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Seismoacoustic coupling induced by the breakup of the 15 February 2013 Chelyabinsk meteor
Laboratoire de Géologie de Lyon: Terre, Planète, Environnement, CNRS UMR 5276, Université Lyon 1, Université de Lyon, Ecole Normale Supérieure de Lyon, Villeurbanne, France
Corresponding author: B. Tauzin, Laboratoire de Géologie de Lyon: Terre, Planète, Environnement, CNRS UMR 5276, Université Lyon 1, Université de Lyon, 2 rue Raphael Dubois, 69622 Villeurbanne Cedex, France. (email@example.com)
 On 15 February 2013 around 03:20:00 UTC, the largest meteor reported since the 1908 Tunguska event was observed as a fireball traveling through the Earth's atmosphere, exploding in an air burst near the city of Chelyabinsk, Russia. The rarity of such an event provides a unique window on the physics of meteoroid collision. We report the fine seismic detection of Rayleigh waves produced by the coupling of ground motion with the incident shock wave at distances up to 4000 km from the event. Combining information from seismic beam-forming analysis, reconstructed trajectory from casual video records, and remote sensing, we identify the Rayleigh waves as being initiated by the shock wave produced by the main blast that occasioned damages and injuries in Chelyabinsk. From the Rayleigh wave observations, we report a magnitude Ms∼3.7 seismic source.
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 The Chelyabinsk meteor is the largest recorded object that entered the Earth's atmosphere since the Tunguska event in 1908 [Ben-Menahem, 1975]. It generated on its way multiple blast events due to meteor fragmentation. The largest was reported by the NASA Near-Earth Object Program (http://neo.jpl.nasa.gov) at about 23 km altitude and is thought to have caused injuries and damages within the city of Chelyabinsk. Multiple fragments of the meteor have also been reported to hit the ground, the largest in the region of the lake Chebarkul, 70 km west-south west of Chelyabinsk. These fragments, millimeters to centimeters in size, are however likely too small to generate seismic waves that can be detected a few hundred kilometers away [Edwards et al.2007].
 Seismic waves are more commonly generated by the sonic shock wave associated with the meteor [Anglin and Haddon, 1987]. When a meteor enters the Earth's atmosphere at hypersonic velocities, it produces a ballistic shock wave within a narrow Mach cone. The induced pressure wave propagates with a wavefront that can be approximated as cylindrical [e.g., ReVelle, 1976]. Additional shock waves with quasi-spherical wavefronts can also be produced by the meteor fragmentation. These shock waves, though experiencing frequency-dependent attenuation as they propagate in the atmosphere, could be detected in the case of Cheylabinsk as infrasound waves recorded at sensors of the Comprehensive Nuclear Test Ban Treaty all over the world [Le Pichon et al., 2013]. These infrasounds impinge the Earth's surface with sufficient energy to induce a measurable seismic signal [Edwards et al.2007].
 In this study, we show that coupling between the meteor's shock wave and ground motion produces Rayleigh waves that can be detected at distances up to 4000 km from Chelyabinsk. These Rayleigh waves can be used to infer the deep internal structure of the Earth. Such Rayleigh waves, precursory to the ground motion associated with the meteor's shock wave, have so far been rarely observed.
2 Seismic Data Analysis
 We analyze 2016 three-component broadband seismograms recorded at seismic stations of the Global Seismographic Network and the International Federation of Digital Seismographic Networks (Figure 1). Among them, we use 73 vertical components recorded at distances up to 4000 km from the Chelyabinsk city (red stations in the map of Figure 1). In Figure 1, these seismograms are sorted by increasing distance and band-pass filtered in the period range 20–60 s. The extraction of the seismic signal associated with the Chelyabinsk meteor is significantly blurred by the coincidental interference with seismic waves of a magnitude 5.8 earthquake that occurred 20 min earlier in the Tonga archipelago (Figure 1). Figure S1 in the supporting information provides a zoomed image of the distance ranging from 0 to 2000 km in Figure 1.
 The first arrivals in the seismograms are P phases radiated by the Tonga earthquake. Travel times computed for the IASP91 reference velocity model [Kennett and Engdahl, 1991] as well as synthetic seismograms computed in a 3-D Earth [Tromp et al., 2010] (Figure S2) indicate the presence of core phases (PKP and PKIKP) as well as P phases reflected under the surface of the Earth (PP). The strongest signal is a dispersed wave train which is framed by the gray curves in Figure 1. This wave train can hardly be explained by the earthquake. First, it is not modeled by the simulation in a realistic Earth's model (Figure S2). Second, its arrival time t does not increase linearly with the distance from the Tonga epicenter (Figure S3). Instead, it increases linearly with the distance d from Chelyabinsk (i.e., t=d/v with an apparent constant velocity v) suggesting that it is emitted in this region. It propagates in the ground with an apparent velocity between 2.7 and 3.5 km/s (Figure 1, gray curves). The wave train is unambiguously identified as Rayleigh waves by the dispersion of the signal with frequency and the recorded elliptical retrograde ground motions occurring essentially in the vertical plane (Figure S4 in the supporting information). Waves from Tonga, although interfering, are weaker by 1 or 2 orders of magnitude (Figure S5). Our observations of absolute travel times, particle motion, and dispersion thus suggest that we isolated meteor-induced Rayleigh waves among waveforms associated with the Tonga earthquake.
