Seismic link at plate boundary

Faical Ramdani∗, Omar Kettani and Benaissa Tadili Mohamed V University, Scientific Institute, Physics of the Earth Laboratory, Rabat, Morocco. ∗Corresponding author. e-mail: [email protected]

Seismic triggering at plate boundaries has a very complex nature that includes seismic events at varying distances. The spatial orientation of triggering cannot be reduced to sequences from the main shocks. Seismic waves propagate at all times in all directions, particularly in highly active zones. No direct evidence can be obtained regarding which earthquakes trigger the shocks. The first approach is to determine the potential linked zones where triggering may occur. The second step is to determine the causality between the events and their triggered shocks. The spatial orientation of the links between events is established from pre-ordered networks and the adapted dependence of the spatio-temporal occurrence of earthquakes. Based on a coefficient of synchronous seismic activity to grid couples, we derive a network link by each threshold. The links of high thresholds are tested using the coherence of time series to determine the causality and related orientation. The resulting link orientations at the plate boundary conditions indicate that causal triggering seems to be localized along a major fault, as a stress transfer between two major faults, and parallel to the geothermal area extension.

1. Introduction (Krishna Mohan and Revathi 2011). This shows that the link between events is a complex feature Plate boundaries are the zones where most earth linked to varying network models (Abe and Suzuki dynamics are focussed. The complexity of tectonic 2006). Links limited to individual events have been boundaries draws attention to them as the largest related to low strain rate environments (Hough et al. earthquakes are felt in these areas and they elicit 2003), visco-elastic relaxation (Lorenzo-Martin et al. the natural hazard of seismic activity. However, the 2006), and solid Earth tides (Cochran et al. 2004). sequences of the main shocks and the triggering By analyzing earthquake pairs over a period of process constrain the seismic hazard assessment. many years, Wan et al. (2004) suggested that Some frequent issues remain as to whether the seis- Coulomb stress triggering may be observed for micity of the interplate zone with a high strain rate thrust earthquakes, while McKernon and Main has random aspects and may be associated with a (2005) limited triggering process to about 150 km. triggering mechanism, and how the seismicity can Extending earthquake activity to a spatial net- be associated with fault patterns and plate motion. work link shows that the alignment of the links is Triggering causes changes in the Coulomb stress on parallel to the Honshu Trench azimuth in Japan a specified fault, which is independent of regional (Tenenbaum et al. 2012) and the direction of the stress but which depends on the fault geometry, San Andreas Fault (SAF) (Jimenez et al. 2008). In the sense of slip, and the coefficient of friction the Ibero–Moroccan region, main shocks and their (King et al. 1994). Restricting the causality con- aftershocks are investigated as local features due to nection to a single predecessor or to an arbitrary fault mechanisms except for some historical event mainshock-aftershock scenario may not be enough studies related to triggering in the Catalan and NE

Keywords. Seismic link; time series; distant earthquakes; causality; plate boundary.

