The repetition of slip during rupture process of earthquake is a debate issue which had never been confirmed clearly in the past big events due to the lack of dense near-field observations and limited resolution in time of source model. The 2011 M9.0 Tohoku-Oki earthquake generated a wealth seismic records which provided us an unprecedented opportunity to study the rupture evolution of giant earthquake at a high spatio-temporal resolution. Here we use teleseismic, local strong motion and near-field coseismic geodetic data to investigate the source rupture process of this event based on the parallel inversion technique. The results reveal a broad slip zone with remarkable large scale repeating slip during the earthquake. The inverted source model shows several time periods of energy release with three main peaks. These energy bursts and temporal rupture snapshots suggest repetition of a large scale slip on the biggest asperity. This rupture behavior resulted in >50 m slips on the slip zone and prolonged the entire rupture process for a long duration of ∼160 seconds. The proposed source model is in a good agreement with the aftershock distribution and can interpret the characteristics of local strong motions. Further investigations of repeating slip during this event are crucial which will deeply transform earthquake science from dynamic point of view.
 The 2011 off the Pacific coast of Tohoku Earthquake (M 9.0) was the fourth largest earthquake in the world from 1900 as well as the most destructive earthquake in Japan over the past several hundred years. This earthquake not only produced strong ground shaking but also resulted in serious tsunamis which caused widespread devastation and fatalities. The Japan Meteorological Agency (JMA) and U.S. Geological Survey (USGS) both reported that the earthquake was located off the Pacific coast of northeast Honshu (Figure 1). According to the USGS's W-phase moment tensor inversion result, faulting during the earthquake is interpreted as reverse faulting on a low-angle plane along the Japan Trench.
 The studies of rupture process of the Tohoku-Oki earthquake have been carried out intensively [Ide et al., 2011; Simons et al., 2011; Ozawa et al., 2011]. However, in most of the studies only one kind of data or few data sets were used to invert the source model, thus the results might not be able to explain other coseismic observations. Furthermore, the resolution, especially in time, of the published models is limited due to the lack of constraints from local observations and inversion technique. Thus, the given source models might not be able to provide good enough information for explaining the real nature of this giant event and for further studies, such as the details of dynamic rupture process and 3-D wavefield simulation. In order to obtain more precise source information in both space and time concerning the origin of this earthquake, especially how the rupture developed into a megathrust event, we perform a joint source inversion using the teleseismic body waves, seafloor and terrestrial GPS coseismic deformation data as well as dense local strong motion records. This large earthquake was well recorded by the teleseismic stations worldwide. The teleseismic data have good data quality and azimuthal coverage of the earthquake, thus providing a good opportunity to arrive at a first-order determination of fault rupture behavior. The near-field GPS coseismic deformation data, including the seafloor geodetic observations [Sato et al., 2011], provide good constraint on the total spatial slip pattern. In addition, the event was well recorded by dense regional seismic networks (e.g., K-NET, KiK-net and F-net) which can provide a further constraint on the details in temporal rupture process. The set of observational data used in this study can cover broad range of frequency band from high (near-field strong motion), middle (teleseismic body wave), and low (GPS) frequency wavefield that is needed to illustrate broadly extended source spectrum for large M9.0 earthquake. We used the full time-space inversion approach through the Parallel NNLS technique [Lee et al., 2006, 2008; Konstantinou et al., 2009] to obtain high resolution source rupture information from the three data sets. By taking the advantage of wealth data and powerful parallel computing technique, the inverted source model enabled us to achieve a high temporal resolution of every 2 seconds. The detailed descriptions of inversion method and data in used are included in the auxiliary material.
