Aftershocks driven by afterslip and fluid pressuresweeping through a fault-fracture meshZachary E. Ross1 , Christopher Rollins1 , Elizabeth S. Cochran2 , Egill Hauksson1 ,Jean-Philippe Avouac1 , and Yehuda Ben-Zion3

1Seismological Laboratory, California Institute of Technology, Pasadena, California, USA, 2United States Geological Survey,Pasadena, California, USA, 3Department of Earth Sciences, University of Southern California, Los Angeles, California, USA

Abstract A variety of physical mechanisms are thought to be responsible for the triggering andspatiotemporal evolution of aftershocks. Here we analyze a vigorous aftershock sequence and postseismicgeodetic strain that occurred in the Yuha Desert following the 2010 Mw 7.2 El Mayor-Cucapah earthquake.About 155,000 detected aftershocks occurred in a network of orthogonal faults and exhibit features of twodistinct mechanisms for aftershock triggering. The earliest aftershocks were likely driven by afterslip thatspread away from the main shock with the logarithm of time. A later pulse of aftershocks swept again acrossthe Yuha Desert with square root time dependence and swarm-like behavior; together with local geologicalevidence for hydrothermalism, these features suggest that the events were driven by fluid diffusion. Theobservations illustrate howmultiple drivingmechanisms and the underlying fault structure jointly control theevolution of an aftershock sequence.

1. Introduction

The Mw 7.2 El Mayor-Cucapah (EMC) earthquake occurred on 4 April 2010 in Baja California on a set ofnorthwest trending faults, rupturing in bilateral fashion [Fletcher et al., 2014; Hauksson et al., 2011; Weiet al., 2011]. In the northwest, the rupture terminated about 60 km from the hypocenter, at the geologicboundary between the Sierra Cucapah range and the Yuha Desert and close to the international border(Figure 1). In this area, an intense aftershock sequence followed—including 40 events with magnitudegreater than 4—and culminated 72 days later in the 15 June 2010 Mw 5.7 Ocotillo earthquake, 20 km fromthe rupture terminus. There is also evidence that significant postseismic deformation occurred in the YuhaDesert [Huang et al., 2016; Pollitz et al., 2012; Rollins et al., 2015; Rymer et al., 2011], which suggests somerelationship with the seismicity.

Various physical mechanisms have been proposed to explain the triggering of aftershocks and theirspatiotemporal evolution. Aftershocks may reflect time-dependent failure in response to coseismic static[Ben-Zion and Lyakhovsky, 2006; Dieterich, 1994; Stein, 1999] or dynamic [Felzer and Brodsky, 2006] stresschanges. They may also be driven by coseismic fluid pressurization [Miller et al., 2004; Mulargia andBizzarri, 2015; Nur and Booker, 1972] or aseismic afterslip [Perfettini and Avouac, 2004]. We used amatched-filter technique to produce a detailed catalog of more than 155,000 aftershocks with M > �2(Figure 1). We show hereafter that the seismicity and geodetic observations of postseismic deformation illumi-nate multiple concurrent—but distinct—physical processes governing the evolution of the EMC sequence.

2. Data

We used continuous seismic data recorded between 4 April 2010 and 26 June 2010 by 112 stations of theSouthern California Seismic Network [Southern California Earthquake Data Center, 2013], which includes atemporary deployment of eight stations in the Yuha Desert following EMC [Kroll et al., 2013]. Only short-period and broadband seismometers were used. All phase data used were produced by SouthernCalifornia Seismic Network (SCSN). The waveform-relocated SCSN catalog [Hauksson et al., 2012] contains22,350 earthquakes in the study region during the period 2000–2016, and these were used as templateevents to search for additional earthquakes. Focal mechanisms used in the study were taken from thecatalog of Yang et al. [2012]. The seismicity catalog produced in this study is available as Data Set S1 inthe supporting information. The GPS data used are the filtered, nondetrended time series published bythe Scripps Orbit and Permanent Array Center [Bock and Haase, 2016].

