Infrasound detection of the Chelyabinsk meteor at the USArray

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Infrasound detection of the Chelyabinsk meteor at the USArray Catherine D. de Groot-Hedlin ∗ , Michael A.H. Hedlin Laboratory for Atmospheric Acoustics, Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093-0225, United States

a r t i c l e

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Article history: Accepted 21 January 2014 Available online xxxx Editor: P. Shearer Keywords: infrasound Chelyabinsk meteor USArray barometers attenuation

a b s t r a c t On February 15, 2013 a small asteroid entered Earth’s atmosphere near Chelyabinsk, Russia. This extremely rare event was recorded by the 400-station USArray deployed in the continental United States and Alaska. These stations recorded infrasound signals from the event at distances from 6000 to 10 000 km across a sector spanning 55◦ that encompassed the North Pole. This dense, extensive network permitted a detailed study of long-range infrasound propagation and source characteristics. We observe long wavetrains at all stations (ranging to over 100 min) but clear variations in the character of the wavetrains across the network. Ray-tracing through a spatially and temporally varying atmospheric model indicates the source excited resonance in the thermospheric duct to all stations. Resonance was also excited in a persistent stratospheric duct between the source and stations in Alaska and along the west coast of the United States due to favorable winds at those azimuths, leading to higher group velocities and frequency content at these stations than those to the east. An attenuation formula derived from parabolic equation simulations is used to estimate infrasound transmission losses at all stations, using simplified models of the effective sound speed along each source-receiver path. Observed variations in signal energies from higher than expected at stations in the thermospheric duct in the eastern United States, to lower than expected in Alaska, at azimuths nearly orthogonal to the asteroid’s Mach cone, lead us to conclude that (1) the source was dominantly isotropic and (2) the model overestimates attenuation in the thermospheric duct. © 2014 Elsevier B.V. All rights reserved.

1. Introduction A small asteroid, measuring from 16 to 21 m in diameter (Brown et al., 2013), entered the Earth’s atmosphere at 03:20:20 UT on February 15, 2013, traveling near Chelyabinsk, Russia, at a shallow angle and high velocity (Borovicka et al., 2013; Zuluaga et al., 2013). Numerous amateur and security videos recorded its descent through the atmosphere; of these, several were used to reconstruct its trajectory (Zuluaga et al., 2013). The meteor fragmented as it descended through the atmosphere. The blast wave that caused damage in the Chelyabinsk region originated between altitudes of 25–30 km (Borovicka et al., 2013). The length of its observed trajectory was 254 km (Borovicka et al., 2013). The Chelyabinsk meteor is estimated to have an explosive yield of 500–600 kT TNT equivalent (Brown et al., 2013), which was previously classified an approximately once-in-a-century event (Brown et al., 2002). The Chelyabinsk meteor is believed to be the largest extraterrestrial object to have entered the atmosphere since the 1908 Tunguska event (Whipple, 1930; Ben-Menahem, 1975).

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Corresponding author. Tel.: +1 858 534 2313; fax: +1 858 534 5332. E-mail address: [email protected] (C.D. de Groot-Hedlin).

0012-821X/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsl.2014.01.031

In recent years there has been a dramatic increase in the density of geophysical instrumentation worldwide. The Global Seismographic Network (GSN) has been deployed principally for seismic monitoring of earthquakes and for research. The International Monitoring System (IMS) comprises several networks of sensors that have been deployed for monitoring of nuclear testing activity. The infrasound network will eventually comprise some 60 arrays of microbarometers for detecting sub-audible signals in the atmosphere. The USArray Transportable Array (TA) is a 400-station broadband seismo-acoustic network that is currently being deployed in stages across the continental United States (Busby et al., 2006). Because of these new deployments, and because of the event’s size, this is the most heavily recorded meteor in history. Shock waves from the meteor transitioned to acoustic signals as the pressure disturbance decreased to a small fraction of ambient atmospheric pressure. The propagation of acoustic waves is governed by local wind speeds and temperatures. Downgoing acoustic waves from this event coupled at the Earth’s free surface to Rayleigh seismic surface waves, which were recorded by stations in GSN at a distance of up to 40◦ from the source (Brown et al., 2013; Tauzin et al., 2013). Infrasound signals from this event were detected at 20 arrays in the IMS, including signals detected nearly 3 days afterward, after encircling the globe several times (Le Pichon et al., 2013). The event was recorded by more than 200 barometers

