京都大学防災研究所年報 第 58 号 B 平成 27 年 6 月
Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No. 58 B, 2015

Seismic Observations of the Sonic Boom Produced by the Chebarkul
Meteorite

Masumi YAMADA and James MORI
Synopsis
The Chebarkul meteorite produced a strong sonic boom throughout Chelyabinsk
Oblast at 03:20 on February 15, 2013 (UTC). Also at that time a large seismic signal
was observed on seismic stations of the IRIS network in the region. We performed awaveform inversion using broadband seismic data from 5 sites to obtain the sourcetime function of the Chebarkul meteorite signal. Assuming a single force for thesource mechanism, the waveform can be explained well with a point source model.
We performed a grid search in space to ﬁnd the location of the source. The bestﬁt source location was determined on the meteor track and 40 km away from Lake
Chebarkul, where the possible meteorite impact was found. We use the modiﬁed
Friedlander equation to estimate a deconvolved form of the source time function, andthe amplitude of the estimated single force is 2.0 × 1011 N with the onset of the pulse
at 03:21:58 (UTC), February 15, 2013. Since the location of the estimated source
is separated from the impact point, we conclude that the single force generating theseismic waves was produced by the blast wave due to the severe fragmentation of thebolide, not the impact of the meteorite on the ground.
Keywords : Chebarkul meteorite, Sonic boom, Seismic waveform, Waveform inversion

1．Introduction

mologically unique since seismic signals producedby the sonic boom were observed as far as 4000 km

The Chebarkul meteorite entered the Earth’s at-from the source (Tauzin et al., 2013; Heimann etmosphere over Russia at 03:20 February 15, 2013

al., 2013) and the trajectory of the meteorite was(UTC) producing a strong sonic boom through-well determined by many visual recordings (Yeo-out Chelyabinsk Oblast. The dazzling light of themans and Chodas, 2013; Borovička et al., 2013;

meteor was widely observed around Russia’s Ural

Zuluaga et al., 2013).

Mountains, and the strong pressure wave damaged

In general, seismic signals from a meteorite di-many buildings, especially window glass. Morerectly record the sonic boom, which is a shock

than 1500 people were injured mostly by the bro-wave associated with a large sound produced by

ken glass, but there were no fatalities. Althoughan object traveling faster than the speed of soundnear-source regions were severely damaged, there

through the atmosphere. It travels through the air

are few direct observations of the shock wave fromat the speed of sound, however the waveforms ob-

the meteorite entry (Brown et al., 2013; Pichon etserved in the seismic data travel at the much fasteral., 2013; Seleznev et al., 2013).

speed of S-waves or surface waves, which indicatesIn this study, we used ground shaking datathat the signals travels through the ground, not inrecorded by broadband seismometers operated by

the air. The signal is observed as far as 2000 km

the Incorporated Research Institutions for Seis-from Chelyabinsk city (see Figure 1). The parti-

mology (IRIS). The Chebarkul meteorite is seis-― 47 ―

cle motion recorded at the closest station (ARU)

three single-force components at each source nodeshows the Rayleigh wave is dominant in the sig-

(Nakano et al., 2008). We compared the residuals

nal. We performed a waveform inversion usingof this process for each point of the grid to de-broadband seismic records to ﬁnd the location oftermine the best ﬁtting location. The normalized

the source. We reconstructed the timing, location,

residuals for this grid are shown in Figure 1.

and force history of the seismic source due to the
Chebarkul meteorite. This seismological ﬁnding of

3．Results

the Chebarkul meteorite helps to understand the
Figure 2 shows the source time functions forcause of damage and mechanism of acoustic cou-

three single force components at the most probablepling.

location (54.8◦ N, 60.9◦E) and the waveform ﬁts
between observed and synthetic data. The best-

