Antipodal Focusing of Seismic Waves for Locating MH370

Malaysian Airlines Flight MH370 likely crashed over deep ocean water, which has made detection by acoustic devices difficult. Satellite doppler indicates a possible high speed dive after loss of power, and recovered fragments of the interior cabin match that scenario. Such an impact would create a pressure wave downward into the Earth. Data recordings from nearly 5,000 active seismometers were analyzed for evidence of the seismic waves traversing the globe. A focusing effect should have amplified the seismic waves by tenfold or more at the antipode on the opposite side of the globe from the origin. A seismometer near the antipode would get a unique signal pattern that shows its displacement. The antipode of the priority MH370 search area is in the southeast USA with good seismometer coverage. Methods of stacking seismometers to reduce noise, and evidence of waves passing distant seismic arrays are explored in search of the crash site.

Distribution of 4,992 active seismometers with public data on March 8, 2014. The 7th arc and its antipode are marked in red.

Background

Despite the large number of seismometers monitoring the Earth at any time, their placement is very sparse in remote areas like the Southern Indian Ocean. The nearest seismometers are not close to the priority MH370 search areas. G.AIS on Amsterdam Island is 500 to 1000 km away, and G.PAF on Kerguelen Island is twice that at 1000 to 2000 km distant. The next nearest seismometers are 2000-3000 km away at G.CRZF Crozet IslandCocos Keeling Island, and on the Australian continent. All of these were investigated with no seismic signals apparent from a 00:19:37 UTC 7th arc impact time.

A possible explanation for the lack of a seismic signal is that fluids only conduct pressure waves, not shear waves, and the pressure wave would be concentrated in the direction that the plane entered the water. Shear waves might be generated at the interface of the deep ocean seabed, but that too is a saturated fluid boundary that varies in depth above the solid crust. It is known that there is a shadow zone for detecting the vertical pressure waves in the form of converted SOFAR T-waves (Taliander and Okal, 1998 p.628.3), where the P-waves are very weak on seismometers that are too close to coastal conversion point. A similar effect may have happened in the impact over abyssal ocean, where the energy was concentrated vertically.

Besides common P-waves and S-waves sensed locally, more teleseismic wave phases propagate throughout the Earth. Downward pressure waves reflecting off the core-mantle boundary (PcP phase) and the inner core (PkP phase) may be detected by remote seismometers. Multiple reflections and refractions can be detected at great distances for strong quakes.

Of particular interest is the phenomenon of antipodal focusing, where waves emitted in all radial directions from a source are eventually focused at its antipode on the opposite side of the globe. The various wave phase paths reach the antipode at different times, with some being more prominent. The focus is imperfect, with variations in the density around the globe acting like distortions of glass in a lens. Some portion of the waves will sum constructively while others will cancel, but the amplification effect may be useful for detection by seismometers up to hundreds of kilometers away from the antipode.

Multiple P-wave phase paths through the Earth to a near-antipodal seismometer.

Estimates of the theoretical amplification factor with synthetic data are over 100x while off-axis real world measurements may reach 25x (2002, White, Global Seismic Focusing at the Antipode.)  A recent report (2014, Retailleau et al, Antipodal focusing of seismic waves observed with the USArray) analyzes antipodal wave arrivals using at 411 stations in the central USA from a 2010 M5.3 quake just west of the 7th arc search area. The report shows amplification over 15x with long period (20-50s) vertical component seismic waves. Higher frequencies examined here may not focus as well, but the major downward (dip) component of an impact could increase the effect. 

Signal arrival patterns near the antipode would be unique. A seismometer off axis from the antipode should receive a complex of arrivals with two peaks in amplitude around the expected time, first from the shorter minor path and then the longer major path through the globe. As the distance from the antipode increases, the peaks move farther apart. If such a split arrival can be found, the distance between the peaks could be used to determine the distance from the true antipode, and thus the origin.

Stacking for Increased Sensitivity

The above referenced Transportable USArray was deployed over different regions for several years, migrating to the northeastern USA by 2014. There are several other arrays of various sizes around the world that have recordings available from the time of the impact. Three isolated arrays in Australia at Pilbara, Warramunga, and Alice Springs are good candidates for detecting P wave reflections from the core-mantle boundary. Arrays have the advantage of being able to stack weak signals using beam-forming methods to better detect the direction and speed of a passing wavefront. Capturing multiple snapshots of a signal also helps to distinguish between local noise sources and a distant origin, which is difficult with individual seismometers.

