Statistic analysis of swarm activities around the Boso Peninsula, Japan: Slow slip events beneath Tokyo Bay?
- Tsubasa Okutani^{1} and
- Satoshi Ide^{2}Email author
https://doi.org/10.5047/eps.2011.02.010
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2011
Received: 24 March 2010
Accepted: 21 February 2011
Published: 21 June 2011
Abstract
Seismicity reflects underground stress states, satisfying scaling laws such as Gutenberg-Richter law and Omori-Utsu law. Standard seismicity models based on these scaling laws, such as the Epidemic Type Aftershock Sequence (ETAS) model, are useful to identify swarm anomalies in seismicity catalogs. Llenos et al. (2009) applied the ETAS model to swarms triggered by slow slip events (SSEs) and found that stressing rate controls the background seismicity μ suggesting that swarms can be utilized to monitor stress change due to various aseismic processes. Following their work, we analyze the 2002 and 2007 Boso swarms triggered by the Boso SSEs (Ozawa et al., 2007) and a swarm beneath Tokyo Bay, in June 2005. A single ETAS model cannot explain the high seismicity during a swarm. Although a combination of three ETAS models for pre-swarm, swarm, and post-swarm periods better explains the data, a simpler model with an ETAS model and a boxcar function is even better. Similarity of the seismicity model, together with the locations and focal mechanisms, suggests that three swarms share a common source of stress, and the possibility of undetected SSE beneath Tokyo Bay.
Key words
1. Introduction
An earthquake swarm is defined as a period of high seismicity without a distinguished mainshock. Despite its prevalence in earthquake catalogs, the background physics still remains unclear (e.g., Vidale and Shearer, 2006). Some swarms are induced by static stress change due to volcanic eruptions, such as the 2000 Izu Islands, Japan swarm (e.g., Toda et al., 2002) induced by the eruption of Miyake Island volcano. The diffusive migration of fluid is also a plausible mechanism, as suggested for the 1965–67 Matsushiro (Ohtake, 1974) and the 1998 Hida (Aoyama et al., 2002) swarms, Japan. Slow slip events, SSE, are another kind of the swarm driving mechanism. Recently, SSE induced swarms have been discovered in various geological environments, such as near the San Andreas Fault, California (Lohman and McGuire, 2007), beneath Kilauea volcano (Montgomery-Brown et al., 2008), Hawaii (Segall et al., 2006), and in subduction zones in Japan (Ozawa et al., 2007; NIED, 2007) and New Zealand (Reyners and Bannister, 2007).
To investigate swarms as anomalies in seismicity catalog, it is important to define the standard seismicity. The Epidemic Type Aftershock Sequence (ETAS) model (e.g., Ogata, 1988, 1999) is one of standard seismicity models and explains the characteristics of seismicity based on a simple assumption that an earthquake sequence is a point process with time-dependent seismicity rate. Each earthquake produces aftershocks following the Omori law and the Gutenberg-Richter law. Llenos et al. (2009) applied the ETAS model to SSE-triggered swarms in three regions and found that the background seismicity rate increases by orders during SSE without significantly changing other characteristics. This property of SSE-triggered swarm may be useful to identify smaller SSE undetectable using current geodetic observation systems.
2. Methods
When an earthquake catalog contains a swarm sequence, we divide it into three subsets: pre-swarm, swarm, and postswarm periods. In the present study, we consider the following four models. (1) Single ETAS model. This is a null hypothesis, one ETAS model with five parameters without change point. (2) Combined ETAS model. We divide the earthquake catalog into three subsets of different periods, pre-swarm, swarm, and post-swarm periods, and fit an ETAS model to each subset. This model has fifteen parameters with two change-points, T_{cp1} and Tcp2, corresponding to the beginning and the end of the swarm period. We can classify each earthquake into two states which are swarm or not, however we can’t determine where the real change point is between the last earthquake in the swarm period and the first earthquake in the post-swarm period. Therefore we define T_{cp2} as the hypocentral time of the last earthquake in the swarm period. (3) Boxcar swarm model. The background seismicity is except during the period of swarm, , when the background rate is This hypothesis has seven parameters (α, c, K, p, , and T_{sw}) and one change-point T_{cp1}. Although we consider T_{sw} as one of the parameters, we may regard it as another change point, which we will discuss later. (4) Exponential swarm model. The background seismicity increases to at the beginning of the period of swarm T_{cp1} and decreases exponentially as ( ) exp(-t/T_{sw}) + The number of parameters are the same as the boxcar model. If swarm is a response to various external forces such as large static stress change due to magma intrusion, volcanic eruption, diffusive migration of fluid, and SSE, an exponential function may better represent transient change of seismicity.
