Understanding deep-water striation patterns and predicting the waveguide invariant as a distribution depending on range and depth

The Waveguide Invariant (WI) theory has been introduced to quantify the orientation of the intensity interference patterns in a range-frequency domain. When the sound speed is constant over the water column, the WI is a scalar with the canonical value of 1. But, when considering shallow waters with a stratified sound speed profile, the WI ceases to be constant and is more appropriately described by a distribution, which is mainly sensitive to source/receiver depths. Such configurations have been widely investigated, with practical applications including passive source localization. However, in deep waters, the interference pattern is much more complex and variable. In fact the observed WI varies with source/receiver depth but it also varies very quickly with source-array range. In this paper, the authors investigate two phenomena responsible for this variability, namely the dominance of the acoustic field by groups of modes and the frequency dependence of the eigenmodes. Using a ray-mode approach, these two features are integrated in a WI distribution derivation. Their importance in deep-water is validated by testing the calculated WI distribution against a reference distribution directly measured on synthetic data. The proposed WI derivation provides a thorough way to predict and understand the striation patterns in deep-water context.