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in the TA at ranges of 6000–10 000 km from the source. The latter dataset is the subject of this study. The high efficiency of infrasound transmission, which makes propagation to great distances possible, results, in part, from the stratification of horizontal wind and air temperature (sound speed is proportional to the square root of the temperature) within the Earth’s atmosphere. This creates transmission ducts, where sound is trapped between reflections at the Earth’s surface and refractions within either the stratosphere or lower thermosphere (Drob et al., 2003). Also, atmospheric attenuation of acoustic energy is significantly lower at infrasonic frequencies within the stratospheric duct than at audible frequencies – e.g. approximately 10−3 dB/km at 2 Hz vs. 1 db/km at 250 Hz (Sutherland and Bass, 2004). However, acoustic absorption increases as atmospheric density decreases, particularly at high frequencies, so that infrasound returns from the thermosphere have much lower frequency content than stratospheric returns (de Groot-Hedlin, 2008; de Groot-Hedlin et al., 2011). Some of the main goals of infrasound studies related to nuclear monitoring efforts are to estimate the source energy from signals recorded at several hundreds of kilometers distance (e.g. Mutschlecner and Whitaker, 2010) and to estimate the seasonal probability of detection for a given source size (Le Pichon et al., 2009). These studies generally rely on simplified models of infrasound propagation, chiefly that the signals are stratospherically ducted. A primary objective of our study is to examine how longrange infrasound propagation depends on atmospheric properties along a broad swath of travel paths using recordings of infrasound signals from the Chelyabinsk meteor at USArray sites, along with time-varying estimates of global winds and temperatures. We compare transmission losses for a large number of infrasound detections across a broad region with the objective of understanding infrasound attenuation within the atmosphere. There have been few opportunities to use a large suite of infrasound recordings of a single event to evaluate infrasound transmission losses over a broad range of propagation paths, due to the scarcity of large events that generate detectable infrasound signals at long distances. Signals analyzed in this study were recorded over a wide area, with some sites located within a stratospheric duct, others within a thermospheric duct, and others located near a boundary where propagation appears to shift from primarily stratospheric to thermospheric ducting. In the next section, we discuss infrasound signals recorded at over 200 pressure sensors deployed at USArray sites in Alaska and the continental United States, and describe the key observations region by region. In Section 3, we discuss the atmospheric specifications used to characterize wind and static sound speed profiles, and apply ray-tracing through time-varying atmospheric models to synthesize several key features of the data. In Section 4, we compare infrasound signal energies using estimates of transmission losses that are based on approximate formulae derived from parabolic equation simulations applied to simplified range independent models (Le Pichon et al., 2013), modified to account for the effects of source altitude. These expressions account for both acoustic absorption and geometrical spreading and are applicable to both thermospherically and stratospherically ducted infrasound propagation. Finally, we compare the results of our propagation modeling with the key observations, and make inferences about global infrasound propagation losses. 2. Infrasound data The USArray, a continental scale seismo-acoustic observatory that includes the USArray Reference Network (USRN) and the USArray Transportable Array (TA), provided atmospheric pressure data for this study. The USRN consists of permanent stations, each

Fig. 1. A global map showing the site of the Chelyabinsk meteor burst (dark grey star) [54.836◦ N, 61.455◦ E] and the USArray barometers. Stations where a signal was detected are shown by black circles; grey triangles indicate stations that did not record a detectable signal. Grey lines marked A through C show infrasound propagation paths with initial directions of 13◦ , 3◦ , and −29◦ from the source, as measured in degrees east of north. Data for stations along these transects are shown in Fig. 2.

equipped with seismometers and barometric pressure sensors, deployed across the United States at an average spacing of 300 km. The TA portion of the USArray comprises approximately 400 similarly equipped seismo-acoustic stations. Each station within the TA forms the node of a nearly Cartesian grid having an average inter-station spacing of 70 km, with the entire grid spanning a footprint of approximately 2 million km2 (Busby et al., 2006). The TA is a rolling network; each station is in operation for 2 yr before being moved from the western trailing edge of the array to the leading, eastern edge of the array. On the date of the Chelyabinsk meteor, the USArray comprised a network of several stations in Alaska, another 27 stations along the northwest coast of the contiguous US, with the remainder of the array located in the Midwest and near the eastern United States. Fig. 1 shows the configuration of the USArray on February 15, 2013 in relation to the site of the Chelyabinsk meteor burst, with black circles indicating stations at which signals were detected; grey triangles mark where signals were not detected. High noise levels over large regions of the US masked infrasound signals from the Chelyabinsk meteor. In all, 415 USArray stations were in operation at the time of the event, and infrasound signals from the meteor were detected at over 200 stations. The Chelyabinsk event is one – albeit particularly large – entry in a growing database of atmospheric events detected by the USArray. This database is TAIRED (Transportable Array Infrasound Reference Event Database) and can be found at http://www.iris.edu/spud/infrasoundevent. We use data from the National Center for Physical Acoustics (NCPA) infrasound sensors deployed at each site to investigate infrasound signals from the meteor. The pass band of these piezoceramic microphones extend from 200 s to 100 Hz. The data are digitized at 1 and 40 sps. Fig. 2 shows infrasound waveform data corresponding to infrasound propagation along paths marked A, B, and C in Fig. 1, corresponding to propagation paths to Alaska, to the US west coast, and to a transect traversing the eastern end of the TA. Traces are bandpassed from 0.008 to 0.12 Hz, a frequency band with a relatively

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frequency content along B being intermediate between those 2 transects. Signals observed along transect C and other TA stations within the Midwest and eastern US have insignificant energy above 0.5 Hz. (4) Arrivals at stations TOLK in Alaska and I04A along transect B have durations of less than 20 min at frequencies above the microbarom band, i.e. above 0.18 Hz. The duration of the infrasound arrivals increases significantly below 0.1 Hz. However, noise levels increase during local daytime hours at low frequencies at most TA stations, so the end of the coda and the signal durations could not be accurately determined at very low frequencies. (5) Extremely low frequency arrivals, with periods from 30 to 40 s, are seen prior to the main arrivals at all 3 stations along Transect A. These can be seen in Fig. 2, and in the spectrogram for TOLK as well (Fig. 3). In addition, analysis of the backazimuth from receiver to source, made at CTBTO (Comprehensive Test ban Treaty Organization) infrasound stations near the USArray stations in Alaska and near the US west coast, show that the apparent source azimuth is deflected eastward of the true source direction (Le Pichon et al., 2013). In the next section, we show that many of these signal characteristics are attributable to variable wind and sound speeds along the infrasound propagation paths that deflect acoustic energy along its travel path. This leads to stratospheric ducting along some paths and thermospheric ducting along others. 3. Atmospheric specifications and infrasound propagation

