Pure and Applied Geophysics

, Volume 173, Issue 1, pp 5–20 | Cite as

Cumulative Coulomb Stress Triggering as an Explanation for the Canterbury (New Zealand) Aftershock Sequence: Initial Conditions Are Everything?

  • Mark Bebbington
  • David Harte
  • Charles Williams


Using 2 years of aftershock data and three fault-plane solutions for each of the initial M7.1 Darfield earthquake and the larger (\(M >6\)) aftershocks, we conduct a detailed examination of Coulomb stress transfer in the Canterbury 2010–2011 earthquake sequence. Moment tensor solutions exist for 283 of the events with \(M \ge 3.6\), while 713 other events of \(M \ge 3.6\) have only hypocentre and magnitude information available. We look at various methods for deciding between the two possible mechanisms for the 283 events with moment tensor solutions, including conformation to observed surface faulting, and maximum \(\Delta\)CFF transfer from the Darfield main shock. For the remaining events, imputation methods for the mechanism including nearest-neighbour, kernel smoothing, and optimal plane methods are considered. Fault length, width, and depth are arrived at via a suite of scaling relations. A large (50–70 %) proportion of the faults considered were calculated to have initial loading in excess of the final stress drop. The majority of faults that accumulated positive \(\Delta\)CFF during the sequence were ‘encouraged’ by the main shock failure, but, on the other hand, of the faults that failed during the sequence, more than 50 % of faults appeared to have accumulated a negative \(\Delta\)CFF from all preceding failures during the sequence. These results were qualitatively insensitive to any of the factors considered. We conclude that there is much unknown about how Coulomb stress triggering works in practice.


Coulomb failure stress Canterbury earthquake sequence Fault plane solutions 



The authors gratefully acknowledge discussions with GS seismologists Matt Gerstenberger, Annemarie Christopherson, Bill Fry, and John Ristau. Two anonymous referees provided helpful feedback.