3. Data and Results
3.1 Earthquake catalogs
We analyze swarm activity in two regions around the Boso Peninsula (Fig. 1). The one is the southeast of the peninsula, where slow slip events have been detected by GPS in 1996, 2002, and 2007. The swarm activities related with the last two SSEs were studied by Llenos et al. (2009). They divided the seismicity catalog into four periods, 2002 pre-swarm, 2002 swarm, 2007 pre-swarm, and 2007 swarm, and determined ETAS parameters for each period to study the temporal change of parameter values. We refer to these swarms as the Boso swarms. About 400 earthquakes equal to or greater than Mj (local magnitude determined by Japan Meteorological Agency, JMA) 2.0 occurred from 1992 to 2007, including two earthquakes greater than M_{J} 5.0 during the 2007 SSE. The hypocenter locations during the two SSEs partially overlaps and the focal mechanisms determined by JMA are low angle thrust dipping to north or northwest. Many of these events have similar waveforms and identified as repeating earthquakes on the subducting plate interface by Kimura et al. (2006). Therefore, despite relatively large scatter in depth, 31.0 km in average with a standard deviation of 9.5 km, in the original catalog, we consider that most of these earthquakes are interplate earthquakes.
We analyze these earthquake sequences by ETAS model and change-point hypothesis explained in the previous section. We neglect the spatial distribution and treat seismicity as a point process. Thus, a data set is a series of hypocentral time t_{ i } and magnitude M_{ i }, from the JMA catalog, within a prescribed space and period. Each combined ETAS model requires two change points: the beginning and the end times of the swarm period, T_{cp1} and T_{cp2}, respectively. The former is relatively easy to identify based on external information. Therefore, when the external information is available, we fix the beginning time, while the latter is determined by minimizing the total AIC. The same beginning time is assumed for the change point T_{cp1} for the boxcar swarm models.
Earthquake catalogs. Time is shown by date (YYYY/MM/DD) and time (hh:mm). N is the number of events and M_{ c } is the minimum magnitude. Times shown by italic fonts are estimated values.
ID | T_{start} | T_{end} | T_{cp1} | T_{cp2} | N | M _{c} |
---|---|---|---|---|---|---|
Boso02 | 1992/01/07 22:20 | 2005/07/09 04:11 | 2002/10/02 06:10 | 2002/10/09 08:32 | 300 | 2.0 |
Boso07 | 2003/02/13 01:50 | 2008/12/20 20:24 | 2007/08/13 09:30 | 2007/08/18 23:16 | 250 | 2.0 |
Tokyo05 | 2000/01/01 15:02 | 2006/06/25 01:47 | 2005/06/01 19:05 | 2005/06/02 03:44 | 250 | 1.0 |
3.2 The result of ETAS modeling
Calculated ETAS parameters by MLE. The number in round brackets is error ratio, assuming that each parameter has log normal distribution.
