Surface Waves and Discontinuities: (Development in Solid Earth Geophysics S.)

In this monograph on surface waves propagating in media with lateral inhomogeneities, the author takes into account the rapid progress made in applying surface waves in many fields of physics and engineering science during the last two decades. The fundamentals of surface waves have been a well-founded part of wave theory for many years. However, the application is connected with various problems which cannot be solved using conventional theory alone, such as input and output of surface wave energy in communication engineering devices, low-loss transfer of energy in wave-guides, the investigation of the Earth's interior using seismic surface waves, etc. A crucial problem common to these fields is the question of the interaction of surface waves with discontinuities. The primary objective of this book is to treat this problem in detail by using a very simple model, the so-called impedance surface. Although there are many books devoted to the propagation of waves in disturbed media, there is no cross-disciplinary treatise for surface waves which also considers seismological aspects.

Table of Contents:
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.