Theoretical Global Seismology

by Dahlen, F. A.; Tromp, Jeroen

• ISBN13: 9780691001166
• ISBN10: 0691001162
• Format: Hardcover
• Copyright: 1998-11-01
• Publisher: Princeton Univ Pr

Summary

After every major earthquake, the Earth rings like a bell for several days. These free oscillations of the Earth and the related propagating body and surface waves are routinely detected at broad-band seismographic stations around the world. In this book, F. A. Dahlen and Jeroen Tromp present an advanced theoretical treatment of global seismology, describing the normal-mode, body-wave, and surface-wave methods employed in the determination of the Earth's three-dimensional internal structure and the source mechanisms of earthquakes. The authors provide a survey of both the history of global seismological research and the major theoretical and observational advances made in the past decade. The book is divided into three parts. In the first, "Foundations," Dahlen and Tromp give an extensive introduction to continuum mechanics and discuss the representation of seismic sources and the free oscillations of a completely general Earth model. The resulting theory should provide the basis for future scientific discussions of the elastic-gravitational deformation of the Earth. The second part, "The Spherical Earth," is devoted to the free oscillations of a spherically symmetric Earth. In the third part, "The Aspherical Earth," the authors discuss methods of dealing with the Earth's three-dimensional heterogeneity. The book is concerned primarily with the forward problem of global seismology--detailing how synthetic seismograms and spectra may be calculated and interpreted. As a long-needed unification of theories in global seismology, the book will be important to graduate students and to professional seismologists, geodynamicists, and geomagnetists, as well as to astronomers who study the free oscillations of the Sun and other stars.

