1 Introduction

Jiaodong Peninsula is part of the Sulu Orogen and separates the Bohai and Yellow seas in eastern North China. The well-known Tancheng-Lujiang fault zone, which cuts through the Moho discontinuity and spreads out across almost the whole eastern part of Chinese mainland, lies to the west of this peninsula, while the Penglai-Weihai fault, also characterized by a high level of activity, crosses the northern side. The Penglai-Weihai fault is part of the Yanshan-Bohai seismic zone; the devastating 1976 M S8.0 Tangshan earthquake occurred within this seismic zone. To the south, the Qianliyan fault strikes to the northeast, while a series of smaller faults that share this orientation spread out over the Jiaodong Peninsula and control the dominant seismic activity in the region (Fig. 1; Zhang et al. 2006).

Fig. 1
figure 1

Map to show the Rushan earthquake swarm (red hexagram) and the regional seismic network (yellow triangles) on the Jiaodong Peninsula. Gray circles mark historical earthquakes (M ≥ 5), while light blue circles denote the two modern events occurred in this region since 1970

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Jiaodong Peninsula is characterized by relatively low earthquake activity. Modern earthquake catalog published by CENC (China Earthquake Networks Center) shows that an average of just 2.33 events with M L ≥ 3.0 have taken place each year in this region since 1970 and that the largest recorded event before 2013 was an earthquake with M L4.5. Records of historical earthquakes indicate that just two medium-strong events (M5.5) have taken place in this region: one in 1046 A.D. and the other in 1939 (Fig. 1). At the same time, however, this region is also well known for the episodic occurrence of earthquake clusters that comprise lots of small magnitude events (Liu et al. 2007; Wang and Zheng 2014).

On October 1, 2013, an earthquake swarm initiated at a location about 15 km to the southeast of the city of Rushan, on the southern edge of Jiaodong Peninsula. This swarm persisted until 2016, and more than 12,000 aftershocks had been detected by December 31, 2015 (Fig. 2a). The biggest event occurred on May 22, 2015, and had a surface-wave magnitude (M S) of 4.6. Although earthquake sequences comprising small-to-medium-sized events are common on the Jiaodong Peninsula (more than 50 have been recorded since 1970), their durations are usually short, encompassing several days up to no more than a month (e.g., the Laoshan swarm in 2003; Zheng et al. 2006). This means that the Rushan earthquake swarm is rather unique for the eastern Chinese mainland, irrespective of its duration or active frequency.

Fig. 2
figure 2

Statistical characteristics of the Rushan earthquake swarm: a M L as a function of time recorded from October 1, 2013; b results of Gutenberg-Richter law fitting; c histogram to show inter-event time (the red solid line denotes the fitted lognormal distribution)

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A number of seismological problems are posed by the Rushan earthquake swarm. In the first place, as active faults appear to be absent from the surface of the epicentral area, and even small branch faults have not been identified (Qu et al. 2015; Zheng et al. 2015b), it remains unclear why such a high frequency swarm took place in the area. Secondly, the Rushan event is reminiscent of the well-known Matsushiro earthquake swarm which was also characterized by high frequency and long duration (Kishimoto et al. 1967). This latter swarm is thought to be a typical fluid-triggered event by CO2-rich water caused by the intrusion of magma (Stuart and Johnston 1975; Cappa et al. 2009). It remains unclear whether, or not, the Rushan earthquake swarm was also triggered by fluid, while the ultimate origin of this series of events also remains unknown.

In order to address these issues, we initially relocated the Rushan earthquake swarm using data from a temporary network that was deployed in the area of the epicenter. We then adapted the mean-shift cluster method to analyze the spatiotemporal rupture features of this swarm. Finally, we applied an epidemic-type aftershock sequence (ETAS) model in order to differentiate externally triggered events from self-excited aftershocks within the Rushan earthquake swarm.

