Beaked whales have been reported to mass strand as result of naval sonar exercises and the ability to mitigate such negative effects is of increasing importance. We present results that suggest that passive acoustic detection of beaked whales is feasible using broadband hydrophone arrays towed at shallow depths. In particular, the presence of delayed surface reflections is an important classification cue indicating that the received sound had been generated by a whale foraging at depth. This contextual information can easily be visualized by time-delay estimation techniques. We show that the use of non-acoustic contextual information of a deep diving foraging whale provides a promising approach to improving the classification performance of a passive acoustic detector of beaked whales.