Open AccessThe Love wave scattering matrix for a continental margin (theoretical) *
Author(s) -
Kazi M. H.
Publication year - 1978
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1978.tb04220.x
Subject(s) - scattering , plane wave , matrix (chemical analysis) , reflection (computer programming) , mathematical analysis , physics , discontinuity (linguistics) , plane (geometry) , diffraction , matrix representation , mathematics , classical mechanics , optics , geometry , quantum mechanics , computer science , chemistry , chromatography , programming language , group (periodic table)
Summary. In this paper, we use the method of integral representation and Schwinger‐Levine variational principle to describe, by means of a scattering matrix, the diffraction of plane, harmonic, monochromatic Love waves, incident normally (from either side) upon the plane of discontinuity in a structure consisting of a half‐space with a surface step—an idealized model of a continental margin. Approximate expressions for the elements of the scattering matrix are obtained through the plane‐wave approximation and their variational improvement is sought through the Schwinger—Levine variational principle. Complex reflection and transmission coefficients can be obtained through a transmission matrix related to the scattering matrix. We obtain the form of the transmission matrix (under both approximations) in some simple cases.