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An Introduction to the Theory of Seismology - K. E. Bullen

An Introduction to the Theory of Seismology

By: K. E. Bullen, Bruce A. Bolt (Editor)

Paperback

Published: 13th January 1986
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This radical revision of Professor Bullen's acclaimed and widely used text provides an introduction to modern seismological theory, with emphasis on both the physical models and the mathematical descriptions of earthquakes and their sources. The essential core of the earlier editions has been retained, particularly the tensor treatment of elasticity, seismic wave travel-time analysis and density in the Earth, although these parts of the text have been brought up to date and expanded. The new part of the book reflects on how the study of earthquakes, seismic waves and seismic risk has been broadened in the past two decades. Thus, this edition includes introductory theory of earthquake sources, seismic wave travel through complex geological zones and viscous and anisotropic media, vibrations of the whole Earth, strong-motion seismology and earthquake prediction and risk. There is an emphasis on statistical and numerical procedures and problems of resolution in inverse theory. Modern class exercises are to be found throughout. The book assumes some background in classical physics and mathematics, including simple differential equations, linear algebra and probability theory. It will be suitable for use in undergraduate courses in geophysics, applied mechanics and geotechnology and for graduate courses in seismology and earthquake engineering. In addition, it will serve as a reference text on seismological problems for professionals concerned with earthquakes, Earth structure and wave motion.

"...an excellent new and updated edition. It wouldn't surprise me if this in turn remains a standard text for many years to come." Geological Magazine "...fills a critical gap in the current literature and will be widely welcomed." Earthquake Spectra

Prefacep. xv
The scope of seismologyp. 1
Early historyp. 1
Developments from 1915 to 1960p. 4
The period since 1960p. 6
Seismology and nuclear explosionsp. 6
Standard global recordingp. 7
Computers and complexityp. 9
Extra-terrestrial seismologyp. 10
The plan of this bookp. 13
Elasticity theoryp. 15
Analysis of stressp. 15
The stress tensorp. 16
Symmetry of the stress tensorp. 18
Use of the Kronecker delta [delta][subscript ij] and alternating tensor [epsiv][subscript ijk]p. 19
The stress quadricp. 20
Elastodynamic equations of motionp. 21
Infinitesimal strainp. 21
The rotation tensorp. 23
The strain tensorp. 23
Cubical dilatationp. 25
The equation of conservationp. 26
Curvilinear coordinatesp. 27
Perfect elasticityp. 28
Stress-strain relations for a perfectly elastic isotropic materialp. 28
Equations of motion in terms of displacementp. 30
Some perfectly elastic substancesp. 31
Young's modulus and Poisson's ratiop. 32
Energy in a perfectly elastic bodyp. 33
Theorems on elastic equilibriump. 36
Solving problems in elasticityp. 38
Non-isotropic materials and transverse isotropyp. 39
Departures from perfect elasticity due to time effectsp. 40
Fluid viscosityp. 41
Kelvin-Voigt modelp. 42
Elastic afterworkingp. 43
Maxwell modelp. 44
Strength of a solidp. 45
Solids and fluidsp. 46
Finite-strain theoryp. 47
Exercisesp. 48
Vibrations and wavesp. 51
Vibrations of systems with one degree of freedomp. 51
Simple harmonic motionp. 51
Damped vibrationsp. 51
Forced vibrationsp. 53
The delta functionp. 54
Green's functionp. 55
Vibrations of systems with more than one degree of freedomp. 58
Eigen-vibrations of systems with finite freedomp. 58
Rayleigh's principlep. 60
Particles on an elastic stringp. 60
Vibrations of continuous systemsp. 61
