COURSE OBJECTIVES:
Introduction to the physics of generation and propagation of body and surface elastic waves, and study of their basic properties in simple Earth models.
COURSE CONTENT
1. Basic theory of elasticity (repetitorium),
23. Navier and wave equations and their
solutions: Helmholtz theorem, elastic potentials,
4. Fourier principle of superposition. Snell's law, ray parameter. P, SV, SH waves.
56. Reflection on the free surface: conversion of phases, coefficients of reflection and conversion.
7. Inhomogeneous waves.
89. Rayleigh waves in half space, eigenfunctions.
1012. Love waves in a layer over halfspace, period equation, dispersion, modes.
1213. Phase and group velocity.
LEARNING OUTCOMES
After completing the course students can:
 Define elastic wave types and their properties.
 Apply the Helmholtz theorem in solving the Navier equation.
 Distinguish between three types of motion (P, SV, SH), and define them.
 Distinguish between homogeneous and inhomogeneous waves, and define them.
 Define boundary conditions end derive reflection and conversion coefficients for P SV waves at the free surface.
 Define boundary conditions end derive reflection and refraction coefficients for SH waves at the boundary between two media.
 Define boundary conditions and derive period equations for surface waves in the simplest Earth models; discuss the period equation for Love waves and argue for the existence of modes and dispersion.
 Analyse and compute eigenfunctions for Rayleigh waves in the homogeneous halfspace.
 Describe the oscillation of particles on the free surface during the passage of Rayleigh waves.
 Define the phase and group velocity, and compute one from the other.
LEARNING MODE:
 Studying textbook and other literature (including lecture notes), attending lectures, ending lectures,
 Derivation of the equations and study of examples.
TEACHING METHODS:
 lectures, discussion
 derivations of the equations
 solving problems
METHODS OF MONITORING AND VERIFICATION:
Attending lectures, solved homework; Attending the Geophysical seminar (at least 75%). Written colloquium and oral exam.
TERMS FOR RECEIVING THE SIGNATURE:
Solved homework, and written report.
EXAMINATION METHODS:
Oral exam.