 We have extracted the average group velocity dispersion for these Rayleigh waves (Figure 2). We band-pass filter the seismograms of Figure 1 from 15 to 60 s by step of 5 s period. We take the envelope of the signals and apply a “delay and sum” approach, i.e., stack these envelopes along linear curves of equation t=d/v+t0, with d the distance from Chelyabinsk. We test values of v within 2.5 km/s and 5 km/s. The result is a time-velocity diagram (Figure S6) whose maximum indicates the origin time t0(T) and the group velocity v(T) for Rayleigh waves at period T. We use a bootstrap resampling approach [Efron and Tibshirani, 1991] to estimate the average dispersion and its associated error. The obtained dispersion relation is classical with longer wavelengths or periods arriving before shorter wavelengths (Figure 2). Indeed, the S wave velocity generally increases with depth in the uppermost 100 km of continents and Rayleigh waves measure a weighted average of the S wave structure over a depth interval that increases with period. Comparison with dispersion curves for the same region [Ritzwoller and Levshin, 1998; Shapiro and Ritzwoller, 2002] confirms that the measured dispersion is typical of a fundamental Rayleigh mode propagating within a Precambrian lithosphere (Figure 2). This is a nice example of how a meteor-induced Rayleigh wave can be used to infer the internal structure of a planetary body with an atmosphere.
 We relocate the source emission of meteor-induced Rayleigh waves using the dispersion relation relating group velocity to frequency and a similar approach developed by Lay  to illuminate near-source structures from teleseismic P waves generated by underground explosions. We use a spatial grid around Chelyabinsk of 1501×1501 km with ∼1 km wide cells. Assuming an origin time for the meteor event (with uncertainties t0(T) on this time considered here), the amplitude at each predicted travel time from a given grid point is taken on the envelope of the corresponding vertical component seismogram. These amplitudes are then backprojected onto the corresponding grid points. By averaging the amplitudes taken from the envelopes of all vertical component seismograms, we produce for every period of Rayleigh wave a map of normalized beam amplitude (Figure S7). The maximum in beam amplitude indicates the best estimate for the location of emission of seismic waves. Our higher-resolution map obtained from the backprojection of 15 s period Rayleigh waves is shown in Figure 3a. The maximum is located south of the city of Chelyabinsk. The resolution is <100 km in the ESE-WNW, but poorer in the NNE-SSW direction, as most stations for which Rayleigh waves could be observed (red stations in the map of Figure 1) are located east or west to Chelyabinsk. This is confirmed by a simple test of beam-forming synthetic seismic signals (Figure S8).
3 Trajectory From Casual Video Records and Remote Sensing
 In a telegram from the International Astronomical Union (IAU), the Astronomical Institute of the Academy of Science, Ondrejov, Czech Republic, reconstructed the meteor trajectory in the atmosphere from seven casual video records. Assuming a trajectory collinear with the probable impact site of Chebarkul Lake, they reported the locations of four successive blasts in an ESE-WNW direction south of 55°N latitude (Figure 3b). We corroborate this trajectory using images from Meteosat-7 and Meteosat-9 that have captured the vapor trail left by the bolide in the atmosphere. These two geostationary meteorological satellites are respectively centered at the longitudes of 57.5°E and 0°E. We rectified and projected the acquired satellite images from the elevation of the trail (Figure S9). We used SEVIRI image in Level 1.0 from Meteosat-7 to compute possible vapor trail trajectories. Meteosat-7 images were preferred as closer to the longitude of the meteor event. We tested elevations between 40 km and 55 km for the eastern extremity of the trail and between 10 and 25 km for the western end. The best match, collinear with the impact site of the Chebarkul Lake, is a vapor trail extending from 45 km altitude to the east to 18 km to the west. The meteor trajectory intersects our broad maximum of seismic beam forming which contains the four blasts (Figure 3b). Seismic beam-forming, casual video records, and remote sensing concur with the main blast (Figure 3b, double red dot) that occasioned damages and injuries in Chelyabinsk being the seismic initiator for the seismic Rayleigh waves.
