Wave Fields in Real Media (eBook)

Wave Propagation in Anisotropic, Anelastic and Porous Media

Jose M. Carcione (Herausgeber)

eBook Download: PDF

2001 | 1. Auflage
414 Seiten
Elsevier Science (Verlag)
978-0-08-054371-0 (ISBN)

Infos

This book examines the differences between an ideal and a real description of wave propagation, where ideal means an elastic (lossless), isotropic and single-phase medium, and real means an anelastic, anisotropic and multi-phase medium. The analysis starts by introducing the relevant stress-strain relation. This relation and the equations of momentum conservation are combined to give the equation of motion. The differential formulation is written in terms of memory variables, and Biot's theory is used to describe wave propagation in porous media. For each rheology, a plane-wave analysis is performed in order to understand the physics of wave propagation. The book contains a review of the main direct numerical methods for solving the equation of motion in the time and space domains. The emphasis is on geophysical applications for seismic exploration, but researchers in the fields of earthquake seismology, rock acoustics, and material science - including many branches of acoustics of fluids and solids - may also find this text useful.

Inhalt

Front Cover 1
WAVE FIELDS IN REAL MEDIA: WAVE PROPAGATION IN ANISOTROPIC, ANELASTIC AND POROUS MEDIA 4
Copyright Page 5
Contents 8
Preface 16
Acknowledgments 21
About the author 22
Basic notation 23
Glossary of main symbols 24
Chapter 1. Anisotropic elastic media 26
1.1 Strain-energy density and stress-strain relation 26
1.2 Dynamical equations 29
1.3 Kelvin-Christoffel equation, phase velocity and slowness 35
1.4 Energy balance and energy velocity 40
1.5 Finely layered media 50
1.6 Anomalous polarizations 54
1.7 Analytical solutions for transversely isotropic media 59
1.8 Reflection and transmission of plane waves 61
Chapter 2. Viscoelasticity and wave propagation 70
2.1 Energy densities and stress-strain relations 71
2.2 Stress-strain relation for 1-D viscoelastic media 74
2.3 Wave propagation concepts for 1-D viscoelastic media 80
2.4 Mechanical models and wave propagation 84
2.5 Constant-Q model and wave equation 98
2.6 Memory variables and equation of motion 102
Chapter 3. Isotropic anelastic media 108
3.1 Stress-strain relation 109
3.2 Equations of motion and dispersion relations 109
3.3 Vector plane waves 111
3.4 Energy balance, energy velocity and quality factor 118
3.5 Boundary conditions and Snell's law 125
3.6 The correspondence principle 127
3.7 Rayleigh waves 127
3.8 Reflection and transmission of cross-plane shear waves 132
3.9 Memory variables and equation of motion 135
3.10 Analytical solutions 137
3.11 The elastodynamic of a non-ideal interface 140
Chapter 4. Anisotropic anelastic media 150
4.1 Stress-strain relations 151
4.2 Wave velocities, slowness and attenuation vector 156
4.3 Energy balance and fundamental relations 158
4.4 The physics of wave propagation for viscoelastic SH waves 165
4.5 Memory variables and equation of motion in the time domain 172
4.6 Analytical solution for SH waves in monoclinic media 178
Chapter 5. The reciprocity principle 180
5.1 Sources, receivers and reciprocity 181
5.2 The reciprocity principle 181
5.3 Reciprocity of particle velocity. Monopoles 183
5.4 Reciprocity of strain 183
5.5 Reciprocity of stress 188
Chapter 6. Reflection and transmission of plane waves 192
6.1 Reflection and transmission of SH waves 193
6.2 Reflection and transmission of qP-qSV waves 214
6.3 Reflection and transmission at fluid/solid interfaces 237
6.4 Reflection and transmission coefficients of a set of layers 240
Chapter 7. Biot's theory for porous media 244
7.1 Isotropic media. Strain energy and stress-strain relations 245
7.2 The concept of effective stress 249
7.3 Anisotropic media. Strain energy and stress-strain relations 259
7.4 Kinetic energy 266
7.5 Dissipation potential 271
7.6 Lagrange's equations and equation of motion 272
7.7 Plane-wave analysis 280
7.8 Strain energy for inhomogeneous porosity 286
7.9 Boundary conditions 291
7.10 Green's function for poro-viscoacoustic media 297
7.11 Poro-viscoela sticity 301
7.12 Anisotropic poro-viscoelasticity 304
Chapter 8. Numerical methods 320
8.1 Equation of motion 320
8.2 Time integration 321
8.3 Calculation of spatial derivatives 326
8.4 Source implementation 331
8.5 Boundary conditions 332
8.6 Absorbing boundaries 333
8.7 Model and modeling design–Seismic modeling 335
8.8 Concluding remarks 337
8.9 Appendix 339
Examinations 352
Chronology of main discoveries 356
A list of scientists 364
Bibliography 370
Name index 396
Subject index 405

Produkt-Details

• Erscheint lt. Verlag: 15.10.2001
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geophysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik
• Themenwelt: Technik
• ISBN-10: 0-08-054371-5 / 0080543715
• ISBN-13: 978-0-08-054371-0 / 9780080543710