J. Earth Syst. Sci. 124, No. 4, June 2015, pp. 697–705 c Indian Academy of Sciences 697 698 Faical Ramdani et al.

Iberian regions (Perea 2009). As zones of perma- zone along the plate boundary. In those particu- nent activity make it difficult to detect causal trig- lar areas, it is more convenient to introduce the gering, it is important to search for the statistical triggering flow direction that considers the link flow of triggering. The use of individual events is between active zones; then, when a threshold link complex as varying fault systems may be in a criti- is reached, the orientation of flow may be esti- cal state of failure before the passage of stress from mated to delimit the direction from the driver to the driver event. Thus, it is useful to consider a zon- the recipient zone in terms of statistical activity. ing characterized by a set of events over a period However, many plate boundaries include a consid- erable number of events that are difficult to pro- of many years before searching for triggering. This cess as we are limited by the running time. In this provides interdependent zones of coeval activity in regard, a specific time window was adopted for which causal triggering may be estimated. We test each of the plate boundary catalogs. Pacific zones a seismic link network from catalogs of and of present abundant background seis- California, Gibraltar as zones of collision, and the micity ranging with various magnitudes, such as Philippines, New Zealand, and Japan as subduc- the Japan and New Zealand regions. We adopted tion zones. Short-time triggering and a long-lived a 10-year time window because it is a reasonable process of two decades are included, and the main period to search for a link between distant regions. objective is to first establish zones of spatial seismic The catalogs have to follow Gutenberg–Richter dependence. The seismic grids represented by time regression from a specific magnitude: the Magni- series are further tested to determine the drivers tude of Completeness (Mc). Mc is calculated from from recipient zones based on the coherence of Zmap by using maximum likelihood solution. How- the time series. Comparing high linked zones with ever, the use of Mc cut-off in these catalogs shows stress field azimuths and local provides that the remaining event number is considerable insight into some possible widespread behaviour of so we then increased our minimum magnitude to seismic triggering in the collision zones. 3 for Japan and New Zealand. In turn, Philippine regions show Mc4.5 which reduced the database too much, so in this case, the lower magnitude cut- off is reduced to 3. The data was obtained from 2. Dataset and methods the Japan University Network Earthquake Cata- logue (JUNEC) and GeoNet of New Zealand for the The databases used in this study include events period spanning from 1988–1998. For other regions that occurred in a relatively large area of the plate (the Philippines, Turkey, California), the catalogs boundary, but they are limited in space because were obtained from the US Geological Survey with linked earthquakes of major events may traverse a time window of 25 years (1988–2012) and the Isti- the entire earth. Since a set of shocks may trig- tuto Geogr´afico Nacional (Spain) for the Gibral- ger events far away from the main shock areas, tar region. The magnitude cut-off was adopted they must be compiled during a relatively impor- (table 1) as we investigated the long-distance link tant time window. In turn, triggered events may of the shocks, and the links related to the lower also trigger events in the main shock source zone. magnitudes were not included. Many earthquakes For this reason, the activity measured between may occur after wave arrivals, so we then enlarged zones represents a cross-correlation in both space the period necessary for triggering and we also and time. Sequences from aftershocks are not the made the distance as large as possible around only factor controlling the threshold link owing to the plate boundaries in order to include most of the wide time span and distant zones within the the events. The plate boundaries were partitioned plate boundaries. Individual shocks cannot repre- into a 1◦ × 1◦ grid. The grids are described by sent the source zones of the triggering in zones a time series of event numbers to each temporal of high activity where shocks occurred in every sample, and the activity within a grid covers a

Table 1. The data used in the link network processing, the magnitude cutoff, score obtained by maximal coefficient R and related distance. Score Distance Region Period Nb events Mc cut-off Rmax PSI (km) Japan 1988–1998 39403 3 1 1.67 143 NZ 2002–2012 40091 3 1 3.13 1072 Gibraltar 1988–2012 6145 2.5 0.75 33.09 631 California 1988–2012 23350 2.8 1 22.19 620 Philippines 1988–2012 9831 3 0.8 35.52 332 Turkey 1988–2012 18136 2.7 0.7 31.11 88 Seismic link at plate boundary 699 period sample of 90 days, and the next sample (figure 1b). When the links of high correlated will cover the next 90-day non-intersecting time regions were established to each grid, we tested period. The prominent factor in determining a link the time series of the grid couple (i, j)inorder between distant regions is that there is at least one to estimate the direction of flow. The goal was period during a 25-year span where both cells are to obtain information on the causality between seismically active. The seismic dependence between the well-correlated grid couple, which shows the the cells increases linearly when the number direction of triggering. The method is based on a of simultaneous active periods increases. Standard frequency average of the slope of the phase coher- cross-correlation includes simultaneous passive ence with respect to the instantaneous mixture periods that may not fit the correlation, e.g., of the independent source (Nolte et al. 2008a). Pearson’s correlation; instead, we suggest a method This method, called the Phase Slope Index (PSI), to compute a coefficient based on cancelling peri- includes the non-linear interaction between the zones, which incorporates waves coming from other ods free from earthquakes and we consider only seismic sources independent from the two zones the number of events in the same temporal sam- under the link. The PSI procedure is more appro- ple. The number of synchronized active periods is priate for a time series than Granger’s causality compiled in regard to the total number of active method (Nolte et al. 2008b) particularly when time temporal samples (T ) in the cell couple i, j.Weuse series are inferred from seismic activity. The Phase the relationship R of two-time series in the form: Slope Index is defined by:  R = α · (eτ − 1) (1) Ψij = |Cij (f)||Cij(f + δf) | with f∈F  × sin [φ(f + δf) − φ(f)] (2) τ = (kij/Tij ) ,α=(1− 1/e) /e, where k is the number of synchronized active peri- where Cij (f) is the complex coherence, φ(f)isthe ij phase spectrum linear and equal to 2πf τ, f is ods in grids i, j, Tij is the total number of active periods in both grids, e is the Napier constant, and the frequency, and τ is the delay time. The slope of A is a constant of normalizing R to boundary con- φ(f) indicates the causal direction from grid 1 to ditions. The relation (1) provides a way to compile grid 2, if it is positive, or from grid 2 to grid 1, if it is inversely negative. The PSI code by MATLAB the synchronized active periods at the two grids input requires epoch and segment length values, as with respect to the entire activity that occurred in the time series is sampled by epoch (epleng) and the grid couple. The relationship is computed inde- each epoch is divided by segment length (sgleng). pendently from the activity in the region as the Since we have postulated that the activity by grid two cells are considered to be individual regions. is sampled over 90 days, this provides the value Figure 1(a) shows the variation of R with the of the epoch sampling data running at 25 years. values of τ for all regions. When the coefficient The sgleng parameter is determined according to R was above a threshold of 0.5, we recorded the the scores obtained by varying sgleng from 1 to associated link number. The number of links was 90. An sgleng of 90 days equal to the epoch value compiled by successive thresholds and by region provides the best scores for the regions where the

