Using nonlinear time warping to estimate North Pacific right whale calling depths in the Bering Sea

Calling depth distributions are estimated for two types of calls produced by critically endangered eastern North Pacific right whales (NPRWs) in the Bering Sea, using passive acoustic data collected with bottom-mounted hydrophone recorders. Nonlinear time resampling of 12 NPRW "upcalls" and 20 "gunshots" recorded in a critical NPRW habitat isolated individual normal mode arrivals from each call. The relative modal arrival times permitted range estimates between 1 and 40 km, while the relative modal amplitudes permitted call depth estimates, provided that environmental inversions were obtained from high signal-to-noise ratio calls. Gunshot sounds were generally only produced at a few meters depth, while upcall depths clustered between 10 and 25 m, consistent with previously published bioacoustic tagging results from North Atlantic right whales. A Wilcoxon rank sum test rejected the null hypothesis that the mean calling depths of the two call types were the same (p = 2.9 × 10^-5); the null hypothesis was still rejected if the sample set was restricted to one call per acoustic encounter (p = 0.02). Propagation modeling demonstrates that deeper depths enhance acoustic propagation and that source depth estimates impact both NPRW upcall source level and detection range estimates.