
An Introduction to the Theory of Seismology
By: K. E. Bullen, Bruce A. Bolt
Paperback | 14 November 1985 | Edition Number 4
At a Glance
520 Pages
Revised
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Preface | p. xv |
The scope of seismology | p. 1 |
Early history | p. 1 |
Developments from 1915 to 1960 | p. 4 |
The period since 1960 | p. 6 |
Seismology and nuclear explosions | p. 6 |
Standard global recording | p. 7 |
Computers and complexity | p. 9 |
Extra-terrestrial seismology | p. 10 |
The plan of this book | p. 13 |
Elasticity theory | p. 15 |
Analysis of stress | p. 15 |
The stress tensor | p. 16 |
Symmetry of the stress tensor | p. 18 |
Use of the Kronecker delta [delta][subscript ij] and alternating tensor [epsiv][subscript ijk] | p. 19 |
The stress quadric | p. 20 |
Elastodynamic equations of motion | p. 21 |
Infinitesimal strain | p. 21 |
The rotation tensor | p. 23 |
The strain tensor | p. 23 |
Cubical dilatation | p. 25 |
The equation of conservation | p. 26 |
Curvilinear coordinates | p. 27 |
Perfect elasticity | p. 28 |
Stress-strain relations for a perfectly elastic isotropic material | p. 28 |
Equations of motion in terms of displacement | p. 30 |
Some perfectly elastic substances | p. 31 |
Young's modulus and Poisson's ratio | p. 32 |
Energy in a perfectly elastic body | p. 33 |
Theorems on elastic equilibrium | p. 36 |
Solving problems in elasticity | p. 38 |
Non-isotropic materials and transverse isotropy | p. 39 |
Departures from perfect elasticity due to time effects | p. 40 |
Fluid viscosity | p. 41 |
Kelvin-Voigt model | p. 42 |
Elastic afterworking | p. 43 |
Maxwell model | p. 44 |
Strength of a solid | p. 45 |
Solids and fluids | p. 46 |
Finite-strain theory | p. 47 |
Exercises | p. 48 |
Vibrations and waves | p. 51 |
Vibrations of systems with one degree of freedom | p. 51 |
Simple harmonic motion | p. 51 |
Damped vibrations | p. 51 |
Forced vibrations | p. 53 |
The delta function | p. 54 |
Green's function | p. 55 |
Vibrations of systems with more than one degree of freedom | p. 58 |
Eigen-vibrations of systems with finite freedom | p. 58 |
Rayleigh's principle | p. 60 |
Particles on an elastic string | p. 60 |
Vibrations of continuous systems | p. 61 |
Seismological considerations | p. 63 |
Plane waves | p. 64 |
Fourier's integral theorem and spectra | p. 65 |
Simple harmonic plane wave | p. 66 |
Vector waves. Polarisation | p. 67 |
Standing waves | p. 69 |
Dispersion of waves | p. 69 |
Energy in plane wave motion | p. 72 |
Propagation of plane waves in a general direction | p. 73 |
The wave equation | p. 73 |
Case of spherical symmetry | p. 74 |
General solution | p. 74 |
Ray theory | p. 75 |
Two-dimensional wave motion | p. 76 |
Scattering | p. 79 |
Diffraction | p. 80 |
Helmholtz and Sturm--Liouville equations | p. 82 |
Exercises | p. 84 |
Body elastic waves | p. 87 |
P and S waves | p. 87 |
Case of plane waves | p. 88 |
Poisson's relation | p. 89 |
Inclusion of the seismic source in infinite media | p. 89 |
Spherical source | p. 89 |
Green's function representation for point sources | p. 91 |
Reciprocity theorem | p. 92 |
Form of ground motion in an earthquake | p. 93 |
The effect of gravity fluctuations | p. 96 |
The effects of elastic imperfections | p. 97 |
Constitutive laws for anelasticity | p. 97 |
Linear models and the Jeffreys power law | p. 99 |
Damping of harmonic waves. The quality factor Q | p. 101 |
Thermodynamical conditions | p. 102 |
Finite-strain effects | p. 103 |
Case of spherical waves | p. 104 |
Exercises | p. 106 |
Surface elastic waves and eigen-vibrations of a sphere | p. 108 |
Waves guided along a plane boundary | p. 108 |
Rayleigh waves | p. 111 |
Stoneley waves | p. 113 |
Love waves | p. 114 |
Nodal planes | p. 116 |