(a) (b)

Figure 1. (a) The variations in the number of links by correlation threshold and by region indicate the power law distribution in both the subduction and collision regions. In (b)thevariationofR versus the relative synchronous activity of the two grids. 700 Faical Ramdani et al.

25-year time span is adopted (figure 2). However, when only 10 years are used, the sample number is reduced and, in that case, the score is 0 and no PSI results are obtained. The reason for this is that the sampling number of the time series has to be at least 100 because of the 1/100 frequency limit. To achieve this sampling rate of the subduction zone (Japan and New Zealand), we re-sampled the time series into 30 days for 10 years of datasets. In this case, there would be a total of 120 samples and the score and the PSI results can be obtained. We then calculated the causality by grid couple using sgleng 90 or sgleng 30 for time series with high thresholds. Investigating the activity by grid couples, we found that several grid couples present significantly reduced activity (one or two events only) during one period of 90 days over the course of 25 years. This particular single, but synchronous, activity to both cells reaches correlation 1 according to equation (1). As shown in figure 3(a), this Dirac type of time series is found in all of the studied regions except Turkey. Those will be distinguished from continuous seismic activity by the other grids (figure 3b). One period of activity and multi- ple periods of activity are then called ts1 and Figure 2. The PSI scores obtained for time series (ts) of (a) ts2, respectively. The multi-period activity shown Turkey and (b) Japan up to a correlation of 0.6 sampled in figure 3(b) presents the complex interactions by an epoch (epleng) of 90 days for Turkey and 30 days for between the grid couple at a large distance. PSI Japan by varying sgleng parameters. It appears that the best coherence is computed to suggest the orientation scores are found when sgleng and epleng are equal for both regions. of causality that predominates the interactions between grids. When causality indicates orienta- tion from grid 1 to grid 2, it cannot mean that

(a) (b)

Figure 3. The time series of threshold link 0.7 and 1 from Turkey and California (a) and show variations of seismicity sampled over quarter (90 days) of a period of 25 years. The coordinates and distances between the two cells are indicated at the top left and the arrow shows the direction of causality from the PSI. In (b), time series of rare synchronous activity in passive zones from Philippines and New Zealand regions. Coordinates of grids separated by a distance (D) are indicated. Causality (arrows) is determined directly from arrival times of events. Seismic link at plate boundary 701 grid 2 has no impact on grid 1. Using cases of ts1, orientation of triggering is hard to assess in the we assigned causality orientation by recording the presence of multiple sources of earthquakes con- timing of the events in both grids. The grid where tinuously active at the plate boundary setting the first event occurred is the driver. By using (figure 4a). PSI we compute the score obtained by each time At the 0.6 threshold, a considerable link is found series and the score we found vary. The best score in all regions. These links disappear at a thresh- obtained by each maximal threshold related to old 0.7 and 0.9, revealing a reduced closed zone distance between grids is shown in table 1. formed by closed structure in triangles such as on the San Andreas Fault. The Turkish network link model does not appear along the Anatolian Fault; 3. Results instead, it is limited to the western off-shore part of the (figure 4b) and it seems that The volume of events varies at each plate bound- it does not follow the EW-oriented Anatolian Fault ary zone, which may have an impact on the result- but is normal to it. The major EW faults, North ing number of links. Figure 1 shows the link Anatolian and Hellenic Arc, are then NS linked in number related to the coefficient R that exhibits the western sections at the place where they are a power law variation as commonly stated for in contact with the continental margin. The Ibero– several statistical seismic correlation distributions. Moroccan region shows that the network link lies Such a high correlated link between two grid zones around the Gibraltar Arc (figure 4c). In subduc- shows evidence for possible triggering, but the tion zones, the network links appear parallel to the