2．Data and Methods

ﬁt source location occurred on the meteor track

We used 5 near-source seismic stations operatedby IRIS (see Figure 1). The closest station is about
200 km from the impact site and others are about
600-1600 km away. All stations have 3 component broadband seismometers with a sampling frequency of 20 Hz. Components with poor S/N ratio
were not used for the analysis.
We processed the broadband records according
to the following procedure. First, we removed themean from the time series and corrected for the instrumental response in all waveforms. The records
were then integrated once, and a noncausal fourthorder Butterworth ﬁlter with corner frequency of
0.01-0.1 Hz was applied to extract signals from microseismic noise. We then decimated the data bya factor of 20, reducing the sampling frequency to
1 Hz. We performed a waveform inversion using
these ﬁltered displacement records.
Following the method of Nakano et al. (2008),
we performed a waveform inversion in the frequency domain to determine the source processof the seismic signal. We calculated Green’s functions at grid points of in a rectangle (from 60.6◦ E
to 61.4◦ E in longitude and from 54.4◦N to 55.0◦N
in latitude) with 0.1◦ interval, using the discrete
wavenumber method (Bouchon, 1979) and theAK135 one-dimensional velocity model (Kennett
et al., 1995). Assuming a single-force mechanism
for the source, we estimated the least-squares solution in the frequency domain for each grid point.
We performed an inverse Fourier transform on thesolution to determine source time functions for(Zuluaga et al., 2013) and 40 km away from Lake
Chebarkul, where a large hole was found in theice covered lake. The normalised residual of the
waveform ﬁt is 0.35 and the ﬁt of the waveforms
are reasonably good. Although we are using the
global AK135 one dimensional velocity model, theresults shows the velocity structure in that region
can be approximated by the simple model. The
vector sum of the maximum force is 1.0 × 1011 N
for a source occurring at 03:21:58 February 15,
2013 (UTC) at the determined location. The vertical component shows a simple pulse with durationof about 100 s. The horizontal components aresubstantially smaller than the vertical component,
which suggests that the source is stronger in thevertical direction.
Since we applied a bandpass ﬁlter to observed
waveforms, the source-time functions obtained
from the waveform inversion have limited information outside of the ﬁlter window. In order to estimate the actual source time function over a wider
bandwidth, we need to correct for the frequencies
which were ﬁltered out of the data. Therefore, weused the approach of Nakano et al. (2008) whichassumes an analytic function for the source-timefunction. We use the modiﬁed Friedlander equation to estimate the form of the source time function, which is widely used to model a blast wave
caused by explosions (Baker, 1973; Martins et al.,2001).
P (t) =― 48 ―

0(t < t0 )t−t00
Ps exp(−β t−tt∗ )(1 − t∗ )(t ≥ t0 )

(1)

56˚

(a)

(b)
60˚
ARU
OBN

Chelyabinsk
55˚

BRVK

50˚

KURK

ABKAR

ZFG
Y&C

40˚
30˚

40˚

50˚

60˚

70˚

80˚

Lake Chebarkul

B.et.al

54˚

0.40

0.50

0.60

53˚
60˚

62˚

64˚

Fig. 1 (a) The normalized residuals of the waveform inversion assuming the source location at each grid
point. The star shows the minimum residual. The results of the damage survey are shown with open
circles (no damage) and solid circles (severe damage). The meteor tracks computed by Yeomans andChodas (2013)(Y&C), Borovička et al. (2013)(B.et.al), and Zuluaga et al. (2013)(ZFG) are also shown.
The shaded area shows the location of maximum brightness in each model. (b) Distribution of seismic
stations used for the analysis. The box shows the region in Figure 1(a)where Ps is the peak overpressure, t0 is the on-

t0 = 117, t∗ = 13, and β = 0.6. The amplitude of

set time of the pressure, t∗ is the positive phasethe estimated single force is 2.0 × 1011N, assuming

duration, which is the time for reaching the refer-a point source at the most probable location. The

ence pressure. β is a parameter to customize theonset of the pulse is estimated to have occurredpressure proﬁle curves. We assume that the actual

at 03:21:58. These numbers are consistent withsingle force is represented by the modiﬁed Fried-

the result of other analysis with seismic waveforms

lander equation with a negative sign, and search(Heimann et al., 2013; Tauzin et al., 2013).

for the 4 unknown parameters (P s, t0 , t∗ , β) in thefunction by minimizing the normalized residual between the observed source-time function and the

4．Discussion

analytic function. For ﬁtting the function, we use
the same bandpass ﬁlter that was applied to theobserved data. The source-time function derived
from this procedure and ﬁts between the observed
and predicted source-time functions are shown in
Figure 3. The obtained parameters in the modiﬁed Friedlander equation are: Ps = 2.0 × 1011 ,The track of the meteor was recorded by manycamerasacrosstheregion(e.g. https://www.youtube.com/v/bXifSi2K278).
The trajectory of the bolide in the atmosphere wasreconstructed from the visual observation, including amateur videos, vehicle cameras, and public
surveillance cameras. Figure 1 shows the trajecto-― 49 ―

(a)UD

Force (x1010N)

