GEOPHYSICAL
RESEARCH
LETTERS,
VOL.
38,
L00G04,
doi:10.1029/2011GL048565, 2011
A shallow strong patch model for the 2011 great Tohoku-oki
earthquake: A numerical simulation
Naoyuki Kato1 and Shingo Yoshida1
Received 16 June 2011; accepted 28 June 2011; published 9 August 2011.
[1] A numerical simulation is conducted for understanding the mechanics of the 2011 great Tohoku-oki earthquake (Mw = 9.0), which widely broke the plate interface at the Pacific plate subducting beneath northern Honshu (Tohoku), Japan. In the model, frictional stress on the plate interface is assumed to obey a rate-and state-dependent friction law. A strong patch (asperity) with higher effective normal stress and a large value of characteristic slip distance is assumed at a shallower part of the plate interface. This strong patch controls the occurrence of great earthquakes that broke the entire seismogenic plate interface with recurrence intervals of several hundred years. The present model explains large coseismic slip at a shallower part of the 2011 great earthquake and accumulation of slip deficit at deeper parts, where smaller M7 class earthquakes repeatedly occurred before the great earthquake. Citation: Kato, N., and S. Yoshida (2011), A shallow strong patch model for the 2011 great Tohoku-oki earthquake: A numerical simulation, Geophys. Res. Lett., 38, L00G04, doi:10.1029/2011GL048565.
1. Introduction
[2] The Mw = 9.0 great Tohoku-oki earthquake on March 11, 2011, broke the entire seismogenic depths of the plate interface between the subducting Pacific plate and the overriding plate at northern Honshu, Japan. Finite fault models estimated from seismic waveforms and tsunami indicate that seismic slip extended about 500 km along the Japan trench and about 200 km along the dip direction and the largest seismic slip greater than 30 m occurred at a shallower part of the fault off Miyagi prefecture and seismic slip tended to decrease with increasing depth [Ammon et al., 2011; Fujii et al., 2011; Hayes, 2011]. Large slip near the hypocenter was supported also by seafloor geodetic observations [Sato et al., 2011].
[3] Large earthquakes of M7 class repeatedly occurred on the plate interface off Miyagi including M7.5 event in 1978 and M7.2 event in 2005 at a deeper part and M7.1 event in 1981 and M7.3 event on March 9, 2011 at a shallower part of the seismogenic zone [e.g., Earthquake Research Committee, 2000; Yamanaka and Kikuchi, 2004; Umino et al., 2006; Wu et al., 2008]. Yamanaka and Kikuchi [2004] pointed out that the sum of moment release by the M7 class interplate earthquakes was significantly smaller than that expected from relative plate motion. Observations of Global Positioning System (GPS) indicate that the plate interface off Miyagi was firmly locked and the slip deficit rate was close to the relative
1Earthquake Research Institute, University of Tokyo, Tokyo, Japan.
Copyright 2011 by the American Geophysical Union. 0094-8276/11/2011GL048565
plate rate [Nishimura et al., 2004; Suwa et al., 2006; Wallace et al., 2009]. Igarashi [2010] estimated the average aseismic slip rate from small repeating earthquakes at the plate interface to find that it was significantly smaller than the relative plate rate. These observations indicate that slip deficit was accumulated off Miyagi and it was not released by M7 class earthquakes or continuous stable sliding. The accumulated slip deficit was expected to be released by larger earthquakes or slow earthquakes [Kanamori et al., 2006]. Historical documents and tsunami deposits indicate that a great earthquake of M > 8 took place off Miyagi in 869 [Minoura et al., 2001; Satake et al., 2008; Sawaietal., 2007, 2008]. Sawai et al. [2007] found four sand sheets due to great tsunamis and estimated the recurrence intervals of great tsunamis as 600 to 1300 years.
[4] Numerical simulations with rate-and state-dependent friction (RSF) laws well describe some important characteristics of earthquake cycles at plate interfaces [Tse and Rice, 1986]. By introducing heterogeneous effective normal stress or frictional properties in the models with RSF laws, Ben-Zion and Rice [1995], Kato and Hirasawa [1999], Hillers et al. [2006], and Kato [2008] succeeded in simulating complex earthquake cycles, where regions of high effective normal stress, larger characteristic slip distance, or velocitystrengthening frictional property may be barriers to rupture propagation.
