Modeling the Waveguide Invariant as a Distribution

The “invariant parameter” called “beta” is often useful for describing the acoustic interference pattern in a waveguide. For some shallow water waveguides, the measured acoustic intensity might contain contributions from several propagating acoustic modes. For each pair of these modes, a different value for the waveguide invariant might apply. If the acoustic intensity is measured over some distributed aperture and finite bandwidth, it may become difficult to assign a single value to beta. In the present work, the waveguide invariant is treated as a distribution. An algorithm for estimating this distribution for a general measurement geometry is developed. The algorithm is exercised for different classes of shallow water waveguides. When the propagation is dominated by modes interacting with the sea surface, the distribution can be sharply peaked. For cases where the sound speed profile creates a duct, the distribution is more diffuse. The effects of source/receiver depth, range, bandwidth and bottom attenuation are quantified.