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PUBLICATIONSGeophysical Research Letters

RESEARCH LETTER10.1002/2017GL074634

Key Points:• Approximately 155,000 aftershocksand geodetic observations illuminatetwo distinct processes driving the2010 El Mayor-Cucapah sequence

• Early aftershocks migrate away fromthe rupture terminus with thelogarithm of time and were likelydriven by afterslip

• Later aftershocks migrate with thesquare root of time and swarm-likebehavior and were likely driven byfluid diffusion

Supporting Information:• Supporting Information S1• Figure S1• Figure S2• Figure S3• Data Set S1• Movie S1• Movie S2

Correspondence to:Z. E. Ross,zross@gps.caltech.edu

Citation:Ross, Z. E., C. Rollins, E. S. Cochran,E. Hauksson, J.-P. Avouac, andY. Ben-Zion (2017), Aftershocks drivenby afterslip and fluid pressure sweepingthrough a fault-fracture mesh, Geophys.Res. Lett., 44, 8260–8267, doi:10.1002/2017GL074634.

Received 17 JUN 2017Accepted 2 AUG 2017Accepted article online 7 AUG 2017Published online 19 AUG 2017

©2017. American Geophysical Union.All Rights Reserved.

3. Methods3.1. Matched-Filter Earthquake Detection

We used a matched-filter algorithm [Ross et al., 2017; Shelly et al., 2016] to detect previously unidentifiedaftershocks in the EMC sequence. The matched-filter technique uses the records of P and S waves frompreviously identified events to scan continuous records and search for similar waveforms across the network[Kato et al., 2016]. P and Swaves templates were constructed using 2.5 s and 4.0 s windows, respectively, start-ing 0.25 s before the pick. If no S pick was available at a given station, a vp/vs ratio of 1.73 was used. P wavetemplates were taken from only the vertical component, while S wave templates used both horizontals.Template events selected had at least 12 phases with a signal-to-noise ratio greater than 5.0. Each templatewas then correlated against the continuous data in 24 h periods on the same stations and channels as thetemplate record. For a given template event and time period, correlation functions were shifted back in timeby an amount equal to the observed travel time of the template and stacked across all stations, channels, andphases. Preliminary detections were then made using a correlation trigger threshold of 8 times the medianabsolute deviation of the stack for the day, with the time of each trigger defining the origin time of thedetected event. Then, returning to the individual phase correlation functions, differential times weremeasured using a threshold of 7 times the median absolute deviation. At least four differential times wererequired for subsequent processing of a detected event, ensuring that the stacked correlation functionwas not dominated by just a single station. Detected events at this stage were assigned a location equal tothat of the best matching template event based on the average correlation coefficient. These steps resultedin a total of 155,795 aftershocks detected (including template events).

Figure 1. Map of Yuha Desert and El Mayor-Cucapah aftershocks. Top right inset shows tectonic setting of study area. Focalmechanisms [Yang et al., 2012] correspond to events with M > 4. Bottom left inset shows seismicity within 2 km of A-A0 ,coseismic slip [Wei et al., 2011], and aseismic slip (see section 3). The green line indicates the coseismic surface rupture fromoptical data [Wei et al., 2011], and black lines indicate faults [Fletcher et al., 2014]. The pink star denotes inferred origin offluid migration.

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Magnitudes were then calculated by taking the median peak amplitude ratio between the template anddetected event and adding the logarithm of this value to the magnitude of the template event [Peng andZhao, 2009]. Amplitude ratios were only calculated for phases with valid differential times. For the smallestevents with low signal-to-noise ratios, individual magnitude values have considerable uncertainty. For a morethorough description of the detection procedure, see Ross et al. [2017].

Each detected event was then correlated with the 200 nearest template events (in spatial distance) to add inadditional differential times, using P and S waves on all three components. For this procedure, windows for Pand S waves were 1.0 and 1.5 s long, respectively [Hauksson et al., 2012]. For each station, we saved at mostone differential time for each phase, choosing the value with the largest positive cross-correlation coefficient.For a given pair of events, a minimum of six differential times with correlation coefficients larger than 0.6 wasfurther required. This process resulted in 24.7 million differential times total for the data set, which were usedto relocate the catalog with the GrowClust algorithm [Trugman and Shearer, 2017]. The relocation parametersused were a minimum correlation coefficient of 0.6 and a minimum of eight differential times, which resultedin 66,337 events being relocated successfully (Figure 1).

3.2. GPS Data Processing and Inversion

To better understand the postseismic deformation in the Yuha Desert, we used GPS data from six nearby sta-tions in an aseismic slip inversion. First, we detrended the data by estimating the secular velocities due tointerseismic deformation, and annual and semiannual oscillations due to tidal, hydrological, thermoelastic,and/or other effects [Ben-Zion and Allam, 2013; Dong et al., 2002]. This was performed using a least squaresfit to the pre-EMC time series, and these signals were then subtracted from the entire time series. To ensurethat the representation of the preseismic signal was robust, we only used stations that had at least 2 years ofdata preceding EMC. A 7 day median filter was applied to the detrended time series, and the position on thefirst postseismic day was set as the zero-reference value. This is generally indistinguishable from the unfil-tered value. To then isolate the localized postseismic deformation in the Yuha Desert, we computed synthetictime series from a model of regional-scale postseismic processes [Rollins et al., 2015] and subtracted the syn-thetic time series from the detrended postseismic GPS time series. The regional-scale model also included ageneric afterslip source in the Yuha Desert, but we excluded this when subtracting the model.

Then, the residual time series were used in a slip inversion on a single right-lateral fault plane aligned withcross section A-A0 (Figure 1). The fault plane was extended 40 km laterally in both directions [Rollins et al.,2015] and downward to 50 km depth to prevent against boundary effects. Weights were determined fromthe variance of the first principal component as in the principal component analysis inversion method[Kositsky and Avouac, 2010]. The inversion was regularized using sensitivity-modulated Laplacian smoothing[Ortega, 2013], which enforces stronger penalization of the Laplacian in poorly resolved areas. The absoluteweight was chosen using the L curve approach of second-order Tikhonov regularization [Aster et al., 2012]. Tocalculate the total moment released, the afterslip distribution was integrated over space andmultiplied by anassumed shear modulus of 30 GPa.

3.3. Cluster Analysis

The highly segmented nature of the seismicity structures in the Yuha Desert promotes the possibility of iden-tifying spatially distinct clusters for detailed examination. We used the DBSCAN algorithm [Ester et al., 1996] toperform the cluster analysis in three dimensions. The algorithm has two parameters, a spherical radius, set to0.4 km, and a minimum number of events, set to 50. Varying the DBSCAN parameters over the ranges0.3–0.6 km radius and 50–200 minimum events had a negligible influence on the results. Applying the pro-cedure to all earthquakes in the catalog resulted in 276 clusters (Figure S1). For each cluster, we then onlykept events withM> 0.5, which was determined to be the magnitude of catalog completeness over the first70 days. A total of 56 clusters had at least 100 events and are used in the skewness and duration analysisdescribed below.

Then two different metrics were calculated for each cluster. The first was the statistical skewness of the origintimes within each cluster [Roland and McGuire, 2009],

s ¼1n

Pni¼1 ti � tð Þ3

1n�1

Pni¼1 ti � tð Þ2

h i3=2; (1)

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where ti is the ith origin time, t is the mean origin time, and n is the number of events in the cluster.

The second metric used was the effective duration, defined here as

IQR ¼ t90 � t10; (2)

where t90 and t10 are the 90th and 10th percentiles of the origin times within a cluster. Error estimates weredetermined by bootstrap resampling of the events within each cluster, calculating each metric for the newsample and repeating the process 1000 times.

4. Results

In the southeastern area beneath the Sierra Cucapah, a long horizontal lineament of aftershocks delineatesthe lower edge of the EMC rupture area [Wei et al., 2011], which is itself relatively devoid of aftershocks(Figure 1, bottom left inset). The northern terminus of the rupture edge coincides with a transition fromcrystalline and volcanic rocks in the south to unconsolidated sedimentary rocks in the north [Fletcher et al.,2014]. Farther north, in the Yuha Desert, the seismicity delineates a complex network of segmented orthogo-nal faults [Kroll et al., 2013] (Figure 1). Individual lineations have typical lengths of 2–3 km, are nonplanar, andpredominantly dip to the northeast. Focal mechanisms in the region are a mixture of strike-slip and normalfaulting [Yang et al., 2012]. Such cross-cutting fault patterns are common in the extensional-transtensionalenvironment of Southern California [Ross et al., 2017; Thatcher and Hill, 1991] and might be interpreted asfault-fracture meshes formed in the presence of fluids [Hill, 1977; Sibson, 1996]. In addition, there is extensivegeological evidence of hydrothermal activity in the Yuha Desert, including an abundance of mineralizationsignatures and metals [Isaac, 1987].

