Aftershocks of the 2012 Off-Coast of Sumatra Earthquake Sequence
AAftershocks of the2012 O ff -Coast of Sumatra Earthquake Sequence Chengping Chai a, ∗ , Charles J. Ammon a , K. Michael Cleveland b a Department of Geosciences, The Pennsylvania State University, University Park, PA 16802, U.S.A. b EES-17:Geophysics, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, U.S.A.
Abstract
Aftershocks of the 2012 O ff -Coast of Sumatra Earthquake Sequence exhibit a complex and dif-fuse spatial distribution. The first-order complexity in aftershock distribution is clear and wellbeyond the influence of typical earthquake location uncertainty. The sequence included rup-ture of multiple fault segments, spatially separated. We use surface-wave based relative centroidlocations to examine whether, at the small scale, the distribution of the aftershocks was influ-enced by location errors. Surface-wave based relative location has delineated precise oceanictransform fault earthquake locations in multiple regions. However, the relocated aftershockso ff the coast of Sumatra seldom align along simple linear trends that are compatible with thecorresponding fault strikes as estimated for the GCMT catalog. The relocation of roughly 60moderate-earthquake epicentroids suggests that the faulting involved in the 2012 earthquake af-tershock sequence included strain release along many short fault segments. Statistical analysisand temporal variations of aftershocks show a typical decay of the aftershocks but a relativelylow number of aftershocks, as is common for intraplate oceanic earthquakes. Coulomb stresscalculations indicate that most of the moderate-magnitude aftershocks are compatible with stresschanges predicted by the large-event slip models. The patterns in the aftershocks suggest thatthe formation of the boundary and eventual localization of deformation between the Indian andAustralian plate is a complicated process. Keywords:
1. Introduction
Across most of the Earth, plate boundaries are well defined geologically and well delineatedby seismic activity. The boundary between the Australian and Indian Plates is one of a few ex-ceptions. Seismicity across the Indian Ocean Basin is characterized by di ff use activity that doesnot define a clear boundary (e.g. Wiens et al., 1985; Delescluse and Chamotrooke, 2007). Somepatterns are clear, for example a change in deformation style occurs from west to east across theNinety-East (90E) Ridge - compressive deformation predominates to the west and strike-slip de-formation dominates in the Wharton Basin to the east (Delescluse and Chamotrooke, 2007). Lack ∗ Corresponding author ([email protected]), now at Oak Ridge National Laboratory, Oak Ridge, TN 37830, U.S.A.
Preprint submitted to Tectonophysics May 13, 2019 a r X i v : . [ phy s i c s . g e o - ph ] M a y f a clearly defined boundary does not preclude the occurrence of very large earthquakes. The2012 O ff the Coast of Sumatra sequence included two great events (e.g. Yue et al., 2012). Theselarge earthquakes and their aftershocks occurred in the northernmost Wharton Basin, which ex-periences NNW oriented compressive stresses as a result of slab pull associated with subductionof the Indian Ocean lithosphere along the Sunda Arc, the continental collision between the Indiaand Eurasia plate to the north, and ridge push associated with Southeast Indian Ridge (Delescluseand Chamotrooke, 2007). The intraplate region has hosted numerous large earthquakes (e.g. An-tolik et al., 2006; Abercrombie et al., 2003; Aderhold and Abercrombie, 2016; Lay et al., 2016),none more spectacular than the 11 April 2012 sequence that began with an M W M W M W M W M W M W M W / s was inferred by Yue et al. (2012), although a later study claimedsupershear-rupture of 5 km / s (Wang et al., 2012). Notable di ff erences exist in the fault systemsinferred in early investigations (Meng et al., 2012; Wang et al., 2012; Yue et al., 2012), but allagree that the rupture was complicated and included strain release on numerous structures.Now, just over five years following the main strain release, information from aftershocks canbe exploited to explore the intraplate structures activated during these impressive earthquakes.In the years since the mainshocks, aftershock activity has continued and the initial, complicatedseismicity patterns have become slightly, but not completely well defined. The United StatesGeological Survey (USGS) catalog includes epicenter locations and depths for several hundredof events. Although of limited spatial extent, high-resolution bathymetric investigations providesome interesting clues to the involvement of en echelon fracture-zone reactivation and of con-jugate fracture-zone and shear-zone participation in deformation across the region (e.g. Cartonet al., 2014; Qin and Singh, 2015; Singh et al., 2017). In this work, we explore the patterns in theUSGS earthquake locations and the GCMT faulting geometries, and then use a surface-wave-based precise, relative epicentroid location technique (Cleveland and Ammon, 2013; Clevelandet al., 2015) to better quantify spatial relationships of moderate-magnitude events within severalof the key subclusters that comprise the overall complex aftershock pattern of this importantearthquake sequence.