Visualizing Phase Arrivals with Section Plots

The timing of various wave paths through layers of the earth has been derived by accumulating statistics on decades of seismic events on thousands of seismometers in the public network. These paths known as phases can be plotted by expected arrival time vs distance around the Earth. They are coded by letters for the type of wave and the layer boundaries they interact with. A good reference is the USGS IASP91 Earthquake Travel Time Curves chart. The ISC Annual Director’s Report contains a similar scatterplot of shallow event travel times.

Tools have been built to make multiple seismic propagation models available for study. They typically reduce the complexity by assuming a spherical Earth without local variations. The InstaSeis toolkit provides a database of synthetic waveforms expected at a given source depth and distance.

Plot of InstaSeis shallow origin waveforms, as time vs distance.

The TauP toolkit has been very useful for delivering average expected arrival times of probable phases given a depth and distance. Adding distant teleseismic phases and extracting for depth=0 gives a travel time reference bitmap, similar to the USGS chart.

TauP global travel time phase map for a surface impact, Time in seconds vs Distance in degrees.

Seismic Section plots are typically a series of seismic waveforms overlaid by distance. Shown is an example of the previously reported Java Anomaly event at 00:15:18 UTC.

A sample Section Plot of close range seismic responses.

By converting three channel signal axis amplitudes into an RGB pixel intensity, data from many more seismometers can be visualized at once, in a diagram similar to the travel time reference charts.

A visual example is a plot of 4,637 phase arrivals from a magnitude 5.3 quake at Kuripan, Sumatra, on the previous day March 7, 2014 at 16:14:53 UTC.

Global phase arrivals by distance from a magnitude 5.3 quake at 16:14:53

When plotted by distance from the known origin, seismometer responses at similar distances are summed, while gaps are interpolated between the two nearest recorders.The farthest seismometers are nearest the antipode. Note that some antipodal focusing can be seen in this example plot between 16:42 and 17:07 UTC.

Arrivals per sorted seismometer from a magnitude 5.3 quake at 16:14:53

More useful for visualizing close arrivals at various arrays is to merely sort by distance, with a full row of pixels for each seismometer. The Y axis becomes the seismometer index count, which can then be referenced in a matching .csv file for distance and lat/lon.

A further variation on visualization of the phase matching for a particular location is to cross correlate the expected TauP phase arrivals (as displayed above) with the signals from each seismometer. The result is a trace through time for each seismometer, showing the likelihood of a particular origin.

Example of phase matching over time, centered on the Kuripan M5.3 quake at 16:14:53 UTC.

This example shows the phase matching results over time from a reduced dataset of 430 seismometers that includes the 100 nearest stations, 100 farthest antipodal stations, plus several prominent arrays for stacking.

By summing the rows of the phase matching plot results, there is a possibility to obtain a relative index over time for detecting an event at a particular location.

Summed phase matching over time for the Kuripan quake.

The origin location used to generate the TauP values can be successively moved over a grid. Some preliminary attempts were made at generating an animated cartographic map over time that might reveal an impact site. The result appears as a spatial stack of signal rings centered on each seismometer, which would sum at matching intersections to indicate a source event. More optimization is needed to reduce the computation time per pixel for mapping.

Antipodal evidence of the 2009 Air France AF447 impact [updated Feb 2019]

To test the validity of using antipodal methods to detect an air crash over deep ocean, an examination was made of data from a known event. Air France flight 447 crashed in the mid-Atlantic en route from Rio de Janeiro to Paris on June 1st, 2009.

The Airbus 330 had airspeed instrumentation problems that caused an unrecognized stall condition from high altitude down to an impact at approximately 02:14:28 UTC. AF447 flight recorders showed the plane falling nose up with the last vertical velocity as 55 m/s = 107 knots, about the same as the ground speed, for an impact angle of 45 degrees. The final speed and angle of attack of the stalled plane would be relatively low compared to various MH370 estimates. Attempts by CTBTO and seismologists in 2009 to locate the AF447 crash site using hydrophones and T-wave seismometers gave no results in the Atlantic region.

While CTBTO hydrophone data from the Azores is unavailable, recordings were obtained from some 3,400 seismometers active at the time. Even with the AF447 crash site known to be 3.066N 30.561W, no sounds are apparent at seismic TauP or T-Wave timings in the Atlantic hemisphere.