2. Spatial Slip Distribution
 Joint source inversion results show that the rupture occurred on a large triangular shaped slip zone with an area of 400 × 200 km2 and the average slip was about 18 m (see Figures 1 and 3a). The slip concentrated in several areas, with one extremely large asperity and two secondly large asperities. These asperities were not only defined from the slip amount but also mainly from the slip characteristics and their developments in temporal rupture process which is discussed in the next section. The largest asperity (denoted by Asperity I) developed around the hypocenter with a maximum slip over 50 m. This asperity covered a broad area of about 200 × 200 km2 with a reverse motion fan spreading originated from the hypocenter. Its slip concentrated in two areas, one (Asperity IA) around the hypocenter at a depth between 10–50 km, and the other (Asperity IB) located slightly north from the hypocenter between about 10–30 km depth. These two areas are highly overlapped on Asperity I. The other two secondly large asperities (Asperity II and III) appeared to the south and north from the hypocenter and were at depths of 10–40 km and 10 km, respectively. Rupture properties on these asperities are both thrust predominately. A close relationship between the fault slip projection onto ground surface and the aftershock distribution can be seen in Figure 1. Most of aftershocks were located to the west of the Japan Trench around the large slip areas, and very few big aftershocks (M > 6) were located inside those asperities. It is noticed that the M7.2 foreshock on March 9 was just located among the two slip concentrated areas on Asperity I.
 A comparison between inverted teleseismic synthetic waveforms and observed data is shown in Figure S1a of the auxiliary material. Peak amplitudes can fit sufficiently well, especially for the stations on the northwest side where waveforms are complex and have larger amplitudes. The teleseismic waveform misfit in the joint inversion is 0.36. Forward synthetic waveforms for the stations not been used in the inversion are also presented in Figure S1a of the auxiliary material. Observed waveforms are generally well retrieved by the forward synthetics, except the PP phase, since this phase is produced from the free surface reflection of P wave leaving a source downwards rather than caused by the source rupture process. Synthetic and observed GPS coseismic displacements are shown in Figure S1b of the auxiliary material. The misfit for GPS data in joint inversion is 0.02. The terrestrial GPS displacement can be well predicted from this model for both amplitudes and azimuths. For the seafloor geodetic observations, the fittings are also good in all five sites. Comparison between the three-component synthetic velocity waveforms and the K-NET observations shows an excellent fit in the vertical component, and a good fit in the horizontal components (E and N), except for some stations at which waveform adjustments have been found (see Figure S1c of the auxiliary material). Since a simplified 1D velocity model is used in this study, a small part of waveform misfit is expected even though the study is targeted in the low frequency region. The misfit for local ground motion waveforms is 0.25. In summary, the total misfit is 0.26 from the joint inversion of three data sets, which provides a reliable coseismic slip distribution of the event.
3. Temporal Rupture Process
 The slip snapshots and accumulated slip are shown in Figure 2 (detailed rupture processes are shown in Figure S4 and Movie S1 of the auxiliary material). In the first 20 seconds, the slip of about 5 m is observed at the middle part of the fault plane close to the hypocenter. Although it is relatively small compared to final slip, the slip might indicate the nucleation of the earthquake. This nucleation is located at 20–25 km in depth, which is comparable to the depth of the JMA hypocenter (24 km). After ∼40 second, a large thrust movement quickly occurred in a broad area above the hypocenter. This area continued to slip at the shallow depths of subduction zone for more than 40 seconds and merged with the initial slip near the hypocenter. In the same time period, the rupture extended to the deeper part of the subduction plane. During 40 to 90 seconds, the rupture forming an extremely large slipped area extended from shallow to deeper subduction zone and becoming the first formed asperity on the fault plane, i.e., Asperity IA. After that, the fault became quiet between 95 and 100 second, and then some small slips are found at the middle fault plane. The rupture front moved slowly to the south and gradually formed the Asperity II between about 100 to 140 seconds. Almost at the same time, the area just above the hypocenter started to slip again which expanded northward and merged with Asperity IA that had slipped before. This produced the second slip concentrated area on Asperity I, i.e., Asperity IB. After 140 second, the rupture front started to propagate to the north along the Japan Trench and formed the last asperity, i.e., Asperity III.
 From the temporal variation in slip, the Tohoku-Oki earthquake appears to be caused primarily in the form of a large scale repeating slip related to the development of the largest asperity. By comparing the moment rate function (see Figure 2) with the rupture snapshots, three time periods of energy release can be identified. We infer that the first energy release time (T1) is related to the rupture nucleation near the hypocenter. In the second energy release time (T2), Asperity IA grew at the shallow part just above the hypocenter. Meanwhile, the rupture front also extended to the deeper part of the subduction zone. The fault plane was quiet at ∼100 seconds, and then the area above hypocenter was initiated to slip again (Asperity IB) between 100 and 140 seconds (T3). These two repeating slip events resulted in a long duration time and extremely large movement (>50 m) on Asperity I. The overall duration of the Tohoku-Oki earthquake is about 160 seconds and the total seismic moment is 0.367 × 1030 dyne-cm, which is equivalent to an earthquake of Mw 9.0.
