Learning the Acoustic Background for Weak Vessel Observability through Temporal Probabilistic Deviations

Rather than learning what vessels sound like, we model the acoustic background itself. This motivates a distinction between vessel presence and vessel observability: the former is a geometric condition, whereas the latter depends on whether the received acoustic signal is distinguishable from the prevailing soundscape. We introduce Probabilistic Background Support Modelling (PBSM), a background-first framework that learns the local operational acoustic background from no-contact recordings and identifies statistically unusual 30-second observations as acoustic departures. Rather than assigning these departures to a predefined acoustic class, PBSM reduces large passive-acoustic datasets to short-duration observations warranting further investigation. An Empirical Background Anomaly Percentile (EBAP) expresses departure relative to the learned background, while a matched 30-second no-contact control accounts for departures caused by temporal representation. Acoustic scoring is blind to vessel position, range, Closest Point of Approach (CPA), and identity. Identified departures are subsequently examined for substantive spectral excess, with AIS-derived vessel geometry introduced only afterward as an independent physical reference. Across eight station-season datasets, short-duration background variability can itself produce substantial acoustic departure, demonstrating that departure alone cannot be interpreted as vessel detection. The prevalence and discriminative value of PBSM departures vary across operational environments, while spectral characterization can retain meaningful acoustic structure even where background departure is prevalent. Where PBSM departure, substantive spectral excess, and vessel proximity converge, increasingly strong acoustic evidence is observed as CPA decreases. The principal contribution is their integration into a background-first evidence chain for acoustic observability: learn the local operational background, identify unusual observations blindly, characterize their spectral structure, and use independent vessel geometry to interpret the resulting evidence.