We perform a back projection method to image the rupture propagation and short-period energy release of the 2012 Off Northern Sumatra earthquake (Mw8.6) using Hi-net data recorded in Japan. The results show a complex pattern of four conjugate faults over about 180 sec. There is a striking correspondence between the lengths and orientations of our rupture pattern with the distribution of aftershocks. Each of the first three stages of the rupture corresponds to a clear lineation in the aftershocks, with lengths of 200 to 400 km. Rupture speeds for several of the fault segments were very high, about 5 km/s, and exceed the local S-wave velocity. This is the first example of an oceanic earthquake with supershear rupture speed.
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 Back-projection analyses of large earthquakes are some of the best methods for observing the spatial distribution of energy radiation within the rupture area. Using relatively high frequencies (about 0.5 to 5 Hz), the directions and speeds of the rupture propagation in this frequency band can often be clearly mapped on the fault plane [e.g.,Ishii et al., 2005; Xu et al., 2009; Yao et al., 2012]. In this study we use our back-projection technique to study the 2012 Off-Northern Sumatra earthquake (Mw8.6), which was a very large oceanic earthquake that occurred on a series of strike-slip faults [Meng et al., 2012; Yue et al., 2012] in the Wharton Basin. For several of the rupture segments, we see very fast rupture speeds that exceed the local shear-wave velocity.
 Rupture speeds for most earthquakes are observed to be in the range of 0.5 to 0.8 times of the shear-wave velocity, however, supershear propagation has been observed recently for several strike-slip earthquakes [e.g.,Bouchon et al., 2001; Bouchon and Vallée, 2003; Eberhart-Phillips et al., 2003; Wang and Mori, 2012]. Rupture speed is a key observation for understanding the controlling stresses and friction during large earthquakes, but is often difficult to accurately determine. Super shear rupture for oceanic events, has not been previously observed, probably because of the difficulty in accurately resolving rupture velocity from teleseismic data.
2. Methods and Data
 To image the rupture process, we use a back-projection method with Hi-net array data recorded in Japan. Our back-projection procedure was developed based onIshii et al. , Xu et al. , and Wang and Mori . This method finds the best source location of the coherent waves for time windows of teleseismic P waves, and determines the amplitude of the short-period radiated energy at each grid point. Time shifts for each station of the stack are calculated using the global velocity model IASPEI 1991 [Kennett, 1991]. We then apply a non-negative least-square inversion algorithm [Lawson and Hanson, 1995] to deconvolve the spatial distribution of the stacked energy with an empirical array response from an Mw5.4 earthquake that occurred in the source region (No.2 in Tablet S1). This procedure corrects for the spatial smear of the back-projection results and produces better spatial resolution of the energy radiation in each time window.
 The P waveforms in this study are from 770 Hi-net stations and recorded at distances of about 45 to 62 degrees from the epicenter in an azimuth range between 37 to 52 degrees (Figure 1). Data are recorded with 1 Hz seismometers all located in boreholes most at depth of 100 to 210 m [Okada et al., 2004]. We filtered the data (vertical components) in the band of 0.5 to 5.0 Hz using two-pole butterworth filters. In our procedure we use a cross correlation of the first 6 sec of the P waves to align the first arrivals at all stations. Then this initial arrival is constrained to be located at the epicenter (2.348°N, 93.073°E), as determined by USGS. For the calculation of the stack amplitudes to determine the source locations, we used 10 sec time windows that are offset by 2 sec. To check the spatial resolution of the source locations in the back projection results, we use the station corrections derived from the procedure described above for the Mw 8.6 earthquake, and apply them in a test to locate six small earthquakes that occurred in the source region (see auxiliary material, Text S1 and Figure S5). The results show that our method has location uncertainties which are about 30 km or less depending on the distance from the epicenter of the Mw 8.6 earthquake.
 The locations of the sources of high-energy radiation in the P wave, as determined in our back projection analysis are shown inFigure 2c. The circles show the locations corresponding to the highest stack amplitude for each time window. The colors of the circles indicate the time, so that the progression of the rupture can be seen. The propagation of the rupture can also be seen quite clearly in Animation S1 provided in the auxiliary material.