2. Earthquake Catalog Aftershock Patterns
We examined the seismicity in the USGS ComCat and International Seismological Centre(ISC) catalogs, and the faulting geometry in the GCMT Catalog to investigate the aftershock2equence of these great oceanic, intraplate earthquakes. We begin with a descriptive review andthen integrate our relocation results with catalog information later in the discussion.The 2012 aftershock pattern reflects the complexity of the initial faulting, and lacks any clearindication of long simple structures originating near the epicenters of either of the two greatearthquakes (Fig. 1). Instead, the aftershocks spread within a two-dimensional pattern stretchingfrom near the Sumatra Trench to the Ninety-East Ridge and between the latitudes of roughly 1.5Nand 4.5N. The region is covered by several kilometers of Bengal-Fan sediments that obscure allbut the largest bathymetric features that could provide more clues to the structures participatingin the deformation. The 2012 aftershock zone has linear dimensions on the order of 500 kmand encompasses roughly 200,000 km . Many of the aftershocks occurred within the first week,immediately showing the complexity of the strain release of the large events and the complexstrain distribution within the Indian-Ocean lithosphere. Early strain release (first day) coveredan area roughly 130,000 km . The evolution of the pattern with time has clarified the overallgeometry of a number of the subclusters. But events within each cluster remain di ff use in someregions, only partly a result of uncertainties in event location.USGS epicentral locations for roughly 730 events within the region occurring since 01 January,2012 are shown in Fig. 2. We extracted hypocenters from the catalog within a polygon definedby the epicentral patterns extending west from the accretionary prism to and including the 90ERidge within the rectangular region bounded by corners at (-7N, 84E) to (7N, 96E). The figureshows aftershock patterns as they evolved from one week to one month to one year followingthe event. The fourth panel shows the 2012 foreshocks and all events in the sequence into April2018 (roughly six years). Most of the area that would eventually be involved in the strain releasewas active within the first week, and the di ff erence between one month and one year is minimal.The USGS event depth estimates are dominated by 511 events with fixed depths at 10 km, but ofthe 212 remaining all are shallower than 40 km, and most are shallower than 35 km. Howeverthe great majority of earthquakes without fixed depths are located below the oceanic crust.Over the last six years some lineations have become more apparent within the aftershocks,including (S, Fig. 2d) one stretching about 140-150 km with an azimuth of roughly 25N, whichis not that di ff erent from the GCMT point source model strike of 17N for the M W ff use is a roughly 200 km pattern(T) including the M W M W ff use nature of theoverall seismicity pattern continues to smaller spatial scales within each of the clusters.
3. Surface-Wave-Based Relative Earthquake Location
Since we are going to use waveform similarity to measure relative travel time di ff erences forsignals from di ff erent events, we must ensure that the earthquakes have similar faulting geome-tries (Cleveland and Ammon, 2013). Closely located earthquakes show similar waveforms atmost stations. Example waveforms from two earthquakes are shown in Fig. S1 of the electronicsupplement. We searched the Global CMT catalog for earthquakes in the focus region. Mostof the o ff -Sumatra aftershocks are strike-slip events, one is a normal faulting event and four arereverse faulting events. We focus our e ff ort on a sixty-one strike-slip faulting earthquakes. Rel-ative surface wave arrival times can be complicated by changes in strike and dip of the strikeslip events, but we examined all the azimuthal time-shift patterns to ensure the data used for therelocations are consistent. For the most part, time di ff erence from nearby event pairs show a con-sistent sinusoidal variation, which is associated with the relative position of the event epicentroid(Cleveland and Ammon, 2013). We have included two examples (Fig. S2 and Fig. S3) in thesupplementary document. The sinusoidal variation can be clearly seen in the figures.Our seismogram analysis procedure is similar to Cleveland and Ammon (2013). We corre-lated short-arc Rayleigh waves and Love waves seismograms to measure the relative time shiftsbetween similar waveforms. We used intermediate period (30-80 s period) signals recorded atstations operating at the time of the event and downloaded from the Incorporated Research Insti-tution for Seismology (IRIS) Data Management Center (DMC). Fig. 3 shows the seismic stationswe used for this study. The instrument-response was removed from the seismograms through afrequency-domain deconvolution. The bandwidth is chosen for several reasons: first, the groupslowness in this band is relatively constant for oceanic lithosphere, which simplifies the locationanalysis; second, the noise in this band is relatively low; third, the period range is relativelyinsensitive to modest changes in source depth (particularly for strike-slip sources); fourth, thelong wavelengths allow linking across relatively long distances. All waveforms were visually4nspected and assigned a quality grade based on the signal-to-noise ratio and character of the sur-face waves. The selected waveforms were graded from A (best) to F (worst) by visual inspectionof the signal quality. Only waveforms with quality better than C are used for further analysis.Examples of waveforms with di ff erent quality grades are shown in Fig. S4.The surface waves were isolated from the seismogram using a group slowness window of(0.2 to 0.4 s / km) and signals from nearby (within 150 km radius) events recorded at the samestation were cross correlated to estimate the relative time shifts and to form an interconnectingnetwork of event pairs. Based on previous studies (Cleveland and Ammon, 2013; Clevelandet al., 2015), only waveforms having normalized cross-correlation values larger than 0.9 fromtwo similar events are used in the relocation. The relative time-shifts from the higher qualitywaveforms are used in a linearized inversion of double-di ff erence time shifts to constrain rela-tive earthquake epicentroid locations. Surface-wave cross correlation time shifts are relativelyinsensitive to modest depth di ff erences. Since we are using signals with wavelengths of severalhundred kilometers, our inversion is in terms of the event spatial and temporal centroids and weuse the term epicentroid to represent the location on Earth’s surface above the rupture’s spatialcentroid. For simplicity, we refer to the time shifts as origin-time shifts, since most events aresmall and the centroid and origin times are close. Double di ff erences are calculated for all linkedevents and an iterative, nonlinear, inversion for the change in latitude, longitude, and origin timeis solved using a truncated SVD. Double-di ff erence partial derivatives are computed assuming auniform slowness (spatially and for the entire bandwidth). We usually select the slowness valueby using a grid search and choosing the value that produces the smallest changes in locationrelative to the original (USGS) locations. This often leads to only slight changes in the totalcentroid of all the epicenters. The inversion includes no direct absolute location constraints,but in practice the initial locations (USGS epicenters) provide some a priori information. Forinversion result assessment, individual event-pair patterns were visually inspected to check thequality of the data, which should exhibit a sinusoidal pattern for events with similar mechanismsand depths.The inversion for relative earthquake locations is the same as that used in Cleveland et al.