**5. Conclusion**

16 Will-be-set-by-IN-TECH

Fig. 6. Solid, dashed and thick dashed lines indicate stress, strength and slip velocity variation, respectively. (a) in a regular asperity. (b) at a point between the two asperities. Consequently, the hierarchical asperity model for M9 can explain qualitatively the characteristics of the 2011 Tohoku earthquake and other M∼9 earthquakes with smaller earthquakes in the source area. Some predicted phenomena here will be examined by the analyses of high quality and dense data sets both on the seafloor and on the land. Modeling of forshock, aftershocks or M ∼ 8 occurrence as the combination of M ∼ 7 asperities in off Miyagi area is for the future work. We will evaluate the predictability of our model quantitatively by constructing more realistic model, which includes asperity distribution, slab geometry, and so on for the Japan trench and other areas.

## **6. Acknowledgement**

We thank Dr. William Stuart for providing subroutines for calculating stress fields due to triangular dislocations coded by him and Dr. Robert Simpson. This work is partly supported by the MEXT project named Evaluation and disaster prevention research for the coming Tokai, Tonankai and Nankai earthquakes.

#### **7. References**

Aochi, H., and S. Ide (2011) Conceptual multi-scale dynamic rupture model for the 2011 Tohoku earthquake. *Earth Planets Space*, Special Issue: First Results of the 2011 Off the Pacific Coast of Tohoku Earthquake.


Bizzarri, A. & Cocco, M. (2003) Slip-weakening behavior during the propagation of dynamic

Blanpied, M.L., Marone, C.J., Lockner, D.A., Byerlee, J.D. & King, D.P. (2001) Quantitative

Boatwright, J. & Cocco, M. (1996) Frictional constraints on crustal faulting. *J. Geophys. Res.*,

Cisternas, M., Atwater, B. F., Torrejon, F., Sawai, Y., Machuca, G., Lagos, M., Eipert, A.,

Christensen, D.H. & Beck, S.L. (1994) The rupture process and tectonic implications of the great 1964 Prince William Sound earthquake. *Pure Appl. Geophys.*, 142, 29-53. Comninou, M. A. & Dundurs, J. (1975) The angular dislocation in a half-space. *J. Elasticity*, 5,

Earthquake Research Committee (2011) The 2011 off the Pacific coast of Tohoku

Fukao, Y. & Furumoto, M. (1985) Hierarchy in earthquake size distribution. *Phys. Earth Planet.*

Hatori, T. (1969) A Study of the Wave Sources of the Hiuganada Tsunamis. *Bull. Earthq. Res.*

Headquarters for Earthquake Research Promotion (2004) Long-term evaluation of seismicity

Hillers, G., Ben-Zion, Y. & Mai, P. M. (2006) Seismicity on a fault controlled by rate- and

G. Hillers, Mai, P. M., Ben-Zion, Y. & Ampuero, J.-P. (2007) Statistical properties of seismicity

Hirose, H. (2011) Tilt records prior to the 2011 Off the Pacific Coast of Tohoku Earthquake.

Hori, T. & Miyazaki, S. (2011) A possible mechanism of M 9 earthquake generation cycles

Ide, S. & Aochi, H. (2005) Earthquakes as multiscale dynamic rupture with heterogeneous fracture surface energy, *J. Geophys. Res.*, 110, B11303, doi:10.1029/2004JB003591. Ide, S. & Beroza, G. C. (2001) Does apparent stress vary with earthquake size? *Geophys. Res.*

Iinuma, T., Ohzono, M., Ohta, Y. & Miura, S. (2011) Coseismic slip distribution of the 2011 off

the 2011 Off the Pacific Coast of Tohoku Earthquake.

state-dependent friction with spatial variations of the critical slip distance. *J. Geophys.*

of fault zones at different evolutionary stages. *Geophys. J. Int.*, 169, 515-533 doi:

*Earth Planets Space*, Special Issue: First Results of the 2011 Off the Pacific Coast of

in the area of repeating M 7 ∼ 8 earthquakes surrounded by aseismic sliding. *Earth Planets Space*, Special Issue: First Results of the 2011 Off the Pacific Coast of Tohoku

the Pacific coast of Tohoku Earthquake (M9.0) estimated based on GPS data - Was the asperity in Miyagi-oki ruptured? *Earth Planets Space*, Special Issue: First Results of

http://www.jishin.go.jp/main/index-e.html, March 13, 2011.

off Hyuga and Southwestern Islands areas along Ryukyu trench.

*Res.*, 111, B01403, doi:10.1029/2005JB003859.

10.1111/j.1365-246X.2006.03275.x.

Tohoku Earthquake.

*Lett.*, 28, 17, 3349-3352.

Earthquake.

2373, doi:10.1029/2002JB002198.

437, doi:10.1038/nature03943.

*Res.*, 103, 9691-9712.

101, 13895–13909.

*Inter.*, 37, 149-168.

*Inst.*, 47, 55-63.

203-216.

ruptures obeying rate- and state-dependent friction laws. *J. Geophys. Res.*, 108, B8,

measure of the variation in fault rheology due to fluid-rock interaction. *J. Geophys.*

Youlton, C., Salgado, I., Kamataki, T., Shishikura, M., Rajendran, C. P., Malik, J. K., Rizal, Y. & Husni, M. (2005) Predecessors of the giant 1960 Chile earthquake. *Nature*,

Earthquake. *Monthly Reports on Evaluation of Seismic Activity in Japan*,

