1. science
2. geology
3. seismology
4. earthquakes

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Seismic link at plate boundary
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Faical Ramdani, Omar Kettani, Benaissa Tadili
Mohamed V- University, Scientific Institute, Physics of the Earth Laboratory
Rabat, Morocco
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Abstract
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Seismic triggering at plate boundaries has a very complex nature that includes seismic events
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at varying distances. The spatial orientation of triggering cannot be reduced to sequences from
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the main shocks. Seismic waves propagate at all times in all directions, particularly in highly
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active zones. No direct evidence can be obtained regarding which earthquakes trigger the
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shocks. The first approach is to determine the potential linked zones where triggering may
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occur. The second step is to determine the causality between the events and their triggered
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shocks. The spatial orientation of the links between events is established from pre-ordered
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networks and the adapted dependence of the spatio-temporal occurrence of earthquakes.
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Based on a coefficient of synchronous seismic activity to grid couples, we derive a network
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link by each threshold. The links of high thresholds are tested using the coherence of time
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series to determine the causality and related orientation. The resulting link orientations at the
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plate boundary conditions indicate that causal triggering seems to be localized along a major
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fault, as a stress transfer between two major faults, and parallel to the geothermal area
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extension.
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Keywords: seismic link, time series, distant earthquakes, causality, plate boundary
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Plate boundaries are the zones where most Earth dynamics are focused. The complexity of
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tectonic boundaries draws attention to them as the largest earthquakes are felt in these areas
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and they elicit the natural hazard of seismic activity. However, the sequences of the main
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shocks and the triggering process constrain the seismic hazard assessment. Some frequent
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issues remain as to whether the seismicity of the interplate zone with a high strain rate has
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random aspects and may be associated with a triggering mechanism, and how the seismicity
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can be associated with fault patterns and plate motion. Triggering causes changes in the
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Coulomb stress on a specified fault, which is independent of regional stress but which
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depends on the fault geometry, the sense of slip, and the coefficient of friction (King et al.,
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1994). Restricting the causality connection to a single predecessor or to an arbitrary
1. Introduction
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mainshock-aftershock scenario may not be enough (Krishna Mohan and Revathi, 2011). This
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shows that the link between events is a complex feature linked to varying network models
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(Abe and Suzuki, 2006). Links limited to individual events have been related to low strain
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rate environments (Hough et al., 2003), visco-elastic relaxation (Lorenzo-Martin et al., 2005),
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and solid Earth tides (Cochran et al., 2004). By analyzing earthquake pairs over a period of
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many years, Wan et al. (2004) suggested that Coulomb stress triggering may be observed for
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thrust earthquakes, while McKernon and Main (2005) limited triggering process to about 150
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km. Extending earthquake activity to a spatial network link shows that the alignment of the
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links is parallel to the Honshu Trench azimuth in Japan (Tanenbaum et al., 2012) and the
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direction of the San Andreas Fault (SAF) (Jimenez et al., 2008). In the Ibero-Moroccan
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region, main shocks and their aftershocks are investigated as local features due to fault
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mechanisms except for some historical event studies related to triggering in the Catalan and
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NE Iberian regions (Perea, 2009). As zones of permanent activity make it difficult to detect
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causal triggering, it is important to search for the statistical flow of triggering. The use of
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individual events is complex as varying fault systems may be in a critical state of failure
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before the passage of stress from the driver event. Thus, it is useful to consider a zoning
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characterized by a set of events over a period of many years before searching for triggering.
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This provides inter-dependent zones of coeval activity in which causal triggering may be
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estimated. We test a seismic link network from catalogs of Turkey and California, Gibraltar as
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zones of collision, and the Philippines, New Zealand, and Japan as subduction zones. Short
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time triggering and a long-lived process of two decades are included, and the main objective
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is to first establish zones of spatial seismic dependence. The seismic grids represented by time
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series are further tested to determine the drivers from recipient zones based on the coherence
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of the time series. Comparing high linked zones with stress field azimuths and local tectonics
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provides insight into some possible widespread behavior of seismic triggering in the collision
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zones.
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2. Dataset and Methods
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The databases used in this study include events that occurred in a relatively large area of the
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plate boundary, but they are limited in space because linked earthquakes of major events may
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traverse the entire Earth. Since a set of shocks may trigger events far away from the main
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shock areas, they must be compiled during a relatively important time window. In turn,
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triggered events may also trigger events in the main shock source zone. For this reason, the
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activity measured between zones represents a cross-correlation in both space and time.