(2015). A spherical-earth version of the double-di ff erence relocation approach (Waldhauseret al., 2000) is applied to measurements from short-arc surface waves. A linearized inversion isconstructed relating the observed and predicted surface-wave arrival time di ff erences to changesin earthquake epicentroid position and origin time. A constant slowness is assumed since thefirst-order seismic structure variations between events are negligible for the 30-80 s period rangein which time shifts are measured. We used slownesses of 0.257 s / km for Rayleigh wave and0.223 s / km for Love wave measurements based on values from a global dispersion model (Ek-str¨om, 2011). We tested the results using a range of reasonable slowness values to verify thatthe general patterns in the relocations are only mildly sensitive to the specific assumed slowness.Larger slowness values produce larger location shifts from the initial locations, lower slownessvalues lead to smaller location shifts. Similar to Cleveland et al. (2015), we allow earthquakeswithin 150 km to be linked as long as at least 12 common stations are available. A linking cri-teria based on the azimuth distributions of stations was also applied to assure linked events havea su ffi cient azimuth coverage. The azimuth coverage is reasonable for the linked events. Thestation coverage for two of the linked events is shown in Fig. S5. After three iterations, the misfitto observations improved significantly as shown in Fig. 4. The RMS misfit for the final locationsis about 1.3 s, reduced from the initial misfit of about 5.2 s. We visually examined data fits forall the linked event pairs. The azimuthal coverage is not optimal for some smaller events dueto sparse station coverage to the south. However, a recognizable cosine pattern exists for most5vents and we ignore poorly constrained events in our subsequent discussion.To verify the relocation results, we performed several synthetic tests similar to Cleveland andAmmon (2013) and Wang et al. (2018). Assuming the station coverage is the same as thatin Fig. S5, surface-wave seismograms for five hypothetical earthquakes were simulated withthe Computer Programs in Seismology package (Herrmann, 2013) using the AK135 velocitymodel (Kennett et al., 1995). We assume these five Mw 5.5 earthquakes were located on a linearfault striking in the N-S direction. The seismograms were computed with the true locations ofthese earthquakes. Incorrect locations were then assigned to these seismic events. The double-di ff erence relocation algorithm was used to improve the earthquake locations from the incorrectones. For the first synthetic test, we assume all the earthquakes have the same strike-slip focalmechanism and focal depth (5 km). The relocation results and a time-shift plot are shown in Fig.S6 and S7, respectively. Though the absolute locations of these earthquakes are shifted togetherto the southeast in respect to the true locations, the relative locations of the earthquakes are wellrecovered. If we shift the centroid of the inverted locations to the centroid of the true locations,the di ff erence between the inverted locations and the true locations are around 1 km on average.For the second test, we assume a di ff erent focal depth (5, 10, 15, 20, and 25 km) for each of thefive earthquakes. The relocation results are almost the same as those for the first test. For thethird, forth and fifth synthetic test, the dip, rake, and strike of the five earthquakes was perturbedbased on distributions measured from real data in the region. We found that variations in strikedoes not change the relocation results. Perturbations on dip and rake leads to larger errors inthe location. However, the inverted locations are much better than the initial locations. Ignoringthe centroid shift, the location errors are less than 2 km for all of these five synthetic tests. Thelocation errors are around 4 km if we account for the centroid shift, which agrees with results byWang et al. (2018).
4. Results
Fig. 5 is a map of the relocated epicentroids (center of focal mechanisms) and the originalUSGS locations (yellow circles). At this scale, the di ff erence in many locations is modest butas described above, the new locations fit the observations significantly better than the initiallocations. Since the location changes are too small to show for the entire study area on one map,we separate the relocated events into clusters and discuss each individually. We summarize theoverall location shift from the USGS catalog in Fig. 6. Origin times after relocation did notchange dramatically except for a few events and the average origin time shift from the USGScatalog times is zero. With one exception, the relocated epicentroids shifted less than 26 km.The 29 April, 2012 event ( M W
5) was shifted 46 km. Even for that event, located near thecenter of the study area, the visual fit to the observed sinusoidal time shift pattern (with azimuth)after inversion is good. On average the epicentroid locations shifted about 10 km from the initialUSGS positions (the median shift was 8 km). The standard deviation of the location shift is 8 km.The location changes are about two times smaller than similar investigations of earthquakes alongoceanic transform faults (Cleveland and Ammon, 2013; Cleveland et al., 2015). We computedformal least-squares uncertainties estimates (Kintner et al., 2018) assuming uncorrelated and auniform data variance of two seconds (double our final RMS misfit, to be conservative). Mostestimated uncertainties are less than three kilometers and the less well-constrained epicentroidsare roughly twice that in both latitude and longitude directions. While these formal uncertaintiesare useful for identifying the better constrained data, they are approximate since they excludeinformation on faulting geometry and slowness uncertainties. The estimated uncertainties are6omparable to what has been found at oceanic transform fault boundaries, where bathymetrycorroborates the results. Including insight gained from experiments with varying the slownessand focal parameters, we feel that less than five kilometers is a reasonable estimate of the relativeepicentroid uncertainties.To explore the relocations, we examine eight event clusters identified in Fig. 5. Maps for theindividual clusters are included in the online supplement. Little of the aftershock region hasdetailed bathymetric information making simple bathymetric validation of the trends di ffi cult.Only one region has detailed bathymetry, so we begin our review with Cluster B. Cluster B locates in the only region with high-resolution bathymetric information. We canuse this information to test the consistency of locations similar to what was done by Clevelandand Ammon (2013); Cleveland et al. (2015) using oceanic transform related bathymetry. InFig. 7, we overlay background seismicity and relocated earthquakes onto a fracture- and shear-zone map that was derived from high-resolution bathymetry and a reflection survey (Singh et al.,2017). Although we have limited absolute location information, event B1 ( M W / / M W / / M W / / M W M W M W M W ff set east fromthe three-event cluster by about 20 km, which may indicate that as much as 20-30 kilometers ofnearby fracture zones participated in the large event (the region between the roughly east-westshear zones in the bathymetric model). Event B5 is o ff to the west, and appears consistent withseismic failure along the conjugate shear zones identified by Singh et al. (2017). The unlabeledevent to the south is discussed with the cluster D, which is south of this region. Changing theslowness moves the events slightly, but never moves events B1-B4 out of the fracture zone region,nor B5 from the shear zone environment, and does not alter any of the relative location trends ofthe events. The biggest impact is on repositioning the cluster centroid by less than about 10-15km. Subcluster A (Fig. S8 in the electronic supplement) locates in the epicentral region of the M W . ff erence in frequency content for events of suchdi ff erent seismic moment. Thus we cannot provide precise locations of events relative to the M W . ◦ o ff the strike of either plane in the GCMT focalmechanisms. Teleseismic body-wave backprojection and finite-fault models (e.g. Yue et al.,2012) suggest failure of a large structure oriented closer to the GCMT strike directions than thesparsely aligned epicentroid locations in this cluster. We do not think these epicentroids identifya single significant structure. Our locations again suggest en echelon faulting, and show littleevidence of aftershock activity on any large scale structure in the M W . Short and long period analyses (Duputel et al., 2012) suggest that significant strain releasealso occurred in the region of Cluster C and A’ (Fig. S9 in the electronic supplement) during the M W .
