Geometric Diffraction Loss in Longitudinal- and Shear-Wave Attenuation Measurements in an Isotropic Half-Space

Polar diagrams of the asymptotic (large R) stresses in an isotropic half-space, due to point-normal and line-tangential harmonic forces applied to the surface, are given for Poisson's ratio of 0.20 and 0.45. A reciprocity-theorem calculation of these stresses helps to give insight into interesting features of the diagrams. An approximate theory of geometric diffraction loss based upon the asymptotic stresses, which neglects all phase fluctuations across the receiver and, hence, cannot be used in the Fresnel region, is derived for the following sources: (a) normal stress applied to a circular area of radius a; (b) infinitely long, narrow strip (of half-width a) of shear stress with displacement normal to the length; mid (c) torsional shear stress applied to a circular area of the half-space. In all cases, the receiver is of the same size, centered on and parallel to the source. The diffraction loss αD (to±0.50 dB) is: Case (a)—αD(dB) = 1.0(λ/a2)z, 3 < (zλ/a2) < 13, which agrees with the same source radiating into a fluid; Case (b)—αD(dB) = 0.40(λ/a2)z, 4 < (zλ/a2) < 15; Case (c)—αD(dB) = 9+1.60(λ/a2)z, 5 < (zλ/a2) < 14, where the diffraction loss in this region is considerably higher than in either Case (a) or (b). In the case of an infinitely long, narrow strip of shear stress with displacement parallel to the length, the entire radiation pattern can be obtained by numerical integration. Using Papadakis' results [.J. Acoust .Soc. Am. 36, 414–422 (1964)], a general diffraction correction of about 0.50 dB (a2/λ) is in order.