2 Data

The Rushan earthquake swarm occurred on the southern seaward side of the Jiaodong Peninsula and was recorded by 14 stations within the Shandong local earthquake network, all located 150 km or less from the epicenter. However, because of local terrain limitations, all these stations were either to the north or the west of the swarm, creating an observational gap of more than 120 degrees (Fig. 1). The station nearest to the earthquake swarm was RSH, approximately 15 km from the epicenter; this station recorded numerous microevents, including some with negative magnitudes (Most microearthquakes with M L ≤ 0.5 are only recorded by RSH station; these events therefore are not located; but still assembled in the catalog for completeness). However, in the aftermath of one event on January 7, 2014 (M L4.6), it became clear that Rushan earthquake swarm was not comparable to previous events; from this point on, a temporary network of 18 seismometers was deployed (Fig. 4), formally initiated on May 6, 2014.

2.1 Seismological characteristics

A catalog of more than 12,000 events are characterized by M C = 0.5 (Fig. 2b); thus, the b value of the Rushan earthquake swarm was less than 0.9 (i.e., 0.8667; Fig. 2b). We utilized a robust regression approach to estimate the b value in order to eliminate the influence of outlier points (Holland and Welsch 1977; Yang and Qu 1999) and confirmed the performance of the calculated inter-event time distribution as in previous work (e.g., Hainzl 2004). However, rather than using a traditional power law model for the probability distribution, we generated a histogram of inter-event times and fitted this to a lognormal distribution (Fig. 2c). This lognormal distribution can also be considered characteristic of a fractal process; the data presented in Fig. 2c show that the fit is relatively good.

2.2 Data from the RSH station

As a temporary seismic network within the area of the epicenter was set up on May 6, 2014, and because the RSH station recorded all swarm activities, we examined differences in the arrival times of Pg and Sg phases recorded at the latter. Although small events cannot be located by just a single station, it is nevertheless possible to extract some meaningful information from variation in t S−P, as these are first-hand data and thus less contaminated by errors than some other phases.

The data show that \(t_{{{\text{S}}\, -\, {\text{P}}}}\) of almost all the aftershocks falls in the interval [1.2, 1.8] second time (Fig. 3). However, prior to April 2014, it is clear that \(t_{{{\text{S}} \,-\, {\text{P}}}}\) values recorded at the RSH station simultaneously increased and decreased following initiation of the Rushan earthquake swarm. Indeed, two remarkable events (both M L ≥ 4) were recorded in the early stages of the swarm: one (M L 4.7) on January 7, 2014, and the other (M L 4.6) on April 4, 2014. The first of these events can be located toward the bottom edge of the \(t_{{{\text{S}}\, -\, {\text{P}}}}\) plot, while the second occurs toward the top edge, perhaps implying that they can be associated with the source diffusion process of the Rushan earthquake swarm. Although we were unable to determine the direction of aftershock migration, the spatial spreading of swarm activity is obvious and similar to the manner in which epicenters spread within fluid-triggered earthquake swarms (Hainzl 2004; Hainzl and Ogata 2005; Bourouis and Cornet 2009; Hainzl et al. 2012; Shelly et al. 2013a, b). It is noteworthy that this spreading tendency disappeared almost completely after April 2014.

Fig. 3
figure 3

Data to show arrival time differences in Pg and Sg phases at the RSH station, the dashed green line shows its mean value. Aftershocks were rare within the area outlined by dashed magenta lines, while blue solid arrows mark swarm spreading directions

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A further point of interest is that an increasingly vacant area formed around a mean value of \(t_{{{\text{S}}\, -\, {\text{P}}}}\) between May 2014 and April 2015, marked by a dashed magenta line in Fig. 3. Throughout this period, aftershocks took place both proximate and distant to this region, while events (M L ≥ 2) within the central area were very rare. The largest recorded such event (M S 4.6 on May 22, 2015) took place at the end of this vacant area; although this phenomenon is reminiscent of ‘seismic quiescence,’ noted by Hauksson et al. (2013) in a discussion of the 2012 Brawley earthquake swarm in Southern California, it evolved more rapidly in this case. Thus, another interpretation might be that the blank area corresponds with a barrier encountered within the source area that was broken leading to the mainshock. Actually this gap is an interesting phenomenon, as pointed out in Wei et al. (2013, 2015); this could be caused by the rupture asperity of the big events in the sequence.

