Quick Search:    advanced search

GSW Home   GeoRef Home   My GSW Alerts   Contact GSW   About GSW   Journals List   Help

This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by KAZI, M. H. Articles by NIAZY, A. Search for Related Content GeoRef GeoRef Citation

Generalization of Higuchi's conditions for Love waves propagating through two welded quarter-spaces with two surface layers on each

DEPARTMENT OF MATHEMATICAL SCIENCES UNIVERSITY OF PETROLEUM AND MINERALS, DHAHRAN, Saudi Arabia
DEPARTMENT OF EARTH SCIENCES UNIVERSITY OF PETROLEUM AND MINERALS, DHAHRAN, Saudi Arabia

Abstract

Higuchi (1932) considered a medium consisting of two quarter-spaces in welded contact, each having a single homogeneous layer of the same thickness overlying a homogeneous half-space, and gave conditions on the rigidities and densities of the two layers and two half-spaces in such a way that the plane Love waves normally incident on the vertical plane generate only reflected and transmitted Love waves without mode conversion or body-wave scattering.

In this paper, we generalize Higuchi's results to two layers overlying a half-space divided by a vertical plane. On one side of the vertical plane, the shear velocities and rigidities for the top and the bottom surface layers, and for the half-space are ß₁, µ₁, ß₂(>ß₁), µ₂(>µ₁), and ß₃(>ß₂), µ₃(>µ₂), respectively. On the other side, the corresponding shear velocities and rigidities for the two layers and the half-space are given by the primed quantities with ß₃' > ß₂' > ß₁' and µ₃' > µ₂' > µ₁'. We show that if the following conditions are satisfied

and

then plane Love waves normally incident on the vertical plane generate only reflected and transmitted Love waves without mode conversion or body-wave scattering. These conditions for the special case under consideration provide a valuable check for various analytical and numerical approximations which ignore the body-wave contributions in similar diffraction problems.