Vo
7、lume 3 1 WAVE FIELDS IN REAL MEDIA:WAVE PROPAGATION IN ANISOTROPIC,ANELASTIC AND POROUS MEDIA Jose M.CARCIONE Istituto Nazionale di Oceanografia e di Geofisica Sperimentale(OSG)Borgo Grotta Giganta 42 C 340 10 Sgonico Trieste,Italy 200 1 PERGAMON An Imprint of Elsevier Science Amsterdam-London-New Y
8、ork-Oxford-Paris-Shannon-Tokyo ELSEVIER SCIENCE Ltd The Boulevard,Langford Lane Kidlington,Oxford OX5 IGB,UK 2001 Elsevier Science Ltd.All rights resewed.This work is protected under copyright by Elsevier Science,and the following terms and conditions apply to its use:Photocopying Single photocopies
9、 of single chapters may be made for personal use as allowed by national copyright laws.Permission of the Publisher and payment of a fee is required for all other photocopying,including multiple or systematic copying,copying for advertising or promotional purposes,resale,and all forms of document del
10、ivery.Special rates are available for educational institutions that wish to make photocopies for non-profit educational classroom use.Permissions may be sought directly from Elsevier Science Global Rights Department,PO Box 800,Oxford OX5 IDX,UK;phone:(144)1865 843830,fax:(+44)1865 853333,e-mail:perm
11、issionselsevier.co.uk.You may also contact Global Rights directly through Elseviers home page(http:Nwww.elsevier.nl),by selecting Obtaining Permissions.In the USA,users may clear permissions and make payments through the Copyright Clearance Center,Inc.,222 Rosewood Drive,Danvers,MA 01923,USA;phone:(
12、+I)(978)7508400,fax:(+I)(978)7504744,and in the UK through the Copyright Licensing Agency Rapid Clearance Sewice(CLARCS),90 Tottenham Court Road,London WIP OLP,UK;phone:(+44)207 631 5555;fax:(+44)207 631 5500.Other countries may have a local reprographic rights agency for payments.Derivative Works T
13、ables of contents may be reproduced for internal circulation,but permission of Elsevier Science is required for external resale or distribution of such material.Permission of the Publisher is required for all other derivative works,including compilations and translations.Electronic Storage or Usage
14、Permission of the Publisher is required to store or use eleclmnically any material contained in this work,including any chapter or part of a chapter.Except as outlined above,no part of this work may be reproduced,stored in a retrieval system or transmitted in any form or by any means,electronic,mech
15、anical,photocopying,recording or otherwise,without prior written permission of the Publisher.Address permissions requests to:Elsevier Science Global Rights Department,at the mail,fax and e-mail addresses noted above.Notice No responsibility is assumed by the Publisher for any injury andlor damage to
16、 persons or property as a matter of products liability,negligence or otherwise,or from any use or operation of any methods,products,instructions or ideas contained in the material herein.Because of rapid advances in the medical sciences,in particular,independent verification of diagnoses and drug do
17、sages should be made.First edition 2001 Library of Congress Cataloging in Publication Data A catalog record from the Library of Congress has been applied for.British Library Cataloguing in Publication Data A catalogue record from the British Library has been applied for.ISBN:0-08-043929-2 ISSN:0950-
18、1401(Series)8 The paper used in this publication meets the requirements of ANSVNISO 239.48-1992(Permanence of Paper).Printed in The Netherlands.This book is dedicated to my parents,Angela and Antonio This Page Intentionally Left BlankContents Preface xv Acknowledgments xx About the author xxi Basic
19、notation xxii Glossary of main symbols xxiii 1 Anisotropic elastic media 1.1.1 Strain-energy density and stress-strain relation 1 1.2 Dynamical equations.4.1.2.1 Symmetries and transformation properties 6.Symmetry plane of a monoclinic medium 7 Transformation of the stiffness matrix.9 1.3 Kelvin-Chr
20、istoffel equation,phase velocity and slowness.10 1.3.1 Transversely isotropic media.11 1.3.2 Symmetry planes of an orthorhombic medium.13 1.3.3 Orthogonality of polarizations.14 1.4 Energy balance and energy velocity.15 1.4.1 Group velocity.17.1.4.2 Equivalence between the group and energy velocitie