Fig. 2. Record sections for stations near each of the transect lines labeled A, B, and C shown in Fig. 1. Each trace is bandpassed from 0.008 to 0.12 Hz. Traces with SNR < 2 are omitted. Blank areas along transects A and B are areas where noise levels are high, not necessarily where signal levels are low. The dashed lines show arrival times corresponding to group velocities of 260 m/s, 280 m/s and 300 m/s.

high SNR for this event for most USArray sensors. The dashed lines in Fig. 2 show arrival times corresponding to group velocities of 260–300 m/s for a source at 54.836◦ N, 61.455◦ E, the site of the meteor’s major flare (Borovicka et al., 2013). Spectrograms and waveforms for a single representative station along each of these transects are shown in Fig. 3. The first column presents data for a station in Alaska, along transect A; data for a west coast station along transect B is shown in the middle column; the rightmost column shows data for a station near the eastern part of the array, along transect C. Each column shows the following: a spectrogram for frequencies up to 3 Hz; a detail of that spectrogram up to the microbarom peak, i.e. up to 0.2 Hz; waveforms bandpassed from 0.008 to 0.12 Hz. Stations with observable signals within the midwestern and eastern parts of the US have characteristics similar to those shown for transect C. From Figs. 2 and 3, the key observational features of the data are: (1) Infrasound arrivals recorded along transects A and B have higher velocities than for transect C. The first arrivals, at stations along transects A and B, have an average velocity of 290 m/s, while for arrivals along transect C the velocity is approximately 270 m/s. (2) Waveform amplitudes are much higher at transect A than along transects B and C, more than would be expected simply due to their shorter travel paths. (3) Infrasound signals along transects A have relatively more energy at high frequencies than those along transect C, with

The characteristics of long-range infrasound signals depend largely on the mode of ducting. Acoustic energy ducted within either the stratospheric or thermospheric duct undergoes cylindrical spreading. Stratospherically ducted infrasound undergoes little intrinsic attenuation at frequencies below 2 Hz (Sutherland and Bass, 2004), whereas thermospheric returns undergo considerable intrinsic attenuation at frequencies above 0.2 Hz (de Groot-Hedlin, 2008). Because thermospheric infrasound signals have spectra that overlap that of the ubiquitous microbarom signals (Le Pichon et al., 2006), they are typically observed only for very energetic sources like bolides (de Groot-Hedlin et al., 2011) or volcanoes (Evers and Haak, 2005; Assink et al., 2012). The mode of infrasound ducting varies both spatially and temporally so accurate atmospheric specifications for a particular region and time of interest are required to investigate long-range propagation. The Naval Research Laboratory (NRL) ground to space (G2S) model of Drob et al. (2003) is used to characterize sound and wind speeds within the atmosphere. This model provides local 1-D profiles of temperature as well as zonal and meridional wind speeds from the ground to approximately 150 km altitude, on a 1◦ × 1◦ grid over the entire globe. The G2S data processing system fuses available operational weather data at lower altitudes to a climatological model above 55 km. Atmospheric specifications were provided to us at three distinct times: at 0300 UT, about 20 min prior to the meteor burst; and at 0600 UT and 1200 UT, nearly 3 and 9 h afterwards. We estimate the altitude of the infrasound duct as the height at which the effective sound speed – the sum of the static sound speeds and wind speeds in the direction of propagation – exceeds the sound speed at the Earth’s surface. We neglect tropospheric ducting which occurs within 10–20 km of the Earth’s surface because the source flared at a higher altitude (Borovicka et al., 2013) and because tropospheric ducts are usually short-lived and have limited lateral extent. As was shown in Fig. 2, infrasound energy from the Chelyabinsk meteor took from 6 h to reach stations in Alaska to over 10 h to reach stations at the southeast of the United

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Fig. 3. Spectrograms and bandpassed waveforms for (left column) Alaska station TOLK at [68.6◦ N, 149.6◦ W] along transect A at a distance of 54.4◦ from the source (middle column) station I04A along transect B at [43.8◦ N, 122.4◦ W], 81.3◦ from the source, and (right column) station R55A along transect C at [38.3◦ N, 80.2◦ W], 81.2◦ from the source. The power spectral densities are in dB with respect to a reference pressure of 20 μPa. Each column shows (top) a spectrogram for frequencies up to 3 Hz; (middle) a detail of that spectrogram up to 0.2 Hz; (bottom) a waveform bandpassed from 0.008 to 0.12 Hz. 225 min of data are shown for each station. Arrival times corresponding to velocities of 300, 280, and 260 m/s are marked on each waveform. Note the change of scale of the band-passed waveforms for transect A vs. transects B and C.

