Skip to main content
SpringerLink
Log in

Complexity in the Earthquake Cycle Increases with the Number of Interacting Patches

  • Published:
Pure and Applied Geophysics Aims and scope Submit manuscript

Abstract

Numerical simulations were performed to examine the effects of heterogeneity of frictional properties on earthquake cycles. In the model, rate- and state-dependent friction was assumed at a planar fault in an infinite uniform elastic medium. Simulated earthquake cycles were compared at model faults with one to four circular patches with velocity-weakening frictional properties. The characteristic slip distances for the patches were varied so that the effects of interactions between patches with different frictional properties could be assessed. Simple periodic, multiperiodic, and aperiodic earthquake cycles were observed in the simulation results. The frequencies of the multiperiodic and aperiodic cycles increased with the number of velocity-weakening patches, suggesting that more complex cycles may occur in a fault as the frictional properties become more heterogeneous. The simulated earthquake cycles were divided into several classes according to the combinations of ruptured patches in the earthquakes. Complex aperiodic earthquake cycles tended to occur when the values of the parameters lay between the parameter ranges for the different patterns. The frequency distribution of simulated earthquake recurrence intervals became more continuous and smooth as the number of patches increased. The simulation results suggest that interactions between many patches with different frictional properties form part of the explanation of realistic complex earthquake cycles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

References

  • Abe, Y., & Kato, N. (2013). Complex earthquake cycle simulations using a two-degree-of-freedom spring-block model with a rate- and state-friction law. Pure and Applied Geophysics, 170, 745–765. https://doi.org/10.1007/s00024-011-0450-8.

    Article  Google Scholar 

  • Abe, Y., & Kato, N. (2014). Intermittency of earthquake cycles in a model of a three-degree-of-freedom spring-block system. Nonlinear Processes in Geophysics, 21, 841–853. https://doi.org/10.5194/npg-21-841-2014.

    Article  Google Scholar 

  • Ampuero, J.-P., & Rubin, A. M. (2008). Earthquake nucleation on rate and state faults aging and slip laws. Journal of Geophysical Research, 113, B01302. https://doi.org/10.1029/2007JB005082.

    Article  Google Scholar 

  • Barbot, S., Lapusta, N., & Avouac, J.-P. (2012). Under the hood of the earthquake machine: Toward predictive modeling of the seismic cycle. Science, 336, 707–710. https://doi.org/10.1126/science.1218796.

    Article  Google Scholar 

  • Becker, T. W. (2000). Deterministic chaos in two state-variable friction sliders and the effect of elastic interactions. In J. B. Rundle, D. L. Turcotte, & W. Klein (Eds.), Geocomplexity and the physics of earthquakes, AGU monograph (Vol. 120, pp. 5–26). Washington, DC: American Geophysical Union.

    Chapter  Google Scholar 

  • Berryman, K. R., Cochran, U. A., Clark, K. J., Biasi, G. P., Langridge, R. M., & Villamor, P. (2012). Major earthquakes occur regularly on an isolated plate boundary fault. Science, 336, 1690–1693. https://doi.org/10.1126/science.1218959.

    Article  Google Scholar 

  • Bizzarri, A., & Cocco, M. (2003). Slip-weakening behavior during the propagation of dynamic ruptures obeying rate- and state-dependent friction laws. Journal of Geophysical Research, 108(B8), 2373. https://doi.org/10.1029/2002JB002198.

    Article  Google Scholar 

  • Carlson, J. M., & Langer, J. S. (1989). Mechanical model of an earthquake fault. Physical Review A, 40, 6470–6484.

    Article  Google Scholar 

  • Chen, T., & Lapusta, N. (2019). On behaviour and scaling of small repeating earthquakes in rate and state fault models. Geophysical Journal International, 218, 2001–2018. https://doi.org/10.1093/gji/ggz270.

    Article  Google Scholar 

  • Chen, K. H., Bürgmann, R., Nadeau, R. M., Chen, T., & Lapusta, N. (2010). Postseismic variations in seismic moment and recurrence interval of repeating earthquakes. Earth and Planetary Science Letters, 299, 118–125. https://doi.org/10.1016/j.epsl.2010.08.027.

    Article  Google Scholar 

  • Cochard, A., & Madariaga, R. (1994). Dynamic faulting under rate-dependent friction. Pure and Applied Geophysics, 142, 419–445.

    Article  Google Scholar 

  • Dieterich, J. H. (1979). Modeling of rock friction: 1. Experimental results and constitutive equations. Journal of Geophysical Research, 84, 2161–2168.

    Article  Google Scholar 

  • Dieterich, J. H. (1992). Earthquake nucleation on faults with rate- and state-dependent strength. Tectonophysics, 211, 115–134.

