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Propagation of large earthquakes as self-healing pulses or mild cracks

Abstract

Observations suggest that mature faults host large earthquakes at much lower levels of stress than their expected static strength1,2,3,4,5,6,7,8,9,10,11. Potential explanations are that the faults are quasi-statically strong but experience considerable weakening during earthquakes, or that the faults are persistently weak, for example, because of fluid overpressure. Here we use numerical modelling to examine these competing theories for simulated earthquake ruptures that satisfy the well known observations of 1–10 megapascal stress drops and limited heat production. In that regime, quasi-statically strong but dynamically weak faults mainly host relatively sharp, self-healing pulse-like ruptures, with only a small portion of the fault slipping at a given time, whereas persistently weak faults host milder ruptures with more spread-out slip, which are called crack-like ruptures. We find that the sharper self-healing pulses, which exhibit larger dynamic stress changes compared to their static stress changes, result in much larger radiated energy than that inferred teleseismically for megathrust events12. By contrast, milder crack-like ruptures on persistently weak faults, which produce comparable static and dynamic stress changes, are consistent with the seismological observations. The larger radiated energy of self-healing pulses is similar to the limited regional inferences available for crustal strike-slip faults. Our findings suggest that either large earthquakes rarely propagate as self-healing pulses, with potential differences between tectonic settings, or their radiated energy is substantially underestimated, raising questions about earthquake physics and the expected shaking from large earthquakes.

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Fig. 1: Geophysical inferences from large earthquakes that can be used to constrain earthquake physics.
Fig. 2: Simulated self-healing pulses on quasi-statically strong but dynamically weak faults versus crack-like ruptures on chronically weak faults.
Fig. 3: The relationship between the rupture mode, radiated energy and stress state of simulated faults.
Fig. 4: Energy-related values for self-healing pulses are substantially different from seismological inferences based on the standard energy budget.

Data availability

Numerical data are accessible through the CaltechDATA repository (https://data.caltech.edu/records/1620). Seismological inferences used in this study are compiled from published literature and publicly available sources. Source data are provided with this paper.

Code availability

The numerical methodology used in this study is described in the Supplementary Materials and references32,49.

References

  1. Brune, J. N., Henyey, T. L. & Roy, R. F. Heat flow, stress, and rate of slip along the San Andreas Fault, California. J. Geophys. Res. 74, 3821–3827 (1969).

    ADS  Google Scholar 

  2. Henyey, T. L. & Wasserburg, G. J. Heat flow near major strike-slip faults in California. J. Geophys. Res. (1896–1977) 76, 7924–7946 (1971).

    ADS  Google Scholar 

  3. Sibson, R. H. Generation of pseudotachylyte by ancient seismic faulting. Geophys. J. R. Astron. Soc. 43, 775–794 (1975).

    ADS  Google Scholar 

  4. Lachenbruch, A. H. & Sass, J. H. Heat flow and energetics of the San Andreas Fault Zone. J. Geophys. Res. Solid Earth 85, 6185–6222 (1980).

    Google Scholar 

  5. Townend, J. & Zoback, M. D. Regional tectonic stress near the San Andreas fault in central and Southern California. Geophys. Res. Lett. 31, L15S11 (2004).

  6. Rice, J. R. Heating and weakening of faults during earthquake slip. J. Geophys. Res. 111, B05311 (2006).

    ADS  Google Scholar 

  7. Suppe, J. Absolute fault and crustal strength from wedge tapers. Geology 35, 1127–1130 (2007).

    ADS  Google Scholar 

  8. Tanikawa, W. & Shimamoto, T. Frictional and transport properties of the Chelungpu fault from shallow borehole data and their correlation with seismic behavior during the 1999 Chi-Chi earthquake. J. Geophys. Res. Solid Earth 114, B01402 (2009).

  9. Nankali, H. R. Slip rate of the Kazerun fault and Main Recent fault (Zagros, Iran) from 3D mechanical modeling. J. Asian Earth Sci. 41, 89–98 (2011).

    ADS  Google Scholar 

  10. Fulton, P. M. et al. Low coseismic friction on the Tohoku-Oki fault determined from temperature measurements. Science 342, 1214–1217 (2013).

    ADS  CAS  PubMed  Google Scholar 

  11. Gao, X. & Wang, K. Strength of stick-slip and creeping subduction megathrusts from heat flow observations. Science 345, 1038–1041 (2014).