6. Relocation brings the four moderate-size aftershocks within Cluster C into a near-linearalignment, but again the alignment is in a direction (NNW) that is at odds with the individualevent faulting geometries and the average faulting geometry of the mainshock. The sparse num-ber of moderate and larger magnitude events again suggests that the aftershocks are occurringalong en echelon structures adjusting to mainshock slip, not illuminating a principal structureinvolved in the large event.
Subcluster D (Fig. S10 in the electronic supplement) is presumably along the southern extentof the M W . M W . M W / /
11) and M W / / Observations are sparse for Cluster E (Fig. S11 in the electronic supplement), which providedsix surface-wave relocatable aftershocks. The general trend of epicentroid locations is 325N (az-imuth), which again is di ffi cult to reconcile with the orientation of the GCMT faulting geometryestimates. The two easternmost events do not link to many other events, but do link to a wellconnected event slightly north. The location of the southernmost event may not be well locatedbecause the correlations do not form a tight, consistent cosine pattern. The easternmost eventshows a pattern that indicates it is east of the trend formed by the other events. Clusters F and G (Fig. S12 in the electronic supplement) are located within the Ninety-EastRidge. Only one pair of events align closely along one of the GCMT strikes. However, therelocation of one of the two events is not well constrained due to lack of event links. The depths ofthese events range from about 12 to 30 km. We observe some systematic Love and Rayleigh wavedi ff erence in misfit for the deepest event, but the overall sinusoidal pattern is robust. Whether the8 ff ect is a result of di ff ering fault strikes or depth is unclear. In any case, the epicentroids forma T-shaped pattern with trends that align in a roughly north-south and ESE-WNW directions.The alignments do not correlate with the GCMT focal mechanism orientations, which remainconsistent with the mechanisms throughout the aftershock area. Cluster H (Fig. S13 in the electronic supplement) is located north of clusters F and G, andconsists of four relocated strike-slip events. Three of the four events have depth estimates (thefourth was fixed) and all are roughly at about 25 km depth. Again, the centroid locations do notform a simple consistent pattern with the fault orientations contained in the GCMT catalog. Eventhree events within 10-20 km of each other do not show any simple pattern.
5. Discussion
The 2012 sequence aftershocks illuminate a complex fault system that includes several longlinear epicentral patterns (Fig. 2) that may be associated with primary structures that failed dur-ing the great events of 2012. But when examined closely with information on individual eventfaulting geometry and precise relative locations, the moderate-magnitude earthquakes show thatthe trends represent structures more complex than simple through-going faults. The relation-ships between location patterns and GCMT faulting geometry (which we believe is accurate) ismuch more complex than what has been seen in typical oceanic transform environments, wherethe epicentroid location and GCMT faulting geometry strike estimates (Cleveland and Ammon,2013; Cleveland et al., 2015) are quite consistent.Very conservatively, the great earthquakes in the 2012 sequence must have ruptured structuresat least a few 10’s of kilometers long, and probably those structures likely approached lengthsof one hundred kilometers. But no such structures are well illuminated by moderate-size after-shocks. In the epicentral region of the mainshock, the alignments are inconsistent with estimatedmainshock faulting geometry, which is of course complicated because it is an average of themoment tensors representing multiple sub-events involved in the earthquake (e.g. Duputel et al.,2012; Yue et al., 2012). The aftershock faulting patterns are generally consistent with the M W M W M W M W ff er enough to requireen echelon rupture of at least two fracture zone segments (e.g. Singh et al., 2017). The relocatedepicentroids in Clusters B and D suggest that if the M W M W . M W M W M W M W ff usenature of the clustering aftershock activity is not an artifact of location, but is an intrinsic charac-teristic of the deformation during the 2012 earthquake sequence. Synthetic experiments indicatesimple linear trends can be recovered with the surface-wave double-di ff erent technique if suchtrends exist.The magnitude and temporal patterns that have evolved over the last five years also show someinteresting character. The temporal history of aftershock activity is summarized in Fig. 8, whichincludes a magnitude time line and an Omori decay histogram. We used a bin width of 28 daysfor the event counts and the Omori display is clipped - the number of events in the first bin (in-cluding the great events) includes 400 events. Roughly 45% of the aftershocks occurred in thefirst week, 58% in the first month, and 78% in the first year. The aftershock decay pattern isnot steady, occasional moderate and strong events within the aftershock area produce aftershocksequences within the tail of the overall distribution. An interesting apparent periodicity seems todominate the first few years of the sequence, which may suggest tidal aftershock triggering, butcould also be an artifact. The decay of aftershocks for the 2012 sequences seems relatively slug-gish. Following a rapid decay in the number of aftershocks in the first week to month, the decayin subsequent years is hard to detect (Fig. 8). A slow decay is expected for intraplate earthquakesince it is consistent with rate-state friction models (Dieterich, 1994) or viscous dissipation pro-cesses (e.g. Ziv and Cochard, 2006) that suggest that the decay rate of aftershocks is inverselyrelated to stress or tectonic loading processes. Stein and Liu (2009) used these ideas to explorethe possibility that large intraplate earthquake aftershock sequences may in fact last for hundredsof years.To better quantify the decay of the 2012 