    Article  Google Scholar 

  • Dieterich, J. H. (2007). Applications of rate- and state-dependent friction to models of fault-slip and earthquake occurrence. Treatise on Geophysics, 4 (pp. 107–129). Amsterdam: Elsevier.

    Chapter  Google Scholar 

  • Dieterich, J. H., & Richards-Dinger, K. B. (2010). Earthquake recurrence in simulated fault systems. Pure and Applied Geophysics, 167, 1087–1184. https://doi.org/10.1007/s00024-010-0094-0.

    Article  Google Scholar 

  • Dragoni, M., & Lorenzano, E. (2017). Dynamics of a fault model with two mechanically different regions. Earth, Planets and Space, 69, 145. https://doi.org/10.1186/s40623-017-0731-2.

    Article  Google Scholar 

  • Dragoni, M., & Tallarico, A. (2016). Complex events in a fault model with interacting asperities. Physics of the Earth and Planetary Interiors, 69, 115–127. https://doi.org/10.1016/j.pepi.2016.05.014.

    Article  Google Scholar 

  • Dublanchet, P., Bernard, P., & Favreau, P. (2013). Interactions and triggering in a 3-D rate-and-state asperity model. Journal of Geophysical Research Solid Earth, 118, 2225–2245. https://doi.org/10.1002/jgrb.50187.

    Article  Google Scholar 

  • Erickson, B., Birnir, B., & Lavallée, D. (2011). Periodicity, chaos and localization in a Burridge–Knopoff model of an earthquake with rate-and-state friction. Geophysical Journal International, 187, 178–198. https://doi.org/10.1111/j.1365-246X.2011.05123.x.

    Article  Google Scholar 

  • Field, E. H. (2007). A summary of previous working groups on California earthquake probabilities. Bulletin of the Seismological Society of America, 97, 1033–1053. https://doi.org/10.1785/0120060048.

    Article  Google Scholar 

  • Gu, J., Rice, J. R., Ruina, A. L., & Tse, S. T. (1984). Slip motion and stability of a single degree of freedom elastic system with rate and state dependent friction. Journal of Mechanics and Physics of Solids, 32, 167–196.

    Article  Google Scholar 

  • Hatakeyama, N., Uchida, N., Matsuzawa, T., & Nakamura, W. (2017). Emergence and disappearance of interplate repeating earthquakes following the 2011M9.0 Tohoku-oki earthquake: Slip behavior transition between seismic and aseismic depending on the loading rate. Journal of Geophysical Research Solid Earth, 122, 5160–5180. https://doi.org/10.1002/2016JB013914.

    Article  Google Scholar 

  • Helmstetter, A., & Shaw, B. E. (2009). Afterslip and aftershocks in the rate-and-state friction law. Journal of Geophysical Research, 114, B01308. https://doi.org/10.1029/2007JB005077.

    Article  Google Scholar 

  • Hillers, G., Mai, P. M., Ben-Zion, Y., & Ampuero, J.-P. (2007). Statistical properties of seismicity along fault zones at different evolutionary stages. Geophysical Journal International, 169, 515–533. https://doi.org/10.1111/j.1365-246X.2006.03275.x.

    Article  Google Scholar 

  • Huang, J., & Turcotte, D. L. (1990). Evidence for chaotic fault interactions in the seismicity of the San Andreas Fault and Nankai Trough. Nature, 348, 234–236.

    Article  Google Scholar 

  • Igarashi, T., Matsuzawa, T., & Hasegawa, A. (2003). Repeating earthquakes and interplate aseismic slip in the northeastern Japan subduction zone. Journal of Geophysical Research, 108(B5), 2249. https://doi.org/10.1029/2002JB001920.

    Article  Google Scholar 

  • Kagan, Y. Y. (1997). Statistical aspects of Parkfield earthquake sequence and Parkfield prediction experiment. Tectonophysics, 270, 207–219.

    Article  Google Scholar 

  • Kanamori, H., & McNally, K. C. (1982). Variable rupture mode of the subduction zone along the Ecuador-Colombia coast. Bulletin of the Seismological Society of America, 72, 1241–1253.

    Google Scholar 

  • Kaneko, Y., Avouac, J., & Lapusta, N. (2010). Towards inferring earthquake patterns from geodetic observations of interseismic coupling. Nature Geoscience, 3, 363–369.

    Article  Google Scholar 

  • Kaneko, Y., Nielsen, S. B., & Carpenter, B. M. (2016). The onset of laboratory earthquakes explained by nucleating rupture on a rate-and-state fault. Journal of Geophysical Research Solid Earth, 121, 6071–6091. https://doi.org/10.1002/2016JB013143.

    Article  Google Scholar 

  • Kato, N. (2004). Interaction of slip on asperities: Numerical simulation of seismic cycles on a two-dimensional planar fault with nonuniform frictional property. Journal of Geophysical Research, 109, B12306. https://doi.org/10.1029/2004JB003001.