5

NS

EW

0
-5
-10
0

200

400

600

Time (s)(b)

max = 1.84µm
min = −3.11µm

max = 1.53µm
min = −0.95µm

max = 1.53µm
min = −1.54µm

max = 1.27µm
min = −0.72µm

max = 1.23µm
min = −1.92µm

ARU

ABKAR
max = 2.42µm
min = −3.46µm

BRVK
max = 1.85µm
min = −1.46µm

KURK

OBN

Obs.
Syn.
Residual = 0.3499

max = 0.65µm
min = −0.79µm

Fig. 2 Seismic waveforms of the Chebarkul meteorite. (a) Estimated single-force source time functions
for the EW, NS, and UD components. The horizontal axis indicates the time after 3:20 February 15,
2013 (UTC). (b) Displacement waveform ﬁts between observed (black) and synthetic (red) data obtained
from the source inversion. The letters on the left show the station code, and the numbers in the top rightshow the maximum and minimum amplitudes.
ries reconstructed by Yeomans and Chodas (2013),

rection, which suggests the signal arrived from the

Borovička et al. (2013), and Zuluaga et al. (2013).

sky. The location of the most probable source time

All of the estimates of the path are quite simi-function is very close to the location of maximum

lar, with only 10-20 km diﬀerence. Therefore, thebrightness and separated from the impact point ofreconstructed trajectory should be reasonably ac-

the meteorite by about 40 km. Therefore, we con-curate. Borovička et al. (2013) and Yeomans andclude that the single force generating the seismic

Chodas (2013) computed the location of maximum

waves was produced by a blast wave due to thebrightness, which may have generated the blast

severe fragmentation of the bolide, and not caused

wave. The location is also shown in Figure 1 asby the impact of the meteorite hitting the ground.

a shaded area. The altitude and timing of the

The location for the fragmentation is consistentmaximum brightness is 25-30 km at 3:20:27-28 inwith a ﬁeld survey of damaged structures (Popova

Borovička et al. (2013) and 23.3 km at 3:20:33 in

et al., 2013). Figure 1 shows the districts with

Yeomans and Chodas (2013).

and without glass damage in Chelyabinsk Oblast.

This information provides an important clue for

The severely damaged region is distributed near

identifying the source of the seismic wave. The

the source region in a north-south direction whichsource time function is dominant in the vertical di-is perpendicular to the meteor track. According to― 50 ―

5．Conclusions

2

Friedlander equation

We performed a waveform inversion using broad-

Force (x1011N)

0band seismic records from 5 sites to obtain thesource-time function of the Chebarkul meteorite−2
2Friedlander equation (10-100s)
Observation (10-100s)0signal.

Assuming a single force for the source

mechanism, the waveforms can be explained wellwith a point source model. We performed a gridsearch in space to ﬁnd the location of the source.

−2
0

50

100

150

200

250

300

The best-ﬁt source location occurred on the meteor track (Zuluaga et al., 2013) and 40 km away

Time (s)from the impact site at Lake Chebarkul. We use
Fig. 3 Comparison of the observed and estimatedthe modiﬁed Friedlander equation to estimate asource-time functions. Top: modiﬁed Friedlander
equation with the most probable coeﬃcients, bot-source time function over a wider frequency band-

tom: band-passed modiﬁed Friedlander equationand observed source-time function.

is 2.0 × 1011 N and the onset of the pulse is at

width. The amplitude of the estimated single force
03:21:58 (UTC), February 15, 2013. Since the location of the estimated source is separated fromthe trajectory report (Yeomans and Chodas, 2013;
Borovička et al., 2013) and result of this analysis,
the height of the fragmentation is about 25 km,
and the travel time of the blast wave is estimatedas 85-90 seconds. The velocity of the blast wave

the impact point, we conclude that the single force
generating the seismic waves was produced by theblast wave associated with the severe fragmentation of the bolide, not due to the ground impactof the meteorite.

(0.28-0.29 km/s) is consistent with the speed of
Acknowledgementssound. We suggest that when the meteorite entered the Earth’s atmosphere, a severe fragmenta-

The authors acknowledge the Incorporated Re-tion of the meteorite at a height of about 25 km

search Institutions for Seismology (IRIS) for thegenerated a sonic boom associated with the blast

use of seismic data. We thank Dr. Hiroyuki Ku-

wave. The sonic boom caused acoustic coupling

magai in Nagoya university, who provided us with

between the atmosphere and the solid earth, pro-a computer program for the waveform inversion.

ducing the observed seismic waves. It is possible

We also thank Dr. Shinya Tsukada in Japan Me-

that the fragmentation occurred over some spa-

teorological Agency for the meaningful discussion.

tial extent, as evidenced by a strong ﬂare at the

We used generic mapping tools (GMT) to draw

time of the explosion which continued for a cou-

the ﬁgures (Wessel and Smith, 1991).

ple of seconds. However, the residual surface of
the waveform inversion has a sharp peak, which

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