# Trajectory of the August 7, 2010 Biwako fireball determined from seismic recordings

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## Abstract

The Biwako fireball on August 7, 2010, produced a strong sonic boom throughout central Japan around 17:00 JST (UTC+9). There were many visual observations and reports of the sound in the Tokai and Kinki regions at that time. We have estimated the trajectory of this fireball and the location of its termination point by analyzing seismograms recorded on a dense local network. The isochrons of the arrival times are close to concentric circles, which suggest that the fireball disappeared due to fragmentation during entry. The fireball trajectory which explains the arrival times of the signal has a relatively high incident angle (55 degrees relative to the horizon) and the source is thought to disappear at a height of 26-km east of Lake Biwa. The azimuthal angle and velocity of the fireball are difficult to determine uniquely from this dataset. We identified an event thought to be due to fragmentation, with a location 3-km ENE and 9-km higher than the termination point. This location is consistent with the trajectory determined from the signal arrival. Based on this trajectory model, the source of the signal spans a horizontal range of 26 to 70 km, and the altitude of the source producing the sonic boom is about 30 to 50 km.

### Key words

2010 Biwako fireball estimation of trajectory sonic boom meteoroid fragmentation## 1. Introduction

The Lake Biwa (Biwako in Japanese) fireball on August 7, 2010, produced a strong sonic boom throughout central Japan at around 17:00 JST (UTC+9). There were numerous reports of the track across the sky and associated sounds in the region. A newspaper reported that the sonic boom was heard by local residents in the Tokai region (Aichi, Gifu, and Mie prefectures) and some people called emergency services to report the strong sound (asahi.com, 2010). Bright flashes were observed as far away as 250 km from the termination point, as reported on an internet bulletin board (Japan Fireball Network, 1999). Local amateur astronomers have searched for the meteoroid which may have reached the ground, but nothing has been found so far (Onishi, 2010).

Past atmospheric trajectories of fireballs have been determined by visual recordings such as photographs and movies (Brown *et al.*, 1994, 2003), infrasound records (Brown *et al.*, 2002; Le Pichon *et al.*, 2002, 2008), and seismic records (e.g., Nagasawa, 1978; Nagasawa and Miura, 1987; Cevolani, 1994; Qamar, 1995; Brown *et al.*, 2002; Cates and Sturtevant, 2002; Le Pichon *et al.*, 2002, 2008; Ishihara *et al.*, 2003, 2004; Rydelek and Pujol, 2004; Pujol *et al.*, 2005). An object flying at supersonic velocity produces a sonic boom, and the acoustic-to-seismic coupled signal is often recorded by seismic arrays. The airwave signal from this fireball was recorded by about 50 seismic stations in Japan (NIED, 2010). This is one of the few events having an airwave signal that has been recorded by a dense seismic network (Walker *et al.*, 2010). In this paper, we estimate the trajectory of the Biwako fireball and the location of the termination point of the signal by analyzing the seismograms, and discuss the characteristic waveforms and mechanism of fireball fragmentation.

## 2. Data

### 2.1 Seismic data

The Biwako fireball produced atmospheric sound waves that were recorded by Hi-net, F-net (both operated by the National Research Institute for Earth Science and Disaster Prevention), the Japan Meteorological Agency high-sensitivity seismic network, and high-sensitivity seismic networks operated by Japanese universities (Okada *et al.*, 2004). Those seismic networks currently have about 20-km spacing throughout Japan, and we identified shockwave signals from the fireball at 49 stations.

*P*-wave arrivals in the seismograms. The characteristics of the time series change over time due to the arrival of seismic waves. Therefore, the time series is divided into two segments, and the autoregressive model is fitted to each segment. The log-likelihood of each multi-variate locally-stationary autoregressive model is computed, and the Akaike information criterion (AIC) is used to determine the best onset time (Akaike, 1974). The onset of the signal is determined as the section that minimizes the AIC. Although this technique can identify the time that the characteristics of the waveforms show the most significant changes, there is a possibility that this onset time is contaminated by an air-coupled Rayleigh wave (Edwards

*et al.*, 2008). The arrival times determined by this method are marked as open triangles in Fig. 1.

