Syllabus
Outlook
Observation of seismic waves
Structure of the seismogram. Body waves and surface waves. Types of seismic waves propagating in the Earth’s interior. Travel-time curves, dispersion curves.
Simple ray theory based on Fermat’s Principle
Fermat’s Principle. Euler’s equations for the extremal. Snell’s law. Seismic rays and travel times in a vertically inhomogeneous medium. Seismic rays and travel times in a spherically symmetric medium. The Wiechert-Herglotz equation.
Elastodynamic equation
Separation of the elastodynamic equation in a homogeneous isotropic medium. Introduction of potentials. Wave equations.
Special solutions of the elastodynamic equation
Plane waves in a homogeneous isotropic medium and in a homogeneous anisotropic medium. Reflection and transmission of plane waves at a plane interface. Total reflection. Stokes’ solution of the elastodynamic equation in a homogeneous isotropic medium. Weyl’s integral. Head waves.
Seismic surface waves
Rayleigh waves on a homogeneous isotropic half-space. Love waves in a layer on a half-space. Matrix formulation of the problems for layered media.
Annotation
Types of seismic waves. Body waves in the Earth’s interior. Ray methods based on variational principles.
Methods based on the equations of continuum mechanics. Seismic surface waves.