earthquake aftershock sequence, we examined thetemporal distribution of the aftershocks by fitting the modified Omori relationship (reviewed inAppendix A Utsu, 1971). In Fig. 9, we show the fit to the modified Omori Law for the 2012 M W M W K , c , and p in the modified Omori relationship are estimated by minimizing themisfit between observations and predictions. The fit associated with the optimal parameters aresatisfactory for both events as shown in Fig. 9. The decay parameter p of 1.0 for the 2012 eventand of 0.8 for the 2005 event is typical comparing to other significant earthquakes (Shcherbakovet al., 2013). The estimated parameters of the modified Omori Law are summarized in Table 1.Fig. 10 includes a plot of the USGS and ISC magnitude distributions of the 2012 M W M W ff erence in the strainrelease pattern with a standard mainshock-aftershock sequence, it is not surprising that the usualpattern is not found. Between magnitudes of 4.0 to 6.5, the b-value is reasonably well approxi-mated by unity (solid line in the figure). These numbers, however, are consistent with what wouldtypically be observed following a magnitude 7 mainshock. The number of events with smallermagnitudes is substantially lower than that expected for the large events in the sequence. Thedashed lines project from the mainshock magnitude and 1.2 unit less (roughly accommodatingBåth’s Law, Båth, 1965) with a slope of minus one. Both lines suggest that we might have ex-pected substantially more aftershocks than were observed. The pattern shows that similar to otherearthquake sequences in oceanic lithosphere such as oceanic transforms (e.g. Boettcher and Jor-dan, 2004) and deep earthquakes (Frohlich, 2006), the 2012 aftershock sequence produced feweraftershocks than typical. Only the large size of the two great earthquakes induced the hundredsof events observed across this broad region. The estimated parameters of the Gutenberg-Richterrelationship are summarized in Table 1. For both the 2005 and 2012 sequences, the frequency-magnitude curve starts to deviate from the linear relationship for events with magnitude less thanfour, which indicates the catalogs are complete for magnitude larger or equal to four.The 2012 great earthquakes were unusual and so it is no surprise that the aftershock patternsare also unusual. Perhaps the lack of aftershocks illuminating large structures is a result of arelatively uniform lithospheric structure (compared to plate boundary and continental regions)around what are likely relatively low-cumulative-o ff set faults (e.g. Hill et al., 2015). A lack ofheterogeneity may result in a lack of focusing of stress onto smaller structures that commonlyin other systems host aftershocks. Although not all, some have argued for super-shear ruptureduring the two great events, which is also consistent with observations of a lack of aftershocksin regions suspected of super-shear rupture along continental transform faults (e.g. Bouchon andKarabulut, 2008).Finally, although complex, the distribution of aftershocks is compatible with the stress changesexpected from models of the large-event slip distributions. First-order compatibility is expectedsince the aftershocks were used to identify likely rupture surfaces in the models. But consistencyextends to regions o ff the fault segments as well. Figure 11 is a plot of the maximum and averagecoulomb stress changes induced by the rupture model (e.g. Yue et al., 2012). The Coulombstress changes were calculated using the Coulomb 3.3 package (Lin and Stein, 2004; Toda et al.,2005) from USGS. We experimented with receiver faults corresponding to both stress-optimalorientations and to a specific orientation. When optimal orientations were chosen, the Coulombstress changes do not agree well with the aftershock locations. Since the faulting geometry ofmost of these aftershocks is similar, we computed stress changes for a fault with a strike similar11o the aftershock GCMT faulting geometry estimates. A range of friction parameters, dip angles,and the auxiliary planes were explored. For reasonable variations in these parameters, Coulombstress changes show similar patterns. We present both the maximum and average stress changes(for a fault with a strike of 107, a dip of 75, and a rake of 180). We do not know a precise depth formany of the aftershocks, which could have occurred at di ff erent depths. Most aftershock depthestimates are within the upper 30 km. Both stress-change patterns are quite similar except veryclose to the mainshock rupture surfaces. The calculations show a reasonable agreement betweenpredicted Coulomb stress increase and the moderate-magnitude aftershock locations. Many ofthe aftershocks that are too small for our location procedure also match with the Coulomb stressincrease. Only a few exceptions exist, but consistent with our discussions above, not all regionsexpected to have increased stress produced aftershocks. The event produced fewer than expectedaftershocks and very few align along the large-event ruptures.
6. Conclusion
The relative relocation of roughly 60 moderate-earthquake epicentroids suggests that after-shock faulting involved in the 2012 o ff -shore Indonesia sequence occurred in a region populatedwith many short fault segments. Unlike observed patterns along relatively mature transformfaults, the relocated events seldom align along simple linear trends that are compatible with thestrikes of the faults as estimated by the GCMT catalog. The lack of long, coherent structuressuggests that the aftershocks are accommodating strain adjustments nearby, but o ff the largerstructures that participated in the 2012 great earthquakes. The 2012 sequence has a relativelylow number of aftershocks, which is similar to other fault ruptures in oceanic lithosphere. Thedecay of the aftershock rates are typical compared to other large events. Taken together, modelsof the rupture and the patterns in the aftershocks suggest that the eventual localization of defor-mation between the Indian and Australian plate is a complicated process still straining a largearea beneath the northeastern Indian ocean.
