Source Depth Discrimination in Shallow Water Using Modal Correlation Scintillation Index

Traditional methods for the source depth discrimination encounter the problem of performance degradation when the surface or internal wave motions cause variations of the source depth. While the modal scintillation index (SI) can classify surface/submerged source by using the fluctuations in the received pressure field. However, calculating the SI requires normal mode functions in advance, which is difficult to obtain accurately in practice (sound speed profile or long enough aperture desired). To address this problem, we propose a method to utilize modal correlation scintillation index to separate surface and submerged sources on a single receiver requiring only knowledge of the water depth. Specifically, we extract the autocorrelations and the cross-correlations of normal modes from the received signal autocorrelation function via warping transform. The variance in the estimated magnitude of the modal autocorrelations and the cross-correlations normalized by the squares of their expected value over some observation intervals are defined as modal autocorrelation scintillation index (MACSI) and modal cross-correlation scintillation index (MCCSI), respectively. The derivation and the simulation results provide that a source near the surface (all products of mode functions sharing a common zero-crossing) will exhibit scintillation indices with large values, while with small values for a submerged source near at least one product extremum. The method can be used to determine the depth of the source with unknown sound speed profile details or sound source range, and no need for the source movement.