This is a technical note about improvements to the calibration of the hydrophone locations, which are critical to getting an accurate back azimuth on a source signal. The information may be helpful to oceanographers doing future research.
This is also a note of appreciation to Warren Gray with Seisintel.com, a seismic survey monitoring service. Warren took a personal interest in this MH370 location project and spent three months, from March to May 2018, researching and obtaining the seismic survey data needed to refine the calibrations.
There were two active hydrophone triads with available data in the Indian Ocean on March 8, 2018 when flight MH370 crashed into the sea. For the purpose of detecting nuclear explosions, The CTBTO operates array H01W near Cape Leeuwin, Australia, and H08S near Diego Garcia. Signals can propagate very long distances across oceans once they enter the SOFAR deep sound conduction channel.
The direction of arrival of a hydroacoustic sound is determined using TDOA (Time Difference Of Arrival) measurements as the wavefront passes each hydrophone. This is typically accomplished by cross-correlating the signals from each hydrophone to get three delay values. The algorithms used for converting the delay values to a bearing despite noise have been discussed in previous posts here and the math is well covered in published scientific reports. Much of this work comes from government research agencies and Curtin University.
Regardless of the algorithm, accuracy of the bearing is essentially dependent on knowing the orientation and placement distances between the hydrophones. It is also limited by the sampling rate used in the recording of the signal data.
Using a selection of various acoustic events from different directions on the day of interest, along with an iterative linear optimization method to minimize delay errors, the placement of the hydrophones relative to each other can be determined. The result has been that the three signals are well aligned in phase at the proper bearing, without any obvious need for nonlinear timing correction by azimuth.
The sampling rate of the signal normally provides a basic limit to measuring the time delay between receivers. The cross correlation peaks showing delay values are only resolved at the sampling rate, regardless of the noise. Noise can be minimized by correlation of longer sample windows from a particular source. The sampling rate of the CTBTO arrays is 250 Hz, which gives a useful resolution of about 0.1 degrees in bearing precision.
To get better bearing precision, a simple approach of oversampling the signals before cross-correlation has been very useful. The best method for resampling the signals has been to fit a smooth spline to the original data points in the recording. There is of course no increase in the bandwidth beyond the Nyquist rate of 125 Hz, but up to 8x oversampling gives a corresponding improvement in the bearing precision to about 0.01 degrees. This is especially useful when running the calibrations.
Improving the relative placements gives very consistent results, but useful bearing accuracy is still dependent on knowing the rotational orientation of the triad array. Some known reference locations for distant events are needed.
Seismic sources do not necessarily conduct into the SOFAR channel above the determined hypocenter of a quake, and the distance error may be hundreds of kilometers. Ice events at a documented location are also rare. Another persistent source of ocean acoustic events in the SOFAR channel are seismic surveys in coastal waters.
Ocean seismic surveys are typically conducted in the search of oil reserves. An array of hydrophones is towed behind a ship, along with a loud impulsive sound source, typically a compressed air cannon. Like sonar, the complex reflections recorded can reveal the structure of the geologic substrata under the seabed. These loud noise sources that repeat several times a minute are towed for weeks on end to survey a large area. The sound clutter from surveys can propagate into the SOFAR channel by following the slope of the coastal shelf into deeper water at around 1000m. Each air cannon blast is like a small impact near the surface. While seismic survey clutter has made detection of an MH370 impact over deep water far more difficult, an accurate ship location can be useful for calibration the hydrophone array rotation.
Only on array H08 was there a known survey source until recently, as shared by Alec Duncan and documented in his report to the ATSB (see Appendix H of The Operational Search for MH370 – Final Report, Oct 2017.)
The orientation of the H08 array was pinned by signals from around bearing 113 degrees, the dominant seismic survey running nearly continuously off the coast of Australia, NE of Exeter.
Repeating signals seen from bearing 324 from H01 on March 7 around 23:23 and H08 bearing 34 throughout the day led to speculation of a possible source in the Bay of Bengal near N11.5 E85.5, which would have put it over deep water. This was perhaps wishful thinking that some portion of strong surface events over deep water might get conducted into the SOFAR channel.