 The inferred spatial slip distribution is characterized by an extremely large asperity. Comparing with other big earthquakes, such as the 1960 Chile earthquake M9.5 [Barrientos and Ward, 1990] and 2004 Sumatra-Andaman earthquake M9.1 [Lay et al., 2005; Ammon et al., 2005], the rupture of the Tohoku-Oki earthquake was concentrated on a relatively small area. However, its maximum slip is >50 m which is rare been seen from other earthquakes, e.g. 1964 Alaska earthquake M9.2 [Ichinose et al., 2007] and 2010 Chile earthquake M8.8 [Lay et al., 2010]. With the extremely large slip on a relatively small ruptured area, the average stress drop, Δσ, is 7 MPa. Kanamori and Anderson  indicated that the interplate earthquake occurred at plate boundary usually has a lower average stress drop (3 MPa) compared to intraplate earthquake which is about 10 MPa. Consequently, the average stress drop of the Tohoku-Oki earthquake could be one of the exceptions that do not follow the scaling relationship of average stress drop with the seismic moment. The moment rate function presents three large peaks related to the repeating ruptures (see Figure 2). The first large peak corresponds to the nucleation which released about 18% of the entire seismic moment that is equivalent to an earthquake of Mw = 8.5. The second peak occurred quickly which released 62% of the seismic moment from the entire rupture, thus representing an event of Mw = 8.8. The third peak, which had a longer duration time and released about 20% seismic moment, was equivalent to an event of Mw = 8.5. This repeating slip behavior on Asperity I caused an extension of the fault along downdip direction that ruptured from shallow to deeper subduction zone. This result is consistent with numerical simulations that only a giant earthquake can extend its fault to the downdip direction along the southern Kuril and Japan trenches [Nanayama et al., 2003].
 In order to understand the rupture process in advance, we measure the rupture velocity (VR) and maximum slip rate (SR). Results show that VR had a large variation during the rupture process (Figure 3b). The rupture started from the hypocenter slowly with VR < 1.5 km/s. On the Asperity IA, the rupture propagated with moderate VR between 1.5 and 2.5 km/s. Ruptures that were at the shallow depths near the Japan Trench speeded up, in some areas have VR > 3.0 km/s. Unlike the rupture velocity, the heterogeneous distribution of maximum slip rate shows a simpler pattern (see Figure 3c). Large SR is observed on the area where repeating slip occurred with a maximum sliding velocity of >100 cm/s. Large SR (>60 cm/s) is also found in the deeper fault plane. These results indicate that when the rupture front reached the biggest asperity around the hypocenter, the slip slowed down and became weak. As the loading force overcame the barrier, large amounts of seismic energy rapidly released, thus causing large slip and high SR on Asperity I, especially at the area where repeating slip occurred.
 It is expected that repeating slip would dominate the characteristics of local seismograms. To confirm this point, we check the acceleration seismograms recorded by K-NET as shown in Figure 4. By tracking the travel times of seismograms, two predominant waveform groups (mark 1, 2 in Figure 4) are observed in the northern stations (above 37.5°N). The wavefronts of these two groups are both centered at about 38.7°N and their travel times delay bilaterally to the north and to the south. The time difference between these two wavefronts is about 40 seconds. Another two waveform groups (mark 3, 4 in Figure 4) can also be found from the northern and southern stations, but their wavefronts are not as obvious as the first two. Comparison between synthetic and observed data shows a good agreement in waveforms (see Figure 4 and Figure S1c of the auxiliary material). This result would confirm the phenomenon of repeating slip.
 We infer that the first waveform group is related to the nucleation near hypocenter that the initial slip occurred on the biggest asperity (T1 in moment rate function, see Figure 2), and the second group is caused by the repeating slip related to the development of Asperity I (T2). Note that the curvature of the second hyperbolic travel time curve (mark 2 in Figure 4) is smaller than the first one (mark 1) which means that the main slip area of second waveform group occurred farther from land. The amplitudes of these two waveform groups are almost equal in accelerograms but not in velocity records (see Figure 4). This could be the case that high-frequency seismic waves were generated when the rupture front initially break the barrier of the fault. After that, a repeating slip occurred on the same fault plane with a smoother interface. This caused a reduction in high-frequency signal even though a larger amount of seismic energy was released and produced larger amplitudes in the velocity waveforms. Although the time difference between seismic energy release of Asperity IA in T2 and that of Asperity IB in T3 is ∼50 seconds, their contributions to waveforms are not indivisible due to long rupture duration times (see mark 2, 3 in Figure 4). Furthermore, the rupture area of Asperity IA extended to the western part of the fault plane close to Honshu. This caused stronger ground shaking compare to Asperity IB that ruptured farther from Honshu. The wavefront of the fourth group (mark 4 in Figure 4) is not obvious, we still can trace its source which came from the development of Asperity II in the southern slip zone (see mark 4 in Figure S4).
Ide et al.  inferred two modes of rupture during the event: shallow, relatively quiet rupture with dynamic overshoot and deep rupture that radiates high frequency wave energetically. Our proposed source model suggests that the repetition of large scale slip near the hypocenter dominated the rupture process. The shallow part of the fault was not relatively quiet; on the contrary, most of the rupture activities, including the peak slip, high VR, large SR and the repeating slip, occurred at the shallow depths. Simons et al.  observed that the sources of high-frequency seismic waves delineate the edges of deepest portions of coseismic slip and do not simply correlate with the locations of peak slip. Our result shows that large slip rate was not only occurred in the deeper subduction zone (SR > 60 cm/s) but also been found in a broad area of the shallow fault plane near the trench (SR > 120 cm/s). The distribution of large rupture velocity (>2.5 km/s) also shows a similar pattern. All of these results imply that the high frequency radiation would come from both deeper and shallow parts of the subduction zone, especially from areas located near the trench. It is noticed that the size of slipped area and its duration time can control the frequency of radiated seismic energy. According to our results, the ruptures in the deep part usually occurred on a smaller area and had shorter durations. This could be the reason why higher frequency seismic waves were observed in this area. At shallow depths, there was a broad slip area with relatively long rupture duration. The initial slip in the shallow part can produce high frequency signal while the repeating ruptures in the same area could further produce the low-frequency signal as discussed above. From this result, we infer that the shallow fault plane radiated a broad frequency band with both high and low frequency signals.
 Based on the results of high resolution joint source inversion analysis, repetition of a large scale slip in area near the hypocenter has been observed during the Tohoku-Oki earthquake. The repeating slip caused an anomalously 50 m slip on the largest asperity which had a dimension of about 200 × 200 km2 developed from shallow to deeper subduction zone. The temporal rupture processes show that the slip nucleated slowly near the hypocenter at the beginning, and then propagated to the shallow part causing the second slip on the biggest asperity. A remarkable slip developed in the deeper subduction zone then enforced the previous ruptured area to slip again. Finally, the rupture front extended to the south and north along the Japan Trench. A relatively large stress drop of 7 MPa is obtained from the inversion result. It is worth noting that this high stress drop was derived from at least twice repeating ruptures in the main asperity. How can a repeating slip occur from a dynamic point of view? Did this rupture behavior cause the shallow dynamic overshoot [Ide et al., 2011]? Further investigations of dynamic rupture process of the Tohoku-Oki earthquake based on high resolution kinematic source model will be crucial to answer these questions.
 We thank Kuo-Fong Ma for fruitful suggestions and discussions. The terrestrial coseismic deformation data are taken from GPS displacement data (version 0.3) provided by the ARIA team at JPL and Caltech. All Original GEONET RINEX data provided to Caltech by the Geospatial Information Authority (GSI) of Japan. The seafloor geodetic observations were provided and processed by Japan Coast Guard. This research was supported by the Taiwan Earthquake Research Center (TEC) and the National Science Council (NSC) with grant number NSC 100-2628-M-001-007-MY3. The TEC contribution number for this article is 00078.