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Sequences from aftershocks are not the only factor controlling the threshold link owing to the
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wide time span and distant zones within the plate boundaries. Individual shocks cannot
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represent the source zones of the triggering in zones of high activity where shocks occurred in
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every zone along the plate boundary. In those particular areas, it is more convenient to
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introduce the triggering flow direction that considers the link between active zones; then,
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when a threshold link is reached, the orientation of flow may be estimated to delimit the
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direction from the driver to the recipient zone in terms of statistical activity. However, many
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plate boundaries include a considerable number of events that are difficult to process as we
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are limited by the running time. In this regard, a specific time window was adopted for each
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of the plate boundary catalogs. Pacific zones of subduction present abundant background
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seismicity ranging with various magnitudes, such as the Japan and New Zealand regions. We
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adopted a 10-year time window because it is a reasonable period to search for a link between
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distant regions. The catalogs have to follow Gutenberg-Richter regression from a specific
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magnitude: the Magnitude of Completeness (Mc). Mc is calculated from Zmap by using
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maximum likelihood solution. However, the use of Mc cutoff in these catalogs shows that the
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remaining event number is considerable so we then increased our minimum magnitude to 3
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for Japan and New Zealand. In turn, Philipppines regions shows Mc4.5 which reduced too
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much the database, so in this case the lower magnitude cutoff is reduced to 3.The data was
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obtained from the Japan University Network (JUNEC) Earthquake Catalogue and GeoNet of
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New Zealand for the period spanning from 1988–1998. For the other regions (the Philippines,
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Turkey, California), the catalogs were obtained from the US Geological Survey with a time
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window of 25 years (1988–2012) and the Istituto Geográfico Nacional (Spain) for the
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Gibraltar region. The Magnitude cutoff was adopted (Table 1) as we investigated the long-
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distance link of the shocks, and the links related to the lower magnitudes were not included.
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Many earthquakes may occur after wave arrivals, so we then enlarged the period necessary for
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triggering and we also made the distance as large as possible around the plate boundaries in
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order to include most of the events. The plate boundaries were partitioned into a 1°×1° grid.
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The grids are described by a time series of event numbers to each temporal sample, and the
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activity within a grid covers a period sample of 90 days, and the next sample will cover the
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next 90-day non-intersecting time period. The prominent factor in determining a link between
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distant regions is that there is at least one period during a 25-year span where both cells are
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seismically active. The seismic dependence between the cells increases linearly when the
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number of simultaneous active periods increases. Standard cross-correlation includes
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simultaneous passive periods that may not fit the correlation, e.g., Pearson’s correlation;
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instead, we suggest a method to compute a coefficient based on canceling periods free from
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earthquakes and we consider only the number of events in the same temporal sample. The
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number of synchronized active periods is compiled in regard to the total number of active
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temporal samples (T) in the cell couple i, j. We use the relationship R of two time series in the
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form:
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
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R = α . (e -1)
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with  = ∑(kij/Tij), α= (1-1/e)/e
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where kij is the number of synchronized active periods in grids i j, Tij is the total number of
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active periods in both grids, e is the Napier constant, and A is a constant of normalizing R to
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boundary conditions. The relation (1) provides a way to compile the synchronized active
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periods at two grids with respect to the entire activity that occurred in the grid couple. The
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relationship is computed independently from the activity in the region as the two cells are
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considered to be individual regions. Figure 1a shows the variation of R with the values of 
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for all regions. When the coefficient R is above a threshold of 0.5, we recorded the associated
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link number. The number of links was compiled by successive thresholds and by region
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(Figure 1b). When the links of high correlated regions were established to each grid, we tested
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the time series of the grid couple (i,j) in order to estimate the direction of flow. The goal was
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to obtain information on the causality between the well-correlated grid couple, which shows
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the direction of triggering. The method is based on a frequency average of the slope of the
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phase coherence with respect to the instantaneous mixture of the independent source (Notle et
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al.,2008a). This method, called the Phase Slope Index (PSI), includes the non-linear
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interaction between the zones, which incorporates waves coming from other seismic sources
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independent from the two zones under the link. The PSI procedure is more appropriate for a
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time series than Granger’s causality method (Notle et al., 2008b) particularly when time
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series are inferred from seismic activity. The Phase Slope Index is defined by:
(1)
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∑
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()
(
)
(
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()
(2)
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( ) is the complex coherence, (f) is the phase spectrum linear and equal to 2 f , f
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where
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is the frequency, and  is the delay time. The slope of (f) indicates the causal direction from
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grid 1 to grid 2, if it is positive, or from grid 2 to grid 1, if it is inversely negative. The PSI
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code by MATLAB input requires epoch and segment length values, as the time series is
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sampled by epoch (epleng) and each epoch is divided by segment length (sgleng). Since we
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have postulated that the activity by grid is sampled over 90 days, this provides the value of the
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epoch sampling data running at 25 years. The sgleng parameter is determined according to the
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scores obtained by varying sgleng from 1 to 90. A sgleng of 90 days equal to the epoch value
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provides the best scores for the regions where the 25-year time span is adopted (Figure 2).
