WAVE FIELDS IN REAL MEDIA
Ouvrage 9780080439297 : WAVE FIELDS IN REAL MEDIA
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.
Contents
Preface. Acknowledgments. About the author. Basic notation. Glossary of
main symbols.
1. Anisotropic elastic media.
1.1. Strain-energy density and stress-strain relation. 1.2 Dynamical
equations. 1.3 Kelvin-Christoffel equation, phase velocity and slowness.
1.4 Energy balance and energy velocity. 1.5 Finely layered media. 1.6
Anomalous polarizations. 1.7 Analytical solutions for transversely
isotropic media. 1.8 Reflection and transmission of plane waves.
2. Viscoelasticity and wave propagation.
2.1 Energy densities and stress-strain relations. 2.2 Stress-strain
relation for 1-D viscoelastic media. 2.3 Wave propagation concepts for
1-D viscoelastic media. 2.4 Mechanical models and wave propagation. 2.5
Constant-Q model and wave equation. 2.6 Memory variable and equation of
motion.
3. Isotropic anelastic media.
3.1 Stress-strain relation. 3.2 Equations of motion and dispersion
relations. 3.3 Vector plane waves. 3.4 energy balance, energy velocity
and quality factor. 3.5 Boundary conditions and Snell's law. 3.6 The
correspondence principle. 3.7 Rayleigh waves. 3.8 Reflection and
transmission of cross-plane shear waves. 3.9 Memory variables and
equation of motion. 3.10 Analytical solutions. 3.11 The elastodynamic of
a non-ideal interface.
4. Anisotropic anelastic media.
4.1 Stress-strain relations. 4.2 Wave velocities, slowness and
attenuation vector. 4.3 Energy balance and fundamental relations. 4.4
The physics of wave propagation for viscoelastic SH waves. 4.5 Memory
variables and equation of motion in the time domain. 4.6 Analytical
solution for SH waves in monoclinic media.
5. The reciprocity principle.
5.1 Sources, receivers and reciprocity. 5.2 The reciprocity principle.
5.3 Reciprocity of particle velocity. Monopoles. 5.4 Reciprocity of
strain. 5.5 Reciprocity of stress.
6. Reflection and transmission of plane waves.
6.1 Reflection and transmission of SH waves. 6.2 Reflection and
transmission of qP-qSV waves. 6.3 Reflection and transmission at
fluid/solid interfaces. 6.4 Reflection and transmission coefficients of
a set of layers.
7. Biot's theory for porous media.
7.1 Isotropic media. Strain energy and stress-strain relations. 7.2 The
concept of effective stress. 7.3 Anisotropic media. Strain energy and
stress-strain relations. 7.4 Kinetic energy. 7.5 Dissipation potential.
7.6 Lagrange's equations and equation of motion. 7.7 Plane-wave
analysis. 7.8 Strain energy for inhomogeneous porosity. 7.9 Boundary
conditions. 7.10 Green's function for poro-viscoacoustic media. 7.11
Poro-viscoelasticity. 7.12 Anisotropic poro-viscoelasticity.
8. Numerical methods.
8.1 Equation of motion. 8.2 Time integration. 8.3 Calculation of spatial
derivatives. 8.4 Source implementation. 8.5 Boundary conditions. 8.6
Absorbing boundaries. 8.7 Model and modeling design - Seismic modeling.
8.8 Concluding remarks. 8.9 Appendix. Examinations. Chronology of main
discoveries. A list of scientists. Bibliography. Name index. Subject
index.
Auteur : CARCIONE
Editeur : PERGAMON PRESS
Nombre de pages : 414
Date de publication : 10 2001
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