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Reflection and diffraction of SH waves due to a line source in a heterogeneous medium

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Abstract

The field due to a line source of harmonic SH waves embedded in a semi infinite medium whose density and rigidity vary exponentially with depth is derived in the integral form. The displacement due to diffraction at any point in the shadow zone is obtained and, by the saddle point method of evaluation of the integral, the field at any point in the illuminated region is also found. Finally, geometrical interpretation is given to the different rays arriving in the illuminated as well as in the shadow zone.

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Abbreviations

b :

shear wave velocity on the free surface

C :

wave velocity

H (1) v (p), H (2) v (p):

Hankel's function of the first and second kind respectively

k :

Fourier transform parameter with respect to x

v :

the displacement

\(\overline V\) :

fourier transform of v with respect to x

X :

grazing angle

α, β :

small positive constants

γ :

positive constant, β−α/2

μ 0 :

coefficient of rigidity at the free surface

μ :

coefficient of rigidity

μ is :

values of μ i at the saddle point (i=1, 2, 3, 4)

ρ :

the density of the medium

ρ 0 :

the density of the medium at the free surface

ω/2π :

frequency of vibration

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Authors and Affiliations

  1. Dept. of Mathematics, Bengal Engineering College, Howrah-3, West Bengal, India

    M. L. Ghosh

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  1. M. L. Ghosh
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Ghosh, M.L. Reflection and diffraction of SH waves due to a line source in a heterogeneous medium. Appl. Sci. Res. 23, 373–392 (1971). https://doi.org/10.1007/BF00413212

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  • DOI: https://doi.org/10.1007/BF00413212

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