2.3 Relocation based on temporary network data

As noted above, 18 temporary seismometers were deployed around the edges of the Rushan earthquake swarm (Fig. 4). Although not perfect, the distribution coverage of these seismometers onto swarm activity was acceptable; thus, these instruments, in concert with adjacent regional stations, comprised a temporary network which was used to more comprehensively monitor swarm activity. We have previously compared location results from regional networks with those of temporary ones (Zheng et al. 2015b) and have demonstrated that catalogs based on the former are often unreliable because precise observations are lacking and station coverage can be poor.

Fig. 4
figure 4

Distribution of temporary seismometers (yellow triangles) and relocated epicenters (black dots). Focal mechanisms of 3 moderate size events also are shown in the map. The RSH permanent station (blue triangle) belongs to the Shandong regional network. Black solid lines on this figure mark local faults; of these, the Rushan fault (strike between 10° and 15°) is dominant, although two other historical earthquakes (M5.5) are also known to have occurred (see Fig. 1). The dip direction of the Rushan fault is ESE, while its dip angle ranges between 75° and 85°

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We generated a relocated swarm catalog by utilizing temporary network data and the hypoDD method (Waldhauser and Ellsworth 2000, Fig. 4). Thus, using the RSH station as the origin, we established N-E-D coordinates to display these relocated results (Fig. 5). The relocation results show the swarm are clustering between 5 and 8 km in depth; and the Rushan earthquake swarm strikes in a WNW direction (Fig. 5a), in agreement with the focal mechanism solution for the January 7, 2014, event (i.e., M L 4.3, strike = 298.5°, dip = 64.3°, rake = 0.3°; Zheng et al. 2015a). In this case, the aftershocks were restricted to within a small region 3 km × 3 km × 1 km in dimensions (Fig. 5a, c, d); this magnitude seismogenic volume is similar to that estimated for earthquake swarms in Vogtland and Western Bohemia (Grünthal et al. 1990).

Fig. 5
figure 5

Hypocenter distribution data collected from the Rushan earthquake swarm between May 6, 2014, and June 30, 2014. This relocation catalog was generated using temporary network observations and the HypoDD method. a Distribution of aftershock epicenters. The colored scale on this figure denotes the times of events from May 6, 2014, onwards. These data show that the aftershock distribution of the Rushan earthquake swarm conforms to a WNW-ESE direction. The bold solid green line drawn between points A and B shows the position of a section with approximately corresponds to the fault plane. b Distance to the first event versus time data for relocated hypocenters. In this case, time is counted as that elapsed from the first event in the catalog. c Sources projected onto the fault plane, the initial coordinates is rotated with the strike angle. d Profiles of hypocenters along the section between A and B, also in a rotated coordinates, the black dashed line denotes a supposed fault. e Evolution of swarm activities with M L ≥ 1.0 (black dots) in different periods (the range for each small diagram is same with that in panel (c)), while gray dots denote all these M L ≥ 1.0 events in relocated catalog. Detailed explanation is provided in Sect. 2.3 above