(a) (b)

(c)

Figure 4. Link network up to threshold 0.7 in Japan (a) and grid sampling used. Link network obtained from threshold 0.5 in Turkey (b) and Gibraltar zone (c). The grids of the region are shown. 702 Faical Ramdani et al. trenches, as shown in Japan. Similarly, the Philip- interaction. 18 individual sites of unique synchro- pines are located between two major faults, the nized event are observed with varying direction. No Manila Trench and the Philippine Trench, and we such individual synchronized events are observed in found that a high threshold link is obtained in the Turkey. The EW-oriented faults in this zone might junction of these major faults, but the intersecting generate an EW link that is not observed. Instead, zone coincides with a secondary transform fault we observed two closed structures, one located to passing near the volcanic zone of Mayon (figure 5a). the north and one located to the south along the More large networks of linked zones in the Ibero– Hellenic Arc (figure 6b). Moroccan region seem to follow the Gibraltar Arc TheJapanmodeloforientedlinksbasedonPSI configuration. The W-direction of causality points outlines NW margin of Honshu (figure 7a) with to the west along the A¸cores–Gibraltar Transform two additional individual synchronized sites. In Fault (figure 5b). A triangular structure showing the presence of the subduction zone, New Zealand the causal direction of the link is found in Cali- exhibits most links along the Alpine Fault, oriented fornia on the San Andreas Fault pointing to SW NE–SW, and another cluster link to the northern direction (figure 6a) that indicates zones of flow subduction zone (figure 7b). In these regions, the

(a) (b)

Figure 5. Most of the 34-oriented links at the 0.7 threshold of Philippines (a) represent stress transfer related to the Manila Trench (MT) and the Philippines Trench (PT). The Ibero–Moroccan region (b) shows a link network at threshold 0.65 with a PSI causal direction (red link) and blue link of individual synchronized event. The arrows show the direction of compression in the region.

(a) (b)

Figure 6. Network link (25) obtained at threshold 1 in California (a). Localized zones of causality flows are shown on the San Andreas Fault (SAF) including 18 links of individual synchronized event. Turkish network provides 21 links determined at threshold 0.7 from PSI with causal direction shows two closed structures located south from the Anatolian Fault and north from the Hellenic Arc (b). Seismic link at plate boundary 703

(a) (b)

