Surface Waves and Discontinuities

1. Introduction. General background. General remarks about wave-guides with discontinuities. 2. Mathematical Aspects. The boundary conditions and their seismological interpretation. The differential operators in closed domains. The differential operators in open domains. 3. The Undisturbed Wave-Guide. The mode conception. The closed wave-guide. The open wave-guide. 4. The Disturbed Wave-Guide. General remarks. The bracket formalism (interrelations with quantum theory). The closed wave-guide with a vertical discontinuity or an impedance jump, respectively. The open wave-guide with vertical discontinuity and an impedance jump. Lateral inhomogeneities and seismic surface waves. 5. The Wiener-Hopf Technique. General remarks. Application of the Wiener-Hopf technique to an impedance jump in an open wave-guide. Application of the Wiener-Hopf technique to an impedance jump in a closed wave-guide. 6. The Three-Dimensional Problem. General remarks. Some special cases. Some remarks concerning Rayleigh waves. 7. Appendix. Calculation of the integrals I 1 , I 2 , I 3 . Perturbation method for complex roots. 8. References. 9. Index.