Dispersion curves | p. 116 |
The differential equation for continuously varying media | p. 117 |
Surface waves in the presence of multiple layers and sources | p. 118 |
Rayleigh waves for a single surface layer | p. 118 |
Matrix theory. Love and Rayleigh waves | p. 121 |
Lamb's problem | p. 124 |
Normal oscillations of an elastic sphere | p. 126 |
The basic equations | p. 126 |
Torsional (toroidal) modes | p. 128 |
Spheroidal and radial modes | p. 129 |
Geometrical description of the oscillations | p. 130 |
Effects of rotation and ellipticity. Terrestrial spectroscopy | p. 132 |
Duality with travelling waves | p. 133 |
Seismic waves in linear visco-elastic media | p. 134 |
Equation of motion. The correspondence principle | p. 134 |
Damped seismic waves | p. 135 |
Damped oscillations of a visco-elastic sphere | p. 136 |
Exercises | p. 137 |
Reflection and refraction of elastic waves | p. 140 |
Formulation | p. 140 |
Laws of reflection and refraction | p. 140 |
General equations for the two media | p. 141 |
Special cases | p. 142 |
Case of incident SH waves | p. 142 |
P wave incident against a free plane boundary | p. 144 |
SV wave incident against a free plane boundary | p. 145 |
Curved boundaries and head waves | p. 146 |
Refraction of dispersed waves | p. 147 |
Scattered seismic waves. Matrix theory | p. 148 |
Exercises | p. 151 |
Seismic rays in a spherically stratified Earth model | p. 153 |
The parameter p of a seismic ray | p. 153 |
Rays in inhomogeneous media. The eikonal equation | p. 154 |
Relations between p, [Delta], T for a given family of rays | p. 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/dp | p. 159 |
Relations between [Delta] and T, corresponding to assigned variations of v with r | p. 160 |
Various cases | p. 160 |
Derivation of P and S velocity distributions from (T, [Delta]) relations | p. 165 |
Herglotz-Wiechert-Bateman inversion | p. 166 |
Bullen's method | p. 167 |
Linear inverse method | p. 168 |
Inversion for low velocity layers | p. 170 |
The tau ([tau]) method | p. 171 |
Special velocity distributions | p. 173 |
Curvature of a seismic ray | p. 173 |
Rays in a homogeneous medium | p. 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 earthquakes | p. 175 |
Special form of the (T, [Delta]) relation for near earthquakes | p. 175 |
Application to a layered crustal structure | p. 176 |
Error, resolution and network design | p. 178 |
Determination of layer thicknesses | p. 178 |
Use of artificial sources. Seismic prospecting | p. 180 |
Exercises | p. 182 |
Amplitudes of the surface motion due to seismic waves in a spherically stratified Earth model | p. 185 |
Energy considerations | p. 185 |
Energy per unit area of wave front in an emerging wave | p. 185 |
Relation between energy and amplitude | p. 187 |
Movements of the surface due to an incident wave | p. 188 |
Amplitude as a function of [Delta] | p. 189 |
Loss of energy during transmission through the medium | p. 191 |
Gradual variation in properties | p. 191 |
Single discontinuity | p. 192 |
Waves which change type | p. 194 |
Amplitudes corresponding to cusps in (T, [Delta]) curves | p. 194 |
Amplitudes of surface seismic waves | p. 195 |
Reflectivity algorithms | p. 196 |
Exercises | p. 199 |
Seismometry | p. 201 |
The horizontal component seismograph | p. 202 |
Effect of tilt | p. 203 |
The vertical component seismograph | p. 204 |
The indicator equation | p. 205 |
Damping of seismographs | p. 206 |
Solution of the indicator equation | p. 207 |
Simple harmonic ground motion | p. 207 |
Impulsive ground motion | p. 208 |
General ground motion response curves | p. 209 |
Computation of the ground motion from a seismogram | p. 211 |
Displacement and velocity meters and accelerometers | p. 211 |
