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Diffraction of Love waves by perfectly rigid and perfectly weak half-planes

DEPARTMENT OF APPLIED MATHEMATICS AND THEORETICAL PHYSICS, SILVER STREET, CAMBRIDGECB3 9EW, U.K.

Abstract

In this paper we investigate the transmission and reflection of Love waves, normally incident on a perfectly rigid half-plane or a perfectly weak half-plane, which lies in a layer of uniform thickness, overlying a semi-infinite solid. The half-plane is parallel to the interface of the two materials and lies in the upper layer. The perfectly rigid half-plane is a domain of vanishing displacement, whereas the perfectly weak half-plane is a domain of vanishing traction. We use the Wiener-Hopf technique based on an approach due to D. S. Jones (1952). Such a method has previously been employed by R. Sato (1961) in his paper on Love waves incident on a change of thickness in the surface layer.

We set up the two boundary value problems, and obtain analytical solutions for transmitted and reflected Love and channel waves in the case of the rigid as well as the weak screen. We draw the following conclusions:

1. Love waves incident on the screens are diffracted by the screens into Love-type modes propagating in the half-strip which overlies the half-space, and channel waves in the upper half-strip.

2. Most of the channel modes die out rapidly with the distance from the edge of the screens.

Finally, we show the connection between the problem of Love waves past a weak screen and Sato's problem of Love waves incident on a vertical step discontinuity in the surface layer, from the thicker to the thinner side.

Footnotes

^* On leave from the Department of Mathematics, Punjab University (New Campus), Lahore, Pakistan.

This article has been cited by other articles:

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