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| Preface | |
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| The scope of seismology | |
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| Early history | |
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| Developments from 1915 to 1960 | |
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| The period since 1960 | |
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| Seismology and nuclear explosions | |
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| Standard global recording | |
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| Computers and complexity | |
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| Extra-terrestrial seismology | |
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| The plan of this book | |
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| Elasticity theory | |
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| Analysis of stress | |
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| The stress tensor | |
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| Symmetry of the stress tensor | |
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| Use of the Kronecker delta [delta][subscript ij] and alternating tensor [epsiv][subscript ijk] | |
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| The stress quadric | |
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| Elastodynamic equations of motion | |
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| Infinitesimal strain | |
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| The rotation tensor | |
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| The strain tensor | |
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| Cubical dilatation | |
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| The equation of conservation | |
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| Curvilinear coordinates | |
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| Perfect elasticity | |
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| Stress-strain relations for a perfectly elastic isotropic material | |
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| Equations of motion in terms of displacement | |
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| Some perfectly elastic substances | |
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| Young's modulus and Poisson's ratio | |
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| Energy in a perfectly elastic body | |
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| Theorems on elastic equilibrium | |
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| Solving problems in elasticity | |
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| Non-isotropic materials and transverse isotropy | |
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| Departures from perfect elasticity due to time effects | |
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| Fluid viscosity | |
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| Kelvin-Voigt model | |
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| Elastic afterworking | |
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| Maxwell model | |
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| Strength of a solid | |
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| Solids and fluids | |
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| Finite-strain theory | |
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| Exercises | |
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| Vibrations and waves | |
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| Vibrations of systems with one degree of freedom | |
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| Simple harmonic motion | |
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| Damped vibrations | |
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| Forced vibrations | |
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| The delta function | |
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| Green's function | |
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| Vibrations of systems with more than one degree of freedom | |
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| Eigen-vibrations of systems with finite freedom | |
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| Rayleigh's principle | |
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| Particles on an elastic string | |
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| Vibrations of continuous systems | |
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| Seismological considerations | |
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| Plane waves | |
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| Fourier's integral theorem and spectra | |
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| Simple harmonic plane wave | |
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| Vector waves. Polarisation | |
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| Standing waves | |
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| Dispersion of waves | |
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| Energy in plane wave motion | |
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| Propagation of plane waves in a general direction | |
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| The wave equation | |
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| Case of spherical symmetry | |
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| General solution | |
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| Ray theory | |
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| Two-dimensional wave motion | |
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| Scattering | |
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| Diffraction | |
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| Helmholtz and Sturm--Liouville equations | |
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| Exercises | |
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| Body elastic waves | |
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| P and S waves | |
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| Case of plane waves | |
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| Poisson's relation | |
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| Inclusion of the seismic source in infinite media | |
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| Spherical source | |
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| Green's function representation for point sources | |
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| Reciprocity theorem | |
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| Form of ground motion in an earthquake | |
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| The effect of gravity fluctuations | |
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| The effects of elastic imperfections | |
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| Constitutive laws for anelasticity | |
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| Linear models and the Jeffreys power law | |
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| Damping of harmonic waves. The quality factor Q | |
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| Thermodynamical conditions | |
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| Finite-strain effects | |
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| Case of spherical waves | |
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| Exercises | |
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| Surface elastic waves and eigen-vibrations of a sphere | |
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| Waves guided along a plane boundary | |
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| Rayleigh waves | |
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| Stoneley waves | |
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| Love waves | |
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| Nodal planes | |
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| Dispersion curves | |
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| The differential equation for continuously varying media | |
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| Surface waves in the presence of multiple layers and sources | |
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| Rayleigh waves for a single surface layer | |
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| Matrix theory. Love and Rayleigh waves | |
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| Lamb's problem | |
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| Normal oscillations of an elastic sphere | |
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| The basic equations | |
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| Torsional (toroidal) modes | |
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| Spheroidal and radial modes | |
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| Geometrical description of the oscillations | |
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| Effects of rotation and ellipticity. Terrestrial spectroscopy | |
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| Duality with travelling waves | |
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| Seismic waves in linear visco-elastic media | |
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| Equation of motion. The correspondence principle | |
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| Damped seismic waves | |
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| Damped oscillations of a visco-elastic sphere | |
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| Exercises | |
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| Reflection and refraction of elastic waves | |
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| Formulation | |
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| Laws of reflection and refraction | |
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| General equations for the two media | |
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| Special cases | |
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| Case of incident SH waves | |
