Syllabus
* Introduction
Body and surface elastic waves, waves on water (tsunami). Main types of surface waves and their characteristics. Examples of seismograms.
* Dispersion relations of surface waves
Derivation of the dispersion relation for Love waves propagating in a layer over half-space. Love waves as an interference phenomenon of SH-waves; derivation of the dispersion relation from the condition of constructive interference. Rayleigh waves in a homogeneous half-space. Dispersion of Rayleigh waves in a layer over a half-space.
* Synthetic seismograms
Modal structure of surface waves, eigenfunctions, elipticity of Rayleigh waves, modal summation, attenuation with distance. Weyl integral, discrete wavenumber method.
* Matrix methods
Model of a layered medium. Matrix for one layer and for a stack of layers. Dispersion relation for Love waves in a layered medium. Thomson-Haskell matrices and their modifications. Thomson-Haskell matrices for Rayleigh waves; the loss-of-precision problem and its causes. Matrix formulations eliminating the loss of precision.
* Analysis of dispersed wave trains
Superposition of two plane harmonic waves with different frequencies and velocities, phase and group velocities. Superposition of a wave packet with a narrow/broad spectrum. Formulae for determining experimental dispersion curves: application of the stationary-phase method, Fourier spectra and frequency-time analysis. Practical determination of dispersion curves from seismograms. Determination of structural model as an inverse problem.
* Seismic noise and array measurements
Methods for determining Green’s functions from cross-correlation of noise measurements in station pairs, tomography from surface waves. Analysis of array data, determination of dispersion curve from seismic noise.
* Examples of structural and source studies using surface waves
Crustal and upper-mantle structure along some profiles. Shallow structure from array measurements, determination of the bedrock depth. Surface and mantle waves in focal mechanism inversion.
Annotation
Body and surface elastic waves, tsunami. Interference character of surface waves, Rayleigh and Love waves in simple structures and their dispersion, ellipticity of Rayleigh waves.
Matrix methods for modeling waves in layered media. Analysis of dispersive signals, determination of phase and group velocities.
Seismic noise, determination of Green’s functions from cross-correlations, array measurements. Examples of structural studies using surface waves.