    Article  Google Scholar 

  • Kato, N. (2012a). Dependence of earthquake stress drop on critical slip-weakening distance. Journal of Geophysical Research, 117, B01301. https://doi.org/10.1029/2011JB008359.

    Article  Google Scholar 

  • Kato, N. (2012b). Fracture energies at the rupture nucleation points of large interplate earthquakes. Earth and Planetary Science Letters, 353–354, 190–197. https://doi.org/10.1016/j.epsl.2012.08.015.

    Article  Google Scholar 

  • Kato, N. (2014). Deterministic chaos in a simulated sequence of slip events on a single isolated asperity. Geophysical Journal International, 198, 727–736. https://doi.org/10.1093/gji/ggu157.

    Article  Google Scholar 

  • Kato, N. (2016). Earthquake cycles in a model of interacting fault patches: Complex behavior at transition from seismic to aseismic slip. Bulletin of the Seismological Society of America, 106, 1772–1787. https://doi.org/10.1785/0120150185.

    Article  Google Scholar 

  • Kato, N., & Hirasawa, T. (1999). Nonuniform and unsteady sliding of a plate boundary in a great earthquake cycle: A numerical simulation using a laboratory-derived friction law. Pure and Applied Geophysics, 155, 93–118.

    Article  Google Scholar 

  • Kato, N., & Tullis, T. E. (2001). A composite rate- and state-dependent law for rock friction. Geophysical Research Letters, 28, 1103–1106. https://doi.org/10.1029/2000GL012060.

    Article  Google Scholar 

  • Kato, N., Lei, X., & Wen, X. (2007). A synthetic seismicity model for the Xianshuihe fault, southwestern China, simulation using a rate- and state-dependent friction law. Geophysical Journal International, 169, 286–300. https://doi.org/10.1111/j.1365-246X.2006.03313.x.

    Article  Google Scholar 

  • Kawamura, H., Hatano, T., Kato, N., Biswas, S., & Chakrabarti, B. K. (2012). Statistical physics of fracture, friction, and earthquakes. Reviews of Modern Physics, 84, 839–884. https://doi.org/10.1103/RevModPhys.84.839.

    Article  Google Scholar 

  • Lay, T., Kanamori, H., Ammon, C. J., Koper, K. D., Hutko, A. R., Ye, L., et al. (2012). Depth-varying rupture properties of subduction zone megathrust faults. Journal of Geophysical Research, 117, B04311. https://doi.org/10.1029/2011JB009133.

    Article  Google Scholar 

  • Liu, Y., & Rice, J. R. (2007). Spontaneous and triggered aseismic deformation transients in a subduction fault model. Journal of Geophysical Research, 112, B09404. https://doi.org/10.1029/2007JB004930.

    Article  Google Scholar 

  • Ma, S., & He, C. (2001). Period doubling as a result of slip complexities in sliding surfaces with strength heterogeneity. Tectonophysics, 337, 135–145.

    Article  Google Scholar 

  • Marone, C., Vidale, J. E., & Ellsworth, W. L. (1995). Fault healing inferred from time dependent variations in source properties of repeating earthquakes. Geophysical Research Letters, 22, 3095–3098.

    Article  Google Scholar 

  • Matsuzawa, T., Igarashi, T., & Hasegawa, A. (2002). Characteristic small-earthquake sequence off Sanriku, northeastern Honshu, Japan. Geophysical Research Letters, 29, 1543. https://doi.org/10.1029/2001GL014632.

    Article  Google Scholar 

  • Matthews, M. V., Ellsworth, W. L., & Reasenberg, P. A. (2002). A Brownian model for recurrent earthquakes. Bulletin of the Seismological Society of America, 92, 2233–2250.

    Article  Google Scholar 

  • Mitsui, Y., & Hirahara, K. (2011). Fault instability on a finite and planar fault related to early phase of nucleation. Journal of Geophysical Research, 116, B06301. https://doi.org/10.1029/2010JB007974.

    Article  Google Scholar 

  • Nadeau, R. M., & Johnson, L. R. (1998). Seismological studies at Parkfield VI: Moment release rates and estimates of source parameters for small repeating earthquakes. Bulletin of the Seismological Society of America, 88, 790–814.

    Google Scholar 

  • Noda, H., & Lapusta, N. (2010). Three-dimensional earthquake sequence simulations with evolving temperature and pore pressure due to shear heating: Effect of heterogeneous hydraulic diffusivity. Journal of Geophysical Research Solid Earth, 115, B12314. https://doi.org/10.1029/2010JB007780.

