Elastic Waves in the Earth - 1st Edition - ISBN: 9780444417985, 9780444601940

Elastic Waves in the Earth

1st Edition

Authors: Walter L. Pilant
eBook ISBN: 9780444601940
Imprint: Elsevier
Published Date: 1st January 1979
Page Count: 506
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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




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About the Author

Walter L. Pilant

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