In reaching out to Alec Duncan, he confirmed that a survey location in the middle of the Bay of Bengal was unlikely to be detected, and also noted that it was atypical for the crustal structure where a survey for energy reserves would be conducted. He inspired a closer look at the signals received at H01 and H08, in particular the airgun repetition rates. While they were not matched in the same time frame, they did appear to have slightly different timings and spectral components. The spectral difference may have been due to different propagation paths, and the shot timing does change over time. The repetition rate would be mostly limited by the time needed to record the local reflections, and thus dependent on the water depth under the ship. It was agreed that two separate surveys were detected:
H01 bearing 324 ends near N16.5 E82.25 off the coast of India
H08 bearing 35 ends near N19.5 E92 off Myanmar.
Alec put out a request to his ship-tracking sources for the previous report, but with no further results on surveys in the Bay of Bengal. He did reveal that there were actually two surveys running off the NW coast of Australia on that day. The analyzed TGS survey that dominated H08 was in shallow coastal water, but another in deeper water was not detected by H08.
In social media at the time, a few MH370 researchers had been using AIS ship tracking services to map out ship locations from 2014, and also to follow the progress of the search ships. With referrals from the Independent Group, requests went out to several vessel tracking services. Of those that responded, none could provide results back to 2014.
Another search found Seisintel.com that among other services, specializes in delivering details on the coverage of past and current seismic surveys using AIS tracking history and other purchased data. Warren Gray said they had been following the MH370 search with interest, and offered their assistance.
Warren quickly located a survey in their inventory from March 2014 that took place off the SE tip of Myanmar, but it was far enough into the Andaman Sea that there was no direct path to either H08 or H01. He then cast a wider net, and found references to two more surveys that fit the criteria nicely. By eventually acquiring the AIS tracking data at their own expense, the Seisintel team delivered detailed survey tracks for the two ships. This provided very precise bearings for calibration of each hydrophone array.
Thanks again go to Warren, who also continued to provide further updates that included their coverage details of the very impressive MH370 search operation being conducted by the Ocean Infinity flagship, Seabed Constructor.
Refining the Bearing Accuracy
For refining the H08 bearings, survey vessel Ramform Explorer reported its location at 00:46:18 on March 8, 2014 as 19.911973°N, 91.971170°E off the coast of Myanmar. This gives the geodesic back azimuth to H08 as bearing 34.733° from true north. The SOFAR path at that moment just misses the coastal shelf of Sri Lanka by 10 km, which might explain why the signal would come and go as the survey tracks were eclipsed or refracted.
The previous H08 bearing to that survey was 34.63, for a small correction of +0.13 degree. Here are the resulting hydrophone locations for that day, still on the original H08 center:
wavespeed = 1.49289; % Simplex AlignFunction. H08 wavespeed profiled from ODV WOA09_March data lat = [ -7.645462902 -7.645396714 -7.627455481 ]; % calibrated against 8 events and one survey ship bearing lon = [ 72.47436657 72.49348008 72.48381441 ]; % 2018may25 subsampled - Ed Anderson centerlat = -7.64607; centerlon = 72.48387;
Checking alignment for H01 was most critical, as the previous references were distant quakes. The tracking locations for survey vessel Viking II off the coast of India were available starting a week later on March 13-29. The tracks were nearly aligned with the hydrophone and their daily progression was constant, The ship also went back to fill in earlier gaps. A best estimate of the ship location on March 8 at 09:35:10 was 16.439316°N, 82.57349°E, for an H01 bearing of 324.178 degrees. This is consistent with the previous quake calibration within 0.2 degrees. The resulting H01 hydrophone location data is:
wavespeed = 1.48221; % H01 wavespeed profiled from ODV WOA09_March data lat = [ -34.89303186 -34.89859383 -34.88306231 ]; % oversampled alignment of 8 sources 2018May28 lon = [ 114.1540075 114.1339111 114.1360596 ]; % rotation to Viking II survey ship GPS @09:35:10 bearing 324.17825 centerlat = -34.8915433; centerlon = 114.1413033;
Further Improvements in Determining Signal Bearings
Algorithm developments for signal visualization with the BearingOverTime plot are continuing. In particular, the previous measure that often worked best is simple covariance between the channels, though many other statistical methods have been attempted. Kurtosis, mutual information, entropy and joint entropy all show promise for broadband impulsive sources where covariance can be low. An enhancement of covariance was inspired by the use in seismic phase analysis of eigenvector calculations in determining the direction of a signal. The ratio of the primary and secondary eigenvalues is similar to comparing the maximum and minimum covariance between the three hydrophone signals. Taking the product of each pair covariance with the eigenvalue ratio acts as an effective filter to remove signal aliases, and narrows the peaks of the bearing plots. This has the benefit of revealing weaker signals and getting sharper results on strong ones.