Figure 7. Japan causal determinations includes 22 from PSI and two inferred directly from the timing of individual events shown by red arrows (a). New Zealand link network of 30 links (b) of threshold 1 lie along Alpine Fault and the Pyusegur Trench (PT). link has a preferred orientation along the transform permanent wave propagation. Only by studying faults and it is normal to the plate motion driven the number of events in several sampling time win- by subduction. dows, we can determine if the two zones may be linked. When two distant and passive grid zones experienced only one event over the course of many 4. Discussion and conclusions years, and that event coincided in both grids within thesamesamplingtimeof90days,theeventmay Triggering processes at a plate boundary exhibit be assumed to be a particular triggering in aseis- a preferred direction for the triggering. Zones that mic region. Since the time delay between the two trigger far away zones through a preferred direc- events may be recorded, it can be interpreted as a tion of triggering will be recipients of the stress real time delay for that particular triggering. How- coming from the regions they have triggered, so ever, both events may be caused by a third previous the system will be closed. While this process works event, and the time delay between these two events repetitively in relatively small scale areas, cluster is not as long as the time it takes for each zone to zones of causal triggering can be observed. The pre- reach critical failure. Otherwise, tidal deformation ferred direction of triggering is a direction where may trigger events occurring in passive regions. the amplitude of the stress transfer is increased. As In a subduction zone, stress transfer is domi- the causality is measured through many years of nantly guided by the direction normal to subduc- activity and the faulting system within a grid is not tion and parallel to the trench zones or the volcanic specified, the causality only includes the far away lines, as it is in Japan. This evidence seems to spatio-temporal stress transfer in statistical terms. be contrary to the absence of widespread trigger- The time delays for static, dynamic, or viscoelastic ing in Japan reported by Harrington and Brodsky relaxation are not distinguished, but the preferred (2006), but it is in agreement with the evidence for direction of the stress transfer is one of the main tidal triggering on reverse faults in Japan (Tanaka parameters in the triggering process. The correla- et al. 2004), and low frequency deep triggering tion between grids shows that an earthquake pri- (Miyazawa and Mori 2005). NE–SW oriented trig- marily presents an instability setting of a zone or a gering flow appears more pronounced in SW direc- fault. This event can also trigger another far away tion than the NE azimuth. This zone is parallel to fault and it can also receive stress from another Japan trench and volcanic lines which favours fluid event and become a second-order failure. Because dynamic released in the extension normal to sub- of this mixture of roles between the recipient and duction. At subcrustal depths, earthquakes due to the driver, it seems more appropriate to compile metastable phase changes in the slab release kinetic the interaction with multi-sources to infer the dom- energy normal to slab penetration. It is noticeable inant flows of triggering. As there is not a zero-time that the most synchronized link stops at the Saga- to decide whether this event triggered some other mi trench to the south, and there is absence of trig- events, and so on, we can consider that each event gered link at maximal threshold in Nankai trough. is due to the stress increase caused by past and Notable observation is that NE–SW oriented linked 704 Faical Ramdani et al. zone of northern Japan is similar to the NE–SW Philippine Fault, causal directions of trigge- linked zones of New Zealand even though both ring parallel this major fault that is normal to regions are not in the same azimuth of subduction. compression-related subduction. Triggering bet- Intriguing observation is that in both subduction ween these two major faults is focused in two clus- zones we found most of the causal links (70%) were ter zones of Manilla Trench and a much larger zone SW oriented consistently. In northern zone of New of the opposed Philippines Trenches forming a tri- Zealand that focuses driver sites is a volcanic area angular beam. Manilla Trench sites appears to be while in the south, the Alpine fault seems to be a recipient of driver sites from Philippine fault zone. recipient zone. Crustal weakness beneath the fault The presence of opposed slab beneath Philippines made it possible repetitive triggering process along favours fluid dynamics and increasing pore pres- the fault. sure within the faults. As triggering flow is mainly In the Gibraltar zone, causal direction outlines oriented to Manilla Trench, this may be an evi- the A¸cores–Gibraltar fault zone strike in the W dence that subduction from Philippines provides direction, globally, that is oblique to the NW– more stress transfer than the opposed subduction SE compression, but in this special case trigger- beneath Manilla Trench. ing is oblique to compression but parallel to the In New Zealand, the causal direction is NE–SW W subduction, as reported by Ramdani et al. oriented along the Alpine Fault and the localized (2014). Model of fault-to-fault stress transfer at the zones in the northern subduction zone. However, regional scale including a closed structure of causal- in this case, triggering only reflects the partial ity is shown in the trenches in the Hellenic Arc and possibilities of the links since only grids that are the eastern boundary of the plate and separated by a distance greater than 2◦ and a mag- the southern Anatolian Fault. In between, these nitude M>3 are used. Lower magnitudes of the closed structures are separated by the EW volcanic near field