    ADS  CAS  PubMed  Google Scholar 

  12. Ye, L., Lay, T., Kanamori, H. & Rivera, L. Rupture characteristics of major and great (Mw > 7.0) megathrust earthquakes from 1990 to 2015: 2. Depth dependence. J. Geophys. Res. Solid Earth 121, 845–863 (2016).

    ADS  Google Scholar 

  13. Chester, F. M. & Chester, J. S. Ultracataclasite structure and friction processes of the Punchbowl fault, San Andreas system, California. Tectonophysics 295, 199–221 (1998).

    ADS  Google Scholar 

  14. Wibberley, C. A. & Shimamoto, T. Earthquake slip weakening and asperities explained by thermal pressurization. Nature 436, 689–692 (2005).

    ADS  CAS  PubMed  Google Scholar 

  15. Tullis, T. in Treatise on Geophysics Vol. 4 (ed. Schubert, G.) 131–152 (2007).

  16. Di Toro, G. et al. Fault lubrication during earthquakes. Nature 471, 494–498 (2011).

    ADS  PubMed  Google Scholar 

  17. Brown, K., Kopf, A., Underwood, M. & Weinberger, J. Compositional and fluid pressure controls on the state of stress on the Nankai subduction thrust: a weak plate boundary. Earth Planet. Sci. Lett. 214, 589–603 (2003).

    ADS  CAS  Google Scholar 

  18. Faulkner, D. R., Mitchell, T. M., Healy, D. & Heap, M. J. Slip on ‘weak’ faults by the rotation of regional stress in the fracture damage zone. Nature 444, 922–925 (2006).

    ADS  CAS  PubMed  Google Scholar 

  19. Bangs, N. et al. Broad, weak regions of the Nankai Megathrust and implications for shallow coseismic slip. Earth Planet. Sci. Lett. 284, 44–49 (2009).

    ADS  CAS  Google Scholar 

  20. Collettini, C., Niemeijer, A., Viti, C. & Marone, C. Fault zone fabric and fault weakness. Nature 462, 907–910 (2009).

    ADS  CAS  PubMed  Google Scholar 

  21. Lockner, D. A., Morrow, C., Moore, D. & Hickman, S. Low strength of deep San Andreas fault gouge from SAFOD core. Nature 472, 82–85 (2011).

    ADS  CAS  PubMed  Google Scholar 

  22. Heaton, T. H. Evidence for and implications of self-healing pulses of slip in earthquake rupture. Phys. Earth Planet. Inter. 64, 1–20 (1990).

    ADS  Google Scholar 

  23. Noda, H., Dunham, E. M. & Rice, J. R. Earthquake ruptures with thermal weakening and the operation of major faults at low overall stress levels. J. Geophys. Res. Solid Earth 114, B07302 (2009).

  24. Allmann, B. P. & Shearer, P. M. Global variations of stress drop for moderate to large earthquakes. J. Geophys. Res. Solid Earth 114, B01310 (2009).

  25. Ide, S. & Beroza, G. C. Does apparent stress vary with earthquake size? Geophys. Res. Lett. 28, 3349–3352 (2001).

    ADS  Google Scholar 

  26. Abercrombie, R. E. & Rice, J. R. Can observations of earthquake scaling constrain slip weakening? Geophys. J. Int. 162, 406–424 (2005).

    ADS  Google Scholar 

  27. Viesca, R. C. & Garagash, D. I. Ubiquitous weakening of faults due to thermal pressurization. Nat. Geosci. 8, 875–879 (2015).

    ADS  CAS  Google Scholar 

  28. Perry, S. M., Lambert, V. & Lapusta, N. Nearly magnitude-invariant stress drops in simulated crack-like earthquake sequences on rate-and-state faults with thermal pressurization of pore fluids. J. Geophys. Res. Solid Earth. 125, e2019JB018597 (2020).

    ADS  Google Scholar 

  29. Beeler, N. M., Wong, T. F. & Hickman, S. H. On the expected relationships among apparent stress, static stress drop, effective shear fracture energy, and efficiency. Bull. Seismol. Soc. Am. 93, 1381–1389 (2003).

    Google Scholar 

  30. Kanamori, H. & Rivera, L. in Earthquakes: Radiated Energy and the Physics of Faulting (eds Abercrombie, R. et al.) 3–13 (AGU, 2006).