[5] We consider a cross section off Miyagi to build a twodimensional (2D) mechanical model for cycles of great earthquakes because it may be assumed that the region of the largest seismic slip controls the great earthquake occurrence. In the present short article, detailed fit to observation data is not intended. We consider a mechanical model that can explain some features of observations as follows: (1) Recurrence of great earthquakes that break the entire seismogenic plate interface, (2) the largest seismic slip at the shallower part of the plate interface during each great earthquake, and
(3) accumulation of slip deficit at the deeper seismogenic plate interface where many M7 class earthquakes took place.
2. The Model
[6] We consider a thrust fault of a dip angle of 20° in a 2D uniform elastic half-space with rigidity of 40 GPa and Poisson’s ratio of 0.25 (Figure 1). Stable sliding with a sliding rate Vpl of 85 mm/y [DeMets et al., 1990] is assumed on the fault at depths deeper than 103 km, and frictional stress obeys the composite rate-and state-dependent friction law [Kato and Tullis, 2003]. Static equilibrium between frictional stress and slip-induced shear stress is assumed and quasi-dynamic approximation during high-speed slip [Rice, 1993] is applied. Refer to Kato and Tullis [2003] for details of simulation method.
Figure 1. A 2D model for earthquake recurrence on a plate interface at a subduction zone. Frictional stress obeys a rate-and state-dependent friction law at depths shallower than 103 km on the plate interface with a dip angle of 20°, and stable sliding with the sliding rate Vpl of 85 mm/y is assumed at depths deeper than 103 km. Velocity-weakening frictional property is assigned for thick-line parts of the plate interface. Numerals 1 to 12 indicate locations where simulated slip histories are shown in Figures 3 and 5. See text for regions A to E.
[7] Several tens of cases of simulation are done by varying model parameters to obtain a model that can explain some important characteristics of observations. Below we examine an example case that can explain some important features of observations. Figure 2 shows depth dependence of friction parameters a and b, which represent the direct velocity effect and the evolution effect on friction, respectively, charac
eff
teristic slip distance L, and the effective normal stress sn assumed in the present model. On the assumption of litho
eff
static pressure and hydrostatic pore pressure, sn is given by (r - rw)gy for y = 20 km, where y is depth, r = 2.8 × 103 kg/m3, rw = 1.0 × 103 kg/m3, and g = 9.8 m/s2. Due to excess pore pressure [Rice, 1992] sn
eff is assumed to be
88.2 MPa for y > 20 km. A large L value of 0.5 m for y = 20 km is assumed for the shallow strong patch, while the L value for y > 20 km is 0.02 m. Seismic slip may be nucleated for a region of velocity-weakening frictional property, which is characterized by a-b < 0. A region of velocitystrengthening friction (a-b > 0), where aseismic sliding is expected to occur, is assumed for 32.5 km < y = 42.5 km because shallower and deeper seismic zones exist on the plate interface off Miyagi [Earthquake Research Committee, 2000]. The existence of velocity-strengthening region is supported by occurrence of small repeating earthquakes [Igarashi, 2010] and afterslip of the 2005 Miyagi-oki earthquake (M7.2) estimated from GPS observation [Miura et al., 2006]. We refer to region A as the shallow patch with higher eff and large L (y = 20.0 km), region B as the intermediate depth velocity-weakening friction region (20.0 km < y =
sn
32.5 km), region C as the intermediate depth velocitystrengthening friction region (32.5 km < y = 42.5 km), region D as the deep velocity-weakening friction region (42.5 km < y = 52.5 km), and region E as the deep velocity-strengthening friction region (y > 52.5 km) as shown in Figure 1.