In contrast to some past observations (e.g., Cates and Sturtevant, 2002; Ishihara *et al.*, 2003), the airwave signals from this event have unclear emergent onsets, a long duration (10–40 s), and no distinct “N” shaped waves. The low apparent velocity (∼0.37 km/s) of the signals across the seismograph network indicates that the source of the signal is in the atmosphere, and is not an earthquake (see Fig. 1).

*et al.*, 2003).

### 2.2 Visual observations

## 3. Methods

*et al.*, 2008). The sites on the ground in the direction of the fireball trajectory record signals due to the fragmentation, while sites on the ground perpendicular to the fireball trajectory record the ballistic wave and signals from the fragmentation (see Fig. 4). Based on this assumption, we estimated the trajectory and termination point of the signal.

*x*

_{0},

*y*

_{0},

*z*

_{0}: coordinates of the trajectory where the signal vanished

*t*_{0}: time when the signal vanished

*γ*: azimuth of the trajectory

*θ*: incident angle of the trajectory relative to the horizontal

*c:* velocity of sound (0.312 km/s)

*v:* velocity of the fireball (20 km/s)

*x*,

*y*,

*z*coordinate system is defined as longitude 136°E, latitude 35°N, and altitude 0 km, and the origin time is 17:00:00 JST. The speed of the sonic wave is assumed to be a constant with the value of 0.312 km/s taken from Nagasawa and Miura (1987). The velocity of the fireball is a parameter which is difficult to constrain because of the trade off with the time the signal vanishes, since the velocity of sound is slow with respect to the observed duration of the signal assuming a range of reasonable fireball velocities (Ishihara

*et al.*, 2003; Edwards

*et al.*, 2008). We computed a misfit surface for each parameter (see Fig. 5) and the result shows that the velocity of the fireball is not sensitive to the root-mean-square residual of the arrival times, so a fixed velocity of 20 km/s was used. (The misfit surface will be discussed in the next section.) Six free parameters (

*x*

_{0},

*y*

_{0},

*z*

_{0},

*t*

_{0},

*γ*,

*θ*) that define the fireball trajectory are solved by minimizing the rms residuals: where

*n*is the number of observations,

*t*

_{pred, i}is the predicted arrival time of the signal at the

*i*th station, and

*t*

_{obs, i}is the measured arrival time of the signal at the

*i*th station. The 6 in the denominator is the number of parameters to be estimated (Montgomery and Runger, 2003).

## 4. Analysis and Results

### 4.1 Estimation of the trajectory

*et al.*, 2010). The uncertainties of the parameters

*x*

_{0},

*y*

_{0},

*z*

_{0},

*t*

_{0},

*γ*,

*θ*are small, since the arrival time of the shock wave is sensitive to these parameters. However, the azimuthal angle

*γ*has a large confidence interval and is difficult to determine uniquely from this dataset, since most of the stations are inside the concentric isochrons and the azimuthal coverage of stations with distances greater than 100 km is poor.

The most probable parameters which determine the trajectory of the fireball.

Parameters | Optimal solution | Search range | Grid interval | Confidence interval |
---|---|---|---|---|

Longitude (deg.) | 136.073 | 136.0–136.2 | 0.001 | 136.055–136.090 |

Latitude (deg.) | 36.149 | 35.0–35.2 | 0.001 | 35.140–35.160 |

Height (km) | 26 | 0–50 | 1 | 22–30 |

Time (sec) | 58 | 50–80 | 1 | 53–65 |

Incident ang. (deg.) | 55 | 30–90 | 1 | 51–60 |

Azimuth (deg.) | 32 | 0–180 | 1 | 16–63 |

RMS (sec) | 6.86 | — | — | — |

### 4.2 Sensitivity analysis

We computed misfit surfaces as a function of each parameter to check the sensitivity of the parameters. The minimum of the rms residuals are computed as a function of two selected parameters (see Fig. 5). The misfit surface for the horizontal location is smooth in both longitude and latitude, and has a single local minimum. Therefore, the solution easily converges to this minimum. The optimal time and altitude of the meteorite dissipation are both sensitive to the velocity of sound and difficult to resolve, but, nevertheless, a broad minimum exists in the surface. Note that these two parameters are also sensitive to the sound velocity. The perturbation of the parameters is about 10% if we change the velocity of the sound by 0.01 km/s. The azimuth of the trajectory is not very well determined by the dataset, as we have seen with the confidence interval. The velocity of the fireball is also significantly insensitive to the data, so we used a constant velocity for this analysis.

