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, SHwaves. 56. Reflection on the free surface: conversion of phases, coefficients of reflection and conversion. 7. Inhomogeneous waves. 89. Rayleigh waves in halfspace, 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 PSV 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 existence of modes and dispersion.
Analyse and compute eigenfunctions for Rayleigh waves in the homogeneous halfspace.
Describe 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.

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