    Article  Google Scholar 

  • Noda, H., Nakatani, M., & Hori, T. (2013). Large nucleation before large earthquakes is sometimes skipped due to cascade-up: Implications from a rate and state simulation of faults with hierarchical asperities. Journal of Geophysical Research Solid Earth, 118, 2924–2952. https://doi.org/10.1002/jgrb.50211.

    Article  Google Scholar 

  • Nussbaum, J., & Ruina, A. (1987). A two degree-of-freedom earthquake model with static/dynamic friction. Pure and Applied Geophysics, 125, 629–656.

    Article  Google Scholar 

  • Rice, J. R. (1993). Spatio-temporal complexity of slip on a fault. Journal of Geophysical Research, 98, 9885–9907.

    Article  Google Scholar 

  • Rice, J. R., & Ruina, A. L. (1983). Stability of steady frictional slipping. Journal of Applied Mechanics, 50, 343–349.

    Article  Google Scholar 

  • Rubin, A. M. (2008). Episodic slow slip events and rate-and-state friction. Journal of Geophysical Research, 113, B11414. https://doi.org/10.1029/2008JB005642.

    Article  Google Scholar 

  • Rubin, A. M., & Ampuero, J.-P. (2005). Earthquake nucleation on (aging) rate and state faults. Journal of Geophysical Research, 110, B11312. https://doi.org/10.1029/2005JB003686.

    Article  Google Scholar 

  • Ruina, A. L. (1983). Slip instabilities and state variable friction laws. Journal of Geophysical Research, 88, 10359–10370. https://doi.org/10.1029/JB088iB12p10359.

    Article  Google Scholar 

  • Scholz, C. H. (1998). Earthquakes and friction laws. Nature, 391, 37–42.

    Article  Google Scholar 

  • Schwartz, S. Y., & Rokosky, J. M. (2007). Slow slip events and seismic tremor at circum-Pacific subduction zones. Reviews of Geophysics. https://doi.org/10.1029/2006RG000208.

    Article  Google Scholar 

  • Strogatz, S. H. (1994). Nonlinear dynamics and chaos. Cambridge, MA: Perseus Books.

    Google Scholar 

  • Sykes, L. R., & Menke, W. (2006). Repeat times of large earthquakes: Implications for earthquake mechanics and long-term prediction. Bulletin of the Seismological Society of America, 96, 1569–1596.

    Article  Google Scholar 

  • Thomas, M. Y., Lapusta, N., Noda, H., & Avouac, J.-P. (2014). Quasi-dynamic versus fully dynamic simulations of earthquakes and aseismic slip with and without enhanced coseismic weakening. Journal of Geophysical Research Solid Earth, 119, 1986–2004. https://doi.org/10.1002/2013JB010615.

    Article  Google Scholar 

  • Tse, S. T., & Rice, J. R. (1986). Crustal earthquake instability in relation to the depth variation of frictional slip properties. Journal of Geophysical Research, 91, 9452–9472.

    Article  Google Scholar 

  • Uchida, N., Matsuzawa, T., Ellsworth, W. L., Imanishi, K., Okada, T., & Hasegawa, A. (2007). Source parameters of a M4.8 and its accompanying repeating earthquakes off Kamaishi, NE Japan: Implications for the hierarchical structure of asperities and earthquake cycle. Geophysical Research Letters., 34, L20313. https://doi.org/10.1029/2007GL031263.

    Article  Google Scholar 

  • Wu, Y., & Chen, X. (2014). The scale-dependent slip pattern for a uniform fault model obeying the rate- and state-dependent friction law. Journal of Geophysical Research Solid Earth, 119, 4890–4906.

    Article  Google Scholar 

  • Yakovlev, G., Turcotte, D. L., Rundle, J. B., & Rundle, P. B. (2006). Simulation based distributions of earthquake recurrence times on the San Andreas fault system. Bulletin of the Seismological Society of America, 96, 1995–2007. https://doi.org/10.1785/0120050183.

    Article  Google Scholar 

  • Zöller, G., & Hainzl, S. (2007). Recurrence time distributions of large earthquakes in a stochastic model for coupled fault systems: The role of fault interaction. Bulletin of the Seismological Society of America, 97, 1679–1687. https://doi.org/10.1785/0120060262.

    Article  Google Scholar 

Download references

Acknowledgements

I am grateful to anonymous reviewers for their helpful comments. This research was partly supported by Japan Society for the Promotion of Science (Grant no. JP19K04032).

Author information

Authors and Affiliations

  1. Earthquake Research Institute, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo, 113-0032, Japan

    Naoyuki Kato

Authors
  1. Naoyuki Kato
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Naoyuki Kato.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kato, N. Complexity in the Earthquake Cycle Increases with the Number of Interacting Patches. Pure Appl. Geophys. 177, 4657–4676 (2020). https://doi.org/10.1007/s00024-020-02555-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-020-02555-4

Keywords

Search

Navigation