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We selected about 2 months of data from our relocated catalog for further analysis in order to examine whether or not the Rushan earthquake swarm was triggered by fluids. The relocated catalog starts long after initiation of the earthquake swarm, and there is no evidence for spatial spreading in the distance-time plot (Fig. 5b). However, detailed examination of Fig. 5c reveals that the focus of the swarm is distributed along the fault plane in a particular order (Fig. 5e). Data recorded from May 6, 2014, onwards show that from the first day through to the tenth day, aftershocks were located together within an area between 6.5 and 7.5 km in depth and between 10 and 11 km horizontally with respect to the RSH station. In contrast, between the 15th day and the 25th day of the swarm, aftershocks were concentrated below 7.5 km, while between the 30th day and the 40th day they were grouped toward the left part of the fault plane. Finally, after 50 days, swarm aftershocks were focused in two area: one toward the top of the fault plane and the other toward the bottom (Fig. 5e). Data show that the aftershocks not only clustered in stages, also migrated in order and that their hypocenters were distributed as irregular forked branches. All these active phenomena are consistent with the process of crack propagation; comparing our data with seismic activity characteristic of other fluid intrusion-triggered earthquake swarms (e.g., Fig. 8 in Hainzl and Fischer 2002; Figs. 2 and 3 in Hainzl et al. 2012; and studies in Jenatton et al. 2007; Bourouis and Cornet 2009; Shelly et al. 2013a, b) implies that the Rushan example was also likely to have been triggered in this way.

3 The fluid-triggering hypothesis

As discussion above, the activity of the Rushan swarm is similar with other fluid-triggered events. Stated by many researchers, variations in pore pressure along a fault plane due to fluid intrusion from a high-pressure source can be described by the diffusion equation as follows:

$$\frac{\delta }{\delta t}P = D\frac{{\delta^{2} }}{{\delta x^{2} }}P.$$
(1)

where D is the hydraulic diffusivity, P is pore pressure, and t is the time since the first contact of the pore pressure source with the host rock (Shapiro et al. 1997; Yamashita 1997).

In this case, however, because available observations from the initial stages of the earthquake swarm are limited, no explicit indications for diffusion were noted. In addition, and as discussed above, a precise location catalog is only available subsequent to May 6, 2014, while the distance-time diagram generated from relocations reveals no indications of hypocenter spreading (Fig. 5b). Nevertheless, as also discussed above (see Sect. 2.3), we are able to hypothesize that aftershocks are distributed as irregular forked branches and that they migrated in clusters. These observations suggest that it would be applicable to perform a fluid-triggering analysis for individual clusters over shorter time periods.

3.1 Cluster analysis

Cluster analysis is a useful tool in seismology and has been widely applied to locate earthquakes (Frohlich and Davis 1990; Davis and Frohlich 1991; Dzwinel et al. 2005; Shearer et al. 2005; Weatherill and Burton 2009; Rehman et al. 2014), split shear-waves (Teanby et al. 2004) and estimate inversion error (Zheng et al. 2015a).

Godano et al. (2013) demonstrated the presence of multiple earthquake clusters in research on an Italian swarm, while Lindenfeld et al. (2012) recorded several similar clusters in a restricted area while researching fluid-triggered earthquake swarms in the East African Rift. However, while cluster analyses traditionally tended to be density-based, incorporating just spatial coordinates, Zaliapin et al. (2008) introduced a statistical method which defined a unified distance between earthquakes in the time-space-energy domain (Zheng et al. 2014); this approach was subsequently shown to be robust and effective via research in Southern California (Zaliapin and Ben-Zion 2011, 2013a, b).

Building on this earlier work, we applied both temporal and spatial cluster analyses to the data from the Rushan earthquake swarm. We adopted a mean-shift criterion to perform a cluster analysis on relocated catalogs generated for the period between May 6, 2014, and June 30, 2014. Although the mean-shift approach is also density-based (Cheng 1995; Comaniciu and Meer 2002), similar to the K-means method applied by many researchers, one advantage is that this technique can be used to detect arbitrary-shaped clusters via an iterative procedure and density estimation.

Results revealed the presence of 16 clusters containing at least 20 events (Fig. 6). Although some isolated events were discarded based on spatiotemporal criteria, the total number retained within our clusters encompassed more than 90% of the relocated catalog. Clusters were labeled with different colors and arranged from the time of origin of the first event in each case (Fig. 6). For events in same cluster, we suppose they are cracks all outspread from a same origin because they have closer time-space distance. Then, we can estimate the hydraulic diffusivity from these events; for detailed analysis see the next section.

