# Quantitative Seismology, 2nd edition

## By Keiiti Aki and Paul Richards

**Paperback**

Sep 2002 , 700 pp

ISBN 9781891389634

**Price:**£76.99, $99.00

This new edition of the classic text by Aki and Richards has at last been updated throughout to systematically explain key concepts in seismology. Now in one volume, the book provides a unified treatment of seismological methods that will be of use to advanced students, seismologists, and scientists and engineers working in all areas of seismology.

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

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