  1. Aki, K., and P. G. Richards. 1980. Quantitative Seismology: Theory and Methods. San Francisco: WH Freeman.Google Scholar
  2. Atzori, S., C. Tolomei, A. Antonioli, J. P. Merryman Boncori, S. Bannister, E. Trasatti, P. Pasquali, and S. Salvi. 2012. The 2010–2011 Canterbury, New Zealand, seismic sequence: Multiple source analysis from INSAR data and modeling. J. Geophys. Res. 117:B08305.Google Scholar
  3. Bannister, S., and K. Gledhill. 2012. Evolution of the 2010–2012 Canterbury earthquake sequence. NZ J. Geol. Geophys. 55:295–304.Google Scholar
  4. Bannister, S., B. Fry, M. Reyners, J. Ristau, and H. Zhang. 2011. Fine-scale relocation of aftershocks of the 22 February mw 6.2 Christchurch earthquake using double-difference tomography. Seismol. Res. Lett. 82:839–845. doi: 10.1785/gssrl.82.6.839.
  5. Beavan, J., M. Motagh, E. J. Fielding, N. Donnelly, and D. Collett. 2012. Fault slip models of the 2010-2011 Canterbury, New Zealand, earthquakes from geodetic data and observations of postseismic ground deformation. NZ J. Geol. Geophys. 55:207–211.Google Scholar
  6. Bebbington, M. 2008. Estimating rate- and state-friction parameters using a two-node stochastic model for aftershocks. Tectonophysics 457:71–85. doi: 10.1016/j.tecto.2008.05.017.
  7. Bebbington, M., and D. S. Harte. 2003. The linked stress release model for spatio-temporal seismicity: formulations, procedures and applications. Geophysical Journal International 154:925–946. doi: 10.1046/j.1365-246X.2003.02015.x.
  8. Borovkov, K., and M. Bebbington. 2003. A stochastic two-node stress transfer model reproducing Omori’s law. Pure and Applied Geophysics 160 (8):1429–1445. doi: 10.1007/s00024-003-2354-8.
  9. Catalli, F., and C. H. Chan. 2012. New insights into the application of the Coulomb model in real-time. Geophys. J. Int. 188:583–599. doi: 10.1111/j.1365-246X.2011.05276.x.
  10. Catalli, F., M. Cocco, R. Console, and L. Chiaraluce. 2008. Modeling seismicity rate changes during the 1997 Umbria-Marche sequence (central Italy) through a rate- and state-dependent model. J. Geophys. Res. 113:B111301.Google Scholar
  11. Cattania, C., S. Hainzl, L. Wang, F. Roth, and B. Enescu. 2014. Propagation of Coulomb stress uncertainties in physics-based aftershock models. J. Geophys. Res. 119:7846–7864. doi: 10.1002/2014JB011183.
  12. Chan, C. H., and R. S. Stein. 2009. Stress evolution following the 1999 Chi-Chi, Taiwan, earthquake: consequences for afterslip, relaxation, aftershocks and departures from Omori decay. Geophys. J. Int. 177:179–192.Google Scholar
  13. Christophersen, A., D. A. Rhoades, S. Hainzl, E. G. C. Smith, andM. C. Gerstenberger. 2013. The Canterbury sequence in the context of global earthquake statistics, GNS Science Consultancy Report 2013/196, GNS Science, Lower Hutt.Google Scholar
  14. Convertito, V., F. Catalli, and A. Emolo. 2013. Combining stress transfer and source directivity: the case of the 2012 Emilia seismic sequence. Sci. Rep. 3:3114.Google Scholar
  15. Cotton, F., R. Archuleta, and M. Causse. 2013. What is sigma of the stress drop? Seismol. Res. Lett. 84:42–48.Google Scholar
  16. Dieterich, J. H. 1994. A constitutive law for rate of earthquake production and its application to earthquake clustering. J. Geophys. Res. 99:2601–2618. doi: 10.1029/93JB02581.
  17. Elliott, J. R., E. Nissen, P. C. England, J. A. Jackson, S. Lamb, Z. Li, M. Oehlers, and B. E. Parsons. 2012. Slip in the 2010–2011 Canterbury earthquakes, New Zealand. J. Geophys. Res. 117:B03401.Google Scholar
  18. Freed, A. M. 2005. Earthquake triggering by static, dynamic, and postseismic stress transfer. Ann. Rev. Earth Planet. Sci. 33:335–367.Google Scholar
  19. Fry, B., and M. C. Gerstenberger. 2011. Large apparent stresses from the Canterbury earthquakes of 2010 and 2011. Seismol. Res. Lett. 82:833–838. doi: 10.1785/gssrl.82.6.833.
  20. Furlong, K. P. 2013. The Intraplate Earthquake Cycle: Strain and Displacement Behaviour During the the Canterbury, NZ Earthquake Sequence, Technical Report NEHRP Award G12AP20031, Pennsylvania State University.Google Scholar