4 Discussion and Conclusion
 The theory of coupling between infrasound waves and elastic ground motion indicates that P and S body waves may be initiated as well as Rayleigh waves [see, for example, Ewing et al., 1957, pp. 183 and 220–238]. These waves are generated when and where the sweep velocity of the infrasonic trace at the Earth's surface precisely matches the propagation velocities of the seismic waves. The strong contrast between infrasonic waves that propagate in the air with velocities close to the sound (c∼0.3 km/s) and seismic waves (Rayleigh, P, and S) that propagate at least 10 times faster requires a very steep shock front incidence. This requires a seismic source in the close vicinity of the meteor ground-projected trajectory. We observe, however, surface waves at distances up to 4000 km from Chelyabinsk. At these distances, our observed Rayleigh waves must thus arrive as precursors of the shock waves. We looked in the records for the shock wave as well as the P and S seismic waves. The lack of seismic stations in the close vicinity of the meteor trajectory and the interference with the Tonga earthquake render their identification difficult, even using methods from array seismology [e.g., Rost and Thomas, 2002]. However, by comparing the observed waveforms with synthetic seismograms computed in a 3-D Earth [Tromp et al., 2010], we identified the shock wave (Figure 4a) and possibly the P and S body waves (Figure S10) at the closest stations from Chelyabinsk.
 Few observations of precursory seismic waves to meteor-induced shock waves have been reported up to now. The closest to the Chelyabinsk event is probably the observation of Rayleigh waves of the 1908 Tugunska event that were recorded as far as 5293 km away from its source region [Ben-Menahem, 1975]. Anglin and Haddon  reported precursory Rayleigh waves associated with a meteoroid above Yellowknife, Canada. Kanamori et al.  and Sorrells et al.  also reported precursory waves to shock fronts but associated with the re-entry in the atmosphere of the Columbia space shuttle.
 The shock waves can have two main origins: ballistic within a narrow Mach cone or ablational due to meteor fragmentation. In these prior studies, Ben-Menahem  invokes a combination of both, Anglin and Haddon  used two orthogonal lines of stations in the vicinity of the meteor track to identify a ballistic shock wave. In the case of the space shuttle studies, it is clear that the shock wave has also a ballistic origin. For the Chelyabinsk meteor, we do not have a dense network of stations near the meteor track. However, there is no clear evidence for a cylindrical symmetry radiation pattern along the projected path of the bolide. As can be seen in Figure 3, the source is not elongated in the ESE-WSW direction of the meteor track although our resolution is good in this direction. Figure 3 would thus be in better agreement with a spherical source due to fragmentation [Edwards et al.2007].
 We estimate an equivalent surface wave magnitude Ms for the Chelyabinsk event (Figure 4b). Using the Praha relation [Karnik et al., 1962] , where A is the amplitude of Rayleigh wave displacement on the vertical component in μm and Δ is the epicentral distance, we find a magnitude Ms=3.7±0.3. This magnitude, comparable to that (Ms∼5) of the Tugunska event [Ben-Menahem, 1975], would correspond to a release of energy of ∼2·1010 J from an equivalent ∼5 T TNT. The NASA Near-Earth Object Program reported an approximate initial diameter for the asteroid of 18 m and a rough estimation of the observed total radiated energy by the fireball of about 90 kT. A rough estimate of the ratio between the seismic energy and the energy released within the atmosphere is ∼5×10−5. Such limited efficiency is consistent with results from observations of coupling between aerial acoustic sources and ground motion [e.g., Brown et al., 2002] and similar to what is reported for the Tugunska event [Toon et al., 1997].
 Present results that use precursory Rayleigh waves induced by the atmospheric breakup of an asteroid to estimate an equivalent seismic source energy give interesting perspectives for planetary seismological missions. For instance, the NASA mission InSight (Interior Exploration using Seismic Investigations, Geodesy, and Heat Transport) plans to land a seismometer on the surface of Mars to investigate among others, the rate of meteorite impacts. Even if the present atmosphere of Mars is about 150 times thinner than the Earth's, atmospheric breakup of interplanetary meteoroids on Mars is predicted and even observed. Popova et al.  predicted atmospheric breakups for bolides smaller than 20 cm in diameter. The recent inventory of fresh Martian impact craters detected between two spacecraft surveys highlights even more atmospheric breakup [Daubar et al., 2013; Malin et al., 2006]. Clusters of impact craters that result from atmospheric breakup are widely observed until 35 m of equivalent crater diameters. Present results thus offer perspectives for impact rate survey on Mars by a seismological space mission.
 This work was supported by a Chaire d'Excellence Fellowship from CNRS. The research has received funding from European Research Council under the European Union'S Seventh Framework Program (PF7/2007-2013)/ERC grant agreement n280168. We thank two anonymous reviewers for their constructive comments. We thank Yanick Ricard for his review and Bertrand Trey for a discussion on present-day impact flux on planetary bodies. We thank the Princeton group for providing 3-D synthetic seismograms calculated based upon the spectral element method. The seismograms have been obtained from the Global ShakeMovie portal (http://global.shakemovie.princeton.edu/). We thank the IRIS and Geoscope Data centers for providing seismological data.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.