Effect of the target scattering function on active waveguide invariance striations

The waveguide invariant has been widely studied and applied in the context of shallow water passive sonar. The invariant provides a simple linear relationship between the frequency content of a moving broadband source and the propagation range, and this relationship is not generally sensitive to small variations in environment parameters. Recent research has shown that a similar structure can be obtained for active sonar geometries, and it has been demonstrated that this structure may be exploited in advanced physics-based processing applications. However, the appearance of the active invariance striations depends on the sonar geometry (source-target-receiver ranges) as well as the scattering properties of the target. Controlled tank measurements with canonical scatterers (sphere, cylinder, plate) were performed to quantify the effect of the scattering function. Additionally, a theoretical formulation is presented to explain the invariance structure as a function of the geometry and target scattering properties. This paper presents results of these measurements, normal mode simulations, and theoretical expressions. The results show that targets which have wide (vertical) scattering patterns can couple ingoing and outgoing propagating modes, and this coupling results in time-frequency striations that are related to source-target-receiver ranges. Conversely, targets with no mode coupling produce striation patterns that correspond only to the time varying bistatic target range.