NDLI: Connections between seismology, waveguide physics and quantum mechanics

Content Provider	IEEE Xplore Digital Library
Author	Malischewsky, P.G.
Copyright Year	2009
Description	Author affiliation: Institute of Geosciences, Friedrich-Schiller University Jena, 07749, Germany (Malischewsky, P.G.)
Abstract	It is well-known that surface waves represent usually the main part of seismograms because of the 2D-character of their propagation. Their interaction with lateral heterogeneities is important not only in seismology but also in non-destructive testing (NDT), solid state physics and other disciplines. If we consider an elastic half-space the differential operator from the Navier equation has an infinite domain of definition with the consequence of a mixed spectrum: the discrete part represented by surface waves and the continuous part represented by body waves. We can identify the surface waves with the bound states of an atom and the body waves with the unbound ones. Conceptions of quantum mecanics like Dirac's perturbation theory and others can be profitably used for the theory of disturbed wave-guides. We present a bra-ket formalism for the Rayleigh and Love waves and observe that contrary to the Love waves, which follow from a standard Sturm-Liouville problem, the eigenvalue problem for Rayleigh waves is a generalized and complicated one. The discrete eigenfunction system of the surface waves is incomplete and it is not yet proven wether the surface waves and body aves together build up a complete system. It is not easy to determine expansion coefficients within any expansion containing surface waves because of the mixed character of the governing operator's eigenspectrum. An approximation technique is proposed to determine the coefficients by minimizing a special functional F2 and the results are compared with an impedance jump problem, the only configuration with an exact solution for reflection and transmission coefficients for surface waves.
Starting Page	144
Ending Page	150
File Size	408377
Page Count	7
File Format	PDF
ISBN	9781424448746
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-05-26
Publisher Place	Russia
Access Restriction	Subscribed
Rights Holder	Day of Diffraction Faculty of Physics, SPbU
Subject Keyword	Surface waves Eigenvalues and eigenfunctions Surface impedance Optical surface waves Quantum mechanics Optical waveguide theory
Content Type	Text
Resource Type	Article

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