Explaining deep seismicity is a long-standing challenge in earth science. Between 300 and 700 km depth, earthquakes are scarce except between ∼530 and ∼600 km, where the majority of events occur. By imaging the seismic rupture process for a set of recent deep earthquakes using the back projection of teleseismic P-waves, we found that the rupture velocities are less than 60% of the shear wave velocity except in the depth range of 530 to 610 km. We propose that large fracture surface energy (Gc) values for deep earthquakes generally prevent the acceleration of dynamic rupture propagation and generation of earthquakes between 300 and 700 km depth, whereas small Gc value in the exceptional depth range promote dynamic rupture propagation and explain the seismicity peak near 600 km.
 Researchers have long tried to explain the seismicity of deep earthquakes. For example, concentrated stresses due to the perturbation of mineral phase transitions in the mantle [Bina, 1997] or the high viscosity of the lower mantle [Vassiliou and Hager, 1988] may be related to the local maximum of deep seismicity at ∼600 km. Alternatively, strength weakening due to the presence of water released by dehydration associated with the equilibrium mineral phase transition from the garnet to the perovskite structure may account for the rise in earthquakes deeper than 530 km [Estabrook, 2004].
 Given the difficulty of estimating fracture properties and observing the stress field in the mantle transition zone (410–660 km), the seismic source processes of deep earthquakes provide very important information for understanding the distribution of deep seismicity. Previous researchers have estimated sub-event locations [e.g., Tibi et al., 2003a] and spatiotemporal slip distributions [e.g., Antolik et al., 1999] by using seismic waveform inversion of teleseismic P- and SH-waves. However, in a compilation of seismic source models of deep earthquakes, the source parameters for individual deep earthquakes are quite varied [Frohlich, 2006]. This discrepancy originates from neglecting the data covariance matrix in waveform inversion [Yagi and Fukahata, 2008, also Introduction of uncertainty of Green's function into waveform inversion for seismic source processes, submitted to Geophysical Journal International, 2010]. Rupture velocities for deep earthquakes estimated using seismic waveforms range from 0.3 to 0.9Vs, where Vs is the shear wave velocity, a considerably wider range than the velocities for shallow earthquakes [Frohlich, 2006; Houston, 2007]. As a result, the stress drop, which is usually estimated assuming a constant rupture velocity, cannot be well constrained, although this value is important for determining the mechanical process of deep earthquakes. Various mechanisms have been proposed to explain deep earthquakes including dehydration of hydrous minerals [Raleigh and Paterson, 1965; Meade and Jeanloz, 1991], thermal shear instabilities [Griggs and Baker, 1968; Ogawa, 1987; Hobbs and Ord, 1988; Kanamori et al., 1998], and the transformational-faulting of metastable olivine [Green and Burnley, 1989; Green and Houston, 1995; Kirby et al., 1996], which are summarized by Houston . However, the uncertainty of seismic source models prevents us from determining the main characteristics of the rupture process and understanding the physical mechanisms of deep earthquakes.
2. Data and Analysis
 Recently, the back projection method has been used to derive a detailed and stable seismic source image from dense seismic network observations [e.g., Ishii et al., 2005; Walker et al., 2005]. Using this method, we can obtain an image of the seismic source process from the observed data without a priori constraints or discarding parameters. We applied the back projection method to 25 large, deep earthquakes (moment magnitude Mw ≥ 7.0, depth ≥ 300 km) for the period since 1994 reported in the U.S. Geological Survey (USGS) catalog, and constructed seismic source models for deep earthquakes. We used teleseismic P-waveforms of Global Seismographic Network (GSN) and Federation of Digital Seismograph Network (FDSN) data downloaded from the Data Management Center of the Incorporated Research Institutions for Seismology (IRIS-DMC).
 For our analysis we used only the vertical component of ground motion observed at epicentral distances between 10° and 100°. The data were shifted and aligned on their first arrival using cross-correlation of the P-waveform, instrument response deconvolved to velocity, and band-pass filtered between 0.25 and 1 Hz. This filter range was selected by trial and error. To reduce the bias due to uneven station distribution, the waveforms were normalized by peak amplitude and then divided by station density. Unlike for shallow earthquakes, we can obtain relatively simple rupture images free from contamination from surface-reflected phases such as pP and sP, which have long lag times for deep events. Assuming potential source grids with spacing of 1 km on the fault plane, we back-projected the seismograms and performed fourth root stacking [Xu et al., 2009] at each gridpoint. Because we do not know which of the two possible fault planes from seismic moment tensor analysis is the correct one, we constructed two seismic rupture models for each event based on the two possible fault planes from the Global Centroid Moment Tensor (CMT) catalog [Dziewonski and Woodhouse, 1983].
 In general, seismic source images obtained using the back projection method are contaminated by distortions related to the station distribution, but the “peak point,” where the relative beam power as a function of time and space reaches its highest amplitude, should be one of the most robust pieces of information (see Figure S1 of the auxiliary material). We perform the backprojections along both possible fault planes and the plane with the greatest peak point amplitude is chosen as the fault plane. Table 1 shows the amplitude ratio of the inferred fault plane to the other. The actual fault planes of 5 earthquakes in the list identified by aftershock distribution [Wiens et al., 1994; Myers et al., 1995; Wiens, 1998; Tibi et al., 2001; Tibi et al., 2003b] are denoted in Table 1. The selected fault planes coincide with the results of the aftershock analysis. As can be seen from the ratio in Table 1, the amplitude ratios of 7 earthquakes are less than 1.07 that is the minimum ratio of the earthquake confirmed by the aftershock analysis. We categorized these 7 earthquakes into an uncertain fault plane earthquake, and plotted results with the two possible planes on later figures.