Seismological considerationsp. 63
Plane wavesp. 64
Fourier's integral theorem and spectrap. 65
Simple harmonic plane wavep. 66
Vector waves. Polarisationp. 67
Standing wavesp. 69
Dispersion of wavesp. 69
Energy in plane wave motionp. 72
Propagation of plane waves in a general directionp. 73
The wave equationp. 73
Case of spherical symmetryp. 74
General solutionp. 74
Ray theoryp. 75
Two-dimensional wave motionp. 76
Scatteringp. 79
Diffractionp. 80
Helmholtz and Sturm--Liouville equationsp. 82
Exercisesp. 84
Body elastic wavesp. 87
P and S wavesp. 87
Case of plane wavesp. 88
Poisson's relationp. 89
Inclusion of the seismic source in infinite mediap. 89
Spherical sourcep. 89
Green's function representation for point sourcesp. 91
Reciprocity theoremp. 92
Form of ground motion in an earthquakep. 93
The effect of gravity fluctuationsp. 96
The effects of elastic imperfectionsp. 97
Constitutive laws for anelasticityp. 97
Linear models and the Jeffreys power lawp. 99
Damping of harmonic waves. The quality factor Qp. 101
Thermodynamical conditionsp. 102
Finite-strain effectsp. 103
Case of spherical wavesp. 104
Exercisesp. 106
Surface elastic waves and eigen-vibrations of a spherep. 108
Waves guided along a plane boundaryp. 108
Rayleigh wavesp. 111
Stoneley wavesp. 113
Love wavesp. 114
Nodal planesp. 116
Dispersion curvesp. 116
The differential equation for continuously varying mediap. 117
Surface waves in the presence of multiple layers and sourcesp. 118
Rayleigh waves for a single surface layerp. 118
Matrix theory. Love and Rayleigh wavesp. 121
Lamb's problemp. 124
Normal oscillations of an elastic spherep. 126
The basic equationsp. 126
Torsional (toroidal) modesp. 128
Spheroidal and radial modesp. 129
Geometrical description of the oscillationsp. 130
Effects of rotation and ellipticity. Terrestrial spectroscopyp. 132
Duality with travelling wavesp. 133
Seismic waves in linear visco-elastic mediap. 134
Equation of motion. The correspondence principlep. 134
Damped seismic wavesp. 135
Damped oscillations of a visco-elastic spherep. 136
Exercisesp. 137
Reflection and refraction of elastic wavesp. 140
Formulationp. 140
Laws of reflection and refractionp. 140
General equations for the two mediap. 141
Special casesp. 142
Case of incident SH wavesp. 142
P wave incident against a free plane boundaryp. 144
SV wave incident against a free plane boundaryp. 145
Curved boundaries and head wavesp. 146
Refraction of dispersed wavesp. 147
Scattered seismic waves. Matrix theoryp. 148
Exercisesp. 151
Seismic rays in a spherically stratified Earth modelp. 153
The parameter p of a seismic rayp. 153
Rays in inhomogeneous media. The eikonal equationp. 154
Relations between p, [Delta], T for a given family of raysp. 156
The relation p = dT/d[Delta]p. 156
Some integral expressions for T, [Delta]p. 157
The functions [zeta] and [zeta]p. 159
Expressions for d[Delta]/dp and dT/dpp. 159
Relations between [Delta] and T, corresponding to assigned variations of v with rp. 160
Various casesp. 160
Derivation of P and S velocity distributions from (T, [Delta]) relationsp. 165
Herglotz-Wiechert-Bateman inversionp. 166
Bullen's methodp. 167
Linear inverse methodp. 168
Inversion for low velocity layersp. 170
The tau ([tau]) methodp. 171
Special velocity distributionsp. 173
Curvature of a seismic rayp. 173
Rays in a homogeneous mediump. 174
Circular rays; the law v = a - br[superscript 2]p. 174
Mohorovicic's law v = ar[superscript b]p. 175
Theory of travel-times in near earthquakesp. 175
Special form of the (T, [Delta]) relation for near earthquakesp. 175
Application to a layered crustal structurep. 176
Error, resolution and network designp. 178
Determination of layer thicknessesp. 178
Use of artificial sources. Seismic prospectingp. 180
Exercisesp. 182
