Earth Planets Space, 63, 1–18, 20101

Trajectory of the August 7, 2010 Biwako Fireball Determined from Seismic

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Recordings

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Masumi Yamada1 and Jim Mori1

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1 Disaster Prevention Research Institute, Kyoto University, Kyoto, Japan

5(Received ; Revised ; Accepted )18

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 thesound in the Tokai and Kinki regions at that time. We estimated the trajectory of this fireball andlocation 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 fireballdisappeared due to fragmentation during entry. The fireball trajectory which explains the arrival
times of the signal has a relatively high incident angle (55 degree relative to the horizon) andthe 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.

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Key words: 2010 Biwako fireball, estimation of trajectory, sonic boom, meteoroid, fragmenta-

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tion

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1.

Introduction

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The Lake Biwa (Biwako in Japanese) fireball on August 7, 2010 produced a strong sonic boom

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throughout central Japan around 17:00 JST (UTC+9). There were numerous reports of the track acrossc The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan;
Copy right⃝
The Geodetic Society of Japan; The Japanese Society for Planetary Sciences.

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M. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGS

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the sky and associated sounds in the region. A newspaper reported that the sonic boom was heard by

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local residents in the Tokai region (Aichi, Gifu, and Mie prefectures) and some people called emergency

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services to report the strong sound (asahi.com, 2010). Bright flashes were observed as far away as 250

27km from the termination point, as reported on an internet bulletin board (Japan Fireball Network, 1999).

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Local amateur astronomers have searched for the meteoroid which may have reached the ground, but

29nothing has been found so far (Onishi, 2010).

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Past atmospheric trajectories of fireballs have been determined by visual recordings such as pho-31

tographs and movies (Brown et al., 1994, 2003), infrasound records (Brown et al., 2002; Le Pichon

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et al., 2002, 2008), and seismic records (e.g. Nagasawa, 1978; Nagasawa and Miura, 1987; Qamar,

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1995; Cevolani, 1994; Brown et al., 2002; Cates and Sturtevant, 2002; Le Pichon et al., 2002; Ishihara

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et al., 2003, 2004; Rydelek and Pujol, 2004; Pujol et al., 2005; Le Pichon et al., 2008). An object fly-35

ing at supersonic velocity produces a sonic boom, and the acoustic-to-seismic coupled signal is often

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recorded by seismic arrays. The airwave signal from this fireball was recorded on about 50 seismic37

stations in Japan (NIED, 2010). This is one of the few events with an airwave signal that is recorded by38

a dense seismic network (Walker et al., 2010). In this paper, we estimate the trajectory of the Biwako

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fireball and location of the termination point of the signal by analyzing the seismograms, and discuss40

the characteristic waveforms and mechanism of fireball fragmentation.

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2.

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2.1

Data

Seismic Data

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The Biwako fireball produced atmospheric sound waves that were recorded by Hi-net, F-net (both44

operated by the National Research Institute for Earth Science and Disaster Prevention), Japan Meteo-

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rological Agency high-sensitivity seismic network, and high-sensitivity seismic networks operated by

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Japanese universities (Okada et al., 2004). Those seismic networks currently have about 20 km spacing

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throughout Japan, and we identified shockwave signals from the fireball at 49 stations.

M. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGS

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Since the onsets of the signal arrival are not very clear, we determined the arrival times as follows.

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First, a band-pass Butterworth filter with typical cutoff frequencies of 2 to 8 Hz was applied to each

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record to look at the frequency range of the infrasound signals. Since we used records from various type51

of sensors, we tried alternative high-pass Butterworth filters if the signal is not clear. The filtered records

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are shown in Figure 1. We used only vertical components for this analysis. The onset of the signal is53

determined by fitting a multi-variate locally stationary autoregressive (MLSAR) model (Takanami and54

Kitagawa, 1991). This technique is widely used to pick P-wave arrivals in the seismograms. The

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characteristics of the time series change over time due to the arrival of seismic waves. Therefore, the56time series is divided into two segments, and the autoregressive model is fit to each segment. The log-

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likelihood of each multi-variate locally stationary autoregressive model is computed, and the Akaike

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information criterion (AIC) is used to determine the best onset time (Akaike, 1974). The onset of the59

signal is determined as a section that minimizes the AIC. Although this technique can identify the time

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that the characteristics of the waveforms have the most significant changes, there is a possibility that61

this onset time is contaminated by the air-coupled Rayleigh wave (Edwards et al., 2008). The arrival

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times determined by this method are marked as open triangles in Figure 1.