  31. Madariaga, R. Dynamics of an expanding circular fault. Bull. Seismol. Soc. Am. 66, 639–666 (1976).

    Google Scholar 

  32. Noda, H. & Lapusta, N. Three-dimensional earthquake sequence simulations with evolving temperature and pore pressure due to shear heating: effect of heterogeneous hydraulic diffusivity. J. Geophys. Res. 115, B12314 (2010).

    ADS  Google Scholar 

  33. Dieterich, J. in Treatise on Geophysics (ed. Schubert, G.) 107–129 (Elsevier, 2007).

  34. Andrews, D. J. Rupture models with dynamically determined breakdown displacement. Bull. Seismol. Soc. Am. 94, 769–775 (2004).

    Google Scholar 

  35. Noda, H. & Lapusta, N. On averaging interface response during dynamic rupture and energy partitioning diagrams for earthquakes. J. Appl. Mech. 79, 031026 (2012).

    ADS  Google Scholar 

  36. Choy, G. L. & Boatwright, J. L. Global patterns of radiated seismic energy and apparent stress. J. Geophys. Res. Solid Earth 100, 18205–18228 (1995).

    Google Scholar 

  37. Pérez-Campos, X. & Beroza, G. C. An apparent mechanism dependence of radiated seismic energy. J. Geophys. Res. Solid Earth 106, 11127–11136 (2001).

    Google Scholar 

  38. Ma, S. & Archuleta, R. J. Radiated seismic energy based on dynamic rupture models of faulting. J. Geophys. Res. Solid Earth 111, https://doi.org/10.1029/2005JB004055 (2006).

  39. Perrin, G., Rice, J. R. & Zheng, G. Self-healing slip pulse on a frictional surface. J. Mech. Phys. Solids 43, 1461–1495 (1995).

    ADS  MathSciNet  MATH  Google Scholar 

  40. Day, S. M. Three-dimensional finite difference simulation of fault dynamics: rectangular faults with fixed rupture velocity. Bull. Seismol. Soc. Am. 72, 705–727 (1982).

    Google Scholar 

  41. Beroza, G. C. & Mikumo, T. Short slip duration in dynamic rupture in the presence of heterogeneous fault properties. J. Geophys. Res. Solid Earth 101, 22449–22460 (1996).

    Google Scholar 

  42. Andrews, D. J. & Ben-Zion, Y. Wrinkle-like slip pulse on a fault between different materials. J. Geophys. Res. Solid Earth 102, 553–571 (1997).

    Google Scholar 

  43. Kanamori, H. & Brodsky, E. E. The physics of earthquakes. Rep. Prog. Phys. 67, 1429–1496 (2004).

    ADS  MathSciNet  Google Scholar 

  44. Cocco, M., Bizzarri, A. & Tinti, E. Physical interpretation of the breakdown process using a rate-and state-dependent friction law. Tectonophysics 378, 241–262 (2004).

    ADS  Google Scholar 

  45. Savage, J. C. & Wood, M. D. The relation between apparent stress and stress drop. Bull. Seismol. Soc. Am. 61, 1381–1388 (1971).

    Google Scholar 

  46. Rice, J. R., Sammis, C. G. & Parsons, R. Off-fault secondary failure induced by a dynamic slip pulse. Bull. Seismol. Soc. Am. 95, 109–134 (2005).

    Google Scholar 

  47. Jiang, J. & Lapusta, N. Deeper penetration of large earthquakes on seismically quiescent faults. Science 352, 1293–1297 (2016).

    ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  48. Kanamori, H., Ross, Z. E. & Rivera, L. Estimation of radiated energy using the KiK-net downhole records—old method for modern data. Geophys. J. Int. 221, 1029–1042 (2020).

    ADS  Google Scholar 

  49. Lapusta, N., Rice, J. R., Ben-Zion, Y. & Zheng, G. Elastodynamic analysis for slow tectonic loading with spontaneous rupture episodes on faults with rate- and state- dependent friction. J. Geophys. Res. 105, 23765–23789 (2000).

    ADS  Google Scholar 

  50. Dieterich, J. H. Modeling of rock friction 1. Experimental results and constitutive equations. J. Geophys. Res. 84, 2161–2168 (1979).

    ADS  Google Scholar 

  51. