Shuyuan Liu, Qinghua Huang (2019). Characteristics of earthquake clustering in and around Japan revealed by single-link cluster analysis. Earthq Sci 32(5-6): 221-228. DOI: 10.29382/eqs-2019-0221-04
Citation:
Shuyuan Liu, Qinghua Huang (2019). Characteristics of earthquake clustering in and around Japan revealed by single-link cluster analysis. Earthq Sci 32(5-6): 221-228. DOI: 10.29382/eqs-2019-0221-04
Shuyuan Liu, Qinghua Huang (2019). Characteristics of earthquake clustering in and around Japan revealed by single-link cluster analysis. Earthq Sci 32(5-6): 221-228. DOI: 10.29382/eqs-2019-0221-04
Citation:
Shuyuan Liu, Qinghua Huang (2019). Characteristics of earthquake clustering in and around Japan revealed by single-link cluster analysis. Earthq Sci 32(5-6): 221-228. DOI: 10.29382/eqs-2019-0221-04
In this study, we apply the single-link cluster (SLC) method to analyze the characteristics of earthquake clustering in Japan. Among the clustering algorithms, the SLC method is effective in characterizing earthquake clusters or isolated events at both global and local scales. The results indicate that link lengths for the whole investigated area in and around Japan follow negative exponential functional or Gamma distribution functional increase. Besides, some difference is revealed among different areas, e.g., link lengths in the area of the Japan Trench and the Kuril Trench are shorter than those in other areas; the densest spatial distribution of the SLC framework is also in the area of the Japan Trench and the Kuril Trench. The close investigations indicate that the α and 1/θ values estimated respectively from the exponential function and Gamma distribution may relate to spatial clustering, which is supported by the results of the distribution of link lengths and the spatial distribution of the SLC framework in the investigated areas.
The circum-Pacific region is the most active earthquake zone, which releases about 75%–80% of the global earthquake energy. Japan lies to the northwest of the circum-Pacific region. This active tectonic region is interacted by four plates: the Eurasian, North America, Pacific, and Philippine Sea plates (Taira, 2001; Bird, 2003). Figure 1 shows the tectonic settings in and around Japan. Most earthquakes distribute along the boundary of plates, such as the subduction zones of the Pacific plate beneath the North America, Eurasian and Philippine Sea plates, and the subduction zones of the Philippine Sea plate beneath the eastern Eurasian plate, where about 20% of worldwide recorded earthquakes occur. Besides, over 100 major earthquakes with M≥7.0 have occurred in this region during last century, including the M9.0 Tohoku earthquake, the biggest event ever recorded in Japan (Huang and Ding, 2012).
Figure
1.
Distribution of earthquakes epiceters with M≥4.5 from the F-net catalog compiled by the National Research Institute for Earth Science and Disaster Resilience (NIED). Earthquakes are scaled to magnitude and colored according to their range of depths. Plate boundaries (the Kuril, Japan, Izu-Bonin and Ryukyu Trenches, and the Nankai Trough) are also included in this figure (Taira, 2001; Bird, 2003)
It should be mentioned that due to the complexity of both the seismogenic process and the underground structure, the understanding of earthquakes is still limited (Kagan, 2013). At the current stage, statistical methods play an important role in seismicity study, e.g., the ETAS model (Ogata, 1998; Zhuang et al., 2002), the ZMAP method (Wiemer and Wyss, 1994), the RTL method (Sobolev and Tyupkin, 1997; Huang, 2004, 2006, 2008), etc.
Clustering is an essential aspect of seismicity (Zhuang et al., 2004; Zaliapin and Ben-Zion, 2013). Gardner and Knopoff (1974) claimed that the sequence of earthquakes with clustering earthquakes removed is considered as Poissonian. In general, the two kinds of earthquakes, namely the background and clustering earthquakes show different statistical and physical features. For example, unlike the background earthquakes, the clustering part which reflects the status of stress release or adjustment is non-Poissonian.
Many clustering techniques have been applied to seismicity analysis. On the basis of the ETAS model, Zhuang et al. (2004) proposed the well-known stochastic reconstruction method to investigate trigger ability, magnitude distribution, diffusion process and scale of triggering region. Making use of probabilities of being a triggered event and a background event, Zhuang et al. (2005) and Jiang and Zhuang (2010) found the correlation between the cluster ratio and seismotectonic structures or potential risk of region strong earthquakes. Furthermore, using the extended version of ETAS model, Zhuang et al. (2018) investigated the direct aftershock distribution with the main shock rupture slip. In addition, Zaliapin and Ben-Zion (2013) used the nearest-neighbor distance of earthquake events in space-time-energy domain to detect and analyze clusters in California. It shows the bimodal distribution of the weak links formed by large distances and the strong links formed by short distances. They applied the method to analyze the magnitude distribution for different types of events, the ability to produce direct offspring, and the cluster size. Besides, Papadopoulou et al. (2016) applied the same methods to global seismicity. Hall et al. (2018) conducted K-means cluster analysis on earthquake clusters in the African-Arabian rift systems. They revealed the correlations of the cluster boundaries with the segmentation of the rift. Wang et al. (2017) introduced ‘seismic density index’ to quantify the degree of clustering seismic energy.
Comparing with non-hierarchical clustering algorithm like the K-means, hierarchical clustering algorithm do not need to predetermine the number of clusters. By definition of distance, hierarchical clustering technique generates agglomerative or divisive cluster as a solution. The single-link cluster (SLC) method, which uses the minimum distance to link events (Sun, 2008), plays an important role in cluster analysis. It does not need any pre-assumption of cluster model, which may provide another perspective of analyzing earthquake clustering features. Frohlich and Davis (1990) showed that the SLC method can identify earthquake nests, isolated events, aftershock sequences, and zones of seismic quiescence, based on the analyses of the earthquake data of the International Seismological Center (ISC). Ma and Zhou (2000) made SLC analysis on the seismic catalogs in China. They found that the northern and western China have different clustering intensity from mesh or chain structure of SLC framework. Moreover, the distribution of the length of spatial and spatio-temporal SLC framework can be better fitted by the dual-exponential and Weibull function respectively.
Because the SLC method provides an effective way to characterize earthquake clusters or isolated events at both global and local scales (Frohlich and Davis, 1990; Ma, 1999; Ma and Zhou, 2000), and Japan locates in an active seismic zone, it would be interesting to investigate the characteristics of seismicity in Japan. In this study, we focus on analyzing the earthquake clustering in and around Japan based on the SLC method.
2.
Data and methods
2.1
Data
The seismic catalogs observed by the National Broadband Seismograph Network in Japan, i.e. later the ‘F-net’ (Full Range Seismograph Network of Japan), are provided by the NIED. The seismic network with 73 active stations nowadays provides the seismic catalogs of Japan and its vicinity (120°E–155°E and 20°N–50°N) since 1997. The catalog contains 31,961 earthquakes within the period January 1997 to April 2017 for events with M≥3.5. We use the Gutenberg-Richter (GR) relation (Gutenberg and Richter, 1956) to check the completeness magnitude for the catalogs. It is complete for earthquakes with a magnitude greater than or equal to the magnitude threshold (Mc) of 4.5, and with a b-value of 0.89. Unless otherwise specified, we only consider the seismicity based on earthquakes with M≥Mc hereinafter.
1) Individual events are linked to their nearest neighbors, namely the two epicenters which have the minimum spherical distance among all, to form event sub-groups, which are also called trees;
2) the process is then repeated, until there is no isolated event;
3) each sub-group is linked to its nearest neighbor, recursively, until all of the trees are linked to produce one tree, i.e. the SLC framework, which link up all the N events by N-1 links.
In the current study, to avoid the requirement of large computer memory and long computation time (Frohlich and Davis, 1990), we adopt an alternative method following the principle of minimum spanning tree to generate the same SLC framework (Gower and Ross, 1969). Clusters will be classified in details once we remove the links whose length is longer than the cutoff value lc.
3.
Results for SLC framework
3.1
Descriptions of linkage
Figure 2 shows the whole SLC framework tree of the seismicity in and around Japan. It provides the clustering characteristics by spatial distance between seismic evets. In general, it is well linked and classified hierarchically by the algorithm. Earthquakes that populate densely in a large area like Japan Trench and Kuril Trench have a mesh link distribution, while earthquakes in the subduction zones like Nankai Trough, Izu-Bonin Trench and Ryukyu Trench have a chain link distribution. In order to compare the characteristics of the distribution of the SLC framework in detail, besides the seismicity in the whole area, we also investigate the seismicity in the following three sub-regions, A: the Ryukyu Trench and the Nankai Trough, B: the Izu-Bonin Trench, and C: the Japan Trench and the Kuril Trench. The polygonal border of the sub-regions, which is shown by the solid lines in Figure 2, is marked roughly based on the boundaries of subduction zones of different plates or seismo-tectonics (Bird, 2003).
Figure
2.
SLC framework of the seismic catalogs of Japan and its vicinity with M≥Mc. The borders of the sub-regions A, B and C are drawn by polygons
Figure 3 shows the cumulative frequency distribution of link lengths for the whole area. The initial increase of the cumulative frequency indicates a concentration tendency at short link lengths and a long “tail” tendency at long link lengths. We consider the exponential function to fit the link lengths distribution,
Figure
3.