States, traveling at velocities between 260 and 290 m/s. The large distances involved and the prolonged duration of travel complicate the task of predicting infrasound transmission and duct height, since winds and temperatures vary with time and location. For the purpose of computing the turning point altitude, winds and temperatures were assumed to vary linearly with time between the model times given above, and the average infrasound propagation velocity was assumed to be 280 m/s. That is, the travel time to a point at a given distance from the source was calculated by applying a velocity of 280 m/s; the winds and temperatures were then given by a linear combination of the atmospheric specifications at either 0300 UT and 0600 UT, or at 0600 UT and 1200 UT, depending on the time from the source. The specifications for 1200 UT were applied at distances where the travel time from the source exceeds 8 h and 40 min. Fig. 4 shows a global map of the altitude of infrasound ducts, computed for a source location corresponding to the Chelyabinsk meteor, at time 03:20:31 UT, 15 February 2015, the time of the meteor’s major flare (Borovicka et al., 2013). As shown, at the time of the Chelyabinsk meteor’s entry into the Earth’s atmosphere, strong eastward winds within the stratosphere at altitudes from 30 to 60 km combined with the static sound speeds to form a stratospheric duct for trajectories to the east of the meteor. The stratospheric duct is absent for trajectories westward of the source, and infrasound is refracted within the thermosphere at altitudes above 100 km. The altitude at which the effective sound speed exceeds that at the Earth’s surface is a proxy for distinguishing between primarily thermospheric vs. primarily stratospheric ducting. Turning altitudes below 65 km suggest stratospheric ducting; higher altitudes imply thermospheric ducting. Thus, Fig. 4 shows that infrasound propagation is highly anisotropic, as expected, since winds must combine with static sound speeds to trap infrasound below the stratopause. A thermospheric duct always exists in any direction at altitudes above 100 km due to large temperature gradients. Fig. 4 shows that most of the US, including stations along transect C, lies within a thermospheric duct from the Chelyabinsk meteor. The Alaska stations are deep within a stratospheric duct for propagation from the Chelyabinsk region. Propagation to stations along the northwest coast of the US (along transect B) is almost directly over

Fig. 4. A global map showing the altitude at which the effective sound speed equals or exceeds the sound speed at the Earth’s surface, for a source location corresponding to the Chelyabinsk meteor burst (star). This suggests where infrasound is primarily stratospherically or thermospherically ducted. The USArray stations are marked by circles, and transects A, B, and C are as shown in Fig. 1. The wind and sound speeds vary with time, as discussed in the text.

the north pole; these stations lie near a boundary between stratospheric and thermospheric ducting. As meteors or other objects move through the air at supersonic speeds, they create elongated bow shock waves along their trajectory, with a shape that depends on details of the object’s shape and velocity (Whitham, 1974). As the shock front propagates away from its source, the pressure disturbance decreases and can be treated as an acoustic perturbation with speeds and travel paths governed by atmospheric temperatures and winds. Acoustic energy generated by a bow wave is highly directional, propagating perpendicularly to the shock wave. Conversely, energy released by a terminal burst is roughly isotropic. In several previous investigations involving infrasound generated by supersonic objects

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Fig. 5. Raypaths show the nature of infrasound propagation to the same stations as shown in Fig. 3: (a) propagation to TOLK; (b) propagation to I04A; (c) propagation to R55A. The background color shows the effective sound speed for horizontal propagation along the travel paths; the raypaths are computed for an advected medium that varies linearly with time, as discussed in the text. For each plot, raypaths are shown for initial launch angles of +45◦ to −45◦ from the source at 30 km altitude, at increments of 10◦ .

(Le Pichon et al., 2002; Cates and Sturtevant, 2002; de GrootHedlin et al., 2008), signals were consistent with acoustic signals propagating at right angles to the bow shocks. In other cases, a terminal burst releases most of a meteor’s energy (Hedlin et al., 2010; Walker et al., 2010), and the infrasound source can be treated as isotropic, similarly to a high altitude explosion (Herrin et al., 2008). Because the Chelyabinsk meteor trajectory traveled westward, at an azimuth of 285◦ (Zuluaga et al., 2013) prior to a major flare, infrasound propagating at right angles to the bow shock would not reach USArray stations within the contiguous US. Although is possible that infrasound generated along the meteor’s trajectory reached the Alaska stations, we assume, for simplicity, that all infrasound signals recorded at all USArray stations originated from the major flare so that it may be treated as an isotropic source at an altitude of about 30 km. Later, we show that this interpretation is consistent with infrasound signals at Alaska as well as the other USArray stations. We use atmospheric ray-tracing to simulate infrasound propagation and gain insight into the several of the key observations made above. Ray-paths were computed using an algorithm developed for an advected medium (Garces et al., 1998). The algorithm accounts for vertical and horizontal refraction as well as lateral deflections resulting from crosswinds. The original algorithm yields travel times for range-independent media, but was applied here to locally 1-D wind and temperature profiles that were updated at every 100 km along the propagation path. We account for Earth sphericity by applying an Earth flattening transformation to the 1-D wind and sound velocities, as in Walker et al. (2013). Again, the winds and temperature profiles were computed for a linear combination of the atmospheric specifications supplied to us at 0300 UT, 0600 UT, and 1200 UT, using total travel times supplied by the ray-tracing algorithm. Fig. 5 shows sample raypaths for each