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In contrast to some past observations (e.g. Cates and Sturtevant, 2002; Ishihara et al., 2003), the64

airwave signals from this event have unclear emergent onsets, long duration (10 - 40 seconds), and65

no distinct “N” shaped waves. The low apparent velocity (∼0.37 km/sec) of the signals across66

the seismograph network indicates that the source of the signal is in the atmosphere, and is not an

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earthquake (see Figure 1).

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Figure 2 shows the distribution of the arrival times of the shockwave. The first arrival was recorded69

at station DP.OHM (Ohmi-Hachiman) east of Lake Biwa, which indicates that the termination of the70

fireball is close to this station. The area where the signals are observed is within 170 km from this71

station. A notable feature of this fireball is that the isochron pattern consists of nearly concentric

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circles, not half-ellipses, as observed in most past studies (Cates and Sturtevant, 2002; Ishihara et al.,

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M. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGS

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2003).

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2.2

Visual Observations

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The Biwako fireball was observed by many people even in daylight around 17:00 local time, early76

evening in summer. Witnesses reported the locations and times of the sightings, durations of the flash,77

and directions of the fireball emergence on an internet bulletin board (Japan Fireball Network, 1999).

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Figure 3 shows the direction of the fireball observed by 34 witnesses. The fireball was observed from79

sites more than 250 km from the fireball trajectory. Although their reports are relatively rough (16-80point compass directions, such as WSW, are usually used), the direction of the fireball is consistent in81

all reports. We can estimate that the explosive signal was produced near Lake Biwa from this figure.

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Some reports describe a fireball traveling with bright illumination twice to three times the size of the83

moon, and splitting into several parts before disappearing. Most of the witnesses reported that the white84

path of the meteor remained for a few minutes in the sky. The diamond symbols in Figure 3 represent85

the sites where sonic booms were observed (asahi.com, 2010). Here, a sonic boom is defined as a strong86

explosive sound with an impact, so sounds resembling distant thunder are excluded. Compared to the87visual observations of the fireball, the observation of the sonic boom is in a more limited area.

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3.

Methods

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We estimated the trajectory of the fireball and termination point of the signal using a method similar90

to Nagasawa and Miura (1987). This method assumes straight-ray theory and a constant velocity of91sound. Since the arrival pattern of the signals are close to concentric circles, we assume that the fireball92

travelled toward the earth and terminated in the air (or at least stop producing atmospheric signals). A

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combination of line and point sources is considered to produce this arrival pattern. First, the fireball is94

moving through the air with high velocity producing nearly cylindrical ballistic waves, with an elliptical95

arrival pattern on the ground. Then, the fireball experiences a catastrophic fragmentation or disruption

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at a termination point, which causes arrivals in a pattern of concentric circles (Edwards et al., 2008).

M. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGS

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The sites on the ground in the direction of the fireball trajectory record signals due to the fragmentation,

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while sites on the ground perpendicular to the fireball trajectory record the ballistic wave and signals

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from the fragmentation (see Figure 4).

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Based on this assumption, we estimated the trajectory and termination point of the signal.

