Fig 1.
A bathymetric map of the continental margin and Cascadia Basin offshore the Pacific Northwest showing the configuration of the seismic network used to track blue whales. A total of 38 ocean bottom seismometers (OBSs) from the first year of the Cascadia Initiative (CI) experiment (triangles) were combined with three stations from the Ocean Networks Canada (ONC) NEPTUNE cabled observatory (circles). The full network was in operation from November 29, 2011, to May 13, 2012. Depths are shown by a color scale with contours at 200 m and 2500 m. The inset figure shows the location of the experiment on the globe. Bathymetric data were obtained from the Global Multi-Resolution Topography (GMRT) Synthesis (data DOI: 10.1594/IEDA.100001) [24] and are available for use under a CC BY 4.0 license. The figure was created with the Generic Mapping Tools software [25].
Fig 2.
Example spectrogram and detections.
(a) Spectrogram of 30 minutes of data with arbitrary scaling from station J53A starting at 03:30:30 UT on December 11, 2011, showing a sequence of strong Northeast Pacific blue whale calls. An earthquake is also apparent at ~1200 s as a vertical band of energy. (b) As for (a) but normalized by subtracting the median at each frequency and shown with a color scale for values that exceed the 90th percentile value. (c) Four-minute segment of the spectrogram from (a) with A and B calls labeled. (d) Cross-correlation kernel that is tuned to the slope of the first half of the B call. (e) Recognition score (RS) for (c) with the minimum threshold of 2.2 shown as a dashed line. Three B calls are strong detections and both the A call and a faint feature early in the spectrogram register as weak detections.
Fig 3.
(a) Histogram with a logarithmic scale showing the call count for Cascadia Initiative station J28A for the automatic detector as a function of the peak recognition score (dark gray) and the calls that were identified independently by an analyst as a definite blue whale (light gray). The scaling of the peak recognition score is arbitrary. (b) Precision (number of true positives divided by the sum of true positive and false positives) of automatic blue whale detections as a function of the minimum peak recognition score determined by treating the analyst identifications as ground truth (solid line and circles) and as inferred by comparing detection rates between the calling and non-calling season for blue whales (dashed line and triangles). (c) Precision-recall curve for the automated detection based on treating the analyst detections as ground truth. The recall is the number of true positives divided by the sum of true positives and false negatives. Labels indicate the threshold for the peak recognition score.
Fig 4.
A histogram showing call detections on station J28A as a function of time in 10-day bins. (a) Calls identified by an analyst as a definite blue whale. (b) Automated detections with peak recognition scores exceeding 4 (light gray), 5 (medium gray) and 6 (dark gray). Dashed vertical lines bound the assumed calling season.
Table 1.
Rate and estimated precision of automated detections.
Table 2.
Localization parameters.
Fig 5.
Correct localization with method 1.
An example of a successful localization using method 1 that used the likelihood function of Eq (3) for a master detection on station J53A at 00:05:35 UT on December 13, 2011. The upper two panels are maps showing (a) the logarithm of the likelihood function L(x) (Eq 3) and (b) the probability density function P(x) (Eq 8) with a color scale. Labeled squares show stations, with filled squares indicating stations with detection times in the solution. The 95% probability area of the location is shown by a bold black contour. (c) Eight spectrograms for 4 minutes of data starting one minute before the master detection with detections used in the solution shown as solid black labeled with the estimated probability the detection is a true positive, other detection times as thin dashed black lines, and the predicted arrival times as dot-dashed red lines. Spectrograms are created with a 4-s-window and 95% overlap, normalized by subtracting the median at each frequency, and shown as a color scale for values that exceed the 90th percentile value. Example A and B calls are labeled on the spectrogram for station J54A.
Fig 6.
Incorrect localization with method 1.
An example of an incorrect localization obtained with a master detection on station J53A at 00:02:30 UT on December 13, 2011, obtained using method 1 plotted using the same conventions as Fig 5.
Fig 7.
Correct localization with method 2.
A correct localization for the same master detection as Fig 6 obtained using method 2 based on Eq (6) that maximizes the number of high probability nearby detections. The upper panels show (a) the function E(x) of Eq (6) with the highest value shown by a black x-mark, and (b) the probability function of Eq (8) plotted using the same conventions as Fig 5. The lower panels show spectrograms plotted using the same convention as Fig 5.
Fig 8.
Characteristics of localizations.
Histograms showing characteristics of the solutions for a 3-day interval from December 13 through December 15, 2011, obtained with a minimum master detection probability of 0.9 and a minimum detection probability of 0.2. (a) The estimated probability of the 4th most probable detection in the localizations from method 1 (Eq 3) shown for all locations, locations within tracks and locations in tracks with at least 20 calls. (b) As for (a) but for the 5th most probable detection for the subset of solutions with at least 5 detections. (c) The number of stations in the solution obtained with the method 1. (d) The maximum value of E(x,t′) (Eq 6) for localizations from method 2 which favors detections with high probabilities near the location.