of the stations with sonograms illustrated in Fig. 3, superimposed on the effective sound speeds. The raypath computations were augmented by estimates of the intrinsic attenuation due to atmospheric viscosity for any given raypath. As described in de Groot-Hedlin et al. (2011), the intrinsic attenuation at infrasound frequencies depends primarily on signal frequency and atmospheric density and is thus strongly dependent on altitude. We compute the intrinsic attenuation vs. altitude for each frequency, and integrate the absorption values for each segment along the path for each ray. This allows us to estimate the travel time, deflection and intrinsic attenuation as a function of frequency for each raypath, given range-varying sound and wind speeds along each path. Because the intrinsic attenuation estimates do not take into account effects like diffraction, dispersion, ray caustics or shadow zones, they cannot be used to provide estimates of overall signal attenuation. Raypaths were computed for a source at 30 km altitude, with initial launch angles ranging from +60◦ to −60◦ , at a uniform increment of 1◦ . Rays were computed up to a maximum altitude of 130 km; rays with higher turning points were excluded due to high attenuation. Fig. 5 shows ray propagation along travel paths to the same stations shown in Fig. 3, superimposed upon the effective sound speeds. As shown in Fig. 5a, sound speeds along the travel path to TOLK vary strongly leading to complicated raypaths. Although some rays are either stratospherically or thermospherically ducted along the entire path, other rays are initially thermospherically ducted and then stratospherically ducted for the remainder of the path, and some become ducted between the stratopause and thermosphere. Rays launched at angles from −32◦ to 30◦ are refracted within the stratosphere along the entire path, and correspond to travel times from 351 to 364 min. This gives a velocity of 288 m/s

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for the earliest stratospheric arrivals, with a total duration of 13 min, similar to the signal duration at frequencies above 0.1 Hz in Fig. 3, suggesting that the duration of the higher frequency signals are due to multi-pathing within the stratosphere. Estimates of intrinsic attenuation indicate that raypaths that are refracted within the thermosphere along the entire path are attenuated by more than 40 dB at frequencies above 0.1 Hz. Attenuation estimates also indicate that, at a period of 25 s, rays refracted at altitudes below 130 km undergo up to 21 dB absorption. Ray-tracing predicts that the thermospheric arrivals have a much longer duration than stratospheric arrivals and both precede and follow the stratospheric arrivals. Several thermospherically ducted rays arrive up to a minute before the stratospheric rays, which could account for the very low frequency precursory arrivals seen at TOLK (Fig. 3). Rays with turning points in the thermosphere arrive up to 392 min after the source time. For propagation to station I04A along transect B, sound speeds do not vary significantly along the propagation path and rays are either stratospherically or thermospherically ducted; little energy transitions between these two modes of ducting as shown in the middle panel of Fig. 5. Ray-tracing predicts that rays launched at angles from −27◦ to 26◦ are refracted within the stratosphere, and have travel times from 515 to 528 min. This gives a velocity of 293 m/s for the earliest stratospheric arrivals, with a total duration of 13 min. This may be compared with signal durations of 10–20 min at frequencies greater than 0.1 Hz for stations along the west coast. Thermospherically ducted rays with turning points below 130 km are multi-pathed as well, with longer durations than the stratospheric returns; ray-tracing predicts thermospheric arrivals at times up to 636 min after the meteor airburst. Given the high attenuation within the thermosphere, these would be observable only at very low frequencies; estimates of intrinsic attenuation indicate that rays refracted below 130 km undergo up to 38 dB attenuation at a period of 25 s. In fact, arrivals are observed at station I04A up to 620–630 min after the source time. Rays that propagate to station R55A along transect C are refracted above 60 km altitude along the entire path. However, as shown in Fig. 5c, some rays are refracted within a thin zone of high effective sound speed within the mesosphere at altitudes from 60 to 80 km, along much of the travel path. Estimates of intrinsic attenuation indicate that at 0.1 Hz, rays with initial propagation angles from −17◦ to 17◦ undergo less than 10 dB attenuation. The travel times associated with these rays range from 567 to 585 min, which gives a velocity of 266 m/s for the first arrivals, consistent with observations of later arrivals along transect C. Rays with higher initial launch angles are slower, refract higher within the thermosphere, and are more highly dispersed, with predicted travel times up to 740 min. Arrivals associated with these rays are more significantly attenuated, and so would be observed only at very long periods, i.e. over 25 s. However, due to a large increase in ambient noise at most TA stations, the end of the infrasound coda from this event is indistinguishable from noise, so the predicted signal duration cannot be compared to observations at these low frequencies. The ray computations explain several key observations made in the previous section. At frequencies greater than 0.1 Hz, the infrasound arrival times and durations along transects A and B are consistent with multi-pathing within the stratosphere. However, the observed signals associated with these raypaths do not form discrete arrivals. We attribute this to the much greater distances involved, and the effects of fine-scale atmospheric structure on acoustic energy, which disperses energy along each raypath. Raytracing also indicates that thermospherically ducted infrasound is highly dispersive and accounts for both the long, low frequency coda at all stations, and also the low frequency arrivals which precede the higher frequency signals at stations in Alaska. Finally, the

ray-tracing results also predict the eastward deflection of the arrivals observed at CTBTO stations near the USArray stations, as infrasound energy from the Chelyabinsk meteor was strongly deflected by eastward stratospheric winds. Rays are deflected to the right (as viewed in the direction of propagation) as they propagate poleward from the source, then to the left from the polar region to the sensors. However, ray-tracing is based on a high frequency approximation to the wavefield. This approximation is valid when acoustic wavelengths considered are significantly smaller than the scale at which the medium varies. Thus, ray-tracing does not provide accurate estimates of the signal strength and cannot be used to explain the relative acoustic energy levels observed along each transect. The parabolic equation (PE) method (Collins, 1993) avoids these limitations and provides accurate solutions to the wave equation that are valid in weakly range dependent media. It is used widely to provide estimates of infrasound attenuation including both geometrical and intrinsic attenuation losses. In the next section, we apply formulations based on PE modeling to address the relative signal energies of the acoustic arrivals along each transect. 4. Signal amplitudes and source pressure An approximate formula for infrasound propagation losses, valid for either stratospheric or thermospheric ducting, is presented in Le Pichon et al. (2012). These authors developed a predictive equation for attenuation based on 9120 PE simulations of infrasound propagation through simplified range- and azimuthallyindependent environmental models. They varied the ratio of the effective sound speed within the stratosphere to that at ground level, V eff -ratio , from 0.85 to 1.18 such that transmission losses for both thermospheric and stratospheric ducting could be examined. The PE simulations incorporate contributions to infrasound absorption due to both classical and relaxation losses. Computations were performed over a set of frequencies, incorporating realistic wind perturbations to the wind models to mimic the effect of gravity waves. Multiple gravity wave realizations were used to derive the approximate formula for the pressure amplitude A at any point along the ground, relative to its value at 1 km. It is given by

