Elastic Wave Diffraction Of A Piston Source And Its Effect On Attenuation Measurement
Name
1988.10 Tang et al.pdf
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583.88 KB
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Author(s)
Tang, X. M.
Toksoz, M. N.
Cheng, C. H.
Date Issued
1988
Publisher
Massachusetts Institute of Technology. Earth Resources Laboratory
Series/Report no.
Earth Resources Laboratory Industry Consortia Annual Report;1988-10
Abstract
The radiation of an elastic wave field from a plane piston source is formulated using
the representation theorem, in which the Green's function for an elastic half space
is employed. On the basis of this formulation, we derive the radiated elastic wave
field for both compressional and shear wave sources. We study the diffraction of
elastic waves incident on a receiver that is coaxially aligned with the source. We
present a procedure in which both numerical and asymptotic techniques are employed
to allow us to evaluate the diffraction effects in any frequency range of interest. We
compare the elastic diffraction with the acoustic diffraction and find that they are
different in the near field of the piston source due to the coupling between shear and
com pressional components in the elastic case. In the far field, however, the elastic
diffraction approaches the acoustic diffraction. With the help of ultrasonic laboratory
measurements, we test the theoretical results and find that the theory and experiments
agree well. An important result of this study is that in attenuation measurements with
pulse propagation techniques where spectral ratio relative to a standard sample or ratio
of samples of the same material but of different lengths is used, it is necessary to correct for diffraction effects. In the attenuation measurement using spectral ratio of a sample and a standard reference sample, the attenuation can be overestimated, while in the attenuation measurement using a spectral ratio of samples of different lengths, the
attenuation can be significantly underestimated, if corrections for diffraction effects
are not made.
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