Elastic Waves in the Earth

1st Edition - January 1, 1979
Author: Walter L. Pilant
Language: English
eBook ISBN:
9 7 8 - 0 - 4 4 4 - 6 0 1 9 4 - 0

Elastic Waves in the Earth provides information on the relationship between seismology and geophysics and their general aspects. The book offers elastodynamic equations and… Read more

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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.

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 RankChapter 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 CoordinatesChapter 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 InvariantsChapter 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 StressChapter 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 MediaChapter 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 MeasurementChapter 7. Source Functions in Infinite Media 7.1. General 7.2. One Dimension 7.3. Two-Dimensional Point Sources 7.4. Three-DimensionaI Point SourcesChapter 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 TheoremChapter 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 SurfaceChapter 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 ConsiderationsChapter 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 ConsiderationsChapter 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 InterfaceChapter 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 SeismologyChapter 14. Waves Along a Solid-Solid Interface 14.1. Real Interface Waves (Stoneley Waves) 14.2. Generalized Interface Waves 14.3. The Impulsive SolutionChapter 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 RaysChapter 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 RaysChapter 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 BelowChapter 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 TechniquesChapter 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 ConsiderationsChapter 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. ModelsChapter 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 ConsiderationsChapter 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 EarthChapter 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 TechniquesChapter 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 SphereChapter 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 ModelsChapter 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 WavesChapter 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. InversionChapter 28. The Seismic Source - Theory 28.1. General 28.2. Point Sources 28.3. Extended Sources 28.4. Applications 28.5. Models of FractureChapter 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 IdentificationChapter 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 PredictionChapter 31. Seismic Noise - Theory 31.1. Wave-Generated Microseisms 31.2. Some Properties of Random SignalsChapter 32. Seismic Noise -Observations 32.1. The Level of Seismic Noise 32.2. The Nature of Seismic Noise 32.3. The Elimination of Seismic NoiseChapter 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 ArraysAppendix A. Papers Relating to Anisotropic MediaAppendix B. Papers Relating to Inhomogeneous MediaAppendix C. Papers Relating to the Scattering of Elastic WavesAppendix D. Additional Reference SourcesBibliographyIndex