A ( f , R , V eff -ratio )



= Ar

10α ( f ) R /20 R

+

R β( f , V eff -ratio ) 1 + 10(δ− R )/σ ( f )

 (1)

,

where A r is the amplitude at 1 km, f is the frequency in Hz, R is the range from the source in km, the parameter δ is the width of the shadow zone (distance between the source and the first recorded stratospheric bounce), assumed constant at 180 km. The values and corresponding uncertainties of the variables α ( f ) and σ ( f ) (with units of km−1 ) and the dimensionless variable β( f , V eff -ratio ) are provided in Le Pichon et al. (2012) for a source at altitude 0 km. Modified parameters provided to us for a source height of 30 km were used in this study. Eq. (1) was derived for a range-independent medium. We introduce weak range dependence to this formula by computing estimates of the transmission loss (TL) at a given frequency as

T L ( f , R ) = −20

 d(log A ( f , R , V eff -ratio )) dR

dR ,

(2)

where the derivative d(log A )/dR is computed at 20 km intervals along the propagation path given the local V eff -ratio value at each step. Eq. (2) was applied to global specifications of winds and temperatures for the date of the Chelyabinsk meteor to compute TL estimates at any point on the Earth’s surface for a 0.1 Hz source. At each point, the V eff -ratio value is calculated as the maximum ratio of the effective sound speed at altitudes from 30 to

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Fig. 6. A global map showing the transmission losses in dB at 0.1 Hz from the Chelyabinsk meteor to any point on the ground. The source altitude is at 30 km at 54.836◦ N, 61.455◦ E. The USArray stations are marked by dots, and transects A, B, and C are as shown in Fig. 1. (The single point at the North Pole indicating a high transmission loss is a numerical artifact and does not affect our computations.)

65 km to that at the ground. Fig. 6 shows the predicted TL for a 0.1 Hz source at the site of the meteor’s major flare, for a medium that varies linearly with time as discussed in the previous section. A comparison of Figs. 4 and 6 indicates the predicted efficiency of stratospheric vs. thermospheric propagation for a 0.1 Hz source. The numerical synthesis predicts that infrasound propagated efficiently within the stratospheric duct eastward of the Chelyabinsk, but was highly attenuated as it propagated westward within the thermospheric duct. The differences in the predicted efficiency of stratospheric vs. thermospheric ducting varies with frequency. At lower frequencies, the differences between stratospheric and thermospheric propagation losses decrease; at higher frequencies, infrasound propagates undergoes much greater attenuation for thermospheric than for stratospheric ducting. Signal energies – given by the sum of the squared pressure amplitudes over the duration of the signal – are compared across the 201 USArray stations that had measurable signals in the 0.04–0.16 Hz band. This band was chosen because it was the only one in which signal amplitudes and durations could be picked consistently across the USArray. Few stations within the larger, eastern part of the USArray had discernible signals at higher frequencies. At lower frequencies, the end of the infrasound coda was indistinguishable from noise due to an increase in noise during daylight hours. Because the maximum signal is in the 0.01–0.03 Hz band (Fig. 3) where the end of the coda from this event cannot be picked accurately, we cannot estimate the total source energy given USArray recordings of this event. Under the assumption that the source is isotropic, variations in infrasound signal energies are attributable to differences in along path TL. Fig. 7a shows estimated signal energies at each station with a signal-to-noise level of at least 2 in the 0.04–0.16 Hz band. Values are plotted as a function of azimuth from receiver to source, such that the Alaska stations are on the left and stations near the east coast are on the right. Stratospherically ducted arrivals are indicated by light grey circles; thermospherically ducted arrivals are shown as dark grey triangles. The Alaska stations have signal energies approximately 16 dB greater than at stations within the remainder of the array within this frequency band. Energy levels at

Fig. 7. Estimates of the signal energy in the 0.04–0.16 Hz band – given by the sum of the squared pressure amplitudes over the duration of the signal – are shown as a function of azimuth from the receiver to source, with Alaska stations to the left and eastern US stations on the right. (a) Signal energy at each receiver. (b) Estimates of the signal energy that would be observed at a range of 1 km from the source, given TL estimates derived for a 0.1 Hz source. Stratospherically ducted arrivals are indicated by light grey circles; thermospherically ducted arrivals are shown as dark grey triangles.

