Separation and Analysis of the Acoustic Field Scattered by a Rigid Sphere

The scattered field calculated when a plane acoustic wave is incident upon an ideally rigid sphere is considered as a composite and resolved into two parts. One part, which includes the specularly reflected contribution to the field, arises out of scattering by the bright hemisphere—the scattering sphere being divided into two regions by the boundary of the geometrical shadow. The second part, owing to scattering by the shadow side of the sphere, includes the major part of the radiation due to creeping waves. This separation is consimilar with the separation of the scattered field that is made in the creeping-wave formulation of scattering theory. The separation is made here, however, by treating the scattering sphere as a spherical radiator and solving a pair of boundary-value problems by classical means. Each of the boundary-value problems is related to one part of the scattered field. Both parts are found to yield scattering components that are related to “image pulses” such as are predicted when scattering problems involving transient signals are analyzed using theory based on the Kirchhoff approximation. It is found, however, that the image-pulse-type returns, which arise out of the exact classical theory, cancel when the two separate parts of the scattered field are added together, so that, in the complete scattered field, no image-pulse-type return is detectable. It is also found that a secondary creeping-wave component originates in the scattering from the bright side of the sphere. This result indicates that the generation of creeping waves may not be a phenomenon taking place solely at the geometrical shadow boundary. Moreover, it is found that the part of the scattered field which yields the specularly reflected return can be very closely approximated by the scattered field that would be predicted by calculations incorporating the Kirchhoff approximation. Interference between the various components, identified as a result of the separation, explain a number of features of the scattering behavior observed when long pulses are incident on the sphere.