The Theory of Earthquakes

Chapter 1: Preface

Chapter 2:  Introduction

Chapter 3: Elasticity  •  Summary  •  Deformation. Strain  •  Stress  •  Hooke’s law  •  Deformable rod  •  Elastic energy  •  Equation of motion. Equilibrium  •  Force in an infinite body  •  Equilibrium with stress equations  •  Boussinesq’s problem  •  Pressure in a cavity •  Gravitational sphere  •  Rotating cylinder  •  General solution  •  Poisson’s equation  •  Mindlin’s problem •  Boussinesq’s problem  •  Concluding remarks

Chapter 4: Elastic Waves  •  Summary  •  Free elastic waves  •  Reflection and refraction  •  Surface waves  •  Vibrations of the sphere  •  Vibrations of rods and plates  •  Wave equation with sources  •  Standard wave equation  •  Kelvin’s problem with Helmholtz potentials  •  A model of seismic focus  •  Tensorial source  •  Explosions. Isotropic source  •  Conservation laws  •  Static solutions  •  Half-space. Standard wave equation  •  Half-space. Elastic waves  •  Near-field approximation  •  Vertical source •  Horizontal source  •  Explosions  •  Force localized on the surface  •  Wave region  •  Waves generated by a vertical source  •  Waves generated by a horizontal source •  Waves generated by explosions  •  The nature of the difficulty  •  Transient solution  •  Calibration of the potentials  •  An antisymmetric moment tensor  •  Structure factor  •  Hertz potentials. Ambiguities and regularization  •  Concluding remarks

Chapter 5: Static Problems  •  Summary  •  Kelvin problem  •  General solution for the half-space  •  Mindlin problem  •  Tensorial force  •  Force on the surface  •  The D-approach  •  Melan and Flamant problems  •  Other approaches  •  Concluding remarks

Chapter 6: Local Waves  •  Summary  •  Introduction  •  Localized force  •  Double couple  •  Tensorial source  •  Isotropic source (explosions)  •  Plane waves  •  Reflection and refraction  •  Inhomogeneous waves  •  Wave attenuation  •  Spherical, conical and other types of waves  •  Summarizing remarks  •  Secondary waves  •  Secondary l-waves  •  Secondary t-waves  •  Secondary waves produced by plane waves  •  Energy balance  •  Waves on the surface, main shock and the long tail  •  Seismic records  •  Preliminary tremor  •  Interaction with the surface  •  Secondary waves  •  The displacement  •  Preliminary tremor, main shock and seismic tail  •  Summary  •  Introduction  •  Elementary seismic sources  •  Primary waves  •  Isotropic sources  •  Structure factor  •  Energy balance  •  Interaction with the surface  •  Secondary waves  • Conclusions  •  Concluding remarks

Chapter 7: Vibrations  •  Summary  •  Half-space  •  Eigenfunctions  •  Harmonic-oscillator equation  •  Surface forces  •  Elastic energy  •  Fluid sphere  •  Solid sphere  •  Spherical coordinates  • Vibrations of the solid sphere  • The case μ =  (fluid sphere)  •  Energy  •  Self-gravitating elastic sphere  •  Earth’s rotation  •  Centrifugal force  •  Inhomogeneities  •  Distribution of energy  •  Sphere in a uniform external field  •  “Cylindrical” elasticity  •  Vibrations of a half-space  •  Introduction  •  General solution  •  General time dependence. Eigenmodes  •  A gradient force. Harmonic oscillations  •  A gradient force-pulse time dependence  •  Force on the surface  •  Static limit  •  Comments  •  Concluding remarks

Chapter 8: Special Problems  •  Summary  •  Elementary waves in a half-space  •  A perturbation scheme  •  An internal discontinuity  •  Secondary waves produced by a discontinuity   •  Explosions  •  Waves produced by a meteorite  •  Vibrations of an elastic slab  •  Seismic radiation  •  Seismographs  •  Periodic force and resonance  •  Gravitational pendulum  •  Seismic signals  •  Determination of the epicentre and focus  •  Determination of the soil displacement, velocity and acceleration •  Determination of the faulting plane  •  Estimation of the seismic moment  •  The three seismic moments  •  The coefficient 3/2 in the Gutenberg-Richter law  •  Rays and “geometrical optics”  •  Travel times  •  Stokes problem  •  Boundary forces  •  Inhomogeneity  •  Surface seismic radiation  •  Concluding remarks

Chapter 9: Fluids  •  Summary  •  Motion of the fluids  •  Connection with the Navier-Cauchy equation  •  Equilibrium of the fluids  •  Gravity waves  •  Entropy (thermal) waves  •  Waves in rotating fluids  •  Axial waves  •  Sound  •  Spherical and cylindrical waves  •  Lateral waves  •  Emission of sound  •  Sound in a narrow tube  •  Scattering of sound  •  Viscosity  •  Energy dissipation  •  Reynolds number and turbulence  •  Sound with viscosity. Attenuation  •  Anelastic matter  •  A generalized damping and attenuation  •  Second viscosity  •  Explosions in seas and oceans  •  Earthquakes below seas and oceans  •  Concluding remarks

Chapter 10:  Elements of Structural Engineering  •  Summary  •  Embedded bar  •  Shock-type excitation  •  Oscillating shock •  Coupled bars  •  Buried bar •  Coupled oscillators  •  Concluding remarks

Chapter 11: Commentaries on the Seismological Problem

Chapter 12: Appendix  •  Spherical coordinates  •  Curvilinear coordinates  •  Green function for the wave equation  •  Orthogonality of eigenmodes  •  Abel inversion formula

Bogaan Felix Apostol is a scientific researcher in the Institute for Earth’s Physics at Magurele-Bucharest, Romania, with publications in scientific journals on the theory of elasticity, the focal mechanism of earthquakes and the statistical analysis of seismic events.