triggering are not included. In case of arc, which shows that the triggered flow in these New Zealand, both the stress transfers along the regions is compression parallel, but not parallel to fault to the south and the triggering in the north- the magma fluid dynamics. The presence of Anato- ern volcanic zones are viable. In terms of trig- lian and Hellenic Fault arcs probably predominate gering flows, the predominant extension setting, the causal flow rather than the EW oriented vol- may first be explained by the fact that extension canic extension. The California causal directions induces a widespread direction of stress transfer, also present closed structures along the northern which is larger than what occurs with undirected parts of San Andreas Fault in the SE direction from stress from compression. Secondly, dynamic fluid 40◦ to 36◦N. This causal structure of the link is relaxation in the lower crust provides long-lived parallel to the SE-oriented volcanic line. However, stress in volcanic eruption zones. Repetitive trig- California triggered zones seem dominated at this gering is estimated by the causal flows of zones of maximum threshold by many individual triggering high seismic dependence. This result is not due to dispersed in the region. Some sites are repetitively the PSI method since the procedure does not take triggered from several sites and sometimes at the into account the geographic location of the grids. same period sample. This may not be an evidence Reversed flow directions parallel to volcanic arc is for direct triggering as it may be explained by the observed in subduction zones. fact that many sites may be triggered at varying The time span and distance scale used in this timings within the same sample of 90 days. How- study seem sufficient to observe some aspects ever, an individual earthquake in a passive site is of the complex earthquake interactions at plate a clear example for triggering. The orientation of boundaries, and the associated correlated events these individual triggering at such large distances are shown from a reasonable period during which does not seem to be related to stress field envi- multi-source triggering may have occurred. This ronment or a particular dynamic process. The pas- approach that compares one grid to all the other sive site experienced permanent passage of seismic grids of the region is crucial in establishing the waves without any response, and sudden occur- regional seismic interdependence. It is justified by rence of an event may be caused by a driver earth- the unknown direction of possible triggering that quake with particular characteristics. Frequency is confined to multiple sources of permanent seis- content or tidal effects may be source of the reac- mic activity at plate boundaries. Individual earth- tion of a passive zone that returns passive just after quakes in a region provide additional stress that the event has occurred. may be sufficient to meet the critical failure at The Philippines lying between EW-opposed varying distances and times. In expanding the subduction (the Manila and Philippines trenches) process to a period as large as 25 years over a shows that the stress transfer switches between distance of more than 1000 km, we can expect to zones lying in the Manila Fault to the west and determine how triggering operates in the presence the eastern Philippine Trench. However, along the of multiple-source events. Transfer from fault-to- Seismic link at plate boundary 705 fault is observed in the presence of major faults Jimenez A, Tiampo K F and Posadas A M 2008 Small world and is limited along the fault in the presence of a in a seismic network: The California case; Nonlin. Process. unique regional fault. The question of why exten- Geophys. 15 389–395. King G C P, Stein R S and Lin J 1994 Static stress changes sion appears to fit the flow direction of trigger- and the triggering of earthquakes; Bull.Seismol.Soc.Am. ing is consistently asked. Crustal relaxation with 84(3) 935–953. volcanic eruptions in geothermal areas provides Krishna Mohan T R and Revathi P G 2011 Earthquake cor- an extension field for triggering in the subduction relations and networks: A comparative study; Phys. Rev. zones. However, in the presence of two major faults, E 83 046109. the triggering may be compression parallel, as is Lorenzo-Martin F, Roth F and Wang R J 2006 Elastic and observed in the Aegean Sea and the Philippines. inelastic triggering of earthquakes in the North Anatolian It is concluded that causal triggering at varying Fault zone; Tectonophys. 424 3–4. Mc Kernon C and Main I G 2005 Regional variations in plate boundaries occurs primarily along a major the diffusion of triggered seismicity; J. Geophys. Res. 110 unique fault or is due to the stress transfer bi- B05S05, doi: 10.1029/2004JB003387. directed between two major faults. It also occurs Miyazawa M J and Mori 2005 Detection of triggered along a geothermal volcanic arc when no parallel deep low-frequency events from the 2003 Tokachi- major fault exists in the enlarged proximity. oki earthquake; Geophys. Res. Lett. 32 L10307, doi: 10.1029/2005GL022539. Nolte G, Ziehe A, Nikulin V, Schlogl A, Kramer N, Brismar Acknowledgements T and Muller K R 2008a Robustly estimating the flow direction of information in complex physical systems; Phys. Rev. Lett. 100 234101. This work has been supported by Mohamed V Uni- Nolte G, Ziehe A, Kr¨amer N, Popescu F and M¨uller K R versity funding from PU project. Authors thank 2008b Comparison of Granger Causality and Phase Slope the Associate Editor, P Dewangan and the anony- Index; JMLR Workshop and Conference Proceedings 6 267–276. mous reviewers for their constructive reviews. Perea H 2009 The Catalan seismic crisis [1427 and 1428; NE Iberian Peninsula]: Geological sources and earthquake triggering; J. Geodyn. 47 259–270. 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MS received 10 June 2014; revised 30 December 2014; accepted 20 January 2015