Modeling signal coherence for a large number of samples

Seabed-reflected sound measurements allow researchers to better understand the ocean environment based on the received signal’s structure. This signal structure is affected by seabed characteristics, like seafloor slope, sediment impedance, and sediment layering. The seabed composition influences both the coherent (signal phase is preserved) and incoherent (signal phase is disrupted) components of the scattered signal. This environmental influence can be studied with the spatial coherence of the scattered field, which is estimated by the magnitude of the complex correlation coefficient (|ρ|) between channels in a normally directed receive array. This work’s primary focus is applying the PDF of the coherence of the scattered field to understand the ocean environment. However, measurements of interest capture transient seafloor properties, like sediment layering, that are non-uniformlypowerful; these variations occur over large scales, which increases the number of measurement points per transmission without maintaining joint independence. To model transient returns with the magnitude coherence PDF (which assumes joint independence), an equivalent number of independent samples is derived and validated for the PDF. Results are presented for multi-channel synthetic data (white Gaussian noise) and for seabed scattered signals; measurements were made with a Kongsberg SBP-29 aboard R/V Sally Ride in 2024.