 In Stage 1 (0 to 56 s), the rupture first moves toward the southeast with a normal rupture speed of 2 to 2.5 km/s. The largest pulse 25 s after the origin time is located about 50 km southeast of the epicenter. Then the rupture changes direction and begins to move toward the west. The second largest pulse occurs at about 45 s and 100 km east of the epicenter. In Stage 2 (56 to 100 s), the rupture appears to change direction and propagate bilaterally in a northeast-southwest direction. The northeast part has larger amplitudes than the southwest part, so the southwest part is not seen very well inFigure 2. However, the distribution of high-frequency energy in both portions, along with the bilateral rupture can be better seen in the animation. In Stage 3 (100 to 156 s), the rupture extends on a second northwest-southeast trending fault southwest of the epicenter and propagates for 56 s over a distance of about 325 km. In Stage 4 (156 to 180 s), the rupture appears to move southward along the Ninety-East Ridge from a point near the end of the Stage 3 rupture.
 Aftershock epicenters determined by USGS are shown along with the rupture pattern in Figure 2. There is a striking correspondence between the complicated rupture pattern from our back projection analysis and the configuration of the aftershock locations. Note that the Stage 1, Stage 2, and Stage 3 ruptures in Figure 2 all correspond to clear lineations, which are 200 to 400 km in length, in the aftershock pattern.
 Early slip distribution studies of this earthquake done soon after the earthquake, do not show the complicated geometry for the rupture process, mainly because the finite fault inversions need to specify the fault geometry a priori. The back projection method has the advantage that it can search over a large area for the sources of the P-wave radiation, without constraining the locations to any predetermined fault geometry, so that these complicated fault structures can be easily identified.
Figure 2ashows the amount of cumulative high-frequency energy for the various portions of the rupture. The second half of the rupture in Stage 3 and 4 has a combined source duration and length comparable with the combined values for Stage 1 and 2, but radiated about one fifth of the energy.
 The rupture speeds for the various fault segments can be seen in Figure 3b which shows the locations of the maximum stack amplitude of each time window, as a function of time. The slopes of these locations as a function of time give the speed. In order to see the rupture speeds for the later portions of the earthquake, we set a second reference point (triangle in Figure 2c) where the rupture of this segment begins at the southeastern end. The rupture of the Stage 1 starts at a speed of 2.0 to 2.5 km/s, which is typical for shallow strike-slip earthquakes, then accelerates to 5.0 km/s from 30 s after the origin time and maintains the high speed to the end of the segment. The trends for Stage 2 and Stage 3 also show very fast rupture speeds of about 5.0 km/sec. Such high rupture speed is faster than local S wave velocity, which is 3.5 to 4.6 km/s for depths of 20 to 50 km [Harmon et al., 2012]. Due to the small amplitudes and heterogeneous source structure for the Stage 4 region, the estimate for the rupture speed is less reliable. The specific values of the rupture speed somewhat depend on the starting point and time window chosen for each segment. Different reference point may give small differences in the rupture velocities. But the estimated rupture speed is always a lower bound of the actual rupture speed. As seen in Figure 3b, the trends of the points all show very fast rupture propagation. For comparison, the slopes corresponding to more typical speed of 2 to 3 km/s are also shown.
 The general source characteristics of oceanic earthquakes are still not well understood. It was often thought that these types of events have unusually long source durations and large amounts of long-period energy, suggesting slow ruptures [e.g.,Okal and Stewart, 1982]. However, Abercrombie and Ekström  concluded that many events did not have anomalously high spectral amplitudes at several hundred seconds. Also, many events have high ratios of radiated energy to moment [Choy and Boatwright, 1995; Choy and McGarr, 2002] indicating complicated ruptures or high stress drop earthquakes. The fast rupture speed of the 2012 event shows that large transform earthquakes can be very energetic.
