Wave Fields in Real Media

Wave Fields in Real Media, 3rd Edition

Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media

Wave Fields in Real Media, 3rd Edition,J. Carcione,ISBN9780080999999


Elsevier Science




229 X 152

A fully revised and updated edition of this essential reference, covering geophysical applications for seismic exploration

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Key Features

  • Examines the fundamentals of wave propagation in anisotropic, anelastic and porous media
  • Presents all equations and concepts necessary to understand the physics of wave propagation, with examples
  • Emphasizes geophysics, particularly, seismic exploration for hydrocarbon reservoirs, which is essential for exploration and production of oil


Authored by the internationally renowned José M. Carcione, Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media examines the differences between an ideal and a real description of wave propagation, starting with the introduction of relevant stress-strain relations. The combination of this relation and the equations of momentum conservation lead to 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.

This 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.

New to this edition:
This new edition presents the fundamentals of wave propagation in Anisotropic, Anelastic, Porous Media while also incorporating the latest research from the past 7 years, including that of the author. The author presents all the equations and concepts necessary to understand the physics of wave propagation. These equations form the basis for modeling and inversion of seismic and electromagnetic data. Additionally, demonstrations are given, so the book can be used to teach post-graduate courses. Addition of new and revised content is approximately 30%.


Researchers in earthquake seismology, rock acoustics and materials science; oil and mining companies dealing with hydrogeology and wave propagation.

J. Carcione

José M. Carcione was born in Buenos Aires, Argentina. He received the degree "Licenciado in Ciencias Físicas" from Buenos Aires University in 1978, the degree "Dottore in Fisica" from Milan University in 1984 and the PhD in Geophysics from Tel-Aviv University in 1987. This year he was awarded the Alexander von Humboldt scholarship for a position at the Geophysical Institute of Hamburg University, where he stayed from 1987 to 1989. From 1978 to 1980 he worked at the "Comisión Nacional de Energía Atómica" at Buenos Aires. From 1981 to 1987 he was a research geophysicist at "Yacimientos Petrolíferos Fiscales", the national oil company of Argentina. Presently, he is a senior geophysicist at the "Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS)" (former "Osservatorio Geofisico Sperimentale") in Trieste. He is the author of the books “Wave fields in real media: Theory and numerical simulation of wave propagation in anisotropic, anelastic, porous and electromagnetic media” (Pergamon Press, 2001; Elsevier Science, 2007, 2015) and "Seismic exploration of hydrocarbons in heterogeneous reservoirs: New theories, methods and applications" (Elsevier Science, 2015), and has published more than 240 peer-reviewed articles. Carcione has been a member of the commission (GEV04) for evaluation of Italian research in the field of Earth Sciences (ANVUR) in the period 2004-2010. Ranked among the top 100 Italian scientists: http://www.topitalianscientists.org/Top_italian_scientists_VIA-Academy.aspx Private webpage: http://www.lucabaradello.it/carcione/ His current research deals with numerical modeling, the theory of wave propagation in acoustic and electromagnetic media, and their application to geophysics.

Affiliations and Expertise

Istituto Nazionale di Oceangrafia e di Geofisica Sperimentale (OGS), Trieste, Italy