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Estimated arrival times of the shockwave are represented with the following function (Nagasawa and102

Miura, 1987). Here, we added an assumption that the object dissipates and the generation of the shock103

wave stops at the termination point of the fireball, so extra parameters are added to the function.

if

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√
tpred = t0 + 1/v( X 2 + Y 2 / tan β − Z)

(1)√
tpred = t0 + 1/c( X 2 + Y 2 + Z 2 )

(2)



√


Z ≥ − tan β X 2 + Y 2 ,

Eq. (1) (region A in Fig. 4)√Z < − tan β X 2 + Y 2 ,

Eq. (2) (region B in Fig. 4),

where,
β = arcsin(c/v)
 







cos γ
0  x − x0 
X   − sin γ


  


  
 Y  = − cos γ sin θ − sin γ sin θ cos θ  y − y 

  
0


  


  
z − z0cos γ cos θ sin γ sin θ sin θZ
105x0 , y0 , z0 : coordinates of the trajectory where the signal vanished106

t0 : time when the signal vanished107

γ : azimuth of the trajectory108θ : incident angle of the trajectory relative to the horizontal

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c : velocity of sound (0.312 km/s)

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M. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGSv : velocity of the fireball (20 km/s)

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The coordinate system used in this analysis is shown in Figure 4. The origin for the x,y,z coordinate

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system is defined as longitude 136◦ E, latitude 35◦ N, and altitude 0 km, and the origin time is 17:00:00

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JST. The speed of the sonic wave is assumed to be a constant with a value of 0.312 km/s taken from115

Nagasawa and Miura (1987). The velocity of the fireball is a parameter which is difficult to constrain

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because of the trade off with the time the signal vanishes, since the velocity of sound is slow with respect

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to the observed duration of the signal assuming a range of reasonable fireball velocities (Ishihara et al.,118

2003; Edwards et al., 2008). We computed a misfit surface for each parameter (see Figure 5) and the119

result shows the velocity of the fireball is not sensitive to the rms residual of the arrival times, so a

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fixed velocity of 20 km/s was used. (The misfit surface will be discussed in the next section.) Six

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free parameters (x0 , y0 , z0 , t0 , γ, θ) that define the fireball trajectory are solved by minimizing the rms

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residuals:vuu
rms = tn
1 ∑(tpred,i − tobs,i )2 ,n − 6 i=1

(3)

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where n is the number of observations, tpred,i is the predicted arrival time of the signal at the ith station,

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and tobs,i is the measured arrival time of the signal at the ith station. The 6 in the denominator is the

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number of parameters to be estimated (Montgomery and Runger, 2003).

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4.

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4.1

Analysis and Results

Estimation of the Trajectory128

We performed a grid search to find the most probable set of parameters of the trajectory model. The

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best fitting parameters of the trajectory that explain the arrival times of the shock wave are shown in

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Table 1. Intervals of the grid search, search ranges, and confidence intervals of the parameters are also

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included in the table. The isochrons of the arrival times based on this model are shown in Figure 2, and132

the residuals of the arrival times are shown in Figure 1. The location of the termination point of theM. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGS

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signal is east of Lake Biwa, and the altitude of 26 km. The 95% confidence interval of each parameter is134

calculated by a bootstrap method with 100 replicates (Efron and Tibshirani, 1993; Walker et al., 2010).

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The uncertainties of the parameters x0 , y0 , z0 , t0 , θ are small, since the arrival time of the shock wave

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is sensitive to these parameters. However, the azimuthal angle γ has a large confidence interval and137

is difficult to determine uniquely from this dataset, since most of the stations are inside the concentric138

isochrons and the azimuthal coverage of stations with distances greater than 100 km is poor.

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4.2

Sensitivity Analysis

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We computed misfit surfaces as a function of each parameter to check the sensitivity of the param-

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eters. The minimum of the rms residuals are computed as a function of two selected parameters (see142

Figure 5). The misfit surface for the horizontal location is smooth in both longitude and latitude, and143

has a single local minimum. Therefore, the solution easily converges to this minimum. The optimal

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time and altitude of the meteorite dissipation are both sensitive to the velocity of sound and difficult to145

resolve, but still a broad minimum exists in the surface. Note that these two parameters are also sensi-

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tive to the sound velocity. The perturbation of the parameters is about 10% if we change the velocity

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of the sound by 0.01 km/s. The azimuth of the trajectory is not very well determined by the dataset, as

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we have seen with the confidence interval. The velocity of the fireball is also significantly insensitive149

to the data, so we used a constant velocity for this analysis.