We first observe that the zone of aftershocks expanded away from the northern EMC rupture terminus withthe logarithm of time, over a distance of 30 km in a ~ 10 day period (Figure 2a). Afterslip following large earth-quakes is also believed to expand spatially with the logarithm of time [Kato, 2007; Perfettini and Avouac,2007], and a similar aftershock migration pattern following the 2004 Parkfield earthquake was inferred tobe driven by afterslip [Peng and Zhao, 2009]. Figure 1 shows the inferred afterslip distribution in the bottomleft inset, with the peak being nearly coincident with the rupture terminus and therefore the origin ofaftershock migration. The GPS vectors and best fitting model are shown in Figure 3a. Over the first 60 daysfollowing EMC, the geodetic data require that postseismic deformation released a moment of~1.44�1018 N m (equivalent to a Mw 6.04 earthquake). This is well in excess of the 9.8�1016 N m momentreleased by all detected aftershocks over the same period of time. If afterslip was the driving process behindthe early aftershocks, it should also have produced geodetic displacements that evolved in time like the

Figure 2. Spatiotemporal evolution of aftershocks. (a) Events are shown as binned counts, while events with M > 3.5 areshown as circles. Aftershock zone expands away from the rupture edge with the logarithm of time, suggestive ofafterslip. (b) Same as Figure 2a but with a square root time scale. Later events migrate away from the rupture edge with thesquare root of time, suggestive of fluid diffusion. Gap of large events (ellipse) is filled in 72 days later during the Ocotillosequence, which may have been triggered by fluids.

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cumulative number of aftershocks [Huang et al., 2017; Perfettini and Avouac, 2004; Villegas-lanza et al., 2016].Notably, we find a close correlation between these quantities at the closest GPS station to the Yuha Desert(Figure 3c). Thus, there is ample evidence that the aftershocks were initially triggered by a pulse ofaseismic afterslip that swept through the Yuha Desert.

Following this episode, a sequence of intensified seismicity punctuated byM> 3.5 events (Figure 2b) initiatednear the northern tip of the EMC rupture and migrated more than 15 km to the northwest with square roottime dependence. These events migrated slower than the afterslip front initially but expanded more rapidlyover the remaining 70 days of the sequence, culminating in theMw 5.7 Ocotillo earthquake. As Figure 4 shows,the overall pattern is well explained by a diffusion process originating from a single point at a depth of 8 km,near the rupture edge at the northern tip of the Sierra Cucapah (pink star in Figure 1). The space-time

evolution of the aftershocks follows r

¼ ffiffiffiffiffiffiffiffiffiffi4πDt

p, where r, D, and t are distance,

diffusivity, and time, respectively[Shapiro et al., 1997]. A diffusivity of6 m2 s�1 best matches the migrationalong A-A0 (Figure 4). These values andthe history of hydrothermalism in theregion suggest a fluid diffusion process,but we note that the elevatedtemperature in the area can lead byitself to a diffusion deformation process[Ben-Zion and Lyakhovsky, 2006]. Themigration appears much slower in thefault-normal direction (Figure 4; MovieS1), suggesting anisotropic permeabilitylikely controlled by fault zone structure.Brittle damage generated by the mainshock and aftershocks is expected tofurther increase the permeability in thefault zone [Hamiel et al., 2004]. The lackof migration across the coseismic rup-ture edge may reflect a permeabilitybarrier related to the change from sedi-mentary to crystalline rocks.

Figure 3. GPS postseismic displacement, afterslip model, and cumulative number of aftershocks. (a) Map of Yuha Desertregion and nearby GPS stations. Blue arrows denote “residual” postseismic displacements after 60 days, corrected for thecontribution of viscoelastic relaxation and afterslip using the model of Rollins et al. [2015]. Red arrows show the cumulativedisplacements predicted from the source model derived from the inversion of the residual time series. (b) Residualpostseismic times series andmodel prediction. Vertical lines denote error bars. (c) Comparison of the cumulative number ofaftershocks, afterslip (shown with 7 day median filter), and total horizontal displacement at P494.

Figure 4. Spatiotemporal evolution of events with M > 3.5, relative topink star in Figure 1. Black lines correspond to predictions from adiffusion model [Shapiro et al., 1997]. Blue line shows the logarithmicinitial expansion of the seismicity.

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Over the ~10 day period following EMC, numerous small earthquakes occurred at the eventual site of theOcotillo earthquake (red ellipse, Figure 2), but most of the area was devoid of large events (M > 3.5).However, 72 days after EMC the Ocotillo earthquake was triggered, which may have resulted from the effectof fluid migration. If true, this suggests that the pore pressure changes had a stronger effect at that time thanthe afterslip stress transfer early in the sequence. Movies S1 and S2 illustrate the migration of aftershocksacross the Yuha Desert region leading to the Ocotillo earthquake.