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| P wave incident against a free plane boundary | |
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| SV wave incident against a free plane boundary | |
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| Curved boundaries and head waves | |
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| Refraction of dispersed waves | |
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| Scattered seismic waves. Matrix theory | |
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| Exercises | |
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| Seismic rays in a spherically stratified Earth model | |
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| The parameter p of a seismic ray | |
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| Rays in inhomogeneous media. The eikonal equation | |
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| Relations between p, [Delta], T for a given family of rays | |
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| The relation p = dT/d[Delta] | |
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| Some integral expressions for T, [Delta] | |
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| The functions [zeta] and [zeta] | |
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| Expressions for d[Delta]/dp and dT/dp | |
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| Relations between [Delta] and T, corresponding to assigned variations of v with r | |
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| Various cases | |
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| Derivation of P and S velocity distributions from (T, [Delta]) relations | |
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| Herglotz-Wiechert-Bateman inversion | |
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| Bullen's method | |
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| Linear inverse method | |
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| Inversion for low velocity layers | |
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| The tau ([tau]) method | |
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| Special velocity distributions | |
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| Curvature of a seismic ray | |
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| Rays in a homogeneous medium | |
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| Circular rays; the law v = a - br[superscript 2] | |
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| Mohorovicic's law v = ar[superscript b] | |
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| Theory of travel-times in near earthquakes | |
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| Special form of the (T, [Delta]) relation for near earthquakes | |
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| Application to a layered crustal structure | |
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| Error, resolution and network design | |
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| Determination of layer thicknesses | |
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| Use of artificial sources. Seismic prospecting | |
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| Exercises | |
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| Amplitudes of the surface motion due to seismic waves in a spherically stratified Earth model | |
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| Energy considerations | |
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| Energy per unit area of wave front in an emerging wave | |
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| Relation between energy and amplitude | |
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| Movements of the surface due to an incident wave | |
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| Amplitude as a function of [Delta] | |
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| Loss of energy during transmission through the medium | |
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| Gradual variation in properties | |
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| Single discontinuity | |
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| Waves which change type | |
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| Amplitudes corresponding to cusps in (T, [Delta]) curves | |
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| Amplitudes of surface seismic waves | |
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| Reflectivity algorithms | |
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| Exercises | |
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| Seismometry | |
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| The horizontal component seismograph | |
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| Effect of tilt | |
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| The vertical component seismograph | |
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| The indicator equation | |
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| Damping of seismographs | |
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| Solution of the indicator equation | |
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| Simple harmonic ground motion | |
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| Impulsive ground motion | |
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| General ground motion response curves | |
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| Computation of the ground motion from a seismogram | |
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| Displacement and velocity meters and accelerometers | |
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| Recording methods and timing | |
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| The dynamic ranges of seismic ground motion | |
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| Microseisms | |
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| Frequency range | |
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| Amplitude range | |
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| Modern seismographs | |
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| The electromagnetic type | |
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| Signal enhancement. Digital processing | |
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| Strong-motion accelerometers and arrays | |
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| Strain, tilt and other measurements | |
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| Portable seismographs and microprocessors. Telemetry | |
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| Ocean-bottom seismographs | |
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| Engineering response spectra | |
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| Exercises | |
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| Construction of travel-time tables | |
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| Parameters of earthquake location | |
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| Calculation of the epicentral distance and azimuth | |
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| Features of seismograms | |
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| Estimation of P travel-time tables | |
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| Equations of condition between hypocentre and table parameters. Geiger's and Inglada's methods | |
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| Application of least-squares theory and inverse theory | |
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| Jeffreys' method of successive approximation. Summary values | |
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| Uniform reduction and robust estimation | |
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| Regional variations and focal depths | |
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| Use of digital computers. Tomography | |
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| Travel-time tables other than P | |
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| Notation used for phases read on seismograms | |
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| Relations between different travel-time tables | |
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| Types of travel-time tables for body waves | |
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| Effect of the Earth's ellipticity | |
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| Travel-times of surface waves | |
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| Numerical results | |
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| The Jeffreys-Bullen seismological tables | |
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| Tables for PKP | |
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| Ellipticity tables | |
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| Statistical treatment of velocity and travel-time table estimation | |
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| Exercises | |
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| The seismological observatory | |
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| Inside the observatory | |
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| Interpretation of seismograms | |
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| Determination of hypocentres and earthquake size | |
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| Group estimation of earthquake parameters | |
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| Abnormal observations. The T-phase. Precursors | |
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| International seismological organisations | |
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| International seismological catalogues | |
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| Global digital networks | |
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| Exercises | |
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| Seismic waves in anomalous structures | |
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| Anisotropic media | |
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| Equation of motion and determinantal conditions | |
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| Surface waves in anisotropic media | |
