Possibility of Mw 9.0 mainshock triggered by diffusional propagation of after-slip from Mw 7.3 foreshock
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For the 2011 off the Pacific coast of Tohoku, Japan, Earthquake, we have investigated the spatio-temporal changes in seismicity from the Mw 7.3 foreshock, March 9, 2011, 11:45, to the Mw 9.0 mainshock, March 11, 14:46 (Japan Standard Time). We found that seismic activities slowly migrated from the source area of the foreshock, which presumably reflected the propagation of the after-slip. The mainshock rupture was initiated when the migration reached the hypocentral location of the mainshock. We also found that the migration slowed down as it expanded, where the migration distance was well fitted by a certain curve proportional to the square root of the duration, suggesting that the propagation was limited by diffusion with a diffusion coefficient of about 104 m2 s−1. This slow slip mechanism differs from nucleation-related pre-slip traditionally applied in earthquake predictions. The obtained value of the diffusion coefficient is of the same order of magnitude as that reported for the migration of a deep non-volcanic tremor. These results appear to be compatible with a conceptual model having strongly coupled patches which, although being separated by decoupled stable regions on this plate-interface, are not mechanically isolated and which became interactive when they broke.
Key wordsTohoku Earthquake foreshock triggering after-slip diffusion
Foreshock-mainshock sequences are also recognized as earthquake doublets, observed in various tectonic settings, which phenomenon has been understood in terms of defined fault segmentations in some form (e.g., Lay and Kanamori, 1980; Engdahl et al., 2007; Nakano et al., 2010). They serve as a type of earthquake triggering and stress transfer (King et al., 1994; Gomberg et al., 2001). This context has particular importance in understanding the current sequence of events, because it has been believed that the plate-interface below the Japan trench contains strongly-coupled patches that are relatively small, and which define strong segmentations as impeding gigantic earthquakes (e.g., Lay and Kanamori, 1981). But, on this occasion, is this view totally wrong? In this paper, we reexamine it in the light of the currently observed foreshock-mainshock sequence.
We concentrate on the data analysis for the 2011 To-hoku Earthquake to clarify the seismicity migration pattern which began at the foreshock and lasted until the main-shock. The background seismicity is also reviewed. An intuitive understanding of the physical background will be given by a model having brittle-ductile mixed fault heterogeneity (Ando et al., 2010; Nakata et al., 2011). We will see below that the seismicity migration follows well the above-mentioned parabolic pattern and that the onset timing of the mainshock corresponds to the arrival of the migration front to the mainshock hypocentral location.
In order to obtain the seismic activity data, we have applied the double-difference earthquake location algorithm of Waldhauser and Ellsworth (2000) to routinely determined P- and S -phase arrival time readings from the Japan Meteorological Agency (JMA). Each event is linked to its neighbors through commonly observed phases, with the average distance between linked events being 20 km. The data was obtained from the Japanese nationwide seismic network and the readings by JMA were obtained during the period between the foreshock and the mainshock. We applied a bootstrap resampling technique to quantify the precision of a given location (see Waldhauser and Ellsworth, 2000); we obtained relative location errors, defined as 1σ, of about 2 km in both horizontal and vertical directions, which is sufficient to discuss the relative locations of the earthquakes during the migration over nearly 40 km.
We choose hypocenters that can reasonably be assumed to be on or around the plate interface (Fig. 1(a)). This is based on the hypocentral depth distribution, which shows a tendency for the hypocenters to be localized to a plane of the presumed plate interface which, despite a certain limitation in the accuracy for these offshore events (Fig. 1(b), lower), is also strongly supported by the CMT solutions, manually determined by the National Research Institute for Earth Science and Disaster Prevention (available at www.fnet.bosai.go.jp), having nodal planes of low-angle reverse faulting (Fig. 1(c)). Note that such features become more obvious in our targeted area, located between the epicenters of the foreshock and mainshock, than in the case of further offshore events. The events of JMA magnitude larger than Mj 1 are included in Figs. 1(a) and (b) but events larger than Mj 2.6 are involved in the following quantitative analysis. To analyze background seismicity, we used the JMA earthquake catalog, and earthquakes smaller than Mj 6 are considered only after January 2000.
Because the propagation of slow slip induces stress perturbation on and around plate interfaces, we can expect the occurrence of earthquakes that are triggered by slow slip in the current sequence, as has been observed along the currently targeted subduction zone (e.g., Miyazaki et al., 2004; Uchida et al., 2004). This situation will also be similar to the generation of a non-volcanic tremor in association with slow slip events (SSEs) observed for the various plate interfaces (Rogers and Dragert, 2003; Obara et al., 2004). Supported by these established observational facts, we can safely interpret the seismic activity change as the marker of the propagation of slow slip, i.e., after-slip.
Figure 1(a) shows the spatio-temporal evolution of seismic activity during the two days between the foreshock and the mainshock. The colors of the epicenters denote the occurrence time of each earthquake so that we can trace temporal changes in the activity. As seen in the gradual changes of the colors, the seismicity migrated and expanded from the focal area of the foreshock, whilst there was an absence of seismicity in some areas. Finally, we can note that the migration reached the hypocentral location of the mainshock.
