Keiiti Aki (Author) Until his death in 2005, Keiiti Aki resided on Réunion Island in the Indian Ocean. His distinguished career included faculty appointments for many years at the Massachusetts Institute of Technology and the University of Southern California.Paul Richards (Author) Paul Richards has taught and conducted research for many years at Columbia University's Lamont-Doherty Earth Observatory, where his work has turned to methods of monitoring earthquakes and underground nuclear explosions. His current research is focused on improving the accuracy with which earthquakes and explosions are routinely located around the world.

• 1. IntroductionSuggestions for Further Reading2. Basic Theorems in Dynamic Elasticity2.1 Formulation2.2 Stress-Strain Relations and the Strain-Energy Function2.3 Theorems of Uniqueness and Reciprocity2.4 Introducing Green's Function for Elastodynamics2.5 Representation Theorems2.6 Strain-Displacement Relations and Displacement-Stress Relations in General Orthogonal Curvilinear CoordinatesSuggestions for Further ReadingProblems3. Representation of Seismic Sources3.1 Representation Theorems for an Internal Surface: Body-Force Equivalents for Discontinuities in Traction and Displacement3.2 A Simple Example of Slip on a Buried Fault3.3 General Analysis of Displacement Discontinuities across an Internal Surface E3.4 Volume Sources: Outline of the Theory and Some Simple ExamplesSuggestions for Further ReadingProblems4. Elastic Waves from a Point Dislocation Source4.1 Formulation: Introduction of Potentials4.2 Solution for the Elastodynamic Green Function in a Homogeneous, Isotropic Unbounded Medium4.3 The Double-Couple Solution in an Infinite Homogeneous Medium4.4 Ray Theory for Far-Field P-waves and S-waves from a Point Source4.5 The Radiation Pattern of Body Waves in the Far Field for a Point Shear Dislocation of Arbitrary Orientation in a Spherically Symmetric MediumSuggestions for Further ReadingProblems5. Plane Waves in Homogeneous Media and Their Reflection and Transmission at a Plane Boundary5.1 Basic Properties of Plane Waves in Elastic Media5.2 Elementary Formulas for Reflection/Conversion/Transmission Coefficients5.3 Inhomogeneous Waves, Phase Shifts, and Interface Waves5.4 A Matrix Method for Analyzing Plane Waves in Homogeneous Media5.5 Wave Propagation in an Attenuating Medium: Basic Theory for Plane Waves5.6 Wave Propagation in an Elastic Anisotropic Medium: Basic Theory for Plane WavesSuggestions for Further ReadingProblems6. Reflection and Refraction of Spherical Waves; Lamb's Problem6.1 Spherical Waves as a Superposition of Plane Waves and Conical Waves6.2 Reflection of Spherical Waves at a Plane Boundary: Acoustic Waves6.3 Spherical Waves in an Elastic Half-Space: The Rayleigh Pole6.4 Cagniard-De Hoop Methods for Line Sources6.5 Cagniard-De Hoop Methods for Point Sources6.6 Summary of Main Results and Comparison between Different MethodsSuggestions for Further ReadingProblems7. Surface Waves in a Vertically Heterogeneous Medium7.1 Basic Properties of Surface Waves7.2 Eigenvalue Problem for the Displacement-Stress Vector7.3 Variational Principle for Love and Rayleigh Waves7.4 Surface-Wave Terms of Green's Function for a Vertically Heterogeneous Medium7.5 Love and Rayleigh Waves from a Point Source with Arbitrary Seismic Moment7.6 Leaky ModesSuggestions for Further ReadingProblems8. Free Oscillations of the Earth8.1 Free Oscillations of a Homogeneous Liquid Sphere8.2 Excitation of Free Oscillations by a Point Source8.3 Surface Waves on the Spherical Earth8.4 Free Oscillations of a Self-Gravitating Earth8.5 The Centroid Moment Tensor8.6 Splitting of Normal Modes Due to the Earth's Rotation8.7 Spectral Splitting of Free Oscillations Due to Lateral Inhomogeneity of the Earth's StructureSuggestions for Further ReadingProblems9. Body Waves in Media with Depth-Dependent Properties9.1 Cagniard's Method for a Medium with Many Plane Layers: Analysis of a Generalized Ray9.2 The Reflectivity Method for a Medium with Many Plane Layers9.3 Classical Ray Theory in Seismology9.4 Inversion of Travel-Time Data to Infer Earth Structure9.5 Wave Propagation in Media Having Smoothly Varying Depth-Dependent Velocity Profiles within Which Turning Points Are Present9.6 Body-Wave Problems for Spherically Symmetric Earth Models in Which Discontinuities are Present between In homogeneous Layers9.7 Comparison between Different MethodsSuggestions for Further ReadingProblems10. The Seismic Source: Kinematics10.1 Kinematics of an Earthquake as Seen at Far Field10.2 Kinematics of an Earthquake as Seen at Near FieldSuggestions for Further ReadingProblems11. The Seismic Source: Dynamics11.1 Dynamics of a Crack Propagating with Prescribed Velocity11.2 Dynamics of Spontaneous Planar Rupture PropagationSuggestions for Further ReadingProblems12. Principles of Seismometry12.1 Basic Instrumentation12.2 Frequency and Dynamic Range of Seismic Signals and Noise12.3 Detection of SignalSuggestions for Further ReadingProblemsAppendix 1: Glossary of WavesAppendix 2: Definition of MagnitudesIndex

"An excellent study and reference book for seismologists well-grounded in the methods of mathematical physics. This updated version of Aki and Richard’s classical geophysical text deserves a place in every serious geophysicist’s library." --The Leading Edge "The continued popularity of this text is testament to the meticulous detail with which important mathematical formulas are derived; there simply is nothing of any importance that is glossed over or omitted." --Pure and Applied Geophysics, 2005 (162)