Elastic Waves in the Earth

Elastic Waves in the Earth

1st Edition - January 1, 1979

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  • Author: Walter L. Pilant
  • eBook ISBN: 9780444601940

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Elastic Waves in the Earth provides information on the relationship between seismology and geophysics and their general aspects. The book offers elastodynamic equations and derivative equations that can be used in the propagation of elastic waves. It also covers major topics in detail, such as the fundamentals of elastodynamics; the Lamb's problem, which includes the Cagniard-de Hoop theory; rays and modes in a radially inhomogeneous earth and in multilayered media, which includes the Thomson-Haskell theory; the elastic wave dissipation; the seismic source and noise; and the seismographs. The book consists of 33 chapters. The first 16 chapters include basic material related to the propagation of elastic waves. Topics covered by these chapters include scalars, vectors, and tensors in cartesian coordinates, stress and strain analysis, equations of elasticity and motion, plane waves, Rayleigh waves, plane-wave theory, and fluid-fluid and solid-solid interfaces. The second half of the book covers various ray and mode theories, elastic wave dissipation, and the observations and theories of seismic source and seismic noise. It concludes by discussing earthquake seismology and different seismographs, like the pendulum seismometer and the strain seismometer.

Table of Contents

  • Chapter 1. Scalars, Vectors, and Tensors in Cartesian Coordinates

    1.1. General

    1.2. Transformation of Coordinates

    1.3. Scalars

    1.4. Vectors

    1.5. Tensors

    1.6. Symmetry Operations on a Tensor of Rank

    Chapter 2. The Analysis of Strain

    2.1. The Deformation of an Elastic Body and the Strain Components

    2.2. The Geometrical Interpretation of the Components wij

    2.3. The Geometrical Interpretation of the Components eij

    2.4. The Strain Quadric of Cauchy

    2.5. Principal Strains

    2.6. Strain Components in Curvilinear Coordinates

    Chapter 3. The Analysis of Stress

    3.1. The Stress Vector and Stress Components

    3.2. Equations of Equilibrium

    3.3. The Stress Quadric, Principal Stresses, and Stress Invariants

    Chapter 4. The Equations of Elasticity

    4.1. Work and the Strain Energy Function

    4.2. Hooke's Law for a Homogeneous Isotropic Medium

    4.3. Three Simple Experiments

    4.4. Strain as a Function of Stress

    Chapter 5. Equations of Motion

    5.1. General

    5.2. Homogeneous, Anisotropic Media

    5.3. Isotropic, Inhomogeneous Media

    5.4. Isotropic, Homogeneous Media

    5.5. Other Types of Media

    Chapter 6. General Solutions of the Isotropic, Homogeneous Medium Equations of Motion

    6.1. Reduction by Wave Potentials

    6.2. Solutions of the Scalar Wave Equation — P-Waves

    6.3. Solutions of the Vector Wave Equation — S-Waves

    6.4. Independent Shear Wave Components — SH- and SV-Waves

    6.5. The Fundamental Elastic Velocities and Their Measurement

    Chapter 7. Source Functions in Infinite Media

    7.1. General

    7.2. One Dimension

    7.3. Two-Dimensional Point Sources

    7.4. Three-DimensionaI Point Sources

    Chapter 8. Boundary Conditions, Uniqueness, Reciprocity, and a Representation Theorem