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4.3

Interpretation of the Model151

A mechanism to produce these concentric isochrons of the arrival times can be explained by an

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explosive fragmentation (Edwards et al., 2008). During a meteoroid entry, the object breaks up suddenly

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because of the increasingly large air pressure. A large amount of light is produced associated with the154

break up. Since these explosive fragmentation events are very brief and take place over small portions

155of the entire trajectory, they are approximated by a point source, and result in the concentric isochrons.

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The non pulse-like waveforms can also be explained with this mechanism. The fragmentation may

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result in separation of the original body into several large fragments. The duration of the fragmentation

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M. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGS

158

is largely unknown, however if fragmentation takes 0.5 second, the meteoroid can travel as far as 10

159

km (assuming a constant velocity) during this time. This distance is comparable to a difference of160

32 seconds in arrival time of the waveforms. Therefore, the extremely long duration of the signal is161

not necessarily unreasonable (Walker et al., 2010). Edwards et al. (2008) explained that observations

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of an explosive point-source events tend to be diffuse, with no distinct arrival time, in contrast to163

the sharp onset of ballistic observations. Waveforms here are very similar to the waveforms of 2002

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Tagish lake fireball (Brown et al., 2002) and 1989 St. Helens fireball (Qamar, 1995), which both show

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concentric isochrons. Similar concentric isochrones were also observed in Arrowsmith et al. (2007) and

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Walker et al. (2010). Multipathing through the atmosphere might also complicate the character of the167

waveforms, however this is generally observed at distances greater than 200 km (Walker et al., 2010)

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which is not the range of the data in this study.

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4.4

Height of the Source

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The airwave signal was observed by seismometers as far away as 150 km, and the bright flashes were171

observed as far away as 250 km from the termination point (Japan Fireball Network, 1999). We try to172estimate the altitude of the termination point from the trajectory model. Figure 4 shows a schematic173

diagram of the fireball trajectory and meteor-generated atmospheric waves. If the source dissipates174

at 26 km altitude, the ballistic wave due to the object flying at supersonic speed cannot be observed

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within 40 km from the epicenter. The signal observed in this near-source region is not impulsive due176

to the fragmentation. Assuming a line source, the height of a source which is observable 150 km

177from the center of the arrival time pattern must be at least 70 km high. Therefore, the source of the178

signal is inferred to be between 26 and 70 km, and could be higher if there is strong attenuation in the179

atmosphere. Reports of the sonic boom concentrate in the Tokai region, about 50-100 km from the180

center of the arrival time pattern. The altitude of the source corresponding to this signal is about 30

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to 50 km high. This height is consistent with past observations; 22 to 34 km for the 2000 Moravka

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fireball and 34 to 87 km for the 2003 Kanto fireball (Pujol et al., 2006). For the Biwako fireball,M. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGS

9183

we located the two fragmentation events at heights of 26 and 35 km. It has been suggested that the184height of fragmentation is where the aerodynamic pressure exceeds the material strength. Cevolani

185(1994) calculated the critical heights of the first fragmentation for meteoroids with different values of186

the material strength. According to the table, the critical height is 45.5 to 56.5 km for dustballs, 14 to

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38 km for stony chondrites, and 3 to 14 km for metal bodies, at velocities of 15 to 30 km/s. From these188

values, we speculate that the material of this fireball may be a stony chondrite.

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5.