First, we investigate the migration pattern on the map view (Fig. 1(a)). The colored tick marks appended inside the gray rectangles show the locations of the migration fronts at 6 hour intervals calculated from Eq. (2) assuming D = 0.78 × 104 m2 s−1 where the color coding corresponds to time after the foreshock (see color bar scale); these intervals become closer as time passes following Eq. (2). In this figure, it is immediately found that the calculated total migration distance bridges a gap between the foreshock focal area and the mainshock epicenter, meaning that the given value of D describes the overall rate of migration well. Comparisons between the colors of the ticks and the epicenters enable a more detailed investigation into the migration process. (Note that we need to trace the front of the migration, which corresponds to the first event at a certain location, whereas some events can be obscured by neighboring later events on this figure.) Although the event locations are spotty, we can see that the overall pattern of their gradual color changes is also well correlated with the tick colors. In particular, it is clearly seen that the migration front extended more than half the total distance during the first half a day, and took another 1.5 days to extend the remaining distance.
Finally, we quantitatively evaluate the other possibilities: (1) linear function fitting and (2) a different migration start point assumed at Lm = 32 as an extreme case considering an extraordinarily larger foreshock focal area. Figure 2(b) shows the used dataset and the obtained least-squares solutions with the root mean squares of the sum of their squared residuals. In order that the dataset on the migration is kept as simple as possible, we eliminated only the obvious aftershocks and the above-mentioned continual activity, so as not to be biased too much by these different phenomena. As a result, we can see that the linear function fittings have larger residuals than the parabolic cases for both assumed starting points (Removing a tricky data point at Lm = 26 changes the residual by less than 10%, and does not change this tendency.) Moreover, we find that the linear cases cannot follow the overall trend if one attempts to explain reasonably all the data points from the foreshock area, Lm ~ 37, to the mainshock hypocenter, Lm = 0, through the recognizable migration front between Lm ~ 5–20 (the reason for the lack of seismicity inbetween is discussed below). These fitting results are basically valid even allowing for possible epicentral determination errors.
4. Discussions and Conclusion
In Fig. 2, we saw an area with an apparent lack of seismicity for Lm ~ 20–35. This apparent deficit seems to be characteristic of this area as exemplified by long-term seismic activity (Fig. 3). We can, perhaps, suppose both decoupling and coupling just to interpret this seismic gap but the slow propagation of the after-slip through the gap is incompatible with the latter because, if such a large coupled patch breaks, the rupture would be accelerated to be a standard earthquake. Therefore we can presume that this area is persistently decoupled as indicated in Fig. 3(b). In this respect, the seismic sequence in January, 1981, provides an interesting perspective because, beyond this gap, the onset of the M 6.6 events on January 23 was largely delayed after the M 7.0 event on January 19. In fact, it suggests that the delay can be explained by a parabolic curve with D = 0.46 × 104 (Fig. 3(c)), which is the same, by an order of magnitude, as that for the current foreshock-mainshock sequence.
The above view is qualitatively supported by physics-based simulations (Ando et al., 2010; Nakata et al., 2011) demonstrating that, if a number of coupled patches almost equally reach their critical stress state, these patches can be ruptured in a sequence even though the patches are sparsely distributed to some extent. We speculate that such a synchronization, which rarely occurs over a great distance, might have happened this time. The simulations further clarify that the degree of the patch interactions is controlled by the patch distributions, and that the parabolic and diffusional slow slip propagation occurs under a certain rheolog-ical fault condition.
The existence of a strict control in after-slip propagation (Eq. (2)) and the possibility of signal detection offer a chance to predict the occurrence of subsequent earthquakes in the preceding hours or days, although we may always expect fluctuations depending on conditions. However, because this phenomenon alone cannot alert us to earthquake generation, in order to accomplish such a prediction we need to know beforehand the locations of coupled patches and their tectonic stress levels. Such evaluations could be made possible by improvements in geodetic (e.g., Hashimoto et al., 2009) and seismic (e.g., Uchida et al., 2004) monitoring for plate coupling, combined with paleo-seismological history reconstruction (e.g., Sawai et al., 2009) to quantify elapsed times since previous earthquakes and their magnitudes. It is also essential to develop proper physical fault models to input these data and to translate them into physical fault states. Since the degree of plate-coupling has localities (Lay and Kanamori, 1981) and the interactive behaviors between fault segments (or patches) are not straightforward, a physics-based understanding is important to compensate for our limited experiences. Earthquake studies following such a direction could be applied to consider other potentially catastrophic earthquakes, such as that on the Nankai subduction zone off southwest Japan.
Suggestions by Y. Yoshida improved the manuscript. We are grateful to the Japan Meteorological Agency (JMA) for the P- and S-phase arrival time readings and the earthquake catalog. The data was processed in collaboration with the JMA and the Ministry of Education, Culture, Sports, Science and Technology (MEXT). This work was partially supported by MEXT KAKENHI (21107007).
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