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7.—High-frequency Scattering in a Certain Stratified Medium*

Published online by Cambridge University Press:  14 February 2012

W. G. C. Boyd
W. G. C. Boyd
Affiliation:
Department of Mathematics, University of Dundee
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Synopsis

The propagation of scalar waves in a certain stratified medium is studied; the field is due to a line source situated on an opaque plane boundary. The exact field can be expressed in terms of a Fourier integral involving Airy functions. By deforming the real axis, which is the contour of integration of the Fourier integral, only in the neighbourhood of the real axis, it is possible to give a simple but rigorous derivation of the asymptotic nature of the field. Two separate cases are considered: the point of observation lying in the illuminated region, when a steepest descents analysis is appropriate, or lying in the shadow region, when the asymptotic field is given by a residue series.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 72 , Issue 2 , 1974 , pp. 93 - 107
Copyright
Copyright © Royal Society of Edinburgh 1974

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References

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