Amplitudes of the surface motion due to seismic waves in a spherically stratified Earth modelp. 185
Energy considerationsp. 185
Energy per unit area of wave front in an emerging wavep. 185
Relation between energy and amplitudep. 187
Movements of the surface due to an incident wavep. 188
Amplitude as a function of [Delta]p. 189
Loss of energy during transmission through the mediump. 191
Gradual variation in propertiesp. 191
Single discontinuityp. 192
Waves which change typep. 194
Amplitudes corresponding to cusps in (T, [Delta]) curvesp. 194
Amplitudes of surface seismic wavesp. 195
Reflectivity algorithmsp. 196
Exercisesp. 199
Seismometryp. 201
The horizontal component seismographp. 202
Effect of tiltp. 203
The vertical component seismographp. 204
The indicator equationp. 205
Damping of seismographsp. 206
Solution of the indicator equationp. 207
Simple harmonic ground motionp. 207
Impulsive ground motionp. 208
General ground motion response curvesp. 209
Computation of the ground motion from a seismogramp. 211
Displacement and velocity meters and accelerometersp. 211
Recording methods and timingp. 212
The dynamic ranges of seismic ground motionp. 214
Microseismsp. 214
Frequency rangep. 216
Amplitude rangep. 217
Modern seismographsp. 217
The electromagnetic typep. 218
Signal enhancement. Digital processingp. 219
Strong-motion accelerometers and arraysp. 221
Strain, tilt and other measurementsp. 224
Portable seismographs and microprocessors. Telemetryp. 224
Ocean-bottom seismographsp. 226
Engineering response spectrap. 226
Exercisesp. 228
Construction of travel-time tablesp. 231
Parameters of earthquake locationp. 231
Calculation of the epicentral distance and azimuthp. 231
Features of seismogramsp. 232
Estimation of P travel-time tablesp. 234
Equations of condition between hypocentre and table parameters. Geiger's and Inglada's methodsp. 234
Application of least-squares theory and inverse theoryp. 236
Jeffreys' method of successive approximation. Summary valuesp. 238
Uniform reduction and robust estimationp. 243
Regional variations and focal depthsp. 245
Use of digital computers. Tomographyp. 248
Travel-time tables other than Pp. 249
Notation used for phases read on seismogramsp. 250
Relations between different travel-time tablesp. 252
Types of travel-time tables for body wavesp. 253
Effect of the Earth's ellipticityp. 254
Travel-times of surface wavesp. 257
Numerical resultsp. 257
The Jeffreys-Bullen seismological tablesp. 257
Tables for PKPp. 260
Ellipticity tablesp. 261
Statistical treatment of velocity and travel-time table estimationp. 263
Exercisesp. 265
The seismological observatoryp. 267
Inside the observatoryp. 267
Interpretation of seismogramsp. 269
Determination of hypocentres and earthquake sizep. 272
Group estimation of earthquake parametersp. 273
Abnormal observations. The T-phase. Precursorsp. 274
International seismological organisationsp. 275
International seismological cataloguesp. 276
Global digital networksp. 277
Exercisesp. 279
Seismic waves in anomalous structuresp. 281
Anisotropic mediap. 281
Equation of motion and determinantal conditionsp. 281
Surface waves in anisotropic mediap. 283
Heterogeneous media. WKBJ approximationp. 284
Topographic and structural variationsp. 286
Finite difference methodsp. 287
Finite element methodsp. 288
Numerical results. A mountain and oceanic-continental transitionp. 295
Variational methodsp. 302
Laboratory model seismologyp. 305
Exercisesp. 306
Seismic waves and planetary interiorsp. 310
Major discontinuities within the Earthp. 310
Existence of a crust. Oceanic and continental structuresp. 310
Existence of a central corep. 312
Discontinuities in the mantlep. 314
Discontinuities in the central corep. 315
Division of the Earth's interior into shellsp. 317
P and S velocity distributions in the Earth and Moonp. 318
