Introduction to the physics of generation and propagation of body and surface elastic waves, and study of their basic properties in simple Earth models.
1. Basic theory of elasticity (repetitorium),
2-3. 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.
5-6. Reflection on the free surface: conversion of phases, coefficients of reflection and conversion.
7. Inhomogeneous waves.
8-9. Rayleigh waves in half space, eigenfunctions.
10-12. Love waves in a layer over half-space, period equation, dispersion, modes.
12-13. Phase and group velocity.
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 half-space.
- 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.
- Studying textbook and other literature (including lecture notes), attending lectures, ending lectures,
- Derivation of the equations and study of examples.
- 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.