Recording methods and timing | p. 212 |
The dynamic ranges of seismic ground motion | p. 214 |
Microseisms | p. 214 |
Frequency range | p. 216 |
Amplitude range | p. 217 |
Modern seismographs | p. 217 |
The electromagnetic type | p. 218 |
Signal enhancement. Digital processing | p. 219 |
Strong-motion accelerometers and arrays | p. 221 |
Strain, tilt and other measurements | p. 224 |
Portable seismographs and microprocessors. Telemetry | p. 224 |
Ocean-bottom seismographs | p. 226 |
Engineering response spectra | p. 226 |
Exercises | p. 228 |
Construction of travel-time tables | p. 231 |
Parameters of earthquake location | p. 231 |
Calculation of the epicentral distance and azimuth | p. 231 |
Features of seismograms | p. 232 |
Estimation of P travel-time tables | p. 234 |
Equations of condition between hypocentre and table parameters. Geiger's and Inglada's methods | p. 234 |
Application of least-squares theory and inverse theory | p. 236 |
Jeffreys' method of successive approximation. Summary values | p. 238 |
Uniform reduction and robust estimation | p. 243 |
Regional variations and focal depths | p. 245 |
Use of digital computers. Tomography | p. 248 |
Travel-time tables other than P | p. 249 |
Notation used for phases read on seismograms | p. 250 |
Relations between different travel-time tables | p. 252 |
Types of travel-time tables for body waves | p. 253 |
Effect of the Earth's ellipticity | p. 254 |
Travel-times of surface waves | p. 257 |
Numerical results | p. 257 |
The Jeffreys-Bullen seismological tables | p. 257 |
Tables for PKP | p. 260 |
Ellipticity tables | p. 261 |
Statistical treatment of velocity and travel-time table estimation | p. 263 |
Exercises | p. 265 |
The seismological observatory | p. 267 |
Inside the observatory | p. 267 |
Interpretation of seismograms | p. 269 |
Determination of hypocentres and earthquake size | p. 272 |
Group estimation of earthquake parameters | p. 273 |
Abnormal observations. The T-phase. Precursors | p. 274 |
International seismological organisations | p. 275 |
International seismological catalogues | p. 276 |
Global digital networks | p. 277 |
Exercises | p. 279 |
Seismic waves in anomalous structures | p. 281 |
Anisotropic media | p. 281 |
Equation of motion and determinantal conditions | p. 281 |
Surface waves in anisotropic media | p. 283 |
Heterogeneous media. WKBJ approximation | p. 284 |
Topographic and structural variations | p. 286 |
Finite difference methods | p. 287 |
Finite element methods | p. 288 |
Numerical results. A mountain and oceanic-continental transition | p. 295 |
Variational methods | p. 302 |
Laboratory model seismology | p. 305 |
Exercises | p. 306 |
Seismic waves and planetary interiors | p. 310 |
Major discontinuities within the Earth | p. 310 |
Existence of a crust. Oceanic and continental structures | p. 310 |
Existence of a central core | p. 312 |
Discontinuities in the mantle | p. 314 |
Discontinuities in the central core | p. 315 |
Division of the Earth's interior into shells | p. 317 |
P and S velocity distributions in the Earth and Moon | p. 318 |
The crust | p. 318 |
The lithosphere | p. 320 |
The deep interior. Recent solutions | p. 321 |
The lunar interior | p. 324 |
The states of the Earth's mantle and core | p. 325 |
Solidity and fluidity | p. 325 |
Anelastic properties | p. 327 |
The Earth's density variation | p. 328 |
Early models of density variation | p. 329 |
Equations for density gradient from seismology | p. 329 |
Extension to inhomogeneous layers. The index [eta] | p. 331 |
The inverse problem of density determination | p. 332 |
Bullen's procedure | p. 332 |
Bullen's compressibility-pressure hypothesis | p. 334 |
Linear inversion. Tradeoff curves | p. 335 |
Direct use of seismic waves | p. 339 |