3. Simulation Results
[8] After some transient slip behavior due to an artificial initial condition, great earthquakes that break the entire seismogenic plate interface repeatedly occur at a recurrence interval of 716 years. If the 2011 great earthquake is the recurrence of the 869 great earthquake, the time interval is 1142 years. Since the largest seismic slip was estimated to be larger than 30 m, the recurrence interval should be longer than several hundred years. Figure 3 shows simulated slip histories for a great-earthquake cycle at twelve points on the plate interface (Figure 1). The largest seismic slip occurs at the shallow pacth (region A) during each great earthquake and seismic slip decreases with increasing depth as shown in Figure 4, where seismic slip is defined as slip with the slip rate equal to or greater than 10 mm/s. Note that seismic slip occurs in region C with velocity-strengthening frictional property, because of large accumulated slip deficit and large stress concentration due to large seismic slip. The simulated depth distribution of seismic slip is similar to that estimated from seismic and tsunami data as described in section 1. Seismic rupture of a simulated great earthquake starts in region B, a little deeper than the boundary between regions A and B
Figure 2. The variation with depth of (top) friction parameters a (thin solid line), b (broken line), (top) a-b (thick solid
eff
line), (middle) L, and (bottom) the effective normal stress sn assumed in the present model.
Figure 3. Simulated slip histories at twelve points on the plate interface for a great earthquake cycle. The locations of the observation points are shown in Figure 1. Broken lines denote stable sliding with sliding rate of 0.3Vpl (28.3 mm/y),
0.5 Vpl (42.5 mm/y), and Vpl (85.0 mm/y) for reference.
(Figure 4). From various simulation results, we find that the seismic rupture start point is significantly influenced by the depth profiles of friction parameters and effective normal stress and it may be located in a deeper part in region B. A smaller earthquake occurs in region B at 2.2 days before the simulated great earthquake (Figure S1 of the auxiliary material).1 This seems to correspond to the M7.3 event on March 9, which took place near the hypocenter of the March 11 great earthquake. It is remarked that the March 9 foreshock occurred slightly up-dip from the main shock hypocenter, which cannot be explained by the present simple 2D model.
1Auxiliary materials are available in the HTML. doi:10.1029/ 2011GL048565.
Figure 4. Depth distribution of seismic slip of a simulated great earthquake. The star denotes the depth of simulated seismic rupture start.
Figure 5. Simulated slip histories for smaller earthquakes at points 4 to 9 on the plate interface. The locations of the observation points are shown in Figure 1.
We simply point out here that an earthquake at a weaker region may trigger a larger earthquake at a stronger region.
[9] Figure 3 indicates that smaller earthquakes repeatedly occur in regions B and D during an interseismic period of great earthquakes, though the average slip rates are significantly smaller than the relative plate rate. The plate interface is virtually locked in regions B and D during each interseismic period of smaller earthquakes. These simulation results are consistent with observations that the average seismic slip rate estimated from repeated occurrence of M7 class earthquakes was much lower than the average plate rate and the geodetically estimated slip deficit rate was close to the average plate rate. The average recurrence interval of M ~ 7.5 earthquakes at the deeper plate interface off Miyagi was 37 years [Earthquake Research Committee, 2000], which is about half of the present simulation value, suggesting that the assumed L or sn
eff at these depths is too large. Figure 5 shows that simulated slip histories on the plate interface when smaller earthquakes take place in regions B and D. An earthquake in region D is followed by an earthquake at the shallower part with a delay of 196 days. This delay time is a typical value but it is variable in the simulation.
[10] Figure 3 indicates further that the aseismic slip rates at the deep velocity-strengthening regions (region E) during an interseismic period are significantly smaller than the relative plate rate, which is consistent with geodetically estimated slip deficit extended deeper than the seismogenic plate interface [Suwa et al., 2006]. Although each simulated smaller earthquake in region D is followed by afterslip in the simulation, the afterslip amplitude is much smaller than the seismic slip amplitude (Figure 5). This is also consistent with GPS observation for the afterslip of the 2005 Miyagi-oki earthquake [Miura et al., 2006]. Note that the afterslip amplitude depends on friction parameters in region C. The accumulated slip deficit in region E is released as significant afterslip of each great earthquake in the simulation. This significant afterslip causes rapid loading at seismogenic plate interface, leading to earlier occurrence of smaller earthquakes in regions B and D (Figure S2 of the auxiliary material).
