Sound Scattering by a Submerged Shell Near the Sea Surface: Source and Receiver Close to the Shell

Abstract

Abstract In previous work we studied the scattering of incident plane sound waves by a spherical elastic shell submerged in water which was arbitrarily near its free surface (H. Huang and G. C. Gaunaurd, Proceedings, 1995a). That study presented an exact solution of the problem valid for any shell depth beneath the free surface, and it used the method of images and the addition theorem for the spherical wave functions. We study the problem again, here, for cases in which the incident waves are now emitted from point sources anywhere in space beneath the free surface (i.e., close to the shell or to the free surface), and the receiver can pick up the scattered returns from arbitrary space positions. Among the many detailed results of the present study, it was found that for a point source near the shell, the scattered field is significantly different from that produced by a plane incident wave. [That field, in turn, is different from that returned in the elementary case of a shell in “free space”, i.e., away from any boundary.] A number of comparisons are shown as the shell and point-source take on positions that are: (1) at different depths beneath the free surface, and (2) at different distances from each other. For point sources more than twenty shell radii away from the shell, the far-field backscattered echo is not much different from that produced by a plane incident wave incident on the shell at the same depth. Our earlier solution can then be used in such cases. For point sources any closer to the shell, the present solution must be used. In such cases, as the shell and point source move further away from the free surface, together, a pattern of rapid oscillations is developed in the resulting form function which is the precise generator of the Lloyd’s mirror effect of elementary acoustics. The scattered field generated by an array of such point sources insonifying the shell, can also be obtained by a linear superposition of the exact solution given here.