### 4.3 Interpretation of the model

A mechanism to produce the concentric isochrons of the arrival times can be explained by an explosive fragmentation (Edwards *et al.*, 2008). During a meteoroid entry, the object breaks up suddenly because of the increasingly large air pressure. A large amount of light is produced associated with the break up. Since these explosive fragmentation events are very brief and take place over small portions of the entire trajectory, they are approximated by a point source, and result in the concentric isochrons.

The non pulse-like waveforms can also be explained with this mechanism. The fragmentation may result in the separation of the original body into several large fragments. The duration of the fragmentation is largely unknown; however, if fragmentation takes 0.5 second, the meteoroid can travel as far as 10 km (assuming a constant velocity) during this time. This distance is comparable to a difference of 32 seconds in the arrival time of the waveforms. Therefore, the extremely long duration of the signal is not necessarily unreasonable (Walker *et al.*, 2010). Edwards *et al.* (2008) explained that observations of explosive point-source events tend to be diffuse, with no distinct arrival time, in contrast to the sharp onset of ballistic observations. Waveforms here are very similar to the waveforms of the 2002 Tagish Lake fireball (Brown *et al.*, 2002) and 1989 St. Helens fireball (Qamar, 1995), which both show concentric isochrons. Similar concentric isochrones were also observed in Arrowsmith *et al.* (2007) and Walker *et al.* (2010). Multipathing through the atmosphere might also complicate the character of the waveforms; however, this is generally observed at distances greater than 200 km (Walker *et al.*, 2010), which is not the range of the data in this study.

### 4.4 Height of the source

The airwave signal was observed by seismometers as far away as 150 km, and bright flashes were observed as far away as 250 km from the termination point (Japan Fireball Network, 1999). We have tried to estimate the altitude of the termination point from the trajectory model. Figure 4 shows a schematic diagram of the fireball trajectory and meteor-generated atmospheric waves. If the source dissipates at 26-km altitude, the ballistic wave due to the object flying at supersonic speed cannot be observed within 40 km from the epicenter. The signal observed in this near-source region is not impulsive due to the fragmentation. Assuming a line source, the height of a source which is observable 150 km from the center of the arrival time pattern must be at least 70-km high. Therefore, the source of the signal is inferred to be between 26 and 70 km, and could be higher if there is strong attenuation in the atmosphere. Reports of the sonic boom concentrate in the Tokai region, about 50–100 km from the center of the arrival-time pattern. The altitude of the source corresponding to this signal is about 30- to 50-km high. This height is consistent with past observations; 22 to 34 km for the 2000 Moravka fireball and 34 to 87 km for the 2003 Kanto fireball (Pujol *et al.*, 2006). For the Biwako fireball, we located two fragmentation events at heights of 26 and 35 km (see Tables 1 and 3). It has been suggested that the height of fragmentation is where the aerodynamic pressure exceeds the material strength. Cevolani (1994) calculated the critical heights of the first fragmentation for meteoroids having different values of material strength. According to these results, the critical height is 45.5 to 56.5 km for dustballs, 14 to 38 km for stony chondrites, and 3 to 14 km for metal bodies, at velocities of 15 to 30 km/s. From these values, we speculate that the material of the Biwako fireball may be stony chondrite.

## 5. Different Models

### 5.1 Point source model

_{i}is the residual sum of squares of model

*i*,

*p*

_{i}is the number of parameters of model

*i*, and

*n*is the number of observations. From the F distribution table, the F value with (

*p*

_{2}−

*p*

_{1},

*n*−

*p*

_{2}) degrees of freedom at a 5% significance level is 3.21. Therefore, the null hypothesis has a low probability of being accepted, and the more complicated model provides a significantly better fit to the data.