4. Summary and Discussion
[11] We conduct a numerical simulation of earthquake cycle at a subduction zone using a 2D model with the rateand state-dependent friction law in order to understand the mechanics of the 2011 great Tohoku-oki earthquake. On the assumption of a strong patch at a shallow part of the plate interface, we can explain some important features of observations as follows: (1) Great earthquakes that break the entire seismogenic plate interface repeatedly occur at a recurrence interval longer than several hundred years. (2) The largest seismic slip of a great earthquake occurs at the shallow part of the plate interface. (3) Slip deficit is accumulated at the deeper part of the plate interface where M7 class earthquakes repeatedly occur during an interseismic period of the great earthquakes. The present simulation result suggests that significant afterslip occurs at a deep aseismic plate interface, where slip deficit is accumulated, leading to rapid loading at the deep seismogenic plate interface, probably resulting in earlier occurrence of M7 class earthquakes. The present model assumed that the shallow strong patch controls the occurrence of great earthquakes and the accumulation of slip deficit at the entire seismogenic plate interface. Each M7 class earthquake at the deeper seismogenic plate interface may relax stress though slip deficit is accumulated because the locked shallow patch prohibits from free slippage. When the strong patch is broken, large seismic slip occurs at the patch and slip occurs also at the deeper plate interface where slip deficit is accumulated. Note that the above features may be reproduced not only by the shallow strong patch but also by large coseismic slip at the shallow patch due to other mechanisms such as thermal pressurization [e.g., Mitsui and Hirahara, 2009; Noda and Lapusta, 2010]. If thermal pressurization occurs only at the shallow patch during each great earthquake, the recurrence interval of earthquakes at the patch would be long and smaller earthquakes would repeatedly occur at deeper parts during the interval.
[12] In the present simulation, great earthquakes of the same magnitude occur repeatedly at a constant recurrence interval. Recurrence of great earthquakes along the Pacific coast of northern Honshu is not sufficiently understood. Recurrence of same magnitude earthquakes in the present model may be too simple to explain possible complex earthquake recurrence in the region.
[13] The strong patch is realized by higher values of
eff
effective normal stress sn and/or large values of characteristic slip distance L in the simulation. Because sn
eff is given by the difference between lithostatic pressure and hydrostatic
eff
pore pressure at depths =20 km, the large contrast of sn comes from higher pore pressure at deeper parts. Higher pore pressure may be justified by pore compaction and sealing in the fault zone at the deeper parts. Larger L values assumed at the shallower depths may be justified by the unconsolidated material at the shallow plate boundary. Moreover, large L may lead to slow source process, which seems to be consistent with less short-period seismic radiation from the shallow patch of the earthquake [Koper et al., 2011]. The maximum L value of 0.5 m assumed in the present model corresponds to the critical slip-weakening distance Dc of 1.5–2.0 m [Kato and Tullis, 2003]. Although some uncertainty is included in estimates of Dc for earthquakes, Dc of 1.5–2.0 m seems to be permissible [e.g., Zhang et al., 2003]. The recurrence interval Tr of great earthquakes is controlled by fracture energy at the strong patch and the theoretical consideration suggests that Tr
p..........
eff
is proportional to .L [Kato, 2010]. We perform numer
n
ical simulations for various values of friction parameters to confirm that qualitatively similar results can be obtained for only higher sn
eff or only larger L at the shallow patch, though too large L leads to slow earthquakes or stable sliding [Kato and Hirasawa, 1997]. Thus, the origin of the strong patch cannot be constrained by the present simulation.
[14] Acknowledgments. We are grateful to S. Miyazaki and an anonymous reviewer for valuable comments, which improved the manuscript. Discussion with T. Igarashi, J. Fukuda, A. Kato and N. Hirata were useful for clarifying our thought. This research was supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan.
References
Ammon, C. J., T. Lay, H. Kanamori, and M. Cleveland (2011), A rupture model of the great 2011 Tohoku earthquake, Earth Planets Space,in press.
Ben-Zion, Y., and J. R. Rice (1995), Slip patterns and earthquake popolations along different classes of faults in elastic solids, J. Geophys. Res., 100, 12,959–12,983, doi:10.1029/94JB03037.
DeMets, C., R. G. Gordon, D. F. Argus, and S. Stein (1990), Current plate motions, Geophys. J. Int., 101, 425–478, doi:10.1111/j.1365-246X.1990. tb06579.x.