Fig. 6
figure 6

Cluster analysis results for relocated hypocenters within the Rushan earthquake swarm for the period between May 6, 2014, and June 30, 2014. Hypocenters in the same color belong to the same cluster, and all are projected onto the fault plane (Fig. 5c). The origin of the coordinates used here was defined as the center of all events within the time period

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In order to extract information on the processes underlying the Rushan earthquake swarm, we further examined the spatial evolution of clusters over time. The data reveal that cluster 1 was active on the left-central side on the fault plane, while clusters 2–4 moved to the right-bottom side (Fig. 6). Similarly, the aftershocks of clusters 5–9 and cluster 11 spread upwards, cluster 10 and clusters 14 and 15 returned to the right-bottom side, while clusters 12 and 13 continued to be active on the right-top side. Although there appears to be no evidence for an overall directional migration of seismicity, the activities of the different clusters nevertheless reveal some order to their occurrences.

3.2 Hydraulic diffusivity of clusters

As shown in previous works (Shapiro et al. 1997; Hainzl 2004; Hainzl and Ogata 2005; Hainzl et al. 2012; Shelly et al. 2013a, b), although D is generally expected to range between 0.01 and 10 m2 s−1 in the crust (Scholz 2002), this can also vary depending on crustal medium. One extreme example was presented by Noir et al. (1997) who reported a D value of about 2 km2/min for a sequence in Central Afar, and a high diffusion rate also characterizes Yellowstone Lake (Farrell et al. 2010).

The swarm activities can be separated into several clusters in time and space domain. We therefore tested the fluid implication hypothesis for the Rushan earthquake swarm by plotting the distance, d, between the first located event and all others within each cluster as a function of time, t. Unsurprisingly, data reveal a diffusion pattern within every d–t diagram (Fig. 7), and the data envelope also corresponds to the theoretical curve defined by \(\sqrt {4\pi Dt}\) (Shapiro et al. 1997). Thus, fitting results (Fig. 7) reveal D values range between 1.2 and 3.5 m2/s. This data range is in accordance with the majority of other examples (Shapiro et al. 1997; Hainzl 2004; Hainzl and Ogata 2005; Hainzl et al. 2012; Shelly et al. 2013a, b).

Fig. 7
figure 7

Data showing the distance between hypocenter and fluid source as a function of earthquake occurrence times for the 16 clusters identified in this study. a Fitted D (red) results for each cluster. b D values for the 16 clusters marked on the first event’s hypocenter in each clusters. The circle size is scaled to first event magnitude. Note that the coordinates of this plot are the same as those in Fig. 6 and that events are sorted by time elapsed since May 6, 2014

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Visually, the curve fits of d–t plots are relative poor in some cases (e.g., clusters 3, 4, 8, 9, 13). In our view, the main reason might be that the clusters are separated mathematically, and the criteria are not calibrated. The spread of small rupture is irregular and, to some extent, randomized in rocks; the cluster analysis can not recreate the rupture process completely and correctly.

When we mark the D values for each cluster on the first event in it (Fig. 7b), it is clear that the hydraulic diffusivities at the edge of the source area are lower than for those in the central area. It is easy to understand combining with Fig. 3: At the start of the Rushan earthquake swarm, ruptures were focused in the central area, but with progress of activity of the swarm, crack activity diffused and rocks in this area became highly crushed. These centrally located rocks subsequently developed higher D values as the result of later shocks.

4 ETAS modeling

The ETAS model is a self-exciting point process that describes temporal and spatial clustering within earthquake catalogs (Ogata et al. 1993). This approach has been widely utilized to analyze and describe the spatiotemporal characteristics of regional seismic activities and aftershock sequences (e.g., Jiang et al. 2007; Kumazawa and Ogata 2014). The ETAS model has also been shown to be an appropriate tool to extract primary fluid signals from earthquake swarms (Hainzl and Ogata 2005; Lei et al. 2008, 2013; Lombardi et al. 2010; Jiang et al. 2012; Eto et al. 2013).