stations along the west coast are on the same order of magnitude as those further east, where the bulk of the array is located. We combine the measured waveform energies with the TL estimates made at 0.1 Hz (Fig. 6), to derive predictions of the signal energies that would be observed in this frequency band at a distance of 1 km from the source. These predictions, shown in Fig. 7b, are based on the assumptions of linear propagation from an isotropic source. If the both the TL estimates (Eq. (2)) and the assumption of linear propagation from an isotropic source were accurate, the estimates of signal energy shown in Fig. 7b would be in agreement at all azimuths. However, Fig. 7b indicates that the estimates for stations at the western edge of the USArray, where infrasound arrivals are primarily stratospherically ducted, are lower than those at the eastern end, where infrasound is thermospherically ducted. That is, the thermospheric arrivals are relatively more energetic than expected. This suggests either that the source preferentially radiated infrasound in this direction, or that TL estimates are incorrect. We note that any significant release of infrasound energy along the meteor’s trajectory would have yielded more energetic arrivals at the Alaska stations. However, since signal energies at Alaska are lower than for stations toward the eastern end of the USArray, supplemental infrasound energy from the meteor’s bow shock is not required to explain the infrasound observations. Thus, we rule out the meteor’s bow shock as a significant source of infrasound energy recorded at any of the USArray stations. The higher estimates of signal energy for stations within the eastern segment of the USArray suggest that either TL is overestimated for thermospheric propagation, or underestimated for stratospheric propagation. To address the latter possibility, we note that the environmental models upon which TL estimates are made are azimuthally independent. This may lead to inaccurate

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TL estimates, particularly for stations that lie near a boundary between regions where infrasound propagation is either primarily stratospherically vs. thermospherically ducted. Fig. 4 indicates that stations near transect B lie along such a boundary; in Fig. 7, it is observed that signal energies at these stations are particularly low. We hypothesize that where there are strong azimuthal variations in stratospheric wind speeds, fine-scale structure may cause infrasound energy to “leak” laterally away from regions where it is stratospherically ducted leading to underestimates in TL. The other possibility, that TL is consistently overestimated for thermospheric ducting, suggests that the atmospheric absorption values used for the environmental models, used in the derivation of Eq. (1), are too high. This possibility had been previously noted in de GrootHedlin et al. (2011), who found that thermospheric arrivals had higher signal energies than expected given standard atmospheric viscosity values (Sutherland and Bass, 2004). 5. Discussion and conclusions Meteoritic events as large as the one that occurred above Chelyabinsk, Russia are not unique in human history. It is only in recent years however that we have deployed broad networks of microbarometers to permit thorough and rapid investigations of them using the atmospheric pressure waves they create. Although the IMS infrasound network recorded signals from the meteor around the globe (Le Pichon et al., 2013), its low density precludes a detailed examination of the nature of infrasound propagation. The USArray network, just recently equipped with pressure sensors, fills in gaps between the global network of infrasound arrays, albeit only in the United States. The data collected by the USArray provide an unprecedented opportunity to further our understanding of the nature of long-range infrasound propagation and assess the utility of atmospheric models for predicting infrasound waveforms. The network’s location with respect to this distant source have allowed us to make finer scale observations of differences in infrasound propagation through stratospheric and thermospheric ducts and examine the nature of propagation at azimuths at which propagation in one duct gives way to propagation in the other. This extremely rare event, recorded with modern, dense, instrumentation provides further evidence of the utility of global-scale atmospheric models. Given the significant time elapsed by propagation of infrasound from the source to even the closest stations in Alaska, it was necessary to accommodate the gradual change of the atmosphere. Raytrace modeling applied to these spatially and temporally varying atmospheric models suggests that a sufficiently large acoustic point source in the atmosphere may cause resonance in stratospheric and thermospheric ducts, leading to extremely protracted waveforms. Thus, the Earth’s atmosphere is akin to a whispering gallery. Infrasound signals recorded in Alaska and at stations along the northwest coast of the U.S. are caused by a combination of stratospheric and thermospheric ducting. For propagation to these sites, rays with shallow launch angles from the source reverberate between the Earth’s surface and stratopause, resulting in signals of approximately from 10 to 16 min duration. Rays with steeper initial launch angles propagate to these sites within the thermosphere and have greater durations than the stratospherically ducted rays. They begin prior to stratospheric arrivals at stations in Alaska and are nearly coincident with stratospheric first arrivals at station I04A along transect B; the trailing thermospherically ducted rays arrive well after the stratospheric signals. These signals are observable only at low frequencies because high frequency energy is absorbed by the upper atmosphere. Stations in the eastern United States provide recordings that are characterized by low-amplitudes, low frequencies and long duration. Ray tracing indicates that these long waveforms consist of