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However, when only 10 years are used the sample number is reduced and, in that case, the
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score is 0 and no PSI results are obtained. The reason for this is that the sampling number of
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the time series has to be at least 100 because of the 1/100frequency limit. To achieve this
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sampling rate of the subduction zone (Japan and New Zealand), we re-sampled the time series
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into 30 days for 10 years of datasets. In this case, there would be a total of 120 samples and
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the score and the PSI results can be obtained. We then calculated the causality by grid couple
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using sgleng 90 or sgleng 30 for time series with high thresholds.
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By investigating the activity by grid couples we found that several grid couples present
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significantly reduced activity (one or two events only) during one period of 90 days over the
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course of 25 years. This particular single, but synchronous, activity to both cells reaches
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correlation 1 according to Equation (1). As shown in Figure 3a, this Dirac type of time series
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is found in all of the studied regions except Turkey. Those will be distinguished from
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continuous seismic activity by the other grids (figure 3b). One period of activity and multiple
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periods of activity are then called ts1 and ts2, respectively. The multi-period activity shown
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in Figure 3b presents the complex interactions between the grid couple at a large distance. PSI
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coherence is computed to suggest the orientation of causality that predominates the
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interactions between grids. When causality indicates orientation from grid 1 to grid 2, it
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cannot mean that grid 2 has no impact on grid 1. Using cases of ts1, we assigned causality
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orientation by recording the timing of the events in both grids. The grid where the first event
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occurred is the driver. By using PSI we compute the score obtained by each timeseries and the
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score we found vary. The best score obtained by each maximal threshold related to distance
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between grids is shown in table 1.
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3. Results
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The volume of events varies at each plate boundary zone, which may have an impact on the
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resulting number of links. Figure 1 shows the link number related to the coefficient R that
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exhibits a power law variation as commonly stated for several statistical seismic correlation
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distributions. Such a high correlated link between two grid zones shows evidence for possible
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triggering, but the orientation of triggering is hard to assess in the presence of multiple
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sources of earthquakes continuously active at the plate boundary setting.
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At the 0.6 threshold a considerable link is found in all regions. These links disappear at a
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threshold 0.7 and 0.9, revealing a reduced closed zone formed by closed structure in triangles
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such as on the San Andreas Fault. The Turkish network link model does not appear along the
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Anatolian Fault; instead, it is limited to the western off-shore part of the Anatolian plate
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(Figure 5) and it seems that it does not follow the EW-oriented Anatolian Fault but is normal
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to it. The major EW faults, North Anatolian and Hellenic Arc, are then NS linked in the
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western sections at the place where they are in contact with the continental margin. The Ibero-
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Moroccan region shows that the network link lies around the Gibraltar Arc (Figure 5). In
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subduction zones, the network links appear parallel to the trenches, as shown in Japan.
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Similarly, the Philippines are located between two major faults, the Manila Trench and the
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Philippine Trench, and we found that a high threshold link is obtained in the junction of these
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major faults, but the intersecting zone coincides with a secondary transform fault passing near
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the volcanic zone of Mayon (Figure 5a). More large networks of linked zones in the Ibero-
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Moroccan region seem to follow the Gibraltar Arc configuration. The W direction of causality
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points to the west along the Açores-Gibraltar Transform Fault (Figure 5b). A triangular
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structure showing the causal direction of the link is found in California on the San Andreas
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Fault pointing to SW direction (Figure 6a) that indicates zones of flow interaction. 18
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individual sites of unique synchronized event are observed with varying direction. No such
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individual synchronized events are observed in Turkey. The EW-oriented faults in this zone
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might generate an EW link that is not observed. Instead, we observed two closed structures,
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one located to the north and one located to the south along the Hellenic Arc (Figure 6b).
