A continuous back-projection analysis using data recorded in North America between March 9, 2011 and April 7, 2011 is applied to the Mw 9.0 2011 Tohoku-oki earthquake and the foreshocks and aftershocks of this event. As with the Mw 8.8 2010 Maule, Chile earthquake, back-projection results of the mainshock show variations in rupture behavior when data filtered to different frequency ranges are used. In particular, there is a relationship between the frequency of data used and the position along the dip direction of the energy release, with the highest-frequency result imaging energy at the down-dip edge of the rupture and progressively lower frequencies showing a continuous shift updip. In addition, these results show that late in the rupture (∼200 seconds after the hypocentral time), energy at all frequencies is imaged very close to the trench at about 37°N, which, with the energy imaged near and updip of the epicenter, may have acted as a tsunami source. Comparing the mainshock rupture area to the area that ruptured during M ≥ 6 foreshocks and aftershocks between March 9th and April 7th shows that total failure of the plate interface nearly doubled compared to the mainshock alone. Building upon the idea that the mainshock occurred through interactions between multiple segments, the results imply that the total failure area of the interface may represent the area that can rupture during a single event as a series of in-phase interface segments.
 Using the back-projection method [Ishii et al., 2007] and data from North America (Figure 1b), we investigate rupture properties of the Mw 9.0 earthquake, as well as the events that preceded and followed the mainshock. Back-projection results using linear stacking provide information on the timing and locations of energy release, as well as the relative amplitude of the energy release (see auxiliary material). The amplitude information is important for assessing the seismic hazards of a rupture (e.g., intensity of ground shaking), but can also obscure low-amplitude features of the rupture that may be important. Applying an additional processing step to the back-projection analysis, a coherency function can be defined that is better suited for imaging the propagation of rupture through time [Ishii, 2011] (see auxiliary material).
 The high-frequency characteristics of the March 11, 2011 mainshock, as well as foreshocks and aftershocks of this event, are analyzed using abundant observations from seismic stations in North America comprised by the following networks: USArray Transportable Array (IRIS and EarthScope), Caltech Regional Seismic Network (Caltech/USGS), Global Seismograph Network (IRIS), International Miscellaneous Stations, University of Utah Regional Network (University of Utah), Berkeley Digital Seismograph Network (Berkeley Seismological Laboratory), University of Oregon Regional Network (University of Oregon), Canadian National Seismograph Network (Geological Survey of Canada), United States National Seismic Network (ANSS Data Collection Center), and ANZA Regional Network (IGPP, University of California, San Diego) (Figure 1b). This group of stations acts as an array over most of North America.
 Though high-frequency data provide the most detailed information regarding the rupture, Kiser and Ishii  show in their study of the 2010 Chile earthquake that back-projection results using lower frequency data can show very different rupture characteristics than their high-frequency counterparts. These differences are interpreted as representing different aspects of the rupture process. A similar multi-frequency back-projection analysis is appropriate for the 2011 Tohoku-oki earthquake, both, because of its large magnitude and because reports from numerous studies have argued that high-frequency energy is concentrated at the downdip edge of the seismogenic zone, while the majority of slip occurred further updip near the epicenter and trench [e.g., Koper et al., 2011; Simons et al., 2011; Ide et al., 2011]. This large slip near the epicenter and trench should generate a strong low-frequency signal, resulting in frequency-dependent release of seismic energy [e.g., Polet and Kanamori, 2000]. To investigate such frequency dependence, the data are bandpass filtered to four frequency ranges: 0.8–2 Hz, 0.25–0.5 Hz, 0.1–0.2 Hz, and 0.05–0.1 Hz.