Table of Contents

Preface	xi
Historical Introduction	3	(22)
Early Theoretical Studies	3	(6)
Dawn of the Observational Era	9	(2)
Spherical Earth Model Refinement	11	(4)
Source-Mechanism Determination	15	(2)
Surface Waves	17	(3)
Lateral Heterogeneity	20	(5)
Part I Foundations
Continuum Mechanics	25	(31)
Eulerian and Lagrangian Variables	26	(1)
Measures of Deformation	27	(5)
Volume and Area Changes	32	(1)
Reynolds Transport Theorem	33	(1)
Measures of Stress	34	(3)
Eulerian Conservation Laws	37	(7)
Lagrangian Conservation Laws	44	(4)
Gravitational Potential Theory	48	(3)
Gravitational Potential Energy	51	(2)
Elastic Constitutive Relation	53	(3)
Equations of Motion	56	(53)
Equilibrium Earth Model	56	(3)
Linear Perturbations	59	(5)
Linearized Conservation Laws	64	(3)
Linearized Boundary Conditions	67	(6)
Linearized Potential Theory	73	(2)
Linearized Elastic Constitutive Relation	75	(10)
Hamilton's Principle	85	(5)
Conservation of Energy	90	(2)
Energy Budget	92	(6)
First-Principles Variational Analysis	98	(2)
Hydrostatic Earth Model	100	(9)
Normal Modes	109	(37)
Non-Rotating Earth Model	110	(13)
Rotating Earth Model	123	(15)
Hydrostatic Earth Model	138	(5)
Response of an Idealized Seismometer	143	(3)
Seismic Source Representation	146	(47)
Stress Glut	147	(4)
Earthquake Fault Source	151	(9)
Burridge-Knopoff Method	160	(5)
Point-Source Approximation	165	(18)
Earthquake Energy Balance	183	(10)
Anelasticity and Attenuation	193	(44)
Linear Isotropic Anelasticity	194	(24)
Non-Rotating Anelastic Earth	218	(7)
Rotating Anelastic Earth	225	(8)
Hydrostatic Anelastic Earth	233	(1)
Response to a Moment-Tensor Source	233	(4)
Rayleigh-Ritz Method	237	(20)
Non-Rotating Elastic Earth	238	(4)
Rotating Elastic Earth	242	(4)
Non-Rotating Anelastic Earth	246	(2)
Rotating Anelastic Earth	248	(2)
Hydrostatic Earth	250	(1)
Effect of a Small Perturbation	250	(2)
Response to a Moment-Tensor Source	252	(5)
Part II The Spherical Earth
Spheroidal and Toroidal Oscillations	257	(70)
Change in Notation	257	(2)
SNREI Earth Model	259	(4)
Equations of Motion	263	(2)
Rayleigh's Principle	265	(1)
Energy Budget and Stability	266	(2)
Radial Scalar Equations	268	(12)
Toroidal Oscillations	280	(9)
Spheroidal Oscillations	289	(31)
Transversely Isotropic Earth Model	320	(7)
Elastic and Anelastic Perturbations	327	(36)
Spherical Perturbation	327	(1)
Application of Rayleigh's Principle	328	(2)
SNREI-to-SNREI Perturbation	330	(5)
Transversely Isotropic Perturbation	335	(1)
An Alternative Derivation	336	(1)
Rogues' Gallery of Frechet Kernels	337	(10)
Anelasticity and Attenuation	347	(4)
Q Kernels, Measurements and Models	351	(7)
Exact Anelasticity	358	(5)
Synthetic Seismograms	363	(42)
Source-Receiver Geometry	363	(3)
Green Tensor	366	(2)
Moment-Tensor Response	368	(6)
Seismometer Response	374	(2)
Wiggly Lines---At Last!	376	(20)
Stacking and Stripping	396	(6)
Alternatives to Mode Summation	402	(3)
Love and Rayleigh Waves	405	(46)
Watson Transformation	406	(1)
Travelling-Wave Decomposition	407	(3)
Surface-Wave Green Tensor	410	(4)
Moment-Tensor Response	414	(4)
Stationary-Phase Approximation	418	(4)
Dispersion Relation and Group Speed	422	(9)
Surface-Wave Seismograms	431	(15)
Surface-Wave Perturbation Theory	446	(5)
Mode-Ray Duality	451	(86)
Ray Theory Primer	452	(13)
Constructive-Interference Principle	465	(17)
Formal Asymptotic Analysis	482	(22)
Asymptotic Miscellany	504	(9)
Body-Wave Response	513	(24)
Part III The Aspherical Earth
Perturbation Theory	537	(59)
Isolated Mode	537	(23)
Degeneracy and Quasi-Degeneracy	560	(17)
Singlet-Sum Synthetic Seismograms	577	(19)
Mode Splitting and Coupling	596	(73)
Hydrostatic Ellipticity	597	(7)
Splitting of an Isolated Multiplet	604	(39)
Multiplet Coupling	643	(26)
Body-Wave Ray Theory	669	(68)
Preliminaries	669	(2)
Whitham's Variational Principle	671	(4)
Kinematic Ray Tracing	675	(6)
Amplitude Variation	681	(12)
Polarization	693	(3)
Effect of Boundaries	696	(6)
Ray-Theoretical Response	702	(4)
Practical Numerical Implementation	706	(15)
Ray Perturbation Theory	721	(16)
Surface-Wave JWKB Theory	737	(230)
Preliminaries	738	(3)
Slow Variational Principle	741	(8)
Surface-Wave Ray Tracing	749	(5)
Amplitude Variation	754	(8)
JWKB Response	762	(4)
Practical Numerical Implementation	766	(12)
Validity of JWKB Theory	778	(4)
Ray Perturbation Theory	782	(14)
Surface-Wave Tomography	796	(15)
Appendixes
Appendix A Vectors and Tensors	811	(27)
A.1 Tensors as Multilinear Functionals	811	(6)
A.2 Tensors as Linear Operators	817	(3)
A.3 Gibbs Notation	820	(2)
A.4 Cartesian and Polar Decomposition	822	(2)
A.5 Grad, Div and All That	824	(2)
A.6 Surfaces	826	(6)
A.7 Spherical Polar Coordinates	832	(6)
Appendix B Spherical Harmonics	838	(39)
B.1 Harmonic Homogeneous Polynomials	839	(2)
B.2 Angular-Momentum Operator	841	(2)
B.3 Construction of a Basis	843	(4)
B.4 Associated Legendre Functions	847	(3)
B.5 Legendre Polynomials	850	(1)
B.6 Real Spherical Harmonics	851	(2)
B.7 Asymptotic Representation	853	(4)
B.8 Spherical-Harmonic Expansions	857	(3)
B.9 Integration Around a Great Circle	860	(2)
B.10 Practical Considerations	862	(2)
B.11 Complex Legendre Functions	864	(4)
B.12 Vector Spherical Harmonics	868	(9)
Appendix C Generalized Spherical Harmonics	877	(55)
C.1 Angular Momentum---Reprise	878	(8)
C.2 Spherical Polar Coordinates	886	(7)
C.3 Construction of a Basis	893	(4)
C.4 Generalized Legendre Functions	897	(4)
C.5 Generalized Expansions	901	(2)
C.6 Gradient of a Tensor Field	903	(6)
C.7 Tensor Products	909	(11)
C.8 Rotation of a Tensor Field	920	(12)
Appendix D Whole Earth Catalogue	932	(35)
D.1 Receiver and Source Vector	933	(3)
D.2 Perturbation Matrices	936	(19)
D.3 Complex-to-Real Basis Transformation	955	(4)
D.4 Self Coupling	959	(8)
Bibliography	967	(32)
Index	999