7. Acknowledgements
This work was supported by the Defense Threat Reduction Agency under Award HDTRA1-11-1-0027. This material is based upon work partially supported by the U.S. Department ofEnergy, O ffi ce of Science, under contract number DE-AC05-00OR22725. The facilities of IRISData Services, and specifically the IRIS Data Management Center, were used for access thewaveforms, related metadata, and / or derived products used in this study. IRIS Data Servicesare funded through the Seismological Facilities for the Advancement of Geoscience and Earth-Scope (SAGE) Proposal of the National Science Foundation under Cooperative Agreement EAR-1261681. The authors thank Monica Maceira and Philip Bingham for helpful comments. Weacknowledge developers of Generic Mapping Tools (Wessel et al., 2013), Obspy (Beyreutheret al., 2010; Megies et al., 2011; Krischer et al., 2015), Numpy (van der Walt et al., 2011),and Matplotlib (Hunter, 2007) for sharing their packages. We also thank University of Califor-nia San Diego for sharing the STRM15 topography data that were used as the background forseveral figures. This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains andthe publisher, by accepting the article for publication, acknowledges that the US governmentretains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the pub-lished form of this manuscript, or allow others to do so, for US government purposes. DOE12ill provide public access to these results of federally sponsored research in accordance withthe DOE Public Access Plan (http: // energy.gov / downloads / doe-public-access-plan). We thankan anonymous review and the Editor Rob Govers for constructive comments and suggestions.13 Indian Plate Australian PlateSunda Plate N i ne t y E a s t R i dge W W W W mm / y r mm / y r Mag 5 4 3M8M7M6M5
Figure 1: Regional seismicity of the o ff -Sumatra region between January 2012 and February 2016. Focal mechanismfrom GCMT catalog are shown with red (strike-slip and one normal faulting) and gray (reverse faulting) beach balls.Magnitude 3 and larger earthquakes from ISC catalog (International Seismological Centre, 2014) are shown as opencircles. Two stars indicate the GCMT centroids of the 2004 M W M W Figure 2: Maps of USGS seismicity showing intraplate events in the vicinity of the 2012 earthquake sequence. Eventswith magnitudes less than 7 are identified by circles scaled logarithmically to four times the expected rupture area foran earthquake with the corresponding magnitude (assuming a simple earthquake model). Epicenters for larger events areindicated by white circles scaled to roughly the rupture area expected for their magnitudes. The panel in the upper leftshows the events occurring within one week of the mainshock ( M W igure 3: A Map showing the seismic stations tried (gray triangles) and used (red triangles). The red box indicates wherethe earthquakes of this study are located. Plate boundaries (blue lines) are based on Bird (2003).
20 15 10 5 0 5 10 15 20
Double Difference Residuals (s) C oun t InitialFinal
Figure 4: Initial and final misfits for the inversion of observations from 61 strike-slip earthquakes. Initial misfit iscomputed based on USGS epicenter locations and origin times. B AFG H EDCA’
Figure 5: Relocated epicentroids (red beach balls) from this study compared to original USGS locations (yellow dots).Black lines indicate location shifts between relocated epicentriods and USGS locations. The green beachballs are the twogreat earthquakes occurred on April 11, 2012. Red beachballs represent other events used in the relocation. Gray linesshow the event links. Open circles show earthquake locations from USGS catalog. The boxes (dashed line bounded)indicate locations for 8 sub clusters. The large solid dots show the two-point locations associated with the M W
10 20 30 40 50
Shift from USGS Epicenter (km) C oun t Shift from USGS Origin Time (s) C oun t Mean: 9.3 kmMedian: 8.2 kmStd. Dev.: 7.8 kmMean: 0.0 sMedian: 0.0 sStd. Dev.: 2.9 s(a)(b)
Figure 6: Histograms show comparison of the epicentroid locations with the original USGS locations. B1B2B3B4 B5
Figure 7: A close view of the relocated epicentroids (red beachballs) around the 2012 / / M W .19
112 0 112 224 336 448 560 672 784 896 1008 1120 1232 1344 1456 1568 1680
Day After Mainshock01020304050 C oun t C oun t M agn i t ude (c)(b)(a) Figure 8: Temporal variation of the seismicity from 2012 to 2017. Top panel shows a simple magnitude timeline starting01 January, 2012. Time reference is the mainshock origin (12 April, 2012, 08:38). Bottom panel shows histogram ofaftershock counts using bin widths of 28 days. The decay of activity was initially rapid (the mainshock bin is clipped),started out with some periodic behavior, and decayed slowly, similar to other intraplate earthquakes. Days after the main shock10 F r equen cy pe r da y w Days after the main shock10 F r equen cy pe r da y w Figure 9: Analysis results of the modified Omori’s law for the 2012 M w w Log [ N ( M ) ] w Log [ N ( M ) ] w Figure 10: Gutenberg-Richter plots for the 2012 M W M W M W aximum Stress Change90˚ 92˚ 94˚−1˚0˚1˚2˚3˚4˚5˚ 90˚ 92˚ 94˚−1˚0˚1˚2˚3˚4˚5˚ 0 100km −0.4−0.20.00.20.4 C hange i n C ou l o m b S t r e ss ( M P a ) Average Stress Change90˚ 92˚ 94˚−1˚0˚1˚2˚3˚4˚5˚ 90˚ 92˚ 94˚−1˚0˚1˚2˚3˚4˚5˚ 0 100km