 The imaged source locations of high-frequency (0.8–2 Hz) energy show a very complex spatio-temporal rupture pattern (Figure 2a). To determine the relative amplitudes of energy release, we use results from linear stacking (Figure 2b), but rupture direction, duration, and velocity are determined by results from the coherency function (see auxiliary material; Figure 2a). At high frequency, this earthquake begins with downdip (northwest) propagation away from the epicenter at a velocity of about 0.8 km/s. This first episode of rupture lasts about 90 seconds (Figure 2a). This rupture episode shows a very diffuse distribution of energy release near its downdip limit. Following this downdip propagation, the rupture moves southwest, parallel to the Japan trench. This southwestward propagation lasts about 60 seconds, and includes the episode of highest amplitude energy release at about 95 seconds after the hypocentral time (Figure 2b). The average rupture velocity of the southwest propagating rupture is very high at about 3.4 km/s. This high speed is in part due to a jump in the rupture of length 70 km (Figure 2a). The rupture velocities to the north and south of this jump are 2.7–3.3 km/s and 1.1–1.7 km/s, respectively. Between 36.5 and 37°N, the along trench strike propagation terminates, and rupture begins to propagate updip (southeast; Figure 2a). This updip propagation is weaker compared to earlier episodes, and lasts for about 20 seconds at a rupture velocity of 2.8–3.3 km/s (Figures 2a and 2b). The last rupture episode propagates to the northeast with a velocity of about 2.1–2.3 km/s and is very close to the trench (Figure 2a). This rupture has lowest amplitude high-frequency energy release and lasts about 45 seconds (Figures 2a and 2b). These results are similar to previous studies that also used back-projection or similar methods [Zhang et al., 2011; Nakahara et al., 2011; Honda et al., 2011; Wang and Mori, 2011a; Koper et al., 2011; Ishii, 2011; Simons et al, 2011]. In particular, imaged energy near the coast of Honshu and a large increase in rupture velocity during southwest propagation seem to be robust features of multiple studies, though imaged energy near the trench late in the rupture is unique to the current study.
 Using lower frequency data (0.25–0.5 Hz) leads to slightly different back-projection results. For example, the rupture now begins with updip (northeast) propagation for 25 seconds at a rupture velocity of 0.4 km/s. The remaining rupture is very similar to the high-frequency results, though the 0.25–0.5 Hz results are updip of the 0.8–2 Hz results (Figure 2c; see auxiliary material). This updip shift in energy release locations continues when using data filtered at 0.1–0.2 Hz. In addition, updip propagation at the beginning of the rupture is more significant with a duration of 45 seconds (Figure 2c; see auxiliary material). Moving to the lowest frequency range (0.05–0.1 Hz), imaged energy is even further updip at the beginning of the rupture and never propagates significantly downdip of the epicenter (Figure 2c; see auxiliary material). At the end of the rupture, energy is imaged slightly east of the trench. This energy is interpreted as being on the plate interface and not in the outer-rise region (see auxiliary material for a discussion on location uncertainty). The updip shift in the imaged energy at lower frequencies agrees well with other back-projection analyses of this event [Ishii, 2011; Wang and Mori, 2011b]. A final observation worth noting is that as the frequency range becomes lower, the relative amplitude of the last episode of energy release (to the south and near the trench) between 180 and 240 seconds increases (Figure 2b).
 Though little is known about the rupture details, the last earthquake in this region that is thought to have produced a similar-sized tsunami as the March 11th event occurred in 869 AD [e.g., Sawai et al., 2008], and produced maximum wave heights between 6 and 9 meters with a minimum magnitude of 8.4 [e.g., Satake et al., 2008]. Tsunami run-up data are sparse for the 869 AD event, and different studies argue for very different slip distributions, especially with respect to distance from the trench [e.g., Satake et al., 2008; Minoura, 2008]. Therefore, it is not clear if the 869 AD event is a predecessor to the 2011 event. Additional smaller events (Mw 7–8) have occurred along this plate interface in the past 200 years that also produced tsunamis (Figure 3a). Our high-frequency back-projection results suggest that parts of four of these patches that ruptured in 1915, 1936, 1938 and 1978 [Hatori, 1987] failed again during the 2011 mainshock, while the low-frequency back-projection results suggest that a segment of the plate interface near the trench that last ruptured in 1897 is also involved in the 2011 earthquake (Figure 3a) [Hatori, 1987]. A noticeable gap in the distribution of past tsunamigenic earthquakes occurs updip of the 1938 event (Figure 3a). This is the region where energy is imaged at all frequencies at the end of the 2011 mainshock. Though additional studies are needed to determine the extent to which this late rupture acted as a tsunami source, the results of this study suggest that this offshore Ibaraki region may be unlikely to produce a tsunamigenic earthquake in the near future if the imaged rupture released most of the cumulative strain. In addition, the back-projection results demonstrate that this section of the plate interface can slip seismically, which will be important for evaluating future seismic hazards.
4. Foreshocks and Aftershocks
 The seismicity preceding and following the Mw 9.0 mainshock is very vigorous. Between March 11th and April 7th, the aftershock sequence of this event included at least four earthquakes with magnitudes greater than 7, and 70 aftershocks with magnitudes greater than or equal to 6.0 according to the JMA catalogue (Figure 1a). These aftershocks have a variety of focal mechanisms, including normal faulting in the outer rise and overriding Okhotsk/North American plate. The Mw 9.0 event is also accompanied by a foreshock sequence that includes a Mw 7.3 event north of the mainshock epicenter and 7 additional earthquakes with magnitudes greater than 6.0 according to the JMA catalogue (Figure 1a).
