Skip to main content

Surface Rupture Effects on Earthquake Moment-Area Scaling Relations

A Correction to this article was published on 11 December 2017

This article has been updated

Abstract

Empirical earthquake scaling relations play a central role in fundamental studies of earthquake physics and in current practice of earthquake hazard assessment, and are being refined by advances in earthquake source analysis. A scaling relation between seismic moment (M 0) and rupture area (A) currently in use for ground motion prediction in Japan features a transition regime of the form M 0A 2, between the well-recognized small (self-similar) and very large (W-model) earthquake regimes, which has counter-intuitive attributes and uncertain theoretical underpinnings. Here, we investigate the mechanical origin of this transition regime via earthquake cycle simulations, analytical dislocation models and numerical crack models on strike-slip faults. We find that, even if stress drop is assumed constant, the properties of the transition regime are controlled by surface rupture effects, comprising an effective rupture elongation along-dip due to a mirror effect and systematic changes of the shape factor relating slip to stress drop. Based on this physical insight, we propose a simplified formula to account for these effects in M 0A scaling relations for strike-slip earthquakes.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Change history

  • 11 December 2017

    The Eq. (10) in the article was displayed incorrectly. The correct version of Eq. (10) should be as follows:

References

  • Dalguer, L. A., Miyake, H., Day, S. M., & Irikura, K. (2008). Surface rupturing and buried dynamic rupture models calibrated with statistical observations of past earthquakes. Bulletin of the Seismological Society of America, 98, 1147–1161. doi:10.1785/0120070134.

    Article  Google Scholar 

  • Fujii, Y., & Matsu’ura, M. (2000). Regional difference in scaling laws for large earthquakes and its tectonic implication. Pure and Applied Geophysics, 157(11–12), 2283–2301.

    Article  Google Scholar 

  • Gallovič, F. (2008). Heterogeneous Coulomb stress perturbation during earthquake cycles in a 3D rate-and-state fault model. Geophysical Research Letters, 35(21).

  • Hanks, T. C., & Bakun, W. H. (2002). A bilinear source-scaling model for M–log A observations of continental earthquakes. Bulletin of the Seismological Society of America, 92(5), 1841–1846.

    Article  Google Scholar 

  • Hanks, T. C., & Bakun, W. H. (2014). M–log A models and other curiosities. Bulletin of the Seismological Society of America, 104(5), 2604–2610.

    Article  Google Scholar 

  • Hillers, G., Ben-Zion, Y., & Mai, P. M. (2006). Seismicity on a fault controlled by rate-and-state dependent friction with spatial variations of the critical slip distance. Journal of Geophysical Research: Solid Earth, 111(B1), B01403.

    Article  Google Scholar 

  • Hillers, G., Mai, P. M., Ben-Zion, Y., & Ampuero, J. P. (2007). Statistical properties of seismicity of fault zones at different evolutionary stages. Geophysical Journal International, 169(2), 515–533.

    Article  Google Scholar 

  • Irikura, K., & Miyake, H. (2001). Prediction of strong ground motions for scenario earthquakes. Journal of Geography (Chigaku Zasshi), 110(6), 849–875.

    Article  Google Scholar 

  • Irikura, K., & Miyake, H. (2011). Recipe for predicting strong ground motion from crustal earthquake scenarios. Pure and Applied Geophysics, 168(1–2), 85–104.

    Article  Google Scholar 

  • Kanamori, H., & Anderson, D. L. (1975). Theoretical basis of some empirical relations in seismology. Bulletin of the Seismological Society of America, 65(5), 1073–1095.

    Google Scholar 

  • Leonard, M. (2010). Earthquake fault scaling: Self-consistent relating of rupture length, width, average displacement, and moment release. Bulletin of the Seismological Society of America, 100(5A), 1971–1988.

    Article  Google Scholar 

  • Marone, C. (1998). Laboratory-derived friction laws and their application to seismic faulting. Annual Review of Earth and Planetary Sciences, 26(1), 643–696.

    Article  Google Scholar 

  • Matsu’ura, M., & Sato, T. (1997). Loading mechanism and scaling relations of large interplate earthquakes. Tectonophysics, 277(1), 189–198.