Table 1. Parameters of the Earthquakes Investigated
Figure 1 shows the locations of these peak points for each of the 25 deep earthquakes in a plot of distance from hypocenter versus time after rupture initiation. As shown in Figure 1, a fast rupture velocity group can be detected from the peak locations of large earthquakes whose distance and time of the peak points are large enough to estimate a stable rupture velocity. In this study, we classified the deep earthquakes into fast-rupture (Vr ≥ 0.6Vs) and slow-rupture groups (Vr < 0.6Vs). Examples of rupture models from each group are shown in Figure 2 (rupture models of 25 deep earthquakes are shown in the auxiliary material). We also estimated an approximate value of average rupture front velocity Vr and plotted a depth profile of Vr/Vs using the peak point of each earthquake (Figure 3a). Rupture velocity estimates based on hypocenter to peak point distance and time are very similar to estimates using smaller local peaks throughout the rupture, i.e., rupture velocity does not seem to significantly change in any of our observations (see auxiliary material). This figure shows that the fast-rupture earthquakes occurred only in the depth range of 530 to 610 km. In this exceptional depth range, about eighty percent of earthquakes were categorized the fast-rupture earthquake. In addition, all earthquakes in the depth range of 570 to 610 km were categorized the fast-rupture earthquake. We calculated Akaike's Information Criterion (AIC) for two models (model 1: the average of rupture velocities are constant with depth of hypocenter, model 2: the average of rupture velocities are variable in the depth rage of 530 to 610 km) and found that model 2 is better than model 1.
 To investigate the variation of rupture velocity among deep earthquakes, we calculated approximate values of their static stress drop using seismic moment from the Global CMT catalog and the rupture area. Following Ishii et al.  and Walker et al. , we estimated the rupture area on the basis of contour of time-integrated beam power. Since the rupture area depends on the cutoff contour, we applied three cutoff contours: 20, 30 and 40% of maximum of the time-integrated beam, and estimated the geometric mean of the static stress drop. The resulting stress drops are shown in Figure 4, as the function of Vr/Vs. In general, high stress drops should promote fast rupture propagation during earthquakes [Olsen et al., 1997]. Nevertheless, our result does not show the clear correlation between the rupture velocity and the stress drop.
4. Discussion and Conclusion
 Slow rupture can be explained by a larger fracture surface energy (Gc), that is, the energy used to produce a new crack surface [Andrews, 1976]. Large Gc should restrain the acceleration of dynamic rupture propagation, as a large stress concentration is necessary to produce new rupture area in a rupture front. Our results suggest that the Gc value of deep fault zones is large enough to restrain dynamic rupture propagation except at the depth range of 530 to 610 km. The depth variation of Gc values matches the observed seismicity distribution for earthquakes of body-wave magnitude Mb ≥ 5.0 in the International Seismological Centre (ISC) catalog for 1964–2007 (Figure 3b).
 In an earlier study, Tibi et al. [2003a] carried out teleseismic body wave inversions for 14 large earthquakes (Mw ≥ 7.0) deeper than 400 km and suggested a possible dependence of the rupture velocities on the thermal state of the slab, with earthquakes in warmer slabs rupturing more slowly. Figure 5 shows the rupture velocity normalized by shear velocity as a function of slab thermal parameter, defined as the product of the vertical subduction rate and the age of the lithosphere when subduction begins [e.g., Molner et al., 1979]. As can be seen in Figure 5, there is no clear correlation between rupture velocity and the slab thermal parameter.
 Our results show that the acceleration of dynamic rupture for deep earthquakes depends on the depth of the source area. Similar patterns of depth dependence have been observed in several studies. Persh and Houston [2004a] found that aftershock productivity is particularly low from 300 to 550 km depth and increases markedly at depths greater than 550 km (Figure 3c). In general, the static stress changes due to large earthquakes trigger aftershocks in and around the seismic source area [e.g., King et al., 1994]. The lack of aftershocks for events from 300 to 550 km suggests that the static stress change is insufficient for triggering aftershocks where large Gc restrains dynamic rupture propagation. In another study, Persh and Houston [2004b] found, by stacking of carefully aligned broadband P waves, that earthquakes deeper than 550 km have shorter and simpler time functions. They concluded that earthquakes deeper than 550 km have fast rupture velocities. Our conclusions are also consistent with the results of Venkataraman and Kanamori , who included source parameters of four deep earthquakes in their study of subduction-zone earthquakes and found that they were of two types: two events have slow rupture velocity with high stress drop and the other events have fast rupture velocity with low stress drop. Their fast-rupture earthquakes occurred only between 530 and 610 km.
 An important issue is the physical significance of the variation of Gc with depth. The large Gc in deep earthquakes may result from special faulting mechanisms, but a mechanism is also needed to account for the relatively small Gc in the exceptional depth range. The decrease of Gc may be explained by weakening due to the presence of water released by dehydration associated with the equilibrium phase transition of garnet to perovskite [Estabrook, 2004]. This reaction starts at ∼18 GPa (530 km depth) in both warm and cold slabs [Ita and Stixrude, 1992; Vacher et al., 1998], which is consistent with the upper limit of fast-rupture earthquakes. Our source models of 25 deep earthquakes suggest that rupture propagation may be controlled by phase transitions in the mantle transition zone and that the zone of deep earthquakes at 530–610 km may result from a decrease in Gc.
 Waveform data were supplied by the IRIS-DMC. We grateful to B. Enescu, S. Ide and A. Hutko for valuable comments that improved the manuscript. We also thank H. Houston and anonymous reviewers for their critical reviews. This study was supported by Grant-in-Aid for Scientific Research, type A, 21246075 of the Japan Ministry of Education, Culture, Sports, Science and Technology and Grant-in-Aid for Construction Technology Development, Ministry of Land, Infrastructure, Transport and Tourism, Japan, to YY.