 To understand the relationship between this series of large earthquakes occurring close in time to the mainshock, we apply the back-projection technique to continuous high-frequency data (0.8–2 Hz) between March 9, 2011 and April 7, 2011 (see auxiliary material). The level of detail at which seismic events in the source region can be investigated by the back-projection technique is demonstrated in Figure 3b where the relative energy release is plotted as a function of time for a one-hour time window after the mainshock. Using traditional techniques, detecting earthquakes immediately after a large event is difficult, and the catalogue is often incomplete. The back-projection approach shows that, in addition to the Mw 9.0 earthquake, both large (Mw > 6.0) and smaller (Mw < 5.5) aftershocks that are in the JMA catalogue are successfully detected (Figure 3b). In addition, two large earthquakes that are reported in the NEIC catalogue, but not the JMA catalogue, are also detected (Figure 3b). Furthermore, additional earthquakes that are not detected in either catalogue (JMA or NEIC) are identified during times immediately following large events (Figure 3b). This demonstrates that the back-projection technique is a useful method for improving the completeness of earthquake catalogues around the times of large events when noise levels are high.
 In addition to detecting foreshocks and aftershocks, the spatial distribution of energy release can be investigated for the largest events (Figure S3). The JMA catalogue shows that these events have a variety of locations that include along the west coast of Japan and in the outer rise. When these events occurring on the overriding plate, as well as events with normal faulting mechanisms, are removed, the spatial distribution of the remaining energy release for events with M ≥ 6 between March 9 and April 7, 2011 shows that there is an almost complete failure of the plate interface between 35.0°N and 41.0°N (Figure 3a). We estimate the area of this failure to be ∼120,000 km2, about 80% of the total seismogenic zone in this latitude range (∼146000 km2) [Heuret et al., 2011]. The majority of the interface failure occurs during the Mw 7.3 foreshock, the Mw 9.0 mainshock, and the series of large events in the 4.5 hours following the mainshock (∼91,000 km2) (Figure 3c). Almost all of the remaining events occur within an area that overlaps with the rupture areas of preceding events. In fact, for many of the regions along the plate interface, high seismicity rates associated with an aftershock sequence do not begin until the cumulative interface failure, as imaged by back-projection, reaches those regions (Figure S4). The northern boundary of interface failure, based upon back-projection results, corresponds to a transition to a region of low interseismic coupling inferred from GPS measurements [e.g., Loveless and Meade, 2010], and the southern boundary of failure matches the location of the northern extent of the subducting Philippine Sea plate [e.g., Shinohara et al., 2011]. In this region, the plate that overrides the Pacific plate changes from the Okhotsk/North American plate to the north to the Philippine Sea plate to the south. It has been suggested that large earthquakes rarely occur along the Pacific plate interface in this region because of the presence of weak serpentinized mantle associated with the subducted Philippine Sea plate [Uchida et al., 2009]. This weak material may not accumulate significant strain, which would explain why interface failure stopped in this region.
 It has been argued that interactions and synchronization between multiple patches of the subduction interface led to the large magnitude of the 2011 mainshock [Ando and Imanishi, 2011; Hori and Miyazaki, 2011; Aochi and Ide, 2011; Mitsui and Iio, 2011]. Given the short time delay between the Mw 7.3 foreshock and the 4.5 hours surrounding the mainshock, it seems plausible that the plate interface that ruptured over this time period could have ruptured in a single event. Using the stress drop of 60 bars to match the Mw 9.0 mainshock as an upper bound, this hypothetical event would have a moment magnitude of 9.2. The recurrence times of these patches are very different, ranging from 21 to 750 years (The Headquarters for Earthquake Research Promotion, 2011, Summary of long-term seismic probability for subduction zone earthquakes), and therefore synchronization of segments is necessary for simultaneous failure. Recent work has focused on determining the distribution of asperities along plate interfaces, where coupling between the subducting and overriding plates is high [e.g., Moreno et al., 2010; Lorito et al., 2011], as a way of evaluating the locations and maximum magnitudes of future large earthquakes. The results of this study emphasize the importance of considering time synchronization of adjacent asperities when evaluating future seismic hazards.
 All of the data used are obtained from the IRIS Data Management Center. Some figures have been generated using the Generic Mapping Tools (GMT) [Wessel and Smith, 1991]. Petros Mpogiatzis assisted with generating some of the figures. The William F. Milton Fund supported E. Kiser during this project. This paper benefitted from constructive comments from two anonymous reviewers.