  21. Gledhill, K., J. Ristau, M. Reyners, B. Fry, and C. Holden. 2011. The Darfield (Canterbury, New Zealand) \(M_W\) 7.1 earthquake of September 2010: A preliminary seismological report. Seismol. Res. Lett. 82:378–386. doi: 10.1785/gssrl.82.3.378.
  22. Hainzl, S., G. B. Brietzke, and G. Zoller. 2010a. Quantitative earthquake forecasts resulting from static stress triggering. J. Geophys. Res. 115 (B11311). doi: 10.1029/2010JB007473.
  23. Hainzl, S., G. Zoller, and R. Wang. 2010b. Impact of the receiver fault distribution on aftershock activity. J. Geophys. Res. 115 (B05315). doi: 10.1029/2008JB006224.
  24. Hainzl, S., B. Enescu, M. Cocco, J. Woessner, F. Catalli, R. Wang, and F. Roth. 2009. Aftershock modeling based on uncertain stress calculations. J. Geophys. Res. 114 (B05309). doi: 10.1029/2008JB006011.
  25. Hanks, T. C., and W. H. Bakun. 2008. \(M - \log A\) observations of recent large earthquakes. Bull. Seismol. Soc. Amer. 98: 490–494. Google Scholar
  26. Hardebeck, J. 2006. Homogeneity of small-scale earthquake faulting, stress and fault strength. Bull. Seismol. Soc. Amer. 96:1675–1688.Google Scholar
  27. Hardebeck, J. L., J. J. Nazareth, and E. Hauksson. 1998. The static stress triggering model: Constraints from two southern California aftershock sequences. J. Geophys. Res. 103:24427–24437.Google Scholar
  28. Harris, R. A. 1998. Introduction to special section: Stress triggers, stress shadows, and implications for seismic hazard. J. Geophys. Res. 103:24347–24358.Google Scholar
  29. Hill, D. P. 2008. Dynamic stresses, Coulomb failure, and remote triggering. Bull. Seismol. Soc. Amer. 98:66–92.Google Scholar
  30. Kaiser, A. E., A. Oth, and R. A. Benites. 2013. Separating source, path and site influences on ground motion during the Canterbury earthquake sequence, using spectral inversions. Paper no. 18 (8 p.) in: Same risks, new realities: New Zealand Society for Earthquake Engineering Technical Conference, April 26--28, 2013, Wellington.Google Scholar
  31. Kanamori, H., and D. L. Anderson. 1975. Theoretical basis of some empirical relations in seismology. Bull. Seismol. Soc. Amer. 65:1073–1095.Google Scholar
  32. King, G. C. P., R. S. Stein, and J. Lin. 1994. Static stress changes and the triggering of earthquakes. Bull. Seismol. Soc. Amer. 84:935–953.Google Scholar
  33. Leonard, M. 2010. Earthquake fault scaling: Self-consistent realting of rupture length, width, average displacement, and moment release. Bull. Seismol. Soc. Amer. 100:1971–1988. doi: 10.1785/0120090189.
  34. Meier, M. A., M. J. Werner, J. Woessner, and S. Wiemer. 2014. A search for evidence of secondary static stress triggering during the 1992 \(M_W\) 7.3 Landers, California, earthquake sequence. J. Geophys. Res. 119:3354–3379. doi: 10.1002/2013JB010385.
  35. Ogata, Y., and J. C. Zhuang. 2006. Space-time ETAS models and an improved extension. Tectonophysics 413:13–23. doi: 10.1016/j.tecto.2005.10.016.
  36. Okada, Y. 1992. Internal deformation due to shear and tensile faults in a half-space. Bull. Seismol. Soc. Amer. 82:1018–1040.Google Scholar
  37. Parsons, T., Y. Ogata, J. C. Zhuang, and E. L. Geist. 2012a. Evaluation of static stress change forecasting with prospective and blind tests. Geophys. J. Int. 188:1425–1440. doi: 10.1111/j.1365-246X.2011.05343.x.
  38. Parsons, T., E. H. Field, M. T. Page, and K. Milner. 2012b. Possible earthquake rupture connections on mapped California faults ranked by calculated Coulomb linking stresses. Bull. Seismol. Soc. Amer. 102:2667–2676.Google Scholar
  39. Quigley, M., R. J. Van Dissen, N. J. Litchfield, P. Villamor, B. Duffy, D. J. A. Barrell, K. Furlong, T. Stahl, E. Bilderback, and D. Noble. 2012. Surface rupture during the 2010 \(M_W\) 7.1 Darfield (Canterbury) earthquake: Implications for fault rupture dynamics and seismic-hazard analysis. Geology 40:55–58. doi: 10.1130/G32528.1.
  40. Rhoades, D. A., E. E. Papadimitriou, V. G. Karakostas, R. Console, and M. Murru. 2010. Correlation of static stress changes and earthquake occurrence in the North Aegean region. Pure Appl. Geophys. 167:1049–1066. doi: 10.1007/s00024-010-0092-2.
  41. Richards-Dinger, K., R. S. Stein, and S. Toda. 2010. Decay of aftershock density with distance does not indicate triggering by dynamic stress. Nature 467:583–586.Google Scholar