α | c | K | ^{ p } | μ | μ _{1} | T _{sw} | ||
---|---|---|---|---|---|---|---|---|
Boso2002 | Single | 0.53 | 0.0007 | 0.032 | 0.90 | 0.02 | — | — |
(1.28) | (4.19) | (1.16) | (1.04) | (1.37) | — | — | ||
Pre | 0.67 | 0.0386 | 0.034 | 1.02 | 0.02 | — | — | |
(1.26) | (2.50) | (1.24) | (1.09) | (1.30) | — | — | ||
Swarm | 8 × 10−^{10} | 0.0003 | 0.054 | 1.0* | 2.21 | — | — | |
(8 × 10^{8}) | (9.13) | (1.73) | — | (1.71) | — | — | ||
Post | 0.17 | 2 × 10^{−5} | 0.041 | 0.80 | 0.02 | — | — | |
(3.39) | (30.0) | (1.31) | (1.09) | (1.93) | — | — | ||
Boxcar | 0.60 | 0.0002 | 0.025 | 0.86 | 0.02 | 2.82 | 7.10 | |
(1.25) | (2.00) | (1.17) | (1.04) | (1.37) | (1.59) | (1.38) | ||
Exp. | 0.64 | 0.0002 | 0.023 | 0.87 | 0.02 | 3.93 | 6.32 | |
(1.23) | (2.00) | (1.17) | (1.05) | (1.34) | (1.54) | (1.43) | ||
Boso2007 | Single | 0.87 | 0.0019 | 0.019 | 1.09 | 0.05 | — | — |
(1.13) | (1.90) | (1.19) | (1.05) | (1.24) | — | — | ||
Pre | 0.39 | 0.0001 | 0.019 | 0.93 | 0.05 | — | — | |
(2.08) | (7.48) | (1.45) | (1.09) | (1.28) | — | — | ||
Swarm | 1.99 | 0.0011 | 0.002 | 1.0* | 5.78 | — | — | |
(1.07) | (3.30) | (1.44) | — | (1.45) | — | — | ||
Post | 0.76 | 0.0019 | 0.024 | 1.04 | 0.05 | — | — | |
(1.29) | (3.92) | (1.40) | (1.10) | (1.56) | — | — | ||
Boxcar | 0.98 | 0.0009 | 0.011 | 1.09 | 0.05 | 5.86 | 5.35 | |
(1.13) | (2.11) | (1.25) | (1.05) | (1.22) | (1.46) | (1.37) | ||
Exp. | 0.62 | 0.0011 | 0.010 | 1.10 | 0.05 | 9.96 | 2.67 | |
(1.12) | (2.01) | (1.24) | (1.05) | (1.22) | (1.52) | (1.42) | ||
Tokyo2005 | Single | 1.03 | 0.0064 | 0.018 | 1.22 | 0.06 | — | — |
(1.12) | (1.66) | (1.22) | (1.05) | (1.20) | — | — | ||
Pre | 0.18 | 0.0007 | 0.036 | 0.93 | 0.03 | — | — | |
(3.72) | (4.61) | (1.28) | (1.08) | (1.31) | — | — | ||
Swarm | 2 × 10^{−7} | 0.0001 | 0.032 | 1.0* | 69.5 | — | — | |
(2 × 10^{6}) | (500) | (2.48) | — | (1.50) | — | — | ||
Post | 1.00 | 0.0009 | 0.028 | 1.01 | 0.04 | — | — | |
(1.39) | (5.12) | (1.40) | (1.10) | (1.73) | — | — | ||
Boxcar | 0.30 | 0.0008 | 0.030 | 1.00 | 0.04 | 70.00 | 0.36 | |
(1.95) | (2.94) | (1.24) | (1.06) | (1.24) | (1.50) | (1.23) | ||
Exp. | 0.22 | 0.0008 | 0.031 | 1.00 | 0.045 | 142.8 | 0.19 | |
(2.33) | (2.91) | (1.25) | (1.06) | (1.23) | (1.49) | (1.37) |
The change of background seismicity seems to be essential characteristics of a swarm sequence. If this is true, we may not have to change all 14 or 15 parameters of the combined model, because the best model maximizes the likelihood with small degrees of freedom. The simplest model would be the one only the background rate is variable, which is boxcar or exponential model. The parameters estimated for the boxcar and exponential models are also shown in Table 2. The end of the swarm period estimated for the boxcar model, T_{cp1} + T_{sw}, does not have to match that of the combined model T_{cp2}, but the estimated end times are eventually identical. The transformed time calculated for the boxcar model is also almost proportional to the cumulative number (Fig. 3), and difference between combined and boxcar models is very small.