Cumulative frequency distribution of link lengths in the whole area. The step of link lengths is chosen as 1 km. The solid line shows both the frequency distribution at each bin and their cumulative distribution. The dash-dotted line and dotted line indicate the cumulative distribution curves of f(l) and g(l), respectively
where (α, A1) are the parameters to be estimated. The cumulative distribution function of equation (1) can be written by
F(l;α,A1)=A1α⋅(1−e−αl).
(2)
To avoid the variations caused by different selections of link length steps, the maximum likelihood estimate (MLE) methods consider every link by probability. Thus, it would not be affected by the man-made way to divide the length bins. One can maximize the log-likelihood function of f(l) to obtain the MLEs (Daley and Vere-Jones, 2003),
lnL=n⋅lnA1−α∑ni=1li−A1α,
(3)
where li denotes the ith link length and n is the number of links. The estimated results are given in Table 1.
Table
1.
Estimated parameters and log-likelihood of f(l; α, A1) and g(l;k,θ,A2) for the whole area
As shown in Table 1, the MLEs of equation (5) are larger than those of equation (1), which means the fitting of the function g(l) is a little better than that of the function f(l). It is consistent with the general knowledge that the Gamma distribution is more inclusive than exponential function. Figure 3 shows that the cumulative distribution of link lengths is almost consistent with the exponential function or the Gamma distribution. We can also obtain the increase rate of cumulative distribution from the tiny difference of the parameters α and 1/θ respectively between equations (1) and (5). These parameters may be related to the information of quantifying clusters. Furthermore, the two fitting curves finally approach to the cumulative distribution line at long length values. The parameter A1/α or A2 is basically equal to the exact number of events.
We made the close analyses to the link lengths distribution in the sub-regions A–C in order to detect and verify more local features in detail. Figure 4 shows the cumulative distribution of link lengths in areas A–C and their fitting cumulative curves. All the estimated parameters for sub-regions A–C are summarized in Table 2.
Table
2.
Estimated parameters and log-likelihood of f(l;α,A1) and g(l;k,θ,A2) for area A–C
Figure
4.
Cumulative frequency distribution of link lengths in area A (a), area B (b), and area C (c). The step of link lengths is chosen as 1 km. The solid line shows both the frequency distribution at each bin and their cumulative distribution. The dash-dotted line and dotted line indicate the cumulative distribution curves of f(l) and g(l), respectively
Similarly to Figure 3, the MLEs of equation (5) are larger than those of equation (1). The value of A1/α or A2 equals to the number of events in each area. Regardless of the exponential function or Gamma distribution, the parameters of both α and 1/θ in area C are the biggest among the three investigated sub-regions. Besides, the α or 1/θ value reflects the increase rate of cumulative distribution. A greater α or 1/θ means that the area is more dominated by short link lengths and vice versa. Notice that the area C mainly contains the Japan Trench and Kuril Trench. The densest links distribute in the Japan Trench and Kuril Trench, and the relatively sparser distribution in the Ryukyu Trench and other trench, as we can see from the SLC framework in Figure 2. Thus, the value α or 1/θ may be also consistent with the density of links.
3.3
Number of links between events
We also analyze the distribution of the number of links between events in different areas. The results are given in Table 3. Different areas show slight difference but quite a similar distribution, e.g., among all number of links, the case of two links is the most dominant one, while the case of higher links rare occurs (i.e., the proportion for the case of 4 links is less than 1%).
Table
3.
The proportion of the different number of links in different area
Area
Number of links
1 links
2 links
3 links
4 links
Whole area*
7751
21.2%
58.3%
20.0%
0.5%
Area A
1424
20.5%
59.8%
19.0%
0.7%
Area B
1137
22.4%
56.1%
20.8%
0.7%
Area C
4371
21.0%
58.4%
20.1%
0.5%
Note: * The whole area includes areas A, B, C and other area in Figure 2
The distribution of link lengths revealed by the SLC method have the characteristics of the exponential function for earthquakes in and around Japan (Figures 3–4). If we take the rescaled length lr=el, we can easily obtain the following relationship from equation (1),
N(lr)∝1(lr)α.
