Wave Fields in Real Media Wave Propagation in Anisotropic, Anelastic and Porous Media-[1st]-[J Jose M Carcione].pdf

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

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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