Quantitative Seismology
2nd Edition

Keiiti Aki
Observatoire Volcanologique du Piton de la Fournaise

Paul G. Richards
Lamont-Doherty Earth Observatory


Table of Contents

1. Introduction
   
Suggestions for Further Reading

2. Basic Theorems in Dynamic Elasticity
   
2.1 Formulation
    2.2 Stress-Strain Relations and the Strain-Energy Function
   
2.3 Theorems of Uniqueness and Reciprocity
    2.4 Introducing Green's Function for Elastodynamics
    2.5 Representation Theorems
    2.6 Strain-Displacement Relations and Displacement-Stress Relations in General   Orthogonal Curvilinear Coordinates
    Suggestions for Further Reading
    Problems

3. Representation of Seismic Sources

    3.1 Representation Theorems for an Internal Surface: Body-Force Equivalents for Discontinuities in Traction and Displacement
    3.2 A Simple Example of Slip on a Buried Fault
    3.3 General Analysis of Displacement Discontinuities across an Internal Surface E
    3.4 Volume Sources: Outline of the Theory and Some Simple Examples
    Suggestions for Further Reading
    Problems

4. Elastic Waves from a Point Dislocation Source
    4.1 Formulation: Introduction of Potentials
    4.2 Solution for the Elastodynamic Green Function in a Homogeneous, Isotropic Unbounded Medium
    4.3 The Double-Couple Solution in an Infinite Homogeneous Medium
    4.4 Ray Theory for Far-Field P-waves and S-waves from a Point Source
    4.5 The Radiation Pattern of Body Waves in the Far Field for a Point Shear Dislocation of Arbitrary Orientation in a Spherically Symmetric Medium
   
Suggestions for Further Reading
    Problems

5. Plane Waves in Homogeneous Media and Their Reflection and Transmission at a Plane Boundary
    5.1 Basic Properties of Plane Waves in Elastic Media
    5.2 Elementary Formulas for Reflection/Conversion/Transmission Coefficients
    5.3 Inhomogeneous Waves, Phase Shifts, and Interface Waves
    5.4 A Matrix Method for Analyzing Plane Waves in Homogeneous Media
    5.5 Wave Propagation in an Attenuating Medium: Basic Theory for Plane Waves
    5.6 Wave Propagation in an Elastic Anisotropic Medium: Basic Theory for Plane Waves
    Suggestions for Further Reading
    Problems

6. Reflection and Refraction of Spherical Waves; Lamb's Problem
    6.1 Spherical Waves as a Superposition of Plane Waves and Conical Waves
    6.2 Reflection of Spherical Waves at a Plane Boundary: Acoustic Waves
    6.3 Spherical Waves in an Elastic Half-Space: The Rayleigh Pole
    6.4 Cagniard-De Hoop Methods for Line Sources
    6.5 Cagniard-De Hoop Methods for Point Sources
    6.6 Summary of Main Results and Comparison between Different Methods
    Suggestions for Further Reading
    Problems

7. Surface Waves in a Vertically Heterogeneous Medium
    7.1 Basic Properties of Surface Waves
    7.2 Eigenvalue Problem for the Displacement-Stress Vector
    7.3 Variational Principle for Love and Rayleigh Waves
    7.4 Surface-Wave Terms of Green's Function for a Vertically Heterogeneous Medium
    7.5 Love and Rayleigh Waves from a Point Source with Arbitrary Seismic Moment
    7.6 Leaky Modes
    Suggestions for Further Reading
    Problems

8. Free Oscillations of the Earth
    8.1 Free Oscillations of a Homogeneous Liquid Sphere
    8.2 Excitation of Free Oscillations by a Point Source
    8.3 Surface Waves on the Spherical Earth
   
8.4 Free Oscillations of a Self-Gravitating Earth
    8.5 The Centroid Moment Tensor
    8.6 Splitting of Normal Modes Due to the Earth's Rotation
    8.7 Spectral Splitting of Free Oscillations Due to Lateral Inhomogeneity of the Earth's Structure
    Suggestions for Further Reading
    Problems

9. Body Waves in Media with Depth-Dependent Properties
    9.1 Cagniard's Method for a Medium with Many Plane Layers: Analysis of a Generalized Ray
    9.2 The Reflectivity Method for a Medium with Many Plane Layers
   
9.3 Classical Ray Theory in Seismology
    9.4 Inversion of Travel-Time Data to Infer Earth Structure
    9.5 Wave Propagation in Media Having Smoothly Varying Depth-Dependent Velocity Profiles within Which Turning Points Are Present
    9.6 Body-Wave Problems for Spherically Symmetric Earth Models in Which Discontinuities are Present between In homogeneous Layers
    9.7 Comparison between Different Methods
    Suggestions for Further Reading
    Problems

10. The Seismic Source: Kinematics
    10.1 Kinematics of an Earthquake as Seen at Far Field
    10.2 Kinematics of an Earthquake as Seen at Near Field
    Suggestions for Further Reading
    Problems

11. The Seismic Source: Dynamics
    11.1 Dynamics of a Crack Propagating with Prescribed Velocity
   
11.2 Dynamics of Spontaneous Planar Rupture Propagation
    Suggestions for Further Reading
    Problems

12. Principles of Seismometry
    12.1 Basic Instrumentation
   
12.2 Frequency and Dynamic Range of Seismic Signals and Noise
    12.3 Detection of Signal
    Suggestions for Further Reading
    Problems

Appendix 1: Glossary of Waves
Appendix 2: Definition of Magnitudes
Index