Axially focused (glory) scattering due to surface waves generated on spheres: Model and experimental confirmation using tungsten carbide spheres

Abstract

When a short tone burst is incident on a tungsten carbide sphere in water, the backscattering response shows a decaying pulse train [L. R. Dragonette, S. K. Numrich, and L. J. Frank, J. Acoust. Soc. Am. 69, 1186–1189 (1981)] which can be attributed to a specular reflection and repeated circumnavigations of other waves. We experimentally investigate the angular dependence of Rayleigh wave contributions as the receiver is moved away from the backscattering axis. It is found that this angular dependence can be approximately described by J0(β γ), where β depends on the frequency of the sinusoidal tone burst used (or equivalently the ka of the sphere) and γ measures the angle relative to the backscattering axis. We show how this form of angular dependence may be attributed to a weak axial focusing along the backward direction. This form is consistent with properties derived from Sommerfeld–Watson transforms for scattering from spheres. Our model includes a prediction of how β will vary with ka. The model is given in a general sense and then specialized to tungsten carbide for experimental confirmation. Experimental results in the range 30<ka<100 are compared with theory. Some implications concerning the backscattering from nonspherical objects are also discussed.