The most probable parameters which determine the trajectory of the fireball from a point source model.

Parameters | Optimal solution | Search range | Grid interval |
---|---|---|---|

Longitude (deg.) | 136.086 | 136.0–136.2 | 0.001 |

Latitude (deg.) | 36.172 | 35.0–35.2 | 0.001 |

Height (km) | 33 | 0–50 | 1 |

Time (sec) | 45 | 40–70 | 1 |

RMS (sec) | 12.07 | — | — |

### 5.2 Back projection method

Since we used the times of the onset of the signal for the location estimation, these arrival times correspond to the location of the end of the terminal explosion. We applied a back projection method to the waveforms in order to find the location where the fireball produced the largest energy.

The waveforms used here are the same as the dataset in Section 2. Since the correlation distance of infrasound at 0.5 to 5 Hz is only several kilometers (Walker *et al.*, 2010), we used the envelopes of the waveforms. The data are processed as follows; envelopes of the waveforms are formed using the maximum absolute value of the waveforms over one-second windows. To remove the effect of stationary noise, the mean over a 10-minute duration is removed. Then, the maximum amplitude of the signal is normalized to one to regularize the amplitude of the envelopes.

*et al.*(2010). However, the stack of the waveform amplitudes (

*Q*) is defined as a function of longitude, latitude, altitude, and time, in our analysis. The maximum for every second

*t*is defined as

*Q*

_{t}. The weighting is set to be one since our station distribution is not greatly skewed. The search range is the same as shown in Table 2. Figure 6 shows

*Q*

_{t}as a function of

*t*. The

*Q*

_{t}has a local maxima between 55 and 60 seconds, and the optimal parameters at those times are shown in Table 3.

The most probable parameters which determine the trajectory of the fireball from a back projection.

Parameters | 55 sec | 56 sec | 57 sec | 58 sec | 59 sec | 60 sec |
---|---|---|---|---|---|---|

Longitude (deg.) | 136.102 | 136.091 | 136.108 | 136.104 | 136.109 | 136.115 |

Latitude (deg.) | 35.169 | 35.168 | 35.162 | 35.168 | 35.163 | 35.163 |

Height (km) | 36 | 35 | 36 | 34 | 35 | 35 |

| 0.521 | 0.537 | 0.533 | 0.515 | 0.533 | 0.519 |

The computed location of the source producing the largest energy is located around 136.105E and 36.165N, about 3-km ENE and 9-km higher than the termination point. This location is consistent with the trajectory determined from the arrivals at the seismic stations, since the path from the source producing the largest energy to the terminal point is similar to the calculated trajectory. Because the source of the largest energy is at a higher altitude than the termination burst, it was recorded a few tens of seconds later at some stations.

## 6. Conclusions

We have estimated the trajectory of the August 7, 2010, Biwako fireball, and the location of its termination point from arrivals at seismic stations. The isochrons of the arrival times are nearly concentric circles, which suggest that the fireball dissipated due to fragmentation during entry. The fireball trajectory which explains the arrival times of the signal has a relatively high incident angle (55 degrees) and the source is thought to disappear at a height of 26-km east of Lake Biwa. The azimuthal angle and velocity of the fireball are difficult to determine uniquely from this dataset. We identified an event thought to be due to fragmentation, with a location 3-km ENE and 9-km higher than the termination point. This location is consistent with the trajectory determined from the arrival time data. Based on this trajectory model, the location of the source of the signal spans a range of 26 to 70 km, and the altitude of the source producing the sonic boom is about 30 to 50 km.

## Notes

### Acknowledgements

The authors thank Yoshihisa Iio of Kyoto University for providing the data observed west of Lake Biwa. We acknowledge the National Research Institute for Earth Science and Disaster Prevention (NIED) and the Japan Meteorological Agency (JMA) for the use of the seismic data. This research was supported by the Program for Improvement of Research Environment for Young Researchers from Special Coordination Funds for Promoting Science and Technology (SCF) commissioned by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.

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