  42. Ristau, J., C. Holden, A. Kaiser, C. Williams, S. Bannister, and B. Fry. 2013. The Pegasus Bay aftershock sequence of the \(M_W\) 7.1 Darfield (Canterbury), New Zealand earthquake. Geophys. J. Int. 195:444–459. Google Scholar
  43. Shaw, B. E. 2013. Earthquake surface slip-length data is fit by constant stress drop and is useful for seismic hazard analysis. Bull. Seismol. Soc. Amer. 103:876–893.Google Scholar
  44. Shcherbakov, R., M. Nguyen, and M. Quigley. 2012. Statistical analysis of the 2010 \(M_W\) 7.1 Darfield earthquake aftershock sequence. NZ J. Geol. Geophys. 55:305–311. Google Scholar
  45. Sibson, R., F. Ghisetti, and J. Ristau. 2011. Stress control of an evolving strike-slip fault system during the 2010–2011 Canterbury, New Zealand, earthquake sequence. Seismol. Res. Lett. 82:824–832. doi: 10.1785/gssrl.82.6.824.
  46. Steacy, S., A. Jimenez, and C. Holden. 2014. Stress trigeering and the Canterbury earthquake sequence. Geophys. J. Int. 196:473–480. doi: 10.1093/gji/ggt380.
  47. Steacy, S., D. Marsan, S. S. Nalbant, and J. McCloskey. 2004. Sensitivity of static stress calculations to the earthquake slip distribution. J. Geophys. Res. 109 (B04303). doi: 10.1029/2002JB002365.
  48. Steacy, S., S. S. Nalbant, J. McCloskey, C. Nostro, O. Scotti, and D. Baumont. 2005. Onto what planes should Coulomb stress perturbations be resolved? J. Geophys. Res. 110 (B05S15). doi: 10.1029/2004JB003356.
  49. Steacy, S., M. C. Gerstenberger, C. Williams, D. A. Rhoades, and A. Christophersen. 2014. A New hybrid Coulomb/statistical model for forecasting aftershock rates. Geophys. J. Int. 196:918–923. doi: 10.1093/gji/ggt404.
  50. Stein, R. S., A. Barka, and J. H. Dieterich. 1997. Progressive failure on the North Anatolian fault since 1939 by earthquake stress triggering. Geophys. J. Int. 128:594–604. doi: 10.1111/j.1365-246X.1997.tb05321.x.
  51. Stirling, M., G. H. McVerry, M. C. Gerstenberger, N. J. Litchfield, R. J. Van Dissen, K. Berryman, P. Barnes, L. Wallace, P. Villamor, R. Langridge, G. Lamarche, S. Nodder, M. Reyners, B. Bradley, D. A. Rhoades, W. D. Smith, A. Nicol, J. Pettinga, K. Clark, and K. Jacobs. 2012. National seismic hazard model for New Zealand: 2010 update. Bull. Seismol. Soc. Amer. 102:1514–1542. doi: 10.1785/0120110170.
  52. Stirling, M., T. Goded, K. Berryman, and N. J. Litchfield. 2013. Selection of earthquake scaling relationships for seismic-hazard analysis. Bull. Seismol. Soc. Amer. 103:1–19. doi: 10.1785/0120130052.
  53. Syracuse, E. M., R. A. Holt, M. K. Savage, J. H. Johnson, C. H. Thurber, K. Unglert, K. N. Allan, S. Karaliyadda, and M. Henderson. 2012. Temporal and spatial evolution of hypocentres and anisotropy from the Darfield aftershock sequence: implications for fault geometry and age. NZ J. Geol. Geophys. 55:287–293.Google Scholar
  54. Toda, S., R. S. Stein, and J. Lin. 2011. Widespread seismicity excitation throughout central Japan following the 2011 \(M=9.0\) Tohoku earthquake and its interpretation by Coulomb stress transfer. Geophys. Res. Lett. 38 (L00G03). Google Scholar
  55. Toda, S., R. S. Stein, G. C. Beroza, and D. Marsan. 2012. Aftershocks halted by static stress shadows. Nature Geoscience 5:410–413. doi: 10.1038/NGEO1465.
  56. Wells, D. L., and K. J. Coppersmith. 1994. New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bull. Seismol. Soc. Amer. 84:974–1002.Google Scholar
  57. Wesnousky, S. G. 2008. Displacement and geometrical characteristics of earthquake surface ruptures: Issues and implications for seismic-hazard analysis and the process of earthquake rupture. Bull. Seismol. Soc. Amer. 98:1609–1632.Google Scholar
  58. Yen, Y. T., and K. F. Ma. 2011. Source-scaling relationship for \(M\) 4.6–8.1 earthquakes, specifically for earthquakes in the collision zone of Taiwan. Bull. Seismol. Soc. Amer. 101:464–481. Google Scholar

Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Mark Bebbington
    • 1
  • David Harte
    • 2
  • Charles Williams
    • 2
  1. 1.IAE, Massey UniversityPalmerston NorthNew Zealand
  2. 2.GNS ScienceLower HuttNew Zealand

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