Fig 9.
A localization plotted using the same conventions as Fig 5 obtained using Eq (3) with a master detection on station J53A at 04:24:41 UT on December 15, 2011, that fits 9 detection times.
Fig 10.
Second ambiguous localization.
A localization plotted using the same conventions as Fig 5 obtained using Eq (3) with a master detection on station J52A at 04:25:22 UT on December 15, 2011, that fits 8 detection times. This solution incorporates the same detections for station J52A and J44A as Fig 9, but otherwise fits a different set of detections.
Fig 11.
Characteristics of a reliable track.
Some characteristics of an example track that is considered reliable, comprising 33 locations on December 14 between 1334 and 1519 UT. (a) Locations of calls in the track (red pluses) and seismic stations (black triangles). (b) Locations of stations that contribute detections to the localization of each call in the track plotted relative to the call location and color coded by the estimated probability that the detection is a true positive. Open circles indicate stations that are missing from the localization but that were recording detections as evidenced by the presence of at least one detection within a time window extending from 60 s before the first detection in the localization to 120 s afterwards. (c). Cumulative count of detections contributing to the call localizations as a function of the range to the location (black solid line) and of stations for which detections are missing in the localization but for which at least one detections is available at the station from 60 s before the first detection to 120 s afterwards (red dashed line). Also shown is the ratio of these two counts (dot-dashed blue line). (d) Histogram showing the time between of successive locations in the track.
Fig 12.
Characteristics of an unreliable track.
As for (a) except for an example track that is considered unreliable, comprising 13 locations on December 13 between 0931 and 1117 UT.
Table 3.
Results of processing data from December 13 through December 15, 2011.
Fig 13.
Statistics of locations in tracks.
Characteristic of the locations within tracks obtained by first assigning detections to locations within tracks using one localization method and then using the other method to obtain the final locations. These plots are for a minimum probability of master detections and all detections of 0.9 and 0.2, respectively but the plots have similar characteristics for tracks obtained with all the choices of minimum probabilities listed in Table 3. (a) Histogram of the travel time misfits normalized to the assumed uncertainties (Table 1) for master detections (dark shading) and all detections (light shading) for locations in tracks with ≥ 20 locations with the final locations obtained using localization method 1 (Eq 3). A solid line shows a Gaussian distribution fit to the histogram which has a standard deviation of 0.96. (b) As for (a) except the final locations are obtained with localization method 2 (Eq 6). The Gaussian distribution fit to the histogram has a standard deviation of 1.35. (c) Histogram of the smallest horizontal 1-σ location error for all tracked locations (light shading) and tracks with ≥20 locations (dark shading) for final locations obtained with localization method 1. (d) As for (c) but for the largest horizontal location error.
Fig 14.
Smooth paths for a long track.
An example of smoothed paths that are fitted to a track comprising 355 call locations between 0021 UT and 1834 UT on December 13, 2011. (a) Smoothed tracks obtained using the method of Eq (15) with three choices of smoothing weight after discarding the 21 outlying locations. Call locations are shown as faint plus symbols with an ellipse illustrating the average location uncertainty. The mean squared normalized spatial misfit is 2.49, 2.07 and 1.81 for smoothing weights α = 108, 106 and 104, respectively. Also show is a smoothed track based on averaging locations temporally by weighting with a Gaussian function with a 20-minute standard deviation. (b) Tracks obtained using the double-difference method of Eq (19). The starting data set comprises 13,174 double-difference times and is constructed by linking each call to up to 8 calls within the next hour if there are four common stations. The solutions were obtained with 5 iterations at each smoothing weight and with poorly fitting double difference times discarded after 3 iterations if the absolute misfit exceeded three times the assumed uncertainty. Totals of 11,999, 11,683 and 11,625 difference times were used in the final solutions for smoothing weights of β = 10, 2, and 0.5, respectively. The mean variances of the double difference time misfits normalized to their assumed uncertainties are 0.58, 0.44, and 0.41. (c-d) Speed as a function of time corresponding to the tracks shown in (a) and (b), respectively.
Fig 15.
Smooth paths for a short track.
As for Fig 14 except for a track with 92 locations from 0132 UT to 0611 UT on December 15, 2011. (a) Solutions are obtained after discarding 11 outlying locations and the mean squared normalized spatial misfit is 2.22, 2.14 and 1.97 for smoothing weights α = 108, 106 and 104, respectively. (b) The starting data set comprises 3638 double difference times and 3204, 3161 and 3159 are used in the final solutions for smoothing weights of β = 10, 2, and 0.5, respectively. The mean variances of the double difference time misfits normalized to their assumed uncertainties are 0.44, 0.37 and 0.36.