Elastic Wave Diffraction of a Piston Source and Its Effect on Attenuation Measurement

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.