21、s 19 1.4.3 Envelope velocity.20 Transversely isotropic media.20.1.4.4 Elasticity constants from phase and group velocities 22.1.4.5 Relationship between the slowness and wave surfaces 24 SH-wave propagation.24 1.5 Finely layered media.25 1.6 Anomalous polarizations.29.1.7 Analytical solutions for tr
22、ansversely isotropic media 34 1.7.1 2-D Greens function.34 1.7.2 3-D Greens function.36 1.8 Reflection and transmission of plane waves.36 1.8.1 Cross-plane shear waves.38 CONTENTS 2 Viscoelasticity and wave propagation 45 2.1 Energy densities and stress-strain relations.46 2.1.1 Fading memory and sy
23、mmetries of the relaxation tensor.48 2.2 Stress-strain relation for 1-D viscoelastic media.49 2.2.1 Complex modulus and storage and loss moduli.49 2.2.2 Energy and significance of the storage and loss moduli.51 2.2.3 Non-negative work requirements and other conditions.51 2.2.4 Consequences of realit
24、y and causality.52 2.2.5 Summary of the main properties.54.Relaxation function 54 Complex modulus.54 2.3 Wave propagation concepts for 1-D viscoelastic media.55 2.4 Mechanical models and wave propagation.59 2.4.1 Maxwell model.61 2.4.2 Kelvin-Voigt model.64 2.4.3 Zener or standard linear solid model
25、.65 2.4.4 Generalized Zener model.69 Nearly constant Q.71 2.4.5 Nearly constant-Q model with a continuous spectrum.73 2.5 Constant-Q model and wave equation.73 2.5.1 Phase velocity and attenuation factor.74 2.5.2 Wave equation in differential form.Fractional derivatives.75 Propagation in Pierre shal
26、e.76 2.6 Memory variables and equation of motion.77 2.6.1 Maxwell model.77 2.6.2 Kelvin-Voigt model.79 2.6.3 Zener model.79 2.6.4 Generalized Zener model.80 3 Isotropic anelastic media 83 3.1 Stress-strain relation.84 3.2 Equations of motion and dispersion relations.84 3.3 Vector plane waves.86 3.3.
27、1 Slowness,phase velocity and attenuation factor.86 3.3.2 Particle motion of the P wave.88 3.3.3 Particle motion of the S waves.90 3.3.4 Polarization and orthogonality.92 3.4 Energy balance,energy velocity and quality factor.93 3.4.1 Pwave.94.3.4.2 S waves 100 3.5 Boundary conditions and Snells law.
28、100 3.6 The correspondence principle.102.3.7 Rayleigh waves 102 3.7.1 Dispersion relation.103 3.7.2 Displacement field.104 3.7.3 Phase velocity and attenuation factor.105 CONTENTS ix.3.7.4 Special viscoelastic solids 106.Incompressible solid 106.Poissons solid 106.Hardtwigs solid 106.3.7.5 Two Rayle
29、igh waves 106 3.8 Reflection and transmission of cross-plane shear waves.107.3.9 Memory variables and equation of motion 110.3.10 Analytical solutions 112.3.10.1 Viscoacoustic media 112.3.10.2 Constant-Q viscoacoustic media 113.3.10.3 Viscoelastic media 114.3.11 The elastodynamic of a non-ideal inte
30、rface 115.3.11.1 The interface model 116.Boundary conditions in differential form 117.3.11.2 Reflection and transmission coefficients of SH waves 117.Energy loss 118 3.11.3 Reflection and transmission coefficients of P-SV waves.119.Energy loss 121 4 Anisotropic anelastic media 125.4.1 Stress-strain
31、relations 126.4.1.1 Model 1:Effective anisotropy 128 4.1.2 Model 2:Attenuation via eigenstrains.128 4.1.3 Model 3:Attenuation via mean and deviatoric stresses.130 4.2 Wave velocities,slowness and attenuation vector.131 4.3 Energy balance and fundamental relations.133.4.3.1 Plane waves.Energy velocit
32、y and quality factor 135.4.3.2 Polarizations 139 4.4 The physics of wave propagation for viscoelastic SH waves.140.4.4.1 Energy velocity 140.4.4.2 Group velocity 142.4.4.3 Envelope velocity 143.4.4.4 Perpendicularity properties 143.4.4.5 Numerical evaluation of the energy velocity 145 4.4.6 Forbidde
33、n directions of propagation.146 4.5 Memory variables and equation of motion in the time domain.147 4.5.1 Strain memory variables.148 4.5.2 Memory-variable equations.150.4.5.3 SH equation of motion 151.4.5.4 qP-qSV equation of motion 151.4.6 Analytical solution for SH waves in monoclinic media 153 5 The reciprocity principle 155.5.1 Sources.receivers and reciprocity 156.5.2 The reciprocity principl
copyright@ 2008-2022 冰豆网网站版权所有
经营许可证编号:鄂ICP备2022015515号-1