A visual example will show the dramatic improvement. For comparison is the best result of a BearingOverTime plot for the original Curtin 01:34:50 signal, reported in 2014 as being on H01 bearing 301.6 with about half a degree of uncertainty.
Contrast on the basic plot could be improved, but it shows how false phantoms of the signal are visible from every direction. The covariance peaks result in a bearing of 301.94 degrees, but a closer look reveals that the most intense portion of the signal appears to be at a slightly lower bearing than the more consistent mix of arrivals. Using the eigenvalue filtering removes most of the aliasing:
Zooming in further on the bearing of interest is now possible with 8x oversampling:
In terms of overall alignment, the bearing 301.0 can probably be taken as a more accurate estimate of the original 301.6 bearing measurement. The averaged bearing from the cross correlation peaks is 300.93, but some components appear to come from a slightly higher bearing. A similar effect is seen on the H08 Java Anomaly signal which could be caused by reflections along a seacoast. For the Curtin event, it may be refractions around Maldives atolls.
This calibration is a best estimate of the the hydrophone positions on the day of the event rather than very old adjustments, but precision is still greater than the accuracy due to other external factors. Horizontal refraction in the SOFAR channel from temperature changes long the path can shift the apparent origin of an event, not only of the target, but the single calibration reference in use on H01.
A second demonstration of the improved filtering shows the bearing components of the LANL Cluster 2 signal, where there were reported to be preamble components at bearing 248.8 deg.
This plot shows little preamble energy content other than the 205.5 degree bearing to an ice event. The slightly different bearing to the second half of the cluster now shows that the two nearly overlapping signals came from different events.
The new calibrations and filtering method have yet to be incorporated into the generation of cartographic overlay maps for use in Google Earth. The previous map code needs to be rewritten for efficiency by precomputing all the covariances over time, and to also take full advantage of the global SOFAR speed mapping completed last year. The speed maps might also be useful for predicting horizontal refraction over each path.
[Feb 2019 update: The plots were regenerated using newer code to correct some errors.]
[ Feb 2019 Note: In a Nature paper published Jan 29, 2019 by Usama Kadri, the patterned H08 sources are noted as, “Signals from military action are intermittent at two locations: 219.2° and 309.7°”. From the time ranges referenced, they are undoubtedly the known seismic survey sources, with the correct bearings near 113 and 34 degrees, respectively. The paper also assigns bearing 241.3 from H08 to his HA_32 arrival at 01:58 UTC. The strong higher frequency signal arrival at 01:59:20 is previously analyzed in detail here as the Java Anomaly event at H08 bearing 92. There is confusion in the paper of a March 7 11:57 event that from his other references (12:11 being over 3 hrs before 03:30) would convert from his notation to 23:57 UTC. No obvious event shows up on H08 near that time above 2 Hz, only a very weak event is on H08 bearing 125 that looks repetetive. A 23:57 UTC H08 signal arrival must have originated about an hour before the presumed 7th arc impact time. ]