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5.1

Different Models

Point Source Model191

We also examined a simple point source model to try to explain the same dataset. If the obseved192

arrivals are produced by the terminal explosion in a very short time frame, the arrival time pattern

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should be explained by a simple point source model. We used the same dataset as in section 2, and the194same method as in section 3 except the velocity of the fireball, and the incident angle and azimuth of195

the trajectory are now set to be zero. The estimated arrival times are computed from equation (1). The

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most probable parameter set from the grid search is shown in Table 2. We compared the two models

197(point source + line source model and simple point source model) with an F-test. The null hypothesis198

is the case where the two models predict the dataset equally well. The F statistic is given by
(
F =

) (
)
RSS1 − RSS2
RSS2/
= 48.11p2 − p1
n − p2(4)

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where RSSi is the residual sum of squares of model i, pi is the number of parameters of model i, and n

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is the number of observations. From the F distribution table, the F value with (p2 − p1 , n - p2 ) degrees

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of freedom at a 5% significance level is 3.21. Therefore, the null hypothesis has a low probability of202

being accepted, and the more complicated model provides a significantly better fit to the data.

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5.2

Back Projection Method

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Since we used times of the onset of the signal for the location estimation, these arrival times

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correspond to the location of the end of terminal explosion. We applied a back projection method

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M. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGS

to the waveforms in order to find the location where the fireball produced the largest energy.

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The waveforms used here are the same as the dataset in section 2. Since the correlation distance208

of infrasound at 0.5 to 5 Hz is only several kilometers (Walker et al., 2010), we used envelopes of

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the waveforms. The data are processed as follows; envelopes of the waveforms are formed using the210

maximum absolute value of the waveforms over one second windows. To remove the effect of stationary211

noise, the mean over a 10 minutes duration is removed. Then, the maximum amplitude of the signal is212

normalized to one to regularize the amplitude of the envelopes.

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The back projection method used here is similar to the reverse time migration technique in Walker

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et al. (2010). However, the stack of the waveform amplitudes (Q) is defined as a function of longitude,

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latitude, altitude, and time in our analysis. The maximum for every second t is defined as Qt . The

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weighting is set to be one since our station distribution is not greatly skewed. The search range is the217

same as shown in Table 2. Figure 6 shows Qt as a function of t. The Qt has a local maxima between

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55 and 60 seconds, the optimal parameters at those times are shown in Table 3.

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The computed location of the source producing the largest energy is located around 136.105E and220

36.165N, about 3 km ENE and 9 km higher than the termination point. This location is consistent221

with the trajectory determined from the arrivals at the seismic stations, since the path from the source

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producing the largest energy to the terminal point is similar to the calculated trajectory. Because the223

source of the largest energy is at a higher altitude than the termination burst, it was recorded a few tens

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of seconds later at some stations.

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6.

Conclusions

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We estimated the trajectory of the August 7, 2010 Biwako fireball and location of its termination

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point from arrivals at seismic stations. The isochrons of the arrival times are nearly concentric circles,

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which suggest that the fireball dissipated due to fragmentation during entry. The fireball trajectory229

which explains the arrival times of the signal has a relatively high incident angle (55 degree) and theM. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGS

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source is thought to disappear at a height of 26 km east of Lake Biwa. The azimuthal angle and velocity

231

of the fireball are difficult to determine uniquely from this dataset. We identified an event thought to232

be due to fragmentation, with a location 3 km ENE and 9 km higher than the termination point. This233

location is consistent with the trajectory determined from the arrival time data. Based on this trajectory

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model, the location of the source of the signal spans a range of 26 to 70 km, and the altitude of the235source producing the sonic boom is about 30 to 50 km.

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Acknowledgments. The authors thank Yoshihisa Iio of Kyoto University for providing data observed west of Lake Biwa. We
acknowledge the National Research Institute for Earth Science and Disaster Prevention (NIED) and 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.

241

References

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M. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGS
Table 1. The most probable parameters which determine the trajectory of the fireball.

Parameters

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266

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Optimal solution

Search Range

Grid interval

Confidence IntervalLongitude (deg.)

136.073

136.0-136.2

0.001

136.055-136.090

Latitude (deg.)