Stratification of the shells | p. 343 |
The upper mantle | p. 343 |
The shell D" | p. 344 |
The outer core (shell E) | p. 345 |
The shell F | p. 346 |
The inner core (shell G) | p. 347 |
Ellipticities of surfaces of equal density within the Earth | p. 348 |
Exercises | p. 348 |
Long-period oscillations and the Earth's interior | p. 350 |
Historical background | p. 350 |
Numerical results for Earth models | p. 352 |
Torsional oscillations | p. 352 |
Spheroidal oscillations | p. 353 |
Modal splitting. The solotone effect | p. 357 |
Estimation of observed eigen-spectra | p. 363 |
Fourier analysis | p. 363 |
Complex demodulation | p. 364 |
Calculation of eigen-frequency, amplitude, phase and Q | p. 366 |
Observations | p. 367 |
Earthquake statistics and prediction | p. 371 |
Energy released in earthquakes | p. 371 |
Case of near earthquakes | p. 372 |
Assumption of spherical symmetry about the source | p. 372 |
Use of surface waves | p. 374 |
Earthquake magnitude | p. 375 |
Magnitude and energy | p. 377 |
Magnitude - frequency of occurrence relation | p. 377 |
Seismicity | p. 379 |
Geography of shallow earthquakes | p. 379 |
Distribution of deep-focus earthquakes | p. 381 |
Tectonic associations | p. 383 |
Reservoir-induced earthquakes | p. 384 |
Foreshocks and aftershocks | p. 386 |
Aftershocks | p. 386 |
Foreshocks | p. 387 |
Swarms | p. 387 |
Earthquake prediction | p. 388 |
Prediction theory | p. 388 |
Periodicities and correlations. Seismicity patterns | p. 389 |
Changes in seismic velocities | p. 391 |
Changes in strain | p. 392 |
Dilatancy model | p. 393 |
Other field parameters. Liquefaction | p. 394 |
Exercises | p. 396 |
The earthquake source | p. 398 |
Elastic rebound model | p. 398 |
Causes of earthquakes | p. 398 |
Strain energy before an earthquake | p. 400 |
Faults and fracture | p. 402 |
Double couple model | p. 405 |
Source mechanism estimation | p. 406 |
Method of fault-plane solutions | p. 406 |
Probability model for group fault-plane solutions | p. 411 |
Moving dislocation source | p. 415 |
Kinematics and dynamics. Near field and far field | p. 415 |
Radiation patterns and directivity | p. 419 |
Synthetic seismograms | p. 423 |
Seismic moment | p. 424 |
Moment tensor | p. 425 |
Estimation of seismic moments | p. 426 |
Exercises | p. 428 |
Strong-motion seismology | p. 432 |
Effects of earthquakes | p. 432 |
Macroseismic data | p. 433 |
Intensity of earthquake effects | p. 433 |
Isoseismal curves and acceleration | p. 435 |
Fault rupture correlations | p. 437 |
Near-field parameters | p. 438 |
Recorded strong ground motion | p. 439 |
Peak ground accelerations, velocity and displacement | p. 439 |
Duration of shaking | p. 443 |
Spectral characteristics | p. 444 |
Local effects. Soil layers and upthrow | p. 446 |
Attenuation | p. 449 |
Array analysis | p. 451 |
Seismic risk | p. 455 |
Statistical theory. Poisson and hazard distributions | p. 455 |
Probability of exceedence of ground motions | p. 456 |
Seismic expectancy maps | p. 460 |
Design of earthquake-resistant structures | p. 462 |
Tsunamis, seiches, and atmospheric oscillations | p. 464 |
Exercises | p. 468 |
Reference velocities and elastic parameters in two Earth models | p. 470 |
Selected bibliography | p. 474 |
References | p. 478 |
Unit conversion table | p. 488 |
Index | p. 489 |
Table of Contents provided by Syndetics. All Rights Reserved. |
ISBN: 9780521283892
ISBN-10: 0521283892
Published: 14th November 1985
Format: Paperback
Language: English
Number of Pages: 520
Audience: Professional and Scholarly
Publisher: Cambridge University Press
Country of Publication: GB
Edition Number: 4
Edition Type: Revised
Dimensions (cm): 22.86 x 15.24 x 2.95
Weight (kg): 0.76
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