In the ETAS model, the rate of aftershock occurrence at time t following the ith earthquake is given as follows:

$$n_{i} (t) = K\exp [\alpha (M_{i} - Mz)]/(t - t_{i} + c)^{p}.$$
(2)

In this expression, p means decay rate of aftershocks, α denotes the discrepancy between different events in generating aftershocks, c is relative to degree of seismic activity in the region, and K is equal to the expected number of aftershocks for an event. As this formula describes a self-exciting process which obeys the modified Omori law, the rate of occurrence of the whole earthquake series at time t is as follows:

$$\lambda (t) = \mu + \sum\nolimits_{i} {n_{i} (t).}$$
(3)

In this expression, μ denotes primary activity at a constant rate of occurrence which can be thought of as background seismicity or activities due to external triggers such as increases in pore pressure (Hainzl and Ogata 2005) or perturbations of stress from large remote earthquakes (Peng et al. 2012). In the case of a fluid-triggered earthquake swarm, μ has been shown to be consistent with variations in pore pressure and can thus be viewed as a proxy for fluid-driven activity (Hainzl and Ogata 2005; Lei et al. 2008, 2013; Jiang et al. 2012).

4.1 Estimating ETAS model parameters

The Rushan region is characterized by low seismic activity. Indeed, as noted above, between January 1, 1970, and September 30, 2013, just 121 weak earthquakes (i.e., M L 2.0 to M L 2.9), 16 medium-sized earthquakes (i.e., M L 3.0 to M L 3.9), and three large-scale events (i.e., M L 4.0 to M L 4.3) are recorded in the CENC catalog within a 50 km radius of the Rushan earthquake swarm. As the vast majority of these earthquakes are related to the NNE faulting Rushan fault and are extremely rare within the epicenter area of the Rushan earthquake swarm, background seismicity can be ignored for the purposes of this research.

ETAS modeling results for the Rushan earthquake swarm are shown in Fig. 8. The catalog is also due to Shandong local earthquake network, same with Fig. 1. But the data we used in ETAS fitting only contain 4256 events with M L ≥ M C. The observed (black) and predicted (red) cumulative numbers of events show that the fit of the estimated model to known earthquakes is fairly consistent. Estimated ETAS model parameters are listed in Table 1.

Fig. 8
figure 8

Estimated ETAS model fit results. The cumulative number of aftershocks is plotted in this figure against ordinary time. The red curve denotes the theoretical cumulative number of detected aftershocks, while the black curve represents the observed cumulative number. An M–t plot of aftershocks is presented beneath the fitted result

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Table 1 Estimated ETAS parameters and corresponding AIC (Akaike information criterion) and BIC (Bayesian information criterion) values
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The final fitting parameter, α = 1.156, is equivalent to the resultant value (1.09) estimated by Lei et al. (2008) in their study of earthquake sequences in the Rongchang gas field that were explicitly induced by water injection, as well as the value (1.17) calculated based on microseismicity of the loading stage in the Three Gorges Reservoir (Jiang et al. 2012). At the same time, however, the α value estimated here is slightly lower than those estimated for non-swarm activities (between 1.2 and 3.1), but higher than those calculated for swarm activity (between 0.35 and 0.85) in Japan (Ogata 1992), and for the Vogtland and Western Bohemia swarm (0.73; Hainzl and Ogata 2005). As discussed by Ogata (1992), α is likely to be large if there are few conspicuously large events within the aftershock sequence. This may provide one explanation for the discrepancies in values given by different researchers.

As our fitted ETAS model reveals a low forcing rate (μ) of ca. 0.15 events per day, a total of about 130 earthquakes are implied throughout the entire period of the swarm period, more than 900 days. This result indicates that about 3% of all events within the Rushan earthquake swarm were externally triggered, while the remainder are the result of Omori-type self-triggered activity.