energy that has reverberated primarily in the thermospheric duct, and is partially reflected by a thin layer within the lower mesosphere. Ray modeling applied to unperturbed atmospheric models shows that waveforms become dispersed simply by reverberation for propagation to ranges of several thousand kilometers. Recent studies indicate that small-scale structure in the atmosphere resulting from gravity waves disperses infrasound energy associated with individual raypaths (Hedlin and Walker, 2012), which may account for the absence of discrete arrivals within the coda. The Chelyabinsk meteor entered the atmosphere just after 03:20 UT and infrasound signals took approximately 6 h to reach USArray stations in Alaska, arriving just after midnight local time. Signals took over 8 h to reach stations along the west coast of the US, arriving after 03:20 local time. For most USArray stations, further to the east, infrasound signals from Chelyabinsk took over 9 h to arrive, yielding onsets after 07:20 local time. Because background noise levels are higher during the daytime than at night, the protracted arrivals blend in with the increasing daytime noise for most USArray stations, particularly at low frequencies. Thus signal energies, which are proportional to the duration, cannot be estimated at very low frequencies. Infrasound from the meteor to most stations was thermospherically ducted, and few of these stations had discernible signals at frequencies above the microbarom peak. Infrasound signal amplitudes and durations could be consistently picked within the 0.04–0.16 Hz band. The analytic expressions of Le Pichon et al. (2012) for attenuation of infrasound propagating in either a stratospheric or a thermospheric waveguide have been used to derive TL estimates, allowing for a quantitative comparison of expected vs. observed signal energies. We computed signal energies within the 0.04–0.16 Hz band and applied TL estimates for a 0.1 Hz source to derive predictions of signal energies that would be observed at a distance of 1 km from an isotropic source. The results indicate that thermospherically ducted infrasound signals observed at the bulk of the USArray stations in the eastern part of the US are larger than would be predicted based on TL estimates (Eq. (2)) applied to an isotropic source. This rules out arrivals from the meteor’s trajectory as a major contributor to infrasound signals observed at the USArray. Acoustic energy generated at a bow shock propagates at right angles to the trajectory. Infrasound energy shed from the bow shock would lead to enhanced signals at the Alaska stations, not at the stations at the eastern end of the array, which are located at azimuths from the source that are significantly off the normal from the bow shock. Therefore an isotropic release of energy from the meteor flare remains the preferred infrasound source model. This is in agreement with the study of Tauzin et al. (2013) who argue that Rayleigh waves radiated from the Chelyabinsk meteor originated from a spherical source, rather than an extended source. Our results indicate that either the TL estimates for stratospheric propagation are underestimated for our source-receiver configuration, or that attenuation for thermospheric propagation is overestimated. In the former case, we hypothesize that finescale atmospheric structure, combined with azimuthal variations in the global stratospheric winds, causes infrasound to “leak” laterally away from the stratospheric duct, leading to low TL estimates. A fully 3-D numerical modeling method, incorporating spatial variations in atmospheric winds and sound speeds would be required to test this hypothesis. However, given that significant lateral leakage seems improbable for the Alaska stations, which lie well within the stratospheric duct, it is more likely that the standard model for atmospheric absorption within the thermosphere is incorrect, indicating that a better understanding of atmospheric absorption at high altitudes is needed.

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Acknowledgements We thank the National Science Foundation’s Earthscope program for providing this dataset and the Incorporated Research Institutions for Seismology Data Management Center (IRIS-DMC) for making the data readily available. NSF provided funding under contract EAR-1147962. Thanks to Kristoffer Walker for valuable discussions and to Douglas Drob for providing the atmospheric data used for this study. We thank Alexis Le Pichon and Lars Ceranna for providing attenuation coefficients for a source at 30 km altitude, and for valuable comments. We also thank three anonymous reviewers for constructive comments. References Assink, J.D., Waxler, R., Drob, D., 2012. On the sensitivity of infrasonic traveltimes in the equatorial region to the atmospheric tides. J. Geophys. Res. 117, D01110. http://dx.doi.org/10.1029/2011JD016107. Ben-Menahem, A., 1975. Source parameters of the Siberian explosion of June 30, 1908, from analysis and synthesis of seismic signals at four stations. Phys. Earth Planet. Inter. 11, 1–35. Borovicka, J., Spurny, P., Shrbeny, L., 2013. Trajectory and orbit of the Chelyabinsk superbolide, Electronic Telegram Central Bureau for Astronomical Telegrams. IAU No. 3423, http://www.icq.eps.harvard.edu/CBET3423.html. accessed 24 October, 2013. Brown, P.G., Spalding, R.E., ReVelle, D.O., Tagliaferri, E., Worden, S.P., 2002. The flux of small near-Earth objects colliding with the Earth. Nature 420, 294–296. http://dx.doi.org/10.1038/nature01238. Brown, P.G., Assink, J., Astiz, L., Blaauw, R., Boslough, M., Borovicka, J., Brachet, N., Brown, D., Campbell-Brown, M., Ceranna, L., Cooke, W., de Groot-Hedlin, C., Drob, D., Edwards, W., Evers, L.G., Gill, J., Garces, M., Hedlin, M., Kingery, A., Laske, G., Le Pichon, A., Mialle, P., Moser, D.E., Saffer, A., Silber, E., Smets, P., Spalding, R.E., Spurny, P., Tagliaferri, E., Uren, D., Weryk, R., Whitaker, R., Krzeminski, Z., 2013. A 500 kiloton airburst over Chelyabinsk and an enhanced hazard from small impactors. Nature. In press. Busby, R.W., Vernon, F.L., Newman, R.L., Astiz, L., 2006. Earth-Scope’s USArray: Advancing eastward. Eos Trans. AGU 87 (52). Fall Meet. Suppl., Abstract U41B-0820. Cates, J.E., Sturtevant, B., 2002. Seismic detection of sonic booms. J. Acoust. Soc. Am. 111, 614–628. Collins, M.D., 1993. A split-step Padé solution for the parabolic equation method. J. Acoust. Soc. Am. 93, 1736–1742. Drob, D.P., Picone, J.M., Garcés, M.A., 2003. The global morphology of infrasound propagation. J. Geophys. Res. 108, 4680. http://dx.doi.org/10.1029/ 2002JD003307. de Groot-Hedlin, C.D., 2008. Finite-difference time-domain synthesis of infrasound propagation through an absorbing atmosphere. J. Acoust. Soc. Am. 124, 1430–1441. de Groot-Hedlin, C.D., Hedlin, M.A.H., Walker, K.T., Drob, D.D., Zumberge, M.A., 2008. Evaluation of infrasound signals from the shuttle Atlantis using a large seismic network. J. Acoust. Soc. Am. 124, 1442–1451.

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