(8)
It means that the α values may have scale-invariant characteristics like fractal dimension. In fact, there are numerous works about the fractal features of seismicity. For example, Smalley et al. (1987) used Poisson process and random fractal approach to fit temporal part of the seismic catalogs of Hebrides island arc. They revealed that the fractal dimension in different regions describes the intensity of the clustering. Corral (2004) analyzed seismic catalogs from USGS, SCSN, and JUNEC, and found that the rescaled time of seismic occurrence in long-term can be described by a unique universal gamma distribution. Davidsen and Goltz (2004) showed that the short- and intermediate-term of seismic waiting time distributions is a power-law decay with different exponent parameters in California and Iceland. However, because the spatial distribution of epicenters forms multi-fractal, the distribution is not universal and depends on different geological area and its size. There are also numerous applications of the detrended fluctuation analysis (DFA) in seismicity study, including the mono- and multi-fractal characteristics of space/magnitude distribution and temporal variation (Telesca et al., 2008; Sarlis et al., 2010, 2018; Varotsos et al., 2011, 2012; Telesca and Chen, 2019).
Therefore, we may use the α values to quantify the intensity of spatial clustering by the length of links. A bigger α value may be related to a denser spatial clustering distribution. Among the whole area and the different areas under investigation, area C has the maximum α value. We also find that area C is more dominated by short link lengths (Figure 4), which is much clear in the normalized frequency distribution (Figure 5, Table 4). The area C is also the densest for clusters as shown in Figure 2. However, the links in area A and area B have more long length parts (Figure 5, Table 4). The cluster densities in area A and area B are also sparser than that in area C (Figure 2). The α values in area A and B are also smaller (Table 2). The parameter 1/θ exhibits the similar characteristics as those of the parameter α. Nevertheless, unlike the temporal fractal characteristics, the spatial distribution may not form a simple mono-fractal (Davidsen and Goltz, 2004). In a sense, comparing to the exponential distribution, the relative larger log-likelihood values for Gamma distribution may show the complexity of spatial fractal dimension. Further work on the spatial multi-fractal would be interesting, but out of the scope of the current work.
Table
4.
The proportion of the range of link length in different area
Besides, in this article we mainly focus on the spatial characteristics of earthquake clustering. However, the catalog we used includes the 2011 M9.0 Tohoku earthquake. Seismicity in the whole area, especially in area C, might be affected by the large number of its aftershocks. In order to clarify whether or not the temporal variation would affect the distribution of “l”, namely the α or 1/θ values, we also analyze the time variation of clustering characteristics before and after the M9.0 Tohoku earthquake for area C and the whole area. The results of the estimated parameters are given in Table 5. As shown in Table 5, the α or 1/θ values are somehow different for the two periods before and after the M9.0 Tohoku event. However, they show the consistent tendency when comparing to the differences among areas, i.e., either before or after the M9.0 event, area C has the maximum α or 1/θ values among the different areas under investigation (Tables 2 and 5). In fact, unlike GR relation, length distribution provides rather different perspective of analyzing clustering characteristics through spatial distance metrics. Therefore, the “l” might be small considering predominant aftershocks occurred near the mainshock. However, such influence may not lead to significant differences in the distribution of “l”. As the further investigation, we calculate the normalized distributions of the link lengths for different areas before and after the M9.0 Tohoku earthquake and the results are given in Figures 6. Although there is a minor difference for the whole area during the two periods (Figure 6a), area C is dominated by smaller “l” comparing to other areas both before and after the M9.0 event (Figures 6b and 6c). This result is consistent with our previous findings for the whole investigated time window in this study (Figure 5, Table 4). Of course, whether the clustering characteristics have changed with time or not should be an interesting topic deserving further study, but out of the scope of the current study.
Table
5.
Estimated parameters and log-likelihood of f(l; α, A1) and g(l;k,θ,A2) for Area C and the whole area before and after the 2011 M9.0 Tohoku earthquake.
Figure
6.
Fitting normalized Gamma distribution of link lengths for the whole area before and after (a) the 2011 M9.0 Tohoku earthquake, and for different areas before (b) and after (c) the M9.0 earthquake
In summary, we employed the SLC method to analyze the features of earthquake clustering in and around Japan, which is located in an active seismic zone. After obtaining the SLC framework in the whole investigated region, we made some close analyses on the distribution of link lengths, focusing on three sub-regions including the main plate boundaries. First, regardless of the whole area or the sub-regions, the link length distribution can be described by both the exponential function and the Gamma distribution. Besides, no matter what form of function, the estimated parameter value α or 1/θ shows comparatively consistent tendency for different areas. In addition, the parameter α or 1/θ may be related to the information of quantifying spatial clustering.
Acknowledgements
We gratefully acknowledge the constructive comments from Jiancang Zhuang and the codes for computing the SLC framework from Yanlu Ma. We also thank two reviews for constructive and helpful comments. Some of the figures are plotted using the GMT software (Wessel and Smith, 1991).
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Table
5.
Estimated parameters and log-likelihood of f(l; α, A1) and g(l;k,θ,A2) for Area C and the whole area before and after the 2011 M9.0 Tohoku earthquake.
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