Passive moving source ocean acoustic tomography with uncertainty quantification using relative arrival times from a ship of opportunity

An ocean acoustic tomography inversion with uncertainty quantification has been performed in the Santa Barbara Channel using relative arrival times obtained from the radiated noise of a ship of opportunity received by two 32-element vertical line arrays, at ranges from approximately 1.8 km at the closest point of approach to approximately 2.5 km at the maximum receiving range. The sound-speed estimate agrees [with a root mean square (rms) difference of 0.71 m/s] with an estimate performed about 40 min later [Gemba et al. (2022). J. Acoust. Soc. Am. 151(2) 861-880] using a controlled source and absolute travel times. The estimate using relative arrival times is less constrained (1.42 m/s rms uncertainty) than with absolute travel times (0.89 m/s rms uncertainty). The relative proximity of the ship noise source to the surface and the geometry at these short ranges result in a depth-varying interference between surface-reflected and direct arrivals. The interference effect on the estimated time delays is larger when computed with respect to a single element but minimal when estimated between adjacent elements. The relevant equations for relative travel time ocean acoustic tomography are presented.