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The Japan model of oriented links based on PSI outlines NW margin of Honshu (Figure 7a)
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with two additional individual synchronized sites. In the presence of the subduction zone,
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New Zealand exhibits most links along the Alpine Fault, oriented NE-SW, and another cluster
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link to the northern subduction zone (Figure 7b). In these regions, the link has a preferred
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orientation along the transform faults and it is normal to the plate motion driven by
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subduction.
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4. Discussion and Conclusions
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Triggering processes at a plate boundary exhibit a preferred direction for the triggering. Zones
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that trigger far away zones through a preferred direction of triggering will be recipients of the
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stress coming from the regions they have triggered, so the system will be closed. While this
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process works repetitively in relatively small scale areas, cluster zones of causal triggering
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can be observed. The preferred direction of triggering is a direction where the amplitude of
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the stress transfer is increased. As the causality is measured through many years of activity
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and the faulting system within a grid is not specified, the causality only includes the far away
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spatio-temporal stress transfer in statistical terms. The time delays for static, dynamic, or
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viscoelastic relaxation are not distinguished, but the preferred direction of the stress transfer is
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one of the main parameters in the triggering process. The correlation between grids shows
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that an earthquake primarily presents an instability setting of a zone or a fault. This event can
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also trigger another far away fault and it can also receive stress from another event and
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become a second order of failure. Because of this mixture of roles between the recipient and
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the driver, it seems more appropriate to compile the interaction with multi-sources to infer the
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dominant flows of triggering. As there is not a zero-time to decide whether this event
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triggered some other events, and so on, we can consider that each event is due to the stress
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increase caused by past and permanent wave propagation. Only by studying the number of
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events in several sampling time windows we can determine if two zones may be linked. When
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two distant and passive grid zones experienced only one event over the course of many years,
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and that event coincided in both grids within the same sampling time of 90 days, the event
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may be assumed to be a particular triggering in aseismic region. Since the time delay between
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the two events may be recorded, it can be interpreted as a real time delay for that particular
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triggering. However, both events may be caused by a third previous event, and the time delay
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between these two events is not as long as the time it takes for each zone to reach critical
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failure. Otherwise, tidal deformation may trigger events occurring in passive regions.
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In a subduction zone, stress transfer is dominantly guided by the direction normal to
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subduction and parallel to the trench zones or the volcanic lines, as it is in Japan. This
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evidence seems to be contrary to the absence of widespread triggering in Japan reported by
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Harrington and Brodsky (2006), but it is in agreement with the evidence for tidal triggering on
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reverse faults in Japan (Tanaka et al., 2004), and low frequency deep triggering (Miyazawa
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and Mori 2005). NE-SW oriented triggering flow appears more pronounced in SW direction
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than the NE azimuth. This zone is parallel to Japan trench and volcanic lines which favors
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fluid dynamic released in the extension normal to subduction. At subcrustal depths,
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earthquakes due to metastable phase changes in the slab release kinetic energy normal to slab
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penetration. It is notable that the most synchronized link stop at the Sagami trench to the
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South, and the absence of triggered link at maximal threshold in Nankai trough. Notable
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observation is that NE-SW oriented linked zone of northern Japan is similar to the NE-SW
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linked zones of New Zealand even though both regions are not in the same azimuth of
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subduction. Intriguing observation is that in both subduction zones we found consistently
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most of causal links (70%) are SW oriented. In northern zone of New Zealand that focuses
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driver sites is a volcanic area while in the South the Alpine fault seems to be recipient zone.
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Crustal weakness beneath the fault made it possible repetitive triggering process along the
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fault.
