# Slip-Weakening Models of the 2011 Tohoku-Oki Earthquake and Constraints on Stress Drop and Fracture Energy

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## Abstract

We present 2D dynamic rupture models of the 2011 Tohoku-Oki earthquake based on linear slip-weakening friction. We use different types of available observations to constrain our model parameters. The distribution of stress drop is determined by the final slip distribution from slip inversions. As three groups of along-dip slip distribution are suggested by different slip inversions, we present three slip-weakening models. In each model, we assume uniform critical slip distance eastward from the hypocenter, but several asperities with smaller critical slip distance westward from the hypocenter. The values of critical slip distance are constrained by the ratio of deep to shallow high-frequency slip-rate power inferred from back projection source imaging. Our slip-weakening models are consistent with the final slip, slip rate, rupture velocity and high-frequency power ratio inferred for this earthquake. The average static stress drop calculated from the models is in the range of 4.5–7 MPa, though large spatial variations of static stress drop exist. To prevent high-frequency radiation in the region eastward from the hypocenter, the fracture energy needed there is in the order of 10 MJ/m^{2}, and the average up-dip rupture speed cannot exceed 2 km/s. The radiation efficiency calculated from our models is higher than that inferred from seismic data, suggesting the role of additional dissipation processes. We find that the structure of the subduction wedge contributes significantly to the up-dip rupture propagation and the resulting large slip at shallow depth.

## Keywords

Tohoku-Oki earthquake dynamic rupture model stress drop fracture energy energy partitioning subduction wedge## Notes

### Acknowledgments

This work was supported by NSF grants EAR-0944288 and EAR-1015704, the Gordon and Betty Moore Foundation, the Japan Nuclear Energy Safety Organization (JNES) and SCEC (funded by NSF EAR-0106924 and USGS 02HQAG0008 cooperative agreements).

