Seismic Waves and Sources

30.06.1981

Englisch

9780387905068

Springer US

Nein

A. Ben-Menahem

1108

Gebundene Ausgabe

earthquake, wave equation, atmosphere, curvilinear coordinates, solution, reflection, seismology, differential equation, refraction, Helmholtz equation, linear differential equation, Deformation, Erdbeben, geometry

PHVG - Geophysik RBG - Geologie und die Lithosphäre PHU - Mathematische Physik

1 Classical Continuum Dynamics.- 1.1. The Stress Dyadic and Its Properties.- 1.2. Geometry of Small Deformations.- 1.3. Linear Elastic Solid.- 1.4. The Field Equations.- 1.5. Lagrangian Formulation.- 1.6. One-Dimensional Approximations.- 1.7. Two-Dimensional Approximations.- 1.8. Representation of Finite Strains.- 2 Waves in Infinite Media.- 2.1. Elementary Solutions of the Wave Equation.- 2.2. Separability of the Scalar Helmholtz Equation.- 2.3. Separability of the Vector Helmholtz Equation.- 2.4. Eigenvector Solutions of the Navier Equation.- 2.5. Plane Waves.- 2.6. Interrelations Among Plane, Cylindrical, and Spherical Waves.- 2.7. Dyadic Plane Waves.- 3 Seismic Plane Waves in a Layered Half-Space.- 3.1. Reflection and Refraction of Plane Waves- General Considerations.- 3.2. Reflection at a Free Surface.- 3.3. Reflection and Refraction at a Solid-Solid Interface.- 3.4. Reflection and Refraction at a Solid-Liquid Interface.- 3.5. Reflection and Refraction at a Liquid-Solid Interface.- 3.6. Surface Waves.- 3.7. Spectral Response of a Multilayered Crust.- 3.8. Generalization of the Matrix Method—the Matrix Propagator.- 3.9. The Inverse Surface-Wave Problem.- 4 Representation of Seismic Sources.- 4.1. A Concentrated Force in a Homogeneous Medium.- 4.2. Dipolar Point Sources.- 4.3. Relations of Betti, Somigliana, and Volterra.- 4.4. Fault-Plane Geometry.- 4.5. Dipolar Sources in a Homogeneous Medium.- 4.6. Stress Distributions on a Spherical Cavity and Their Equivalent Sources.- 4.7. Radiations from a Finite Moving Source.- 4.8. Radiation of Elastic Waves by Volume Sources.- 5 Surface-Wave Amplitude Theory.- 5.1. Surface-Wave Amplitudes in Simple Configurations.- 5.2. Generalization to a Vertically Inhomogeneous Half-space.- 5.3. Surface Waves from a Finite Moving Source.- 6 Normal-Mode Solution for Spherical Earth Models.- 6.1. Introduction.- 6.2. Oscillations of a Homogeneous Sphere.- 6.3. Oscillations of a Radially Inhomogeneous Self-Gravitating Earth Model.- 6.4. Effect of the Rotation of the Earth.- 6.5. Energy Integrals.- 6.6. Source Effects.- 6.7. Numerical Procedures.- 7 Geometric Elastodynamics: Rays and Generalized Rays.- 7.1. Asymptotic Body Wave Theory.- 7.2. Ray-Amplitude Theory.- 7.3. Ray Theory in Vertically Inhomogeneous Media.- 7.4. Asymptotic-Wave Theory in Vertically Inhomogeneous Media.- 7.5. Breakdown of the GEA: Caustics.- 7.6. Theoretical Seismograms.- 7.7. Spectral Asymptotic Approximations.- 7.8. Initial Motions.- 7.9. Normal-Mode versus Ray Solutions for Vertically Inhomogeneous Media.- 8 Asymptotic Theory of the Earth’s Normal Modes.- 8.1. Jeans’ Formula.- 8.2. Watson’s Transformation of the Spectral Field.- 8.3. Surface Waves on a Sphere.- 8.4. Mode-Ray Duality.- 8.5. Ray Analysis in a Homogeneous Sphere.- 8.6. SH-Fild Analysis in a Uniform Shell Overlying a Fluid Core.- 8.7. Generalized Rays in Spherical-Earth Models.- 9 Atmospheric and Water Waves and Companion Seismic Phenomena.- 9.1. The Navier-Stokes Equation.- 9.2. Sound Waves.- 9.3. Gravity Waves in Liquids.- 9.4. Acoustic-Gravity Waves in the Atmosphere.- 9.5. Waves Generated by Atmospheric Explosions.- 9.6. Coupled Air-Sea Waves.- 9.7. Rayleigh Waves from Atmospheric Explosions.- 10 Seismic Wave Motion in Anelastic Media.- 10.1. The Specific Dissipation Parameter.- 10.2. Linear Viscoelastic Solid.- 10.3. Pulse Propagation in Unbounded Anelastic Media.- 10.4. Attenuation of Seismic Waves in the Earth.- Appendices.- A. Algebra and Calculus of Dyadics.- B. Orthogonal Curvilinear Coordinates.- C. The Material Derivative.- D. Bessel and Legendre Functions.- E. Asymptotic Evaluation of Special Integrals.- F. Generalized Functions.- G. The Airy Integral.- H. Asymptotic Solutions of Second-Order Linear Differential Equations.- I. Generalized Spherical Harmonics.- J. Transformation of Wave Functions under Translation and Rotation of the Coordinate Axes.- K. The Mathematics of Causality.- L. Models of the Earth and the Atmosphere.- List of Symbols.- Author Index.

0 mm