Earthquake Research Committee (2000), Long-term forecast of Miyagi-oki earthquakes (in Japanese), report, 18 pp., Headquarters for Earthquake Res. Promotion, Tokyo, Japan.
Fujii, Y., K. Satake, S. Sakai, M. Shinohara, and T. Kanazawa (2011), Tsunami source of the 2011 off the Pacific coast of Tohoku, Japan earthquake, Earth Planets Space, in press.
Hayes, G. (2011), Rapid source characterization of the 03-11-2011 Mw 9.0 off the Pacific coast of Tohoku earthquake, Earth Planets Space, in press.
Hillers, G., Y. Ben-Zion, and P. M. Mai (2006), Seismicity on a fault controlled by rate-and state-dependent friction with spatial variations of the critical slip distance, J. Geophys. Res., 111, B01403, doi:10.1029/ 2005JB003859.
Igarashi, T. (2010), Spatial changes of inter-plate coupling inferred from sequences of small repeating earthquakes in Japan, Geophys. Res. Lett., 37, L20304, doi:10.1029/2010GL044609.
Kanamori, H., M. Miyazawa, and J. Mori (2006), Investigation of the earthquake sequence off Miyagi prefecture with historical seismograms, Earth Planets Space, 58, 1533–1541.
Kato, N. (2008), Numerical simulation of recurrence of asperity rupture in the Sanriku region, northeastern Japan, J. Geophys. Res., 113, B06302, doi:10.1029/2007JB005515.
Kato, N. (2010), Dependence of earthquake stress drop on critical slipweakening distance, Abstract S33E-08 presented at 2010 Fall Meeting, AGU, San Francisco, Calif., 13–17 Dec.
Kato, N., and T. Hirasawa (1997), A numerical study on seismic coupling along subduction zones using a laboratory-derived friction law, Phys. Earth Planet. Inter., 102,51–68, doi:10.1016/S0031-9201(96)03264-5.
Kato, N., and T. Hirasawa (1999), Nonuniform and unsteady sliding of a plate boundary in a great earthquake cycle: A numerical simulation using a laboratory-derived friction law, Pure Appl. Geophys., 155,93–118, doi:10.1007/s000240050256.
Kato, N., and T. E. Tullis (2003), Numerical simulation of seismic cycles with a composite rate-and state-dependent friction law, Bull. Seismol. Soc. Am., 93, 841–853, doi:10.1785/0120020118.
Koper, K. D., A. R. Hutko, T. Lay, C. J. Ammon, and H. Kanamori (2011), Frequency-dependent rupture process of the 11 March 2011 Mw 9.0 Tohoku earthquake: Comparison of short-period P wave back-projection images and broadband seismic rupture models, Earth Planets Space, in press.
Minoura, K., F. Imamura, D. Sugawara, Y. Kono, and T. Iwashita (2001), The 869 Jogan tsunami deposit and recurrence interval of large-scale tsunami on the Pacific coast of northeast Japan, J. Nat. Disaster Sci., 23,83–88.
Mitsui, Y., and K. Hirahara (2009), Coseismic thermal pressurization can notably prolong earthquake recurrence intervals on weak rate and state friction faults: Numerical experiments using different constitutive equations, J. Geophys. Res., 114, B09304, doi:10.1029/2008JB006220.
Miura, S., T. Iinuma, S. Yui, N. Uchida, T. Sato, K. Tachibana, and
A. Hasegawa (2006), Co-and post-seismic slip associated with the 2005 Miyagi-oki earthquake (M7.2) as inferred from GPS data, Earth Planets Space, 58, 1567–1572.
Nishimura, T., T. Hirasawa, S. Miyazaki, T. Sagiya, T. Tada, S. Miura, and
K. Tanaka (2004), Temporal change of interplate coupling in northeastern Japan during 1995–2002 estimated from continuous GPS observations, Geophys. J. Int., 157, 901–916, doi:10.1111/j.1365-246X.2004.02159.x.
Noda, H., and N. Lapusta (2010), Three-dimensional earthquake sequence simulations with evolving temperature and pore pressure due to shear heating: Effect of heterogeneous hydraulic diffusivity, J. Geophys. Res., 115, B12314, doi:10.1029/2010JB007780.
