Probabilistic Estimation of Merchant Ship Source Levels in an Uncertain Shallow-Water Environment

The estimation of ship source levels (SSLs) in shallow-water environments can be complicated by sound interaction with the seabed. Uncertainty in seabed properties influences SSL estimates, and it is of interest to mitigate and quantify such effects. This article proposes a probabilistic approach to ship radiated noise recorded on a vertical line array (VLA) of hydrophones to infer SSL and properties of a mud-sand shallow water seabed on the New England Shelf. The approach, trans-dimensional Bayesian marginalization, samples probabilistically over complex spectral source strengths, source depths/ranges, and number of seabed layers and geoacoustic parameters of each layer. The Bayesian information criterion is applied to determine the appropriate number of (point) sources used to describe a ship. Radiated noise due to two merchant ships passing the VLA at beam aspect at 3.2−3.4-km range is considered. The SSL estimates agree well with reference spectra from shallow-water studies on large ensembles of merchant ships. The average SSL uncertainty (in terms of one-half the interquartile range interval) is 3.2 dB/Hz for low-frequency narrowband (20−120 Hz) and 1.8 dB/Hz for broadband noise (190−590 Hz). Seabed layering and geoacoustic parameter estimates agree reasonably well with mud-over-sand seabed models from other inversions in the area.