A method is presented for passive localization of impulsive acoustic sources in a stratified ocean by measuring relative times of direct and surface-reflected arrivals at two hydrophones. The proposed method is based on ray theory and takes into account the effects of refraction on the geometry of acoustic paths ͑ray bending͒ and travel times, generalizing previous approaches based on the homogeneous-ocean assumption ͑straight-line localization͒. If the hydrophone depths are known, then the source depth and distance from each hydrophone can be estimated from the three differential arrival times. If in addition the hydrophone separation is known, the bearing of the source can be estimated as well. Apart from the effects on ray geometry and travel times, stratification affects localization by introducing shadow zones and caustics. For source locations in the neighborhood of caustics, the localization problem accepts two solutions, one of which is the true source location and the other one which is an artifact ͑ghost solution͒. This ambiguity can be resolved in the case of tracking moving sources since as the source moves away from the caustic only the track corresponding to the true source position will be continued. The present method has been developed primarily for monitoring the dive behavior of sperm whales producing acoustic clicks, yet it is general and can be applied for the localization and tracking of any kind of impulsive acoustic source in the ocean.

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A series of underwater acoustic localization experiments were conducted in the Eastern Mediterranean Sea to test the performance of a Bayesian method for localization of pulsed acoustic sources exploiting time differences between direct and surface-reflected arrivals at two hydrophones of known depth. The experiments involved a controlled source (pinger) at various depths/ranges as well as vocalizing sperm whales encountered off southern Crete. The localization method provides primarily range and depth information. In addition, if the location of the hydrophones in the horizontal is known, horizontal localization can be performed as well, subject to left–right ambiguity; this was applied for whale localization. The localization results confirmed the anticipated behavior of range, depth, and bearing estimation errors, which, according to theory, depend mainly on the source azimuth. In particular, range and depth estimation errors are larger for source locations close to broadside to the array and smaller towards endfire, and they increase with range. Conversely, bearing estimation errors are larger close to endfire and smaller towards broadside. Localizations in this paper were performed to ranges of about 3.5 km. The limiting factors for localization to longer ranges were the loss of ability to resolve direct and surface-reflected arrivals as well as the self-noise of the hydrophones.