Wave Fields in Real Media, 3rd Edition

  • Dedication
  • Preface
  • About the Author
  • Basic Notation
  • Glossary of Main Symbols
  • Chapter 1: Anisotropic Elastic Media
    • Abstract
    • 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 The best isotropic approximation
    • 1.8 Analytical solutions
    • 1.9 Reflection and transmission of plane waves
  • Chapter 2: Viscoelasticity and Wave Propagation
    • Abstract
    • 2.1 Energy densities and stress–strain relations
    • 2.2 Stress–strain relation for 1D viscoelastic media
    • 2.3 Wave propagation in 1D viscoelastic media
    • 2.4 Mechanical models and wave propagation
    • 2.5 Constant-Q Model and wave equation
    • 2.6 Equivalence between source and initial conditions
    • 2.7 Hysteresis cycles and fatigue
    • 2.8 Distributed-order fractional time derivatives
    • 2.9 The concept of centrovelocity
    • 2.10 Memory variables and equation of motion
  • Chapter 3: Isotropic Anelastic Media
    • Abstract
    • 3.1 Stress–strain relation
    • 3.2 Equations of motion and dispersion relations
    • 3.3 Vector plane waves
    • 3.4 Energy balance, velocity and quality factor
    • 3.5 Boundary conditions and snell law
    • 3.6 The correspondence principle
    • 3.7 Rayleigh waves
    • 3.8 Reflection and transmission of SH waves
    • 3.9 Memory variables and equation of motion
    • 3.10 Analytical solutions
    • 3.11 Constant-Q P- and S-waves
    • 3.12 Wave equations based on the burgers model
    • 3.13 The elastodynamic of a non-ideal interface
  • Chapter 4: Anisotropic Anelastic Media
    • Abstract
    • 4.1 Stress–strain relations
    • 4.2 Fracture-induced anisotropic attenuation
    • 4.3 Stiffness tensor from oscillatory experiments
    • 4.4 Wave velocities, slowness and attenuation vector
    • 4.5 Energy balance and fundamental relations
    • 4.6 Propagation of SH waves
    • 4.7 Wave propagation in symmetry planes
    • 4.8 Memory variables and equation of motion
    • 4.9 Analytical solution for SH waves
  • Chapter 5: The Reciprocity Principle
    • Abstract
    • 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
    • 5.6 Reciprocity principle for flexural waves
  • Chapter 6: Reflection and Transmission of Plane Waves
    • Abstract
    • 6.1 Reflection and transmission of SH waves
    • 6.2 Reflection and transmission of qp–qSV waves
    • 6.3 Interfaces separating a solid and a fluid
    • 6.4 Scattering coefficients of a set of layers
  • Chapter 7: Biot Theory for Porous Media
    • Abstract
    • 7.1 Isotropic media – stress–strain relations
    • 7.2 The concept of effective stress
    • 7.3 Pore-pressure buildup in source rocks
    • 7.4 The asperity-deformation model
    • 7.5 Anisotropic media – stress–strain relations
    • 7.6 Kinetic energy
    • 7.7 Dissipation potential
    • 7.8 Lagrange equations and equation of motion
    • 7.9 Plane-wave analysis
    • 7.10 Strain energy for inhomogeneous porosity
  • Chapter 8: The Acoustic-Electromagnetic Analogy
    • Abstract
    • 8.1 Maxwell equations
    • 8.2 The acoustic–electro magnetic analogy
    • 8.3 A Viscoelastic form of the electromagnetic energy
    • 8.4 The analogy for reflection and transmission
    • 8.5 The single-layer problem
    • 8.6 3D Electromagnetic theory and the analogy
    • 8.7 Plane-wave theory
    • 8.8 Electromagnetic diffusion in anisotropic media
    • 8.9 Analytical solution for anisotropic media
    • 8.10 Elastic medium with fresnel wave surface
    • 8.11 Finely layered media
    • 8.12 The time-average and crim equations
    • 8.13 The kramers–kronig dispersion relations
    • 8.14 The reciprocity principle
    • 8.15 Babinet principle
    • 8.16 Alford rotation
    • 8.17 Cross-property relations
    • 8.18 Poro-acoustic and electromagnetic diffusion
    • 8.19 Electro-seismic wave theory
  • Chapter 9: Numerical Methods
    • Abstract
    • 9.1 Equation of Motion
    • 9.2 Time Integration
    • 9.3 Calculation of Spatial Derivatives
    • 9.4 Source Implementation
    • 9.5 Boundary Conditions
    • 9.6 Absorbing Boundaries
    • 9.7 Model and Modelling Design. Seismic Modelling
    • 9.8 Concluding Remarks
    • 9.9 Appendix
  • Examinations
  • Chronology of Main Discoveries
  • Leonardo’s Manuscripts
  • A List of Scientists
  • Bibliography
  • Name Index
  • Subject Index
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