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In the Gibraltar zone, causal direction outlines the Açores-Gibraltar fault zone strike in the W
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direction, globally, that is oblique to the NW-SE compression, but in this special case
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triggering is oblique to compression but parallel to the W subduction, as reported by Ramdani
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et al. (2014). Model of fault-to-fault stress transfer at the regional scale including a closed
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structure of causality is shown in the trenches in the Hellenic Arc and the eastern boundary of
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the Aegean Sea plate and the southern Anatolian Fault. In between, these closed structures are
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separated by the EW volcanic arc, which shows that the triggered flow in these regions is
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compression parallel, but not parallel to the magma fluid dynamics. The presence of
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Anatolian and Hellenic Fault arcs probably predominate the causal flow rather than the
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volcanic extension EW oriented. The California causal directions also present closed
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structures along the northern parts of San Andreas Fault in the SE direction from 40°N to
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36°N. This causal structure of the link is parallel to the SE-oriented volcanic line. However,
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California triggered zones seem dominated at this maximum threshold by many individual
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triggering dispersed in the region. Some sites are repetitively triggered from several sites and
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sometimes at the same period sample. This may not be evidence for direct triggering as it may
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be explained by the fact that many sites may be triggered at varying timing within the same
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sample of 90 days. However, the individual earthquake in a passive site is the clear example
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for triggering. The orientation of these individual triggering at such large distance seems not
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related to stress field environment or a particular dynamic process. The passive site
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experienced permanent passage of seismic waves without any response, and sudden
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occurrence of an event may be caused by a driver earthquake with particular characteristics.
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Frequency content or Tidal effects may be source of the reaction of a passive zone that returns
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passive just after the event has occurred.
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The Philippines lying between EW-opposed subduction (the Manila and Philippines
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Trenches) shows that the stress transfer switches between zones lying in the Manila Fault to
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the west and the eastern Philippine Trench. However, along the Philippine Fault, causal
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directions of triggering parallel this major fault that is normal to compression related
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subduction. Triggering between these two major faults is focused in two cluster zones of
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Manilla trench and a much larger zone of the opposed Philippines trenchs forming a triangular
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beam. Manilla trench sites appears to be recipient of driver sites from Philippine fault zone.
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The presence of opposed slab beneath Philippines favours fluid dynamics and increasing pore
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pressure within the faults. As triggering flow is mainly oriented to Manilla trench this may be
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evidence for that subduction from Philippines provides more stress transfer than the opposed
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subduction beneath Manilla trench.
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In New Zealand, the causal direction is NE-SW oriented along the Alpine Fault and the
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localized zones in the northern subduction zone. However, in this case, triggering only
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reflects the partial possibilities of the links since only grids that are separated by a distance
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greater than 2° and a magnitude M>3 are used. Lower magnitudes of the near field triggering
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are not included. In the case of New Zealand, both the stress transfers along the fault to the
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south and the triggering in the northern volcanic zones are viable. In terms of triggering
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flows, the predominant extension setting, may first be explained by the fact that extension
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induces a widespread direction of stress transfer, which is larger than what occurs with
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undirected stress from compression. Secondly, dynamic fluid relaxation in the lower crust
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provides long-lived stress in volcanic eruption zones. Repetitive triggering is estimated by the
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causal flows of zones of high seismic dependence. This result is not due to the PSI method
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since the procedure does not take into account the geographic location of the grids. Reversed
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flow directions parallel to volcanic arc is observed in subduction zones.
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The time span and distance scale used in this study seem sufficient to observe some aspects of
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the complex earthquake interactions at plate boundaries, and the associated correlated events
292
are shown from a reasonable period during which multi-source triggering may have occurred.
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This approach that compares one grid to all of the grids of the region is crucial to establishing
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the regional seismic interdependence. It is justified by the unknown direction of possible
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triggering that is confined to multiple sources of permanent seismic activity at plate
296
boundaries. Individual earthquakes in a region provide additional stress that may be sufficient
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to meet the critical failure at varying distances and times. In expanding the process to a period
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as large as 25 years over a distance of more than 1000 km we can expect to determine how
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triggering operates in the presence of multiple source events. Transfer from fault-to-fault is
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observed in the presence of major faults and is limited along the fault in the presence of a
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unique regional fault. The question of why extension appears to fit the flow direction of
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triggering is consistently asked. Crustal relaxation with volcanic eruptions in geothermal areas
303
provides an extension field for triggering in the subduction zones. However, in the presence
304
of two major faults, the triggering may be compression parallel, as is observed in the Aegean
305
Sea and the Philippines. It is concluded that causal triggering at varying plate boundaries
306
occurs primarily along a major unique fault or is due to the stress transfer bi-directed between
307
two major faults. It also occurs along a geothermal volcanic arc when no parallel major fault
308
exists in the enlarged proximity.