36.14935.0-35.2

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

-

-

-

of the September 15, 2007, Carancas crater. Meteoritics & Planetary Science, 43, 1797–1809.
Le Pichon, A., Guérin, J., Blanc, E., and Reymond, D. (2002). Trail in the atmosphere of the 29 December 2000 meteor as recorded in Tahiti: Characteristics
and trajectory reconstitution. Journal of Geophysical Research, 107, 4709.

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Onishi, M. (2010). Search for a meteor which might have reached around Biwako. Kyoto Shimbun, November 7, 2010. local news section, (in Japanese).

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Pujol, J., Rydelek, P., and Bohlen, T. (2005). Determination of the trajectory of a fireball using seismic network data. Bulletin of the Seismological Society

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Pujol, J., Rydelek, P., and Ishihara, Y. (2006). Analytical and graphical determination of the trajectory of a fireball using seismic data. Planetary and Space
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Takanami, T. and Kitagawa, G. (1991). Estimation of the arrival times of seismic waves by multivariate time series model. Annals of the Institute of

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seismic networks and infrasound arrays. Journal of Geophysical Research, 115, B12329.

M. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGS

13

/s
5km
0.3 m/s7k
0.3 km/s
0.39
Fig. 1. Waveforms ordered as a function of distance from the termination point. The open triangles show the observed arrival times. The station code andresidual of the arrival time (tpred − tobs ) are added on the right side. Alternate seismograms are shown in black and gray for clarity.

14

M. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGS(sec)

Fig. 2. Observed arrival times of the shockwave (color of the small circle at stations) and predicted arrival times of the shockwave based on the trajectorymodel (color contors). The large circles indicate distances of 50, 100, and 150 km from the estimated termination point of the signal.

M. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGS

15

ToyamaNaganoLake Biwa
Fukui

Gifu

Kyoto
Hyogo

Shiga

Aichi

Mie
Osaka
Nara
Wakayama

Fig. 3. Directions of the fireball observed by 34 witnesses. The diamond symbols show the sites where sonic booms were heard. Star shows the termination
point of the signal. The large circles show distances of 50, 100, 150, and 200 km from the estimated termination point of the signal.

16

M. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGSz (up)
(km)
100

y (north)

fireball

Z


Y

50



x (east)

X

(B)



dispersed wave

0(A)
sonic boom observation
fireball observation
impulsive wave

50

100

150 (km)Fig. 4. Schematic diagram of meteor-generated atmospheric waves. In region A, the signal is explained by a line souce, and in region B by a point source.
Coordinate systems used in the analysis are shown in right-hand side. Origins for the x,y,z coordinate system are longitude 136E, latitude 35N, and 0
km altitude, respectively. See the text for details.

M. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGS

Fig. 5.

17

Misfit surface for parameters. The rms residuals are computed as function of two out of six of the parameters to see the trade-off between

parameters.

0.54
0.52
0.5

Q

t

0.48
0.46
0.44
0.42
0.4
40

50

60

70

Time (sec)Fig. 6. Amplitudes of the stack of the waveforms from the back projection analysis, as a function of time.

18

M. YAMADA AND J. MORI: DETECTION OF BIWAKO FIREBALL TRAJECTORY FROM SEISMIC RECORDINGS
Table 2. The most probable parameters which determine the trajectory of the fireball from point source model.

Parameters

Optimal solution

Search Range

Grid intervalLongitude (deg.)

136.086

136.0-136.2

0.001

Latitude (deg.)

36.17235.0-35.2

0.001

Height (km)

33

0-50

1

Time (sec)

45

40-70

1

RMS (sec)

12.07

-

-

Table 3. The most probable parameters which determine the trajectory of the fireball from back projection.

289

Parameters

55sec

56sec

57sec

58sec

59sec

60sec

Longitude (deg.)

136.102

136.091

136.108

136.104

136.109136.115

Latitude (deg.)

35.16935.16835.16235.16835.16335.163Height (km)

36

35

36

34

35

35

Qt

0.521

0.537

0.533

0.515

0.533

0.519

M.Yamada (e-mail: masumi@eqh.dpri.kyoto-u.ac.jp) and Jim Mori