 Past earthquakes with supershear rupture speeds in Turkey, Alaska, and Tibet [Bouchon et al., 2001; Bouchon and Vallée, 2003; Eberhart-Phillips et al., 2003; Wang and Mori, 2012] have all been shallow strike-slip events that have occurred onshore. This event is the first time that supershear rupture speed has been observed for an oceanic strike-slip earthquake. Since oceanic strike-slip faults tend to be some of the straightest and structurally simplest faults in the world, their configurations are conducive to supershear ruptures, which have generally been observed to occur on straight fault segments. Since it is often difficult to accurately determine rupture speed using only teleseismic observations, it is possible that many supershear ruptures on oceanic faults have gone undetected.
Satriano et al. also studied this event using a back projection method with broadband data from Europe. Their results, using a wider frequency band, show three subparallel faults trending in a nearly north-south direction, which is quite different from our configuration inFigure 2. We also analyzed data from Europe with our back projection method, using the high-frequency bands of 0.5 to 5.0 Hz, which are similar to the Hi-net data from Japan. Our results using the European data are quite similar to the results from the Japanese data (see Figures S3 and S4 in theauxiliary material), although in this letter, we do not investigate the lower frequency aspects for this earthquake. The results from the European data for the higher frequency band do not seem to be as robust as for the Japanese data, probably because of the larger number of Hi-net stations and the more consistent waveforms of the borehole data (See Figure S5 in theauxiliary material). The better quality of results using Japanese data compared to the European data, is opposite of the conclusion from Meng et al. . Using theoretical calculations, that study concluded that the European data should provide better results than Hi-net. However, the difference between surface and borehole observations and the number of stations, which are not accounted in the array response calculations, contribute to better performance for the Hi-net array, as also noted byKoper et al. .
 Another reason that supports our results, is the pattern we obtain for the rupture propagation correlates well with the linear segments seen in the aftershock distribution (Figure 2b).
 An unusual feature of this earthquake is that it does not appear to follow the usual scaling relationship between seismic moment (Mo) and fault lengths of oceanic strike-slip earthquakes (Figure 4). Usually the seismic moment is proportional to the cube of the fault length, the horizontal extent of the fault [Kanamori and Anderson, 1975], and for earthquakes larger than Mw 7.7 (Mo = 5 × 1020 Nm), the seismic moment becomes proportional to the fault length due to a finite thickness of a seismogenic zone [e.g., Scholz, 1982; Romanowicz and Ruff, 2002]. Our back-projection analyses show four different fault segments for this event from which we estimate the fault lengths and moments. The overall shape of our energy source time function resembles the moment rate function obtained from other studies such as Shao et al. (http://www.geol.ucsb.edu/faculty/ji/big_earthquakes/2012/04/10/sumatra.html), so we infer it can be used to estimate the moments. The fraction of the estimated seismic energy for Stages 1, 2, 3, and 4 are 55%, 24%, 16%, and 5%, respectively. Multiplying these values by the total seismic moment, 9 × 1021 Nm, we obtain an estimate of the seismic moment from each stage. The values for Stage 1 are quite different from the scaling relationship, while the other values for the other stages are generally consistent. This observation implies that the faulting during Stage 1 may have a wider (deeper) fault or a higher stress drop compared to other oceanic events.
 Back projection analyses have the advantage of imaging the rupture of complex earthquakes without specifying a fault geometry. This aspect was particular useful for studying the 2012 Off Northern Sumatra earthquake, where we identified ruptures on four separate faults with varying orientation. Clarifying the fault geometry, allowed us to better estimate the rupture speed, which we found to be very fast. Values of about 5 km/s on several segments exceed the local S-wave velocity. This is the first example of an oceanic earthquake with supershear rupture; however, past oceanic events with fast rupture speeds on long straight faults may have been overlooked.
 This work was partly supported by NSFC grant 41004020 (D.W.). T.U. is a JSPS Research Fellow. Hi-net data were obtained from National Research Institute for Earth Science and Disaster Prevention (NIED). European station data were obtained from Deutsches GeoForschungsZentrum (GFZ) and ORFEUS Data Centre. All the figures were created using the Generic Mapping Tools (GMT) ofWessel and Smith .
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.