## References

- Ampuero, J. P. (2009),
*SEM2DPACK, A spectral element method tools for 2D wave propagation and earthquake source dynamics*, User’s Guide, version 2.3.6. Available online at http://www.sourceforge.net/projects/sem2d/. - Andrews, D. J. (1985),
*Dynamic plane-strain shear rupture with a slip-weakening friction law calculated by a boundary integral method*, Bull. Seismol. Soc. Am.,*75*, 1–21.Google Scholar - Aochi, H., and Ide, S. (2011),
*Conceptual multi-scale dynamic rupture model for the 2011 off the Pacific coast of Tohoku Earthquake*, Earth Planets Space,*63*, 761–765.Google Scholar - Duan, B. (2012),
*Dynamic rupture of the 2011 Mw 9.0 Tohoku-Oki earthquake: Roles of a possible subducting seamount*, J. Geophys. Res.,*117*, B05311.Google Scholar - Freund, L. B., Dynamic fracture mechanics (Cambridge Univ. Press, Cambridge 1990).Google Scholar
- Fujiwara, T., Kodaira, S., No, T., Kaiho, Y., Takahashi, N., and Kaneda, Y. (2011),
*The 2011 Tohoku-Oki earthquake: Displacement reaching the trench axis*, Science,*334*, 1240.Google Scholar - Goto, H., Yamamoto, Y., and Kita, S. (2012),
*Dynamic rupture simulation of the 2011 off the Pacific coast of Tohoku Earthquake: Multi-event generation within dozens of seconds*, Earth Planets Space,*64*, 1167–1175.Google Scholar - Huang, Y., Meng, L., and Ampuero, J.-P. (2012),
*A dynamic model of the frequency-dependent rupture process of the 2011 Tohoku-Oki earthquake*, Earth Planets Space,*64*, 1061–1066.Google Scholar - Hyndman, R. D., Yamano, M., and Oleskevich, D. A. (1997),
*The seismogenic zone of subduction thrust faults*, Island Arc,*6*, 244–260.Google Scholar - Ide, S., Baltay, A., and Beroza, G. C. (2011),
*Shallow dynamic overshoot and energetic deep rupture in the 2011 Mw 9.0 Tohoku-Oki earthquake*, Science,*332*, 1426–1429, 2011.Google Scholar - Igarashi, T., Matsuzawa, T., and Hasegawa, A. (2003),
*Repeating earthquakes and interplate aseismic slip in the northeastern Japan subduction zone*, J. Geophys. Res.,*108*, 2249.Google Scholar - Iinuma, T., Hino, R., Kido, M., Inazu, D., Osada, Y., Ito, Y., Ohzono, M., Tsushima, H., Suzuki, S., Fujimoto, H., and Miura, S. (2012),
*Coseismic slip distribution of the 2011 off the Pacific Coast of Tohoku Earthquake (M9.0) refined by means of seafloor geodetic data*, J. Geophys. Res.,*117*, B07409.Google Scholar - Ito, Y., Tsuji, T., Osada, Y., Kido, M., Inazu, D., Hayashi, Y., Tsushima, H., Hino, R., and Fujimoto, H. (2011),
*Frontal wedge deformation near the source region of the 2011 Tohoku-Oki earthquake*, Geophys. Res. Lett.,*38*, L00G05.Google Scholar - Kanamori, H., and Rivera, L., Energy partitioning during an earthquake, Earthquakes: Radiated energy and the physics of faulting (AGU Monograph Series 170, Washington D. C., 2006) pp. 3–14.Google Scholar
- Kaneko, Y., Lapusta, N., and Ampuero, J.-P. (2008),
*Spectral element modeling of spontaneous earthquake rupture on rate and state faults: Effects of velocity-strengthening friction at shallow depth*, J. Geophys. Res.,*113*, B09317.Google Scholar - Kato, N., and Yoshida, S. (2011),
*A shallow strong patch model for the 2011 great Tohoku-oki earthquake: a numerical simulation*, Geophys. Res. Lett.,*38*, L00G04,Google Scholar - Kido, M., Osada, Y., Fujimoto, H., Hino, R., and Ito, Y. (2011),
*Trench-normal variation in observed seafloor displacements associated with the 2011 Tohoku-Oki earthquake*, Geophys. Res. Lett.,*38*, L24303.Google Scholar - Kimura, G., Hina S., Hamada, Y., Kameda, J., Tsuji, T., Kinoshita, M., and Yamaguchi, A. (2012),
*Runaway slip to the trench due to rupture of highly pressurized megathrust beneath the middle trench slope: The tsunamigenesis of the 2011 Tohoku earthquake off the east coast of northern Japan*, Earth Planet. Sci. Lett.,*339–340*, 32–45.Google Scholar - Kiser, E., and Ishii, M. (2012),