Figure 11: Maximum (left) and average (right) static coulomb stress changes in the depth range of 0-30 km using the finitefault model from Yue et al. (2012). Circles identify USGS aftershock locations, the focal mechanisms identify GCMTfaulting estimates shown at the centroid locations estimated in this study. Warm colors indicate regions of increasedstress in a favorable orientation to produce faulting, cooler colors show regions where aftershock faulting is less likely. able 1: Summary of the Estimated Parameters of the Empirical Relationships Event Date Magnitude a-value b-value
K C p / /
28 8.6 7.2 1.0 124 0.07 0.82012 / /
11 8.6 7.0 1.0 61 0.02 1.023 ppendix A. Gutenberg-Richter Relationship & Modified Omori Law
The frequency-magnitude statistics of an earthquake sequence have been found to fit theGutenberg-Richter relationship (Gutenberg and Richter, 1954) log N ( ≥ M ) = a − bM (A.1)where N ( ≥ M ) is the cumulative number of earthquakes with magnitudes larger than or equalto M . a and b are constants.The temporal change of an earthquake sequence can be modeled by the modified Omori law(Utsu, 1971) r ( t ) = K ( t + C ) p (A.2)where r ( t ) is the occurrence rate of aftershocks at time t . K , c , and p are constants. ReferencesReferences
Abercrombie, R. E., Antolik, M., Ekstr¨om, G., 2003. The June 2000 M-w 7.9 earthquakes south of Sumatra: Deformationin the India-Australia Plate. Journal of Geophysical Research 108 (B1), ESE 6 1–16.Aderhold, K., Abercrombie, R. E., May 2016. Seismotectonics of a di ff use plate boundary: Observations o ff the Sumatra-Andaman trench. Journal of Geophysical Research 121 (5), 3462–3478.Ammon, C. J., Ji, C., Thio, H.-K., Robinson, D., Ni, S., Hjorleifsdottir, V., Kanamori, H., Lay, T., Das, S., Helmberger,D., Ichinose, G., Polet, J., Wald, D., 2005. Rupture Process of the 2004 Sumatra-Andaman Earthquake. Science308 (5725), 1133–1139.Antolik, M., Abercrombie, R. E., Pan, J., Ekstr¨om, G., 2006. Rupture characteristics of the 2003 Mw7.6 mid-IndianOcean earthquake: Implications for seismic properties of young oceanic lithosphere. Journal of Geophysical Research111 (B4), B04302.Båth, M., 1965. Lateral inhomogeneities of the upper mantle. Tectonophysics 2 (6), 483–514.Beyreuther, M., Barsch, R., Krischer, L., Megies, T., Behr, Y., Wassermann, J., May 2010. ObsPy: A Python Toolbox forSeismology. Seismological Research Letters 81 (3), 530–533.Bird, P., Mar. 2003. An updated digital model of plate boundaries. Geochemistry Geophysics Geosystems 4 (3), 1027.Boettcher, M. S., Jordan, T. H., Dec. 2004. Earthquake scaling relations for mid-ocean ridge transform faults. Journal ofGeophysical Research 109 (B12), B12302.Bouchon, M., Karabulut, H., Jun. 2008. The Aftershock Signature of Supershear Earthquakes. Science 320 (5881),1323–1325.Carton, H., Singh, S. C., Hananto, N. D., Martin, J., Djajadihardja, Y. S., Udrekh, Franke, D., Gaedicke, C., Jan. 2014.Deep seismic reflection images of the Wharton Basin oceanic crust and uppermost mantle o ff shore Northern Sumatra:Relation with active and past deformation. Journal of Geophysical Research 119 (1), 32–51.Cleveland, K. M., Ammon, C. J., Jun. 2013. Precise relative earthquake location using surface waves. Journal of Geo-physical Research 118 (6), 2893–2904.Cleveland, K. M., VanDeMark, T. F., Ammon, C. J., Oct. 2015. Precise relative locations for earthquakes in the northeastPacific region. Journal of Geophysical Research 120 (10), 6960–6976.Delescluse, M., Chamotrooke, N., Feb. 2007. Instantaneous deformation and kinematics of the India-Australia Plate.Geophysical Journal International 168 (2), 818–842.DeMets, C., Gordon, R. G., Argus, D. F., Apr. 2010. Geologically current plate motions. Geophysical Journal Interna-tional 181 (1), 1–80.Dieterich, J., 1994. A Constitutive Law for Rate of Earthquake Production and Its Application to Earthquake Clustering.Journal of Geophysical Research 99 (B2), 2601–2618.Duputel, Z., Kanamori, H., Tsai, V. C., Rivera, L., Meng, L., Ampuero, J.-P., Stock, J. M., Oct. 2012. The 2012 Sumatragreat earthquake sequence. Earth and Planetary Science Letters 351-352, 247–257.Ekstr¨om, G., Dec. 2011. A global model of Love and Rayleigh surface wave dispersion and anisotropy, 25-250 s. Geo-physical Journal International 187 (3), 1668–1686. kstr¨om, G., Nettles, M., Dziewo´nski, A. M., Jun. 2012. The global CMT project 2004–2010: Centroid-moment tensorsfor 13,017 earthquakes. Physics of the Earth and Planetary Interiors 200-201, 1–9.Frohlich, C., 2006. Deep earthquakes. Cambridge university press.Gutenberg, B., Richter, C. F., 1954. Seismicity of the Earth and Associated Phenomena. Princeton Univ. Press, NewJersey.Herrmann, R. B., 2013. Computer Programs in Seismology: An Evolving Tool for Instruction and Research. Seismolog-ical Research Letters 84 (6), 