Syllabus
*
1. Main types of elastic waves and their properties Body waves, surface waves. Wave dispersion. *
2. Historical development of the theory of elasticity and of the theory of seismic surface waves Theory of elasticity in the 17th and 18th centuries. Propagation of light and the theory of elasticity. Mathematical theory of elasticity. Beginnings of seismology. Studies of other types of surface waves (channel waves and higher modes, PL waves and leaking modes, microseisms). *
3. Principles of continuum mechanics Mathematical models in physics. Displacement vector. Strain tensor. Stress vector and stress tensor. Stress-strain relations. Equations of motion. *
4. Separation of the elastodynamic equations in a homogeneous isotropic medium Wave equations for potentials. Expressions of the displacement and stress in terms of potentials. Special expressions for P-SV and SH problems. Plane waves. Surface waves as superpositions of body waves. *
5. Rayleigh waves in a homogeneous isotropic half-space Potentials for a plane harmonic Rayleigh wave; displacement and stress components; boundary conditions. Velocity of Rayleigh waves. Polarization. *
6. Love waves in a layer on a half-space Dispersion equation and its solutions. Derivation of the dispersion relation from the condition of constructive interference. Methods of computing the group velocity. *
7. Rayleigh waves in a layer on a half-space Dispersion equation. Another form of the dispersion equation. *
8. Matrix methods for Love waves in a layered medium Model of the medium. Matrix for one layer and for a stack of layers. Dispersion equation. Forms of the dispersion equation; Thomson-Haskell matrices. *
9. Matrix methods for Rayleigh waves in a layered medium Thomson-Haskell matrices and their modifications. Associated matrices and reduced associated matrices. Knopoff's method. Computing reflection and transmission coefficients. *
10. Matrix formulation of some body-wave problems Motion of the surface of a layered medium caused by an incident SH wave. Reflection and transmission coefficients of SH waves for a transition zone. Spectral ratio of the horizontal and vertical components of P waves. Reflection and transmission coefficients of P and SV waves for a transition zone. *
11. Wave propagation in dispersive media Superposition of two plane harmonic waves in a non-dispersive and in dispersive medium. Propagation of a plane wave with a narrow spectrum, and with a broad spectrum. The peak and trough technique for estimating group and phase velocities from observations. Determination of phase velocities from Fourier spectra. Time-frequency analysis. *
12. Examples of structural studies by surface waves Short-period surface waves generated by explosions and their interpretation. Surface waves generated by earthquakes and their application in studies of the Earth's crust and upper mantle. * References: - M. Bath: Introduction to Seismology. Birkhäuser Verlag, Basel 1979 (second edition). - T.A. Proskuryakova, O. Novotny, E.V. Voronina: Studies of the Earth's Structure by the Surface-Wave Method (Central Europe). Nauka, Moscow
1981. (In Russian). - B.L.N. Kennett: Seismic Wave Propagation in Stratified Media. Cambridge University Press, New York
1983. - V.I. Kejlis-Borok (ed.): Seismic Surface Waves in a Laterally Inhomogeneous Earth. Kluwer Academic Publishers, Dordrecht
1989. - X. Chen: A systematic and efficient method of computing normal modes for multilayered half-space. Geophys. J. Int. 115 (1993), 391-409. - O. Novotný: Seismic Surface Waves. UFBA, Salvador, Bahia 1999 (Lecture notes).
Annotation
Main types of elastic waves and their properties. Historical development of the theory of elasticity and of the theory of seismic waves.
Separation of the elastodynamic equations. Rayleigh and Love waves in simple models of the medium.
Matrix methods for Love and Rayleigh waves in a layered medium. Matrix formulation of some body-wave problems.
Wave propagation in dispersive media.