4.2 Variation of forcing rate μ

We adapted the method proposed by Hainzl and Ogata (2005) to extract the forcing rate μ, estimating the ETAS parameter using a moving time window with size fixed at 30 days and the moving step set as one day. Although all five parameters were fitted in each time window, initial values were set to those determined for the whole sequence (Table 1). We obtained variation in the occurrence rate of interpreted primary fluid signals, μ, as a function of time elapsed within the Rushan earthquake swarm (Fig. 9). In order to investigate the correlation between μ and swarm seismicity, the variation in monthly frequency with time was also calculated (Fig. 9).

Fig. 9
figure 9

The relationship between seismic activity and the rate of occurrence of primary fluid signals within the Rushan earthquake swarm. The gray dots in this figure denote the magnitude of all M L ≥ 0.5 events, the solid cyan line marks a histogram of monthly swarm frequencies, and the magenta line is the rate of occurrence. Times on the horizontal axis are counted from October 1, 2013

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Results show that variation in μ is roughly coincident with swarm activity; thus, when μ is high, aftershocks were active and intense. In other words, a high proportion of fluid-induced events usually occurred subsequent to significant earthquakes. We therefore infer that as the source area became even more crushed by large ruptures due to major events, new fractures emerged and caused the development of additional fluid-triggered cracks.

5 Discussion and conclusions

Fluid-driven earthquake swarms have been studied from a number of perspectives (Legrand et al. 2011; Horálek and Šílený 2013; Leclère et al. 2013; Braunmiller et al. 2014; D’Hour et al. 2016; Schultz et al. 2015). The prevailing consensus is that such swarms are triggered by the rupture of a zone containing confined high-pressure aqueous fluid into a preexisting crustal fault system, which prompts release of accumulated stress (Shelly et al. 2013a, b). However, no such outcropped fault has been located to date within the area of the Rushan earthquake swarm, even during detailed prospecting investigations for gold (Fig. 4; Hu et al. 2013; Zheng et al. 2015b). In addition, and even more perplexing, as this earthquake swarm is located more than 10 km away from the nearest fault traces, we have suggested that it might occur on a blind fault (Qu et al. 2015; Zheng et al. 2015b). The Rushan earthquake swarm is tectonically located at the boundary between two rock mass units (Zheng et al. 2015b); we therefore suggest that, for some reason, the boundary between these two masses was broken and a new fault developed. Cluster analysis of D combined with ETAS modeling further suggests that the reason underlying the development of the Rushan earthquake swarm is deep fluid action.

A relocated catalog for the Rushan earthquake swarm generated using data from a temporary seismic network and the hypoDD method reveals the presence of at least 16 activity clusters between May 6, 2014, and June 30, 2014. The data also show that each of these clusters was itself characterized by a distinct hypocenter spreading process and that the D value of each ranged between 1.2 and 3.5 m2/d. Results also show lower D values at the margins of the source area than in the center, which may also imply differences in the degrees to which rocks were crushed.

Sibson (1996) studied the structural permeability of fluid-driven fault fracturing, while Yamashita (1999) modeled the spatiotemporal variation in rupture activity assuming fluid migration along a narrow and porous fault zone. The results of both these studies showed that when an inhomogeneity is introduced into a permeability spatial distribution, high complexity rupture activity can result, both spatially and temporally. The multi-cluster activity of the Rushan earthquake swarm reported in this study is in accordance with this earlier work.

We have estimated the parameters of the Rushan earthquake swarm using ETAS modeling. The final fitting parameter (α = 1.156) reported in this paper is equivalent to those previously calculated for earthquake sequences induced by water injection. Calculated μ for the Rushan swarm (just 0.15 events per day) also indicates that around 3% of events were fluid-triggered. Finally, the variation in μ we report here is approximately coincident with earthquake swarm activity, which might imply that the Rushan event was fluid-driven. Taken in combination with our cluster analysis, the migration of underground fluid likely exerted a marked influence on swarm activity.