*The March 11, 2011 Tohoku-oki earthquake and cascading failure of the plate interface*, Geophys. Res. Lett.,*39*, L00G25.Google Scholar - Kodaira, S., No, T., Nakamura, Y., Fujiwara, T., Kaiho, Y., Miura, S., Takahashi, N., Kaneda, Y., and Taira, A. (2012),
*Coseismic fault rupture at the trench axis during the 2011 Tohoku-oki earthquake*, Nature Geosci.,*5*, 646–650.Google Scholar - Koketsu, K., Yokota, Y., Nishimura, N., Yagi, Y., Miyazaki, S., Satake, K., Fujii, Y., Miyake, H., Sakai, S., Yamanaka, Y., and Okada, T. (2011),
*A unified source model for the 2011 Tohoku earthquake*, Earth Planet. Sci. Lett.,*310*, 480–487.Google Scholar - Kozdon, J. E., and Dunham, E. M. (2013),
*Rupture to the trench: Dynamic rupture simulations of the 11 March 2011 Tohoku earthquake*, Bull. Seismic. Soc. Am.,*103*, 1275–1289.Google Scholar - Lay, T., Ammon, C. J., Kanamori, H., Xue, L., and Kim, M. J. (2011),
*Possible large near-trench slip during the 2011 Mw 9.0 off the Pacific coast of Tohoku earthquake*, Earth, Planets Space,*63*, 687–692.Google Scholar - Lay, T., Kanamori, H., Ammon, C. J., Koper, K. D., Hutko, A. R., Ye, L., Yue, H., and Rushing, T. M. (2012),
*Depth-varying rupture properties of subduction zone megathrust faults*, J. Geophys. Res.,*117*, B04311.Google Scholar - Lee, S.-J., Huang, B.-S., Ando, M., Chiu, H.-C., and Wang, J.-H. (2011),
*Evidence of large scale repeating slip during the 2011 Tohoku-Oki earthquake*, Geophys., Res. Lett.,*38*, L19306.Google Scholar - Ma, S., and Hirakawa, E. T. (2013),
*Dynamic wedge failure reveals anomalous energy radiation of shallow subduction earthquakes*, Earth Planet. Sci. Lett.,*375*, 113–122.Google Scholar - Madariaga, R. (1983),
*High-frequency radiation from dynamic earthquake fault models*, Ann. Geophys.,*1*, 17–23.Google Scholar - Meng, L., Inbal, A., and Ampuero, J.-P. (2011),
*A window into the complexity of the dynamic rupture of the 2011 Mw 9 Tohoku-Oki earthquake*, Geophys. Res. Lett.,*38*, L00G07.Google Scholar - Newman, A. (2011), Written Communication, May 3, 2011.Google Scholar
- Noda, H., and Lapusta, N. (2012),
*On averaging interface response during dynamic rupture and energy partitioning diagrams for earthquakes*, J. Appl. Mech.,*79*, 031026.Google Scholar - Noda, H., and Lapusta, N. (2013),
*Stable creeping fault segments can become destructive as a result of dynamic weakening*, Nature,*493*, 518–523.Google Scholar - Sato, H., Ishikawa, T., Ujihara, N., Yoshida, S., Fujita, M., Mochizuki, M., and Asada, A. (2011),
*Displacement above the hypocenter of the 2011 Tohoku-Oki earthquake*, Science,*332*, 1395.Google Scholar - Simons, M.,
*et al*. (2011),*The 2011 magnitude 9.0 Tohoku-Oki earthquake: Mosaicking the megathrust from seconds to centuries*, Science,*332*, 1421–1425.Google Scholar - Tajima, F., Mori, J., and Kennett, B. L. N. (2013),
*A review of the 2011 Tohoku-Oki earthquake (Mw 9.0): Large-scale rupture across heterogeneous plate coupling*, Tectonophysics,*586*, 15–34.Google Scholar - Tobin, H. J., and Saffer, D. M. (2009),
*Elevated fluid pressure and extreme mechanical weakness of a plate boundary thrust, Nankai Trough subduction zone*, Geology,*37*, 679-682.Google Scholar - Wei, S., Graves, R., Helmberger, D., Avouac, J.-P., and Jiang, J. (2012),
*Sources of shaking and flooding during the Tohoku-Oki earthquake: A mixture of rupture styles*, Earth Planet. Sci. Lett.,*333–334*, 91–100.Google Scholar - Yagi, Y., and Fukahata, Y. (2011),
*Rupture process of the 2011 Tohoku-oki earthquake and absolute elastic strain release*, Geophys. Res. Lett.,*38*, L19307.Google Scholar - Yoshida, S., and Kato, N. (2011),
*Pore pressure distribution along plate interface that causes a shallow asperity of the 2011 great Tohoku-oki earthquake*, Geophys. Res. Lett.,*38*, L00G13.Google Scholar - Yue, H., and Lay, T. (2011),
*Inversion of high-rate (1sps) GPS data for rupture process of the 11 March 2011 Tohoku earthquake (Mw 9.1)*, Geophys. Res. Lett.,*38*, L00G09.Google Scholar