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Acknowledgments
311
This work has been supported by Mohamed V-University founding from PU project.
312
P. Dewangan and anonymous reviewers are thanked for reviews.
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in Japan; Bull Seismological Society America 96: 871-878.
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Hough S E, Seeber L and Armbruster J G 2003 Intraplate Triggered Earthquakes:
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the 2003 Tokachi-oki earthquake; Geophys. Res. Lett 32: L10307; doi:
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Perea, H 2009 The Catalan seismic crisis [1427 and 1428; NE Iberian Peninsula]:
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Geological sources and earthquake triggering; Journ of Geodynamics 47:259–270
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Ramdani F Kettani O and Benaissa Tadili B 2014 Evidence for subduction beneath
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Gibraltar Arc and Andean regions from k-means earthquake centroids J Seismol DOI
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Tanaka S Ohtake M and Sato H 2004 Tidal triggering of earthquakes in Japan related
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to the regional tectonic stress; Earth, Planets, and Space 56: 511-515
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Wan Y G, Wu Z L and Zhou G W 2004 Focal mechanism dependence of static stress
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triggering of earthquakes; Tectonophys 390 164: 235-243
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Figure Captions
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398
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Figure 1. The variations in the number of links by correlation threshold and by region indicate
400
the power law distribution in both the subduction and collision regions. In (b) the variation of
401
R versus the relative synchronous activity of the two grids.
402
403
Figure 2. The PSI scores obtained for time series (ts) of Turkey (a) and Japan (b) up to a
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correlation of 0.6 sampled by an epoch (epleng) of 90 days for Turkey and 30 days for Japan
405
by varying sgleng parameters. It appears that the best scores are found when sleng and epleng
406
are equal for both regions.
407
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Figure 3. The time series of threshold link 0.7 and 1 from the Turkey and California (a) and
409
show variations of seismicity sampled over quarter (90 days) of a period of 25 years. The
410
coordinates and distances between the two cells are indicated at the top left and the arrow
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shows the direction of causality from the PSI. In (b), time series of rare synchronous activity
412
in passive zones from Philippines and New Zealand regions. Coordinates of grids separated
413
by a distance (D) are indicated. Causality (arrows) is determined directly from arrival times of
414
events.
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Figure 4. Link network up to threshold 0.7 in Japan (a) and grid sampling used. Link network
417
obtained from threshold 0.5 in Turkey in (b) and Gibraltar zone (c). The grids of the region
418
are shown.
419
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Figure 5. Most of the 34-oriented links at the 0.7 threshold of the Philippines (a) represent
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stress transfer related to the Manila Trench (MT) and the Philippines Trench (PT).
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The Ibero-Moroccan region (b) shows a link network at threshold 0.65 with a PSI causal
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direction (red link) and blue link of individual synchronized event. The arrows show the
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direction of compression in the region.
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Figure 6. Network and 25 are obtained at threshold 1 in California (a). Localized zones of
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causality flows are shown on the San Andreas Fault (SAF) including 18 links of individual
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synchronized event. Turkish network provides 21 links determined at threshold 0.7 from PSI
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with causal direction shows two closed structures located south from the Anatolian Fault and
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north from the Hellenic Arc (b).
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Figure 7. Japan causal determinations includes 22 from PSI and two inferred directly from the
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timing of individual events shown by red arrows (a). New Zealand link network of 30 links
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(b) of threshold 1 lie along Alpine fault and the Pyusegur Trench (PT).
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Table1. The data used in the link network processing, the magnitude cutoff, score obtained by
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maximal coefficient R and related distance
Region
Jap
NZ
Gibr
Cal
Phil
Turk
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480
481
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Period
Nb
events
M-cutoff
Rmax
scorePSI
Distance,
km
1988-1998
2002-2012
1988-2012
1988-2012
1988-2012
1988-2012
39403
40091
6145
23350
9831
18136
3
3
2.5
2.8
3
2.7
1
1
0,75
1
0.8
0,7
1,6743
3,1282
33,09
22,187
35,523
31,113
143
1072
631
620
332
88
16
489
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(a)
(b)
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Figure 1
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Figure 2
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Figure 3
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Figure 4
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581
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(b)
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Figure 5
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Figure 6
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Figure 7