    8.1. Boundary Conditions

    8.2. Type Boundary Value Problems

    8.3. Uniqueness

    8.4. Reciprocity

    8.5. A Representation Theorem

    Chapter 9. Plane Waves Incident upon a Plane Free Surface

    9.1. Plane-Wave Solutions of the Scalar Wave Equation

    9.2. P-Waves Incident Upon a Free Surface

    9.3. SV-Waves Incident Upon a Free Surface

    9.4. SH-Waves Incident Upon a Free Surface

    9.5. Phase Shifts, Allied Function, and Hilbert Transforms

    9.6. Particle Motion at the Free Surface

    Chapter 10. Rayleigh Waves - Free Surface Phenomena

    10.1. Straight-Crested or Inhornogeneous Waves

    10.2. RayIeigh-Waves

    10.3. RayIeigh-Waves in Cylindrical Coordinates

    10.4. Other Considerations

    Chapter 11. Lamb's Problem

    11.1. Genera I

    11.2. Motion Due to a Surface Vertical Force

    11.3. A Surface Horizontal Force

    11.4. Pseudo-Waves

    11.5. Other Considerations

    Chapter 12. Reflection and Transmission of Body-Waves at a Plane Interface

    12.1. P-Waves Incident Upon an Interface Between Two Elastic Media

    12.2. SV-Waves Incident Upon an Interface Between Two Elastic Media

    12.3. SH-Waves Incident Upon an Interface Between Two Elastic Media

    12.4. Reflection and Transmission From a Generalized Interface

    Chapter 13. Generalized Plane-Wave Theory and Head-Waves

    13.1. A Point Source Near a Fluid-Fluid Interface

    13.2. Plane-Wave Theory

    13.3. Head-Waves

    13.4. Applications to Seismology

    Chapter 14. Waves Along a Solid-Solid Interface

    14.1. Real Interface Waves (Stoneley Waves)

    14.2. Generalized Interface Waves

    14.3. The Impulsive Solution

    Chapter 15. One Layer Over A Half-Space - Ray Theory

    15.1. General

    15.2. Travel-Time Curves for Reflected Rays

    15.3. Travel-Time Curves for Refracted Rays

    Chapter 16. One Layer Over a Half-Space - Mode Theory

    16.1. General

    16.2. Love Modes (SH)

    16.3. Rayleigh Modes (P-SV)

    16.4. Impulsive Response of the Surface-Wave Modes Phase and Group Velocity

    16.5. Orthogonality of Modes in Two Dimensions

    16.6. Some Relations Between Modes and Rays

    Chapter 17. Many Layers Over a Half-Space - Ray Theory

    17.1. Travel-Time Curves for Reflected Rays

    17.2. Travel-Time Curves for Refracted Rays

    17.3. Rays Incident Upon a Plane-Layered Structure From Below

    Chapter 18. Many Layers Over a Half-Space - Body-Wave Observations

    18.1. General

    18.2. Reflection Seismology

    18.3. Refraction Seismology

    18.4. Time-Term Analysis

    18.5. Crustal Transfer Functions

    18.6. Advanced Inversion Techniques

    Chapter 19. Many Layers Over a Half-Space - Mode Theory

    19.1. Rayleigh-Waves From Surficial Stress Distributions

    19.2. The Rayleigh-Wave Problem for Sources at Depth

    19.3. Love-Waves from Surficial Stress Distributions

    19.4. Surface-Waves When Liquid Layers Are Present

    19.5. Other Considerations

    Chapter 20. Many Layers Over a Half-Space - Surface-Wave Observations

    20.1. General

    20.2. The Determination of Phase and Group Velocity

    20.3. Observations

    20.4. Interpretation

    20.5. Models

    Chapter 21. Asymptotic Ray Theory

    21.1. Some Properties of the Scalar Wave Equation in Inhomogeneous Media

    21.2. Fermat's Principle

    21.3. Rays in a Vertically Inhomogeneous Medium

    21.4. Rays in a Medium With Uniform Gradients

    21.5. Inversion for a Vertically Inhomogeneous Medium

    21.6. Other Considerations

    Chapter 22. A Radially Inhomogeneous Earth - Ray Theory

    22.1. General

    22.2. Rays in a Radially Inhomogeneous Earth

    22.3. Inversion for a Radially Inhomogeneous Earth

    22.4. Diffraction by the Core of the Earth

    Chapter 23. A Radially Inhomogeneous Earth - Body-Wave Observations

    23.1. Seismic Phases and Travel-Time Curves

    23.2. The Construction of Travel-Time Curves

    23.3. The Location of the Source Region

    23.4. Observations

    23.5. Advanced Inversion Techniques

    Chapter 24. A Radially Inhomogeneous Earth - Mode Theory

    24.1. General

    24.2. The Nature of Spherical Wave Motion

    24.3. Surface-Waves on a Spherical Earth

    24.4. Modes and Rays in a Sphere

    Chapter 25. A Radially Inhomogeneous Earth - Free Oscillations and Mantle Waves

    25.1. The Periods of Free Oscillation

    25.2. Mantle Waves

    25.3. Inversion

    25.4. Realistic Earth Models

    Chapter 26. Elastic Wave Dissipation - Theory

    26.1. The Constant "Q" Model

    26.2. An Almost Constant Q Model

    26.3. Mechanisms of Attenuation

    26.4. The Dissipation of Surface-Waves, Rod and Plate Waves

    Chapter 27. Elastic Wave Dissipation - Observations

    27.1. General

    27.2. Attenuation of Body-Waves

    27.3. Attenuation of Surface-Waves and Free Oscillations

    27.4. Inversion

    Chapter 28. The Seismic Source - Theory

    28.1. General

    28.2. Point Sources

    28.3. Extended Sources

    28.4. Applications

    28.5. Models of Fracture

    Chapter 29. The Seismic Source - Observations

    29.1. General

    29.2. Spatial Parameters at the Source

    29.3. Moment, Magnitude and Energy Release

    29.4. Nuclear Detection and Identification

    Chapter 30. Seismicity

    30.1. Global Extent

    30.2. Variation with Depth

    30.3. Variation with Time

    30.4. Microearthquakes

    30.5. Aftershocks and Foreshocks

    30.6. The Problem of Prediction

    Chapter 31. Seismic Noise - Theory

    31.1. Wave-Generated Microseisms

    31.2. Some Properties of Random Signals

    Chapter 32. Seismic Noise -Observations

    32.1. The Level of Seismic Noise

    32.2. The Nature of Seismic Noise

    32.3. The Elimination of Seismic Noise

    Chapter 33. Seismographs and Earthquake Seismology

    33.1. General

    33.2. The Pendulum Seismometer

    33.3. Pendulum Seismometer with Moving Coil Sensing and Galvanometric Recording

    33.4. The Strain Seismometer

    33.5. Special Installations, Seismic Networks, and Seismic Arrays

    Appendix A. Papers Relating to Anisotropic Media

    Appendix B. Papers Relating to Inhomogeneous Media

    Appendix C. Papers Relating to the Scattering of Elastic Waves

    Appendix D. Additional Reference Sources



Product details

  • No. of pages: 506
  • Language: English
  • Copyright: © Elsevier 1979
  • Published: January 1, 1979
  • Imprint: Elsevier
  • eBook ISBN: 9780444601940

About the Author

Walter L. Pilant

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