Rice, J. R. (1992), Fault stress states, pore pressure distribution, and the weakness of the San Andreas fault, in Fault Mechanics and Transport Properties of Rocks, editedbyB.Evans and T.-F. Wong, pp. 475–503, Academic, San Diego, Calif., doi:10.1016/S0074-6142(08)62835-1.
Rice, J. R. (1993), Spatio-temporal complexity of slip on a fault, J. Geophys. Res., 98, 9885–9907, doi:10.1029/93JB00191.
Satake, K., Y. Namegaya, and S. Yamaki (2008), Numerical simulation of the AD 869 Jogan tsunami in Ishinomaki and Sendai plains (in Japanese with English abstract), Annu. Rep. Active Fault Paleoearthquake Res., 8, 71–89.
Sato, M., T. Ishikawa, N. Ujihara, S. Yoshida, M. Fujita, M. Mochizuki, and A. Asada (2011), Displacement above the hypocenter of the 2011 Tohoku-oki earthquake, Science, 332, 1395, doi:10.1126/science. 1207401.
Sawai, Y., et al. (2007), A study on paleotsunami using handy geoslicer in Sendai Plane (Sendai, Natori, Iwanuma, Watari, and Yamamoto) (in Japanese with Englsih abstract), Miyagi, Japan, Annu. Rep. Active Fault Paleoearthquake Res., 7,47–80.
Sawai, Y., Y. Fujii, O. Fujiwara, T. Kamataki, J. Komatsubara, Y. Okamura,
K. Satake, and M. Shishikura (2008), Marine incursions of the past 1500 years and evidence of tsunamis at Suijin-numa, a coastal lake facing the Japan Trench, Holocene, 18,517–528, doi:10.1177/ 0959683608089206.
Suwa, Y., S. Miura, A. Hasegawa, T. Sato, and K. Tachibana (2006), Interplate coupling beneath NE Japan inferred from three-dimensional displacement field, J. Geophys. Res., 111, B04402, doi:10.1029/ 2004JB003203.
Tse, S. T., and J. R. Rice (1986), Crustal earthquake instability in relation to the depth variation of frictional slip properties, J. Geophys. Res., 91, 9452–9472, doi:10.1029/JB091iB09p09452.
Umino, N., T. Kono, T. Okada, J. Nakajima, T. Matsuzawa, N. Uchida,
A. Hasegawa, Y. Tamura, and G. Aoki (2006), Revisiting the three M~7 Miyagi-oki earthquakes in the 1930s: possible seismogenic slip on asperities that were re-ruptured during the 1978 M = 7.4 Miyagi-oki earthquake, Earth Planets Space, 58, 1587–1592.
Wallace, L. M., R. J. Beavan, S. Miura, and R. McCaffrey (2009), Using global positioning system data to assess tectonic hazards, in Volcanic and Tectonic Hazard Assessment for Nuclear Facilities, edited by
C. B. Connor, N. A. Chapman, and L. J. Connor, pp. 156–175, Cambridge Univ. Press, Cambridge, U. K., doi:10.1017/CBO9780511635380.007.
Wu, C., K. Koketsu, and H. Miyake (2008), Source processes of the 1978 and 2005 Miyagi-oki, Japan, earthquakes: Repeated rupture of asperities over successive large earthquakes, J. Geophys. Res., 113, B08316, doi:10.1029/2007JB005189.
Yamanaka, Y., and M. Kikuchi (2004), Asperity map along the subduction zone in northeastern Japan inferred from regional seismic data,
J. Geophys. Res., 109, B07307, doi:10.1029/2003JB002683.
Zhang, W., T. Iwata, K. Irikura, H. Sekiguchi, and M. Bouchon (2003), Heterogeneous distribution of the dynamic source parameters of the 1999 Chi-Chi, Taiwan, earthquake, J. Geophys. Res., 108(B5), 2232, doi:10.1029/2002JB001889.
N. Kato and S. Yoshida, Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi Bunkyo-ku, Tokyo 113-0032, Japan. (nkato@eri.utokyo.ac.jp)