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| Heterogeneous media. WKBJ approximation | |
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| Topographic and structural variations | |
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| Finite difference methods | |
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| Finite element methods | |
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| Numerical results. A mountain and oceanic-continental transition | |
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| Variational methods | |
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| Laboratory model seismology | |
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| Exercises | |
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| Seismic waves and planetary interiors | |
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| Major discontinuities within the Earth | |
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| Existence of a crust. Oceanic and continental structures | |
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| Existence of a central core | |
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| Discontinuities in the mantle | |
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| Discontinuities in the central core | |
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| Division of the Earth's interior into shells | |
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| P and S velocity distributions in the Earth and Moon | |
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| The crust | |
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| The lithosphere | |
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| The deep interior. Recent solutions | |
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| The lunar interior | |
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| The states of the Earth's mantle and core | |
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| Solidity and fluidity | |
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| Anelastic properties | |
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| The Earth's density variation | |
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| Early models of density variation | |
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| Equations for density gradient from seismology | |
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| Extension to inhomogeneous layers. The index [eta] | |
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| The inverse problem of density determination | |
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| Bullen's procedure | |
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| Bullen's compressibility-pressure hypothesis | |
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| Linear inversion. Tradeoff curves | |
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| Direct use of seismic waves | |
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| Stratification of the shells | |
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| The upper mantle | |
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| The shell D" | |
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| The outer core (shell E) | |
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| The shell F | |
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| The inner core (shell G) | |
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| Ellipticities of surfaces of equal density within the Earth | |
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| Exercises | |
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| Long-period oscillations and the Earth's interior | |
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| Historical background | |
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| Numerical results for Earth models | |
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| Torsional oscillations | |
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| Spheroidal oscillations | |
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| Modal splitting. The solotone effect | |
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| Estimation of observed eigen-spectra | |
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| Fourier analysis | |
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| Complex demodulation | |
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| Calculation of eigen-frequency, amplitude, phase and Q | |
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| Observations | |
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| Earthquake statistics and prediction | |
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| Energy released in earthquakes | |
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| Case of near earthquakes | |
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| Assumption of spherical symmetry about the source | |
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| Use of surface waves | |
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| Earthquake magnitude | |
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| Magnitude and energy | |
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| Magnitude - frequency of occurrence relation | |
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| Seismicity | |
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| Geography of shallow earthquakes | |
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| Distribution of deep-focus earthquakes | |
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| Tectonic associations | |
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| Reservoir-induced earthquakes | |
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| Foreshocks and aftershocks | |
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| Aftershocks | |
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| Foreshocks | |
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| Swarms | |
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| Earthquake prediction | |
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| Prediction theory | |
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| Periodicities and correlations. Seismicity patterns | |
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| Changes in seismic velocities | |
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| Changes in strain | |
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| Dilatancy model | |
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| Other field parameters. Liquefaction | |
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| Exercises | |
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| The earthquake source | |
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| Elastic rebound model | |
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| Causes of earthquakes | |
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| Strain energy before an earthquake | |
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| Faults and fracture | |
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| Double couple model | |
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| Source mechanism estimation | |
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| Method of fault-plane solutions | |
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| Probability model for group fault-plane solutions | |
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| Moving dislocation source | |
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| Kinematics and dynamics. Near field and far field | |
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| Radiation patterns and directivity | |
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| Synthetic seismograms | |
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| Seismic moment | |
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| Moment tensor | |
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| Estimation of seismic moments | |
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| Exercises | |
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| Strong-motion seismology | |
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| Effects of earthquakes | |
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| Macroseismic data | |
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| Intensity of earthquake effects | |
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| Isoseismal curves and acceleration | |
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| Fault rupture correlations | |
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| Near-field parameters | |
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| Recorded strong ground motion | |
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| Peak ground accelerations, velocity and displacement | |
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| Duration of shaking | |
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| Spectral characteristics | |
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| Local effects. Soil layers and upthrow | |
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| Attenuation | |
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| Array analysis | |
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| Seismic risk | |
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| Statistical theory. Poisson and hazard distributions | |
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| Probability of exceedence of ground motions | |
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| Seismic expectancy maps | |
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| Design of earthquake-resistant structures | |
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| Tsunamis, seiches, and atmospheric oscillations | |
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| Exercises | |
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| Reference velocities and elastic parameters in two Earth models | |
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| Selected bibliography | |
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| References | |
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| Unit conversion table | |
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| Index | |