The evolving behavior is also reflected in the characteristics of individual aftershock clusters that occur as partof the broader sequence. A variety of empirical relationships have been developed to characterize the spatial,temporal, and magnitude progression of clusters [Utsu, 2002], and the parameters which govern these rela-tionships are often used to classify clusters into end-member categories of bursts and swarms [Zaliapin andBen-Zion, 2013]. Bursts are primarily composed of a single large main shock and aftershocks dominated byone generation with a power law decay rate and are associated with brittle processes in relatively coldregions [Ben-Zion and Lyakhovsky, 2006]. Swarms tend to have complex spatiotemporal histories with noidentifiable main shock and are associated with ductile processes in relatively hot areas and possibly fluidmigration or aseismic slip [Hauksson et al., 2017; Shelly et al., 2016; Vidale and Shearer, 2006]. We identifiedclusters as groupings of events that are spatially compact (Figure S1). The clusters trend from large positiveskewness to nearly zero skewness (symmetric) with increasing time after the EMC main shock (Figure 5).Bursts are associated with strongly positive skewness, while swarms are associated with near-zero skewness.We next examine cluster duration, defined as the time range spanned by the middle 80% of events. For clus-ters that had their largest event within the first few days after EMC, there are a wide range of cluster durations.From days 10 to 70, the cluster duration increases moderately with the time to the largest event in the cluster.Together, these complementary metrics suggest that the behavior of the EMC aftershocks evolved fromburst-like to swarm-like with time.

5. Discussion

To summarize, the Yuha Desert aftershocks of EMC exhibit the following features: (1) they delineate an ortho-gonal mesh of fault segments, (2) they expanded along strike away from the northern edge of the EMCrupture with a logarithmic time dependence, (3) they correlate spatially with and follow the same logarithmictime evolution as postseismic deformation, (4) seismicity accounts for only 6.8% of the postseismic deforma-tion, (5) another sequencemigrated away from the edge of the EMC rupture with the square root of time, and(6) aftershocks evolved from burst-like to swarm-like with time. The combination of afterslip and fluid migra-tion together with the underlying volumetric fault structure provides the most likely explanation for all theseobservations. We propose that the EMC rupture arrested at the onset of the Sierra Cucapah, where it encoun-tered a zone dominated by rate-strengthening frictional behavior [Kaneko et al., 2010]. From there, a pulse ofafterslip initiated, expanding rapidly across the Yuha Desert and triggering aftershocks throughout. Fluidspercolated throughout the deformation zone, starting from a point near the tip of the EMC rupture, and

Figure 5. Cluster evolution metrics. Points represent clusters with at least 100 events. Clusters trend from large positiveskewness and short duration to near-zero skewness and long duration, with increasing time to the largest event. Thesepatterns suggest that clusters become swarm-like over the course of the sequence.

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resulted in renewed seismic activity in the form of swarms and larger magnitude events. This second phaseultimately led to the Mw 5.7 Ocotillo earthquake 72 days after EMC. A similar association of creep, swarm-likeseismicity, fluids, and barrier effects has been suggested from studies of subduction megathrusts [Holtkampand Brudzinski, 2014; Moreno et al., 2014].

For most earthquake sequences, it is difficult to uniquely identify whether a fluid source triggered the earlyevents in a sequence or whether early earthquakes started the fluid migration. This sequence is a rare excep-tion with no such ambiguity, as the EMC hypocenter is located 60 km to the southeast of the inferred origin offluidmigration. This study demonstrates that diverse patterns in aftershock sequences can result from severalcooperating mechanisms under typical seismotectonic conditions for transtensional regimes. In fluid-saturated areas within or near a rupture, there is likely to be elevated aftershock rates, swarm-like activity,volumetric migration, and/or delayed triggering of large aftershocks. The spatiotemporal evolution of after-shocks in such regions is strongly affected by fault zone permeability, which is controlled by the dominantfault structures and reactivated at the time of large events.

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AcknowledgmentsWe thank the field teams from UCRiverside and UC Santa Barbara whoinstalled the temporary stations in theYuha Desert. The paper benefitted fromconstructive comments by twoanonymous reviewers and Shiqing Xu.All waveform data used are available atthe Southern California Earthquake DataCenter (scedc.caltech.edu), and all GPSdata used are available at SOPAC(sopac.ucsd.edu). The earthquakecatalog produced is available insupporting information as Data Set S1.This research was supported byUSGS/NEHRP grant G16AP00147; NSFawards: EAR-1550704 and EAR-1551411;and by the Southern CaliforniaEarthquake Center, which is funded byNSF Cooperative Agreement EAR-1033462 and USGS CooperativeAgreement G12 AC20038.

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