Three-dimensional passive acoustic tracking of sperm whales (Physeter macrocephalus) in ray-refracting environments.

A wide-aperture towed passive acoustic array is used to obtain ranges and depths of acoustically active sperm whales in the Gulf of Mexico in June 2004, by extending a technique previously reported [Thode, J. Acoust. Soc. Am. 116, 245-253 (2004)] to explicitly account for ray-refraction effects arising from a depth-dependent sound speed profile. Under this expanded approach, three quantities are measured from an impulsive sound: the time difference between direct-path arrivals on a forward and rear subarray, the time difference between the direct and surface-reflected paths on the rear subarray, and the acoustic bearing measured on the rear subarray. These quantities, combined with independent measurements of hydrophone depths and cable inclination, are converted into range-depth position fixes by implementing an efficient numerical procedure that uses a ray-tracing code to account for ray-refraction effects caused by depth-dependent sound speed profiles. Analytic expressions that assume a constant waterborne sound speed are also derived. Foraging depths of various sperm whales over 10 days in June, 2004 are estimated using the numerical technique.