Sperm whale three-dimensional track, swim orientation, beam pattern, and click levels observed on bottom-mounted hydrophones.

In an earlier paper [Nosal and Frazer Appl. Acoust. 61, 1187-1201 (2006)], a sperm whale was tracked in three-dimensions using direct and surface-reflected time differences (DRTD) of clicks recorded on five bottom-mounted hydrophones, a passive method that is robust to timing errors between hydrophones. This paper refines the DRTD method and combines it with a time of (direct) arrival method to improve the accuracy of the track. The position and origin time of each click having been estimated, pitch and yaw are then obtained by assuming the main axis of the whale is tangent to the track. Roll is then found by applying the bent horn model of sperm whale phonation, in which each click is composed of two pulses, p0 and p1, that exit the whale at different points. With instantaneous pitch, roll, and yaw estimated from time differences, amplitudes are then used to estimate the beam patterns of the p0 and p1 pulses. The resulting beam patterns independently confirm those obtained by Zimmer et al. [J. Acoust. Soc. Am. 117, 1473-1485 (2005); 118, 3337-3345 (2005)] with a very different experimental setup. A method for estimating relative click levels is presented and used to find that click levels decrease toward the end of a click series, prior to the "creak" associated with prey capture.