Calculated AIC for each model. The AIC values include the change point penalties calculated by Monte Carlo simulation. The number in brackets is change point penalty term. The lower number of each cell is AIC improvement, which is the difference of AIC for combined ETAS and boxcar models from the single ETAS model.
Single | Combined | Boxcar | Exponential | |
---|---|---|---|---|
Boso2002 | 1844.7 (0) | 1807.3 (9.3) | 1800.4 (0) | 1799.7 (0) |
0 | −37.4 | −44.3 | −45.0 | |
Boso2007 | 881.4(0) | 822.8 (9.1) | 814.1 (0) | 823.0 (0) |
0 | −58.6 | −67.3 | −58.4 | |
Tokyo2005 | 1012.0 (0) | 1005.1 (24.7) | 981.4(9.1) | 984.2 (9.1) |
0 | −6.9 | −30.6 | −27.8 |
4. Discussion and Conclusion
The boxcar swarm model successfully explains seismicity rate change during a swarm. However the boxcar function is just one example and the other type of function may be better approximation. In fact, the exponential swarm model is comparable for the 2002 Boso and the 2005 Tokyo Bay swarms, but the specific shape of the function is not appropriate for the 2007 Boso swarm. Probably some swarm seismicity prefers a boxcar function with definite end time rather than an exponential function that decreases gradually. Although we have not tested other functions, we expect that it is difficult to find a simple function universally applicable for various swarm activity instead of a boxcar function. Therefore, we conclude that a boxcar function is preferable as the first degree assumption of swarm activity, and only the increase of the background seismicity is essential for swarm seismicity.
It should be noted that this is not the first paper that proposes the possibility of SSE beneath Tokyo Bay. Hirose et al. (2000) used tiltmeter and strainmeter records from 1985 to 1994 and a rectangular fault model to conclude that an SSE occurred beneath Tokyo Bay on December 9, 1989 at about 20 km south of the 2005 Tokyo Bay swarm area. The size of SSE is M_{w} 6.0 and the duration is about one day. Although the seismic activity on the day is not high, we cannot derive definite conclusion because the detection threshold at that time is worse than the current level. The relation between SSE and swarm may not be simple.
The stochastic analysis of seismicity little constrains the size of the possible SSE. However, if the SSE obeys the scaling law of slow earthquakes proposed by Ide et al. (2007), the size is determined simply by the duration. For the Boso swarms of about one week, the scaling law estimates the size of the corresponding SSE as M_{w} 5.8–6.5, which marginally covers the observational values of 6.4– 6.6. The 1989 Tokyo Bay SSE determined by Hirose et al. (2000) is also about the upper limit of the predicted range. The duration of the 2005 Tokyo Bay swarm is about a half day, which corresponds to an SSE of M_{w} 5.0–5.7. This is close to the detection limit of SSE using Hi-net tiltmeters and very sensitive geodetic instruments can detect it. This size is small compared to the Boso events, but might have significant effects on stress accumulation to the source area of the next Kanto earthquake.
In summary, our study revealed that the swarm activities beneath the Boso peninsula and Tokyo Bay are successfully explained by a boxcar function swarm model including an ETAS model. Both swarms are located on the top of Philippine Sea plate and have mechanisms consistent with the plate motion. In addition to the well-observed SSEs corresponding to the Boso swarms, we expect a smaller undetected SSE for the Tokyo Bay swarm. This is small, but may be observable using today’s best observational system.
Declarations
Acknowledgments
We thank Y. Ogata for helpful discussions to understand history of point process model up to ETAS model and the AIC penalty of change point problem. We also thank the Japan Meteorological Agency for providing earthquake catalogs and the Generic Mapping Tools software freely distributed by Wessel and Smith (1991) for mapping the distribution of earthquakes and swarm sequences. Comments from two anonymous reviewers are helpful for revision. This work was supported by JSPS KAKENHI (20340115), MEXT KAKENHI (21107007), and Special Project for Earthquake Disaster Mitigation in Tokyo Metropolitan Area.
Authors’ Affiliations
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