1081–1088.Hill, E. M., Yue, H., Barbot, S., Lay, T., Tapponnier, P., Hermawan, I., Hubbard, J., Banerjee, P., Feng, L., Natawidjaja,D., Sieh, K., May 2015. The 2012 Mw 8.6 Wharton Basin sequence: A cascade of great earthquakes generated bynear-orthogonal, young, oceanic mantle faults. Journal of Geophysical Research 120 (5), 3723–3747.Hunter, J. D., 2007. Matplotlib: A 2D Graphics Environment. Computing in Science & Engineering 9 (3), 90–95.International Seismological Centre, 2014. On-line Bulletin. Internatl. Seismol. Cent., Thatcham, United Kingdom,http: // ff use oceanic deformation zone between theIndian and Australian Plates. Geophysical Research Letters 43 (15), 7937–7945.Lin, J., Stein, R. S., Feb. 2004. Stress triggering in thrust and subduction earthquakes and stress interaction between thesouthern San Andreas and nearby thrust and strike-slip faults. Journal of Geophysical Research 109 (B2), 589.McGuire, J. J., Beroza, G. C., Jun. 2012. A Rogue Earthquake O ff Sumatra. Science 336 (6085), 1118–1119.Megies, T., Beyreuther, M., Barsch, R., Krischer, L., Wassermann, J., 2011. ObsPy - What can it do for data centers andobservatories? Annals of Geophysics 54 (1), 47–58.Meng, L., Ampuero, J. P., Stock, J., Duputel, Z., Luo, Y., Tsai, V. C., Aug. 2012. Earthquake in a Maze: CompressionalRupture Branching During the 2012 Mw 8.6 Sumatra Earthquake. Science 337 (6095), 724–726.Qin, Y., Singh, S. C., Sep. 2015. Seismic evidence of a two-layer lithospheric deformation in the Indian Ocean. Naturecommunications 6, 8298.Shcherbakov, R., Goda, K., Ivanian, A., Atkinson, G. M., Nov. 2013. Aftershock Statistics of Major Subduction Earth-quakes. Bulletin of the Seismological Society of America 103 (6), 3222–3234.Singh, S. C., Hananto, N., Qin, Y., Leclerc, F., Avianto, P., Tapponnier, P. E., Carton, H., Wei, S., Nugroho, A. B.,Gemilang, W. A., Sieh, K., Barbot, S., Jan. 2017. The discovery of a conjugate system of faults in the Wharton Basinintraplate deformation zone. Science Advances 3 (1), e1601689.Stein, S., Liu, M., Nov. 2009. Long aftershock sequences within continents and implications for earthquake hazardassessment. Nature 462 (7269), 87–89.Tajima, F., Kanamori, H., 1985. Global Survey of Aftershock Area Expansion Patterns. Physics of the Earth and PlanetaryInteriors 40 (2), 77–134.Toda, S., Stein, R. S., Richards-Dinger, K., Bozkurt, S. B., 2005. Forecasting the evolution of seismicity in southernCalifornia: Animations built on earthquake stress transfer. Journal of Geophysical Research 110 (B5), 97.Utsu, T., Mar. 1971. Aftershocks and Earthquake Statistics(2) : Further Investigation of Aftershocks and Other Earth-quake Sequences Based on a New Classification of Earthquake Sequences. Journal of the Faculty of Science,Hokkaido University. Series 7, Geophysics 3 (4), 197–266.van der Walt, S., Colbert, S. C., Varoquaux, G., 2011. The NumPy Array: A Structure for E ffi cient Numerical Computa-tion. Computing in Science & Engineering 13 (2), 22–30.Waldhauser, F., Waldhauser, F., Ellsworth, W. L., Ellsworth, W. L., Dec. 2000. A Double-Di ff erence Earthquake LocationAlgorithm: Method and Application to the Northern Hayward Fault, California. Bulletin of the Seismological Societyof America 90 (6), 1353–1368.Wang, D., Mori, J., Uchide, T., Nov. 2012. Supershear rupture on multiple faults for the Mw 8.6 O ff Northern Sumatra,Indonesia earthquake of April 11, 2012. Geophysical Research Letters 39 (21), L21307.Wang, X., Bradley, K. E., Wei, S., Wu, W., feb 2018. Active backstop faults in the Mentawai region of Sumatra, Indonesia,revealed by teleseismic broadband waveform modeling. Earth and Planetary Science Letters 483, 29–38. ei, S., Helmberger, D., Avouac, J.-P., Jul. 2013. Modeling the 2012 Wharton basin earthquakes o ff -Sumatra: Completelithospheric failure. Journal of Geophysical Research 118 (7), 3592–3609.Wessel, P., Smith, W. H. F., Scharroo, R., Luis, J., Wobbe, F., Nov. 2013. Generic Mapping Tools: Improved VersionReleased. Eos, Transactions American Geophysical Union 94 (45), 409–410.Wiens, D. A., DeMets, C., Gordon, R. G., Stein, S., Argus, D., Engeln, J. F., Lundgren, P., Quible, D., Stein, C.,Weinstein, S., Woods, D. F., Jul. 1985. A di ff use plate boundary model for Indian Ocean tectonics. GeophysicalResearch Letters 12 (7), 429–432.Yue, H., Lay, T., Koper, K. D., Oct. 2012. En echelon and orthogonal fault ruptures of the 11 April 2012 great intraplateearthquakes. Nature 490 (7419), 245–249.Zhang, H., Chen, J., Ge, Z., Nov. 2012. Multi-fault rupture and successive triggering during the 2012 Mw 8.6 Sumatrao ff shore earthquake. Geophysical Research Letters 39 (22), L22305.Ziv, A., Cochard, A., 2006. Quasi-dynamic modeling of seismicity on a fault with depth-variable rate-and state-dependentfriction. Journal of Geophysical Research 111 (B8), B08310.shore earthquake. Geophysical Research Letters 39 (22), L22305.Ziv, A., Cochard, A., 2006. Quasi-dynamic modeling of seismicity on a fault with depth-variable rate-and state-dependentfriction. Journal of Geophysical Research 111 (B8), B08310.