    Article  Google Scholar 

  • Miyakoshi, K., Irikura, K., & Kamae, K. (2015). Re-examination of scaling relationships of source parameters of the inland crustal earthquakes in Japan based on the waveform inversion of strong motion data. Journal of Japan Association for Earthquake Engineering, 15–7, 141–156. (in Japanese with English abstract).

    Google Scholar 

  • Murotani, S., Matsushima, S., Azuma, T., Irikura, K., & Kitagawa, S. (2015). Scaling relations of source parameters of earthquakes occurring on inland crustal mega-fault systems. Pure and Applied Geophysics, 172(5), 1371–1381.

    Article  Google Scholar 

  • Okada, Y. (1992). Internal deformation due to shear and tensile faults in a half-space. Bulletin of the Seismological Society of America, 82(2), 1018–1040.

    Google Scholar 

  • Romanowicz, B., & Rundle, J. B. (1993). On scaling relations for large earthquakes. Bulletin of the Seismological Society of America, 83(4), 1294–1297.

    Google Scholar 

  • Rubin, A. M., & Ampuero, J. P. (2005). Earthquake nucleation on (aging) rate and state faults. Journal of Geophysical Research: Solid Earth, 110(B11), B11312.

    Article  Google Scholar 

  • Scholz, C. H. (1982). Scaling laws for large earthquakes: consequences for physical models. Bulletin of the Seismological Society of America, 72(1), 1–14.

    Google Scholar 

  • Scholz, C. H. (1998). Earthquakes and friction laws. Nature, 391(6662), 37–42.

    Article  Google Scholar 

  • Shaw, B. E. (2009). Constant stress drop from small to great earthquakes in magnitude-area scaling. Bulletin of the Seismological Society of America, 99(2A), 871–875.

    Article  Google Scholar 

  • Shaw, B. E., & Wesnousky, S. G. (2008). Slip-length scaling in large earthquakes: The role of deep-penetrating slip below the seismogenic layer. Bulletin of the Seismological Society of America, 98(4), 1633–1641.

    Article  Google Scholar 

  • Somerville, P., Irikura, K., Graves, R., Sawada, S., Wald, D., Abrahamson, N., et al. (1999). Characterizing crustal earthquake slip models for the prediction of strong ground motion. Seismological Research Letters, 70(1), 59–80.

    Article  Google Scholar 

  • Song, S. G., Beroza, G. C., & Segall, P. (2008). A unified source model for the 1906 San Francisco earthquake. Bulletin of the Seismological Society of America, 98(2), 823–831.

    Article  Google Scholar 

  • Streit, J. E., & Cox, S. F. (2001). Fluid pressures at hypocenters of moderate to large earthquakes. Journal of Geophysical Research: Solid Earth, 106(B2), 2235–2243.

    Article  Google Scholar 

  • Wells, D. L., & Coppersmith, K. J. (1994). New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bulletin of the Seismological Society of America, 84(4), 974–1002.

    Google Scholar 

  • Bodin, P., & Brune, J. N. (1996). On the scaling of slip with rupture length for shallow strike-slip earthquakes: Quasi-static models and dynamic rupture propagation. Bulletin of the Seismological Society of America, 86(5), 1292–1299.

    Google Scholar 

  • Mai, P. M., & Beroza, G. C. (2000). Source scaling properties from finite-fault-rupture models. Bulletin of the Seismological Society of America, 90(3), 604–615.

    Article  Google Scholar 

  • Causse, M., & Song, S. G. (2015). Are stress drop and rupture velocity of earthquakes independent? Insight from observed ground motion variability. Geophysical Research Letters, 42(18), 7383–7389.

    Article  Google Scholar 

Download references

Acknowledgements

This study was based on the 2015 research project ‘Improvement for uncertainty of strong ground motion prediction’ by the Nuclear Regulation Authority (NRA), Japan.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yingdi Luo.

Additional information

A correction to this article is available online at https://doi.org/10.1007/s00024-017-1725-5.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Luo, Y., Ampuero, JP., Miyakoshi, K. et al. Surface Rupture Effects on Earthquake Moment-Area Scaling Relations. Pure Appl. Geophys. 174, 3331–3342 (2017). https://doi.org/10.1007/s00024-017-1467-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-017-1467-4

Keywords

  • Earthquake scaling relations
  • surface rupture effects
  • earthquake cycle model
  • rate-and-state friction
  • analytical dislocation model
  • numerical crack model