Wave Fields in Real Media book cover

Wave Fields in Real Media

Wave propagation in anisotropic, anelastic and porous 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.

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Published: October 2001

Imprint: Pergamon

ISBN: 978-0-08-043929-7

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.

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