Open AccessThe asymptotic structure of the surface wave dispersion diagram for plane‐stratified earth models with several turning points
Author(s) -
Kerry N. J.
Publication year - 1981
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.1981.tb02747.x
Subject(s) - dispersion (optics) , reflection (computer programming) , mathematical analysis , asymptotic analysis , turning point , shear (geology) , shear waves , surface wave , surface (topology) , plane (geometry) , mathematics , point (geometry) , geology , mechanics , physics , geometry , optics , acoustics , computer science , petrology , period (music) , programming language
Summary Asymptotic approximations to the dispersion equations for trapped waves in stratified elastic media are obtained under conditions such that shear waves have more than one turning point. These approximate equations are then solved to examine quantitatively the interaction between crustal and channel type surface wave modes. Asymptotic expressions for the reflection and transmission coefficients for the same media are also found in order to provide a more rigorous justification of some previous results. Finally a non‐uniformity of the initial asymptotic solution is identified and a uniformly valid solution indicated.