The crustp. 318
The lithospherep. 320
The deep interior. Recent solutionsp. 321
The lunar interiorp. 324
The states of the Earth's mantle and corep. 325
Solidity and fluidityp. 325
Anelastic propertiesp. 327
The Earth's density variationp. 328
Early models of density variationp. 329
Equations for density gradient from seismologyp. 329
Extension to inhomogeneous layers. The index [eta]p. 331
The inverse problem of density determinationp. 332
Bullen's procedurep. 332
Bullen's compressibility-pressure hypothesisp. 334
Linear inversion. Tradeoff curvesp. 335
Direct use of seismic wavesp. 339
Stratification of the shellsp. 343
The upper mantlep. 343
The shell D"p. 344
The outer core (shell E)p. 345
The shell Fp. 346
The inner core (shell G)p. 347
Ellipticities of surfaces of equal density within the Earthp. 348
Exercisesp. 348
Long-period oscillations and the Earth's interiorp. 350
Historical backgroundp. 350
Numerical results for Earth modelsp. 352
Torsional oscillationsp. 352
Spheroidal oscillationsp. 353
Modal splitting. The solotone effectp. 357
Estimation of observed eigen-spectrap. 363
Fourier analysisp. 363
Complex demodulationp. 364
Calculation of eigen-frequency, amplitude, phase and Qp. 366
Observationsp. 367
Earthquake statistics and predictionp. 371
Energy released in earthquakesp. 371
Case of near earthquakesp. 372
Assumption of spherical symmetry about the sourcep. 372
Use of surface wavesp. 374
Earthquake magnitudep. 375
Magnitude and energyp. 377
Magnitude - frequency of occurrence relationp. 377
Seismicityp. 379
Geography of shallow earthquakesp. 379
Distribution of deep-focus earthquakesp. 381
Tectonic associationsp. 383
Reservoir-induced earthquakesp. 384
Foreshocks and aftershocksp. 386
Aftershocksp. 386
Foreshocksp. 387
Swarmsp. 387
Earthquake predictionp. 388
Prediction theoryp. 388
Periodicities and correlations. Seismicity patternsp. 389
Changes in seismic velocitiesp. 391
Changes in strainp. 392
Dilatancy modelp. 393
Other field parameters. Liquefactionp. 394
Exercisesp. 396
The earthquake sourcep. 398
Elastic rebound modelp. 398
Causes of earthquakesp. 398
Strain energy before an earthquakep. 400
Faults and fracturep. 402
Double couple modelp. 405
Source mechanism estimationp. 406
Method of fault-plane solutionsp. 406
Probability model for group fault-plane solutionsp. 411
Moving dislocation sourcep. 415
Kinematics and dynamics. Near field and far fieldp. 415
Radiation patterns and directivityp. 419
Synthetic seismogramsp. 423
Seismic momentp. 424
Moment tensorp. 425
Estimation of seismic momentsp. 426
Exercisesp. 428
Strong-motion seismologyp. 432
Effects of earthquakesp. 432
Macroseismic datap. 433
Intensity of earthquake effectsp. 433
Isoseismal curves and accelerationp. 435
Fault rupture correlationsp. 437
Near-field parametersp. 438
Recorded strong ground motionp. 439
Peak ground accelerations, velocity and displacementp. 439
Duration of shakingp. 443
Spectral characteristicsp. 444
Local effects. Soil layers and upthrowp. 446
Attenuationp. 449
Array analysisp. 451
Seismic riskp. 455
Statistical theory. Poisson and hazard distributionsp. 455
Probability of exceedence of ground motionsp. 456
Seismic expectancy mapsp. 460
Design of earthquake-resistant structuresp. 462
Tsunamis, seiches, and atmospheric oscillationsp. 464
Exercisesp. 468
Reference velocities and elastic parameters in two Earth modelsp. 470
Selected bibliographyp. 474
Referencesp. 478
Unit conversion tablep. 488
Indexp. 489
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521283892
ISBN-10: 0521283892
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 520
Published: 13th January 1986
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 23.5 x 15.88  x 3.18
Weight (kg): 0.83
Edition Number: 4
Edition Type: Revised