A Waveguide-Invariant-Based Warping Operator and Its Application to Passive Source Range Estimation

A formula for the instantaneous phase of the cross-correlation function of two different modes using the relationship between the horizontal wavenumber difference and frequency described by the waveguide invariant is deduced in this paper. Based on the formula, a waveguide-invariant-based warping operator suitable for both reflected and refracted modes in shallow water at low frequency is presented, providing an effective tool to filter the cross-correlation function of modes from the signal autocorrelation function. Using the phase of the filtered cross-correlation component in the frequency domain, a passive source ranging method on a single hydrophone is proposed. Simulated and experimental data using impulsive signals verify the validity of the derived warping operator and source ranging method.