The antipode of the AF447 crash is in Papua New Guinea at 3.066S 149.439E in the Bismarck Sea. Data from the nearest recorder AU.MANU (257km) is unavailable. The closest active site is AU.RABL in Rabaul at 327km (2.94 deg). The data is relatively clean except for a repeating local noise source at 13.85Hz (probably a compressor pump). The next nearest recorder is IU.PMG in Port Moresby at 744 km (6.69 deg) from the antipode. IU.PMG is uncluttered at the time of interest.

There are responses on IU.RABL and IU.PMG that appear near the expected times for antipodal phase arrivals. Two spectral plots are shown for the same time frame that would encompass the PPPP and SKKS phases. The predicted IASP91 TauP phase arrival times centered at the antipode are SKKS=02:46:50 and PPPP=02:47:22 UTC.

Signal arrivals at AU.RABL – 327 km from the AF447 antipode.
Signal arrivals at IU.PMG – 744 km from the AF447 antipode.

The spread of the major and minor path signal arrivals would approximately double as the distance from the antipode is doubled. That appears to be the case when comparing the two plots. If the signals were typical local or even teleseismic P and S phases, the arrivals at one seismometer would lead the other rather than spreading.

Notable is that the spectral energy is concentrated above 8 Hz, and in a narrow frequency band around 17 Hz with greater distance. Seismic studies at low frequencies report that focusing might be expected only within about 1-2 degrees distance from the antipode. These plots hint that higher frequency components may be emphasized at increased distance from the antipode, which would have put these signals out of the bandwidth previously examined.

Also note that the coloration of the plot shows some frequency separation between N-S (red) and E-W (green) signal components, possibly due to different global paths. A strong magenta coloration on SKKS phases at the more distant seismometer shows that the E-W and vertical (blue) channels are more prominent. AF447 entered the water on a magnetic heading of 270 during the stall per the flight data recorder. This matches the orientation of the debris field. A larger E-W than N-S acoustic component appears to be consistent with a 45 degree downward impact of AF447 on a west heading.

A unique feature of the antipodal split arrivals from major and minor paths around the globe is that the signals should be very similar. This makes them a good candidate for weak signal detection by autocorrelation methods. The nearer AU.RABL signal autocorrelation is corrupted by a repeating resonant source, but a plot of the IU.PMG autocorrelation shows promise.

Autocorrelation plot of antipodal signals for AF447, with expected phase arrivals.

The SKKS phases appear to be about 18 seconds early, with PPPP phases just a few seconds early. Adjusting the predicted TauP timing would suggest spreading around SKKS=02:46:32 and PPPP=02:47:19 UTC at the antipode.

Negative results for the priority search area

Examination of seismometers that are nearest to antipodal from various candidate sites along the 7th Arc have not yet provided any obvious seismic indications of an impact. It could be that there are no viable seismometers close enough to the impact antipode, or that more advanced processing algorithms may be needed. The early antipodal analyses were done in 2018 without autocorrelation matching, and without emphasis on the more prominent SKKS and PPPP phases. The first look at data antipodal to AF447 likewise had negative results, but improved methods may have revealed promising insights.

Ongoing research

The quality of the section plots is dependent on detecting phases from an isotropic source like a plane impact. The current plots are based on simple signal variance which is related to amplitude. Development continues on using higher order statistical measures like kurtosis and entropy. The seismic visualization methods used here have mostly been developed from first principles. More sophisticated methods for detecting and locating small tele-seismic events may be worth pursuing. Seismic research may also be incorporated to improve the methods here. Seismologists have recently trained deep neural networks against a large corpus of human-picked seismic phases with excellent results.

MH370 Data

In case it is useful for reference, a global plot of 4,730 seismometer variance responses (filtered for higher frequencies) after 00:19:37 is shown, with a distance origin on the 01:15:18 Java Anomaly event. The corresponding .csv file and 54MB source .png file of seismometers are also indexed by distance.

Reference global phase arrivals by distance from a Java anomaly at 00:19:37 and 01:15:18 UTC. (Click for large .pdf file).

It is clear why the Java event was not recorded in the catalogs. The response was relatively weak, and only notable at nearby seismometers. There is faint evidence of a weak 00:19:37 event at the location of the later anomaly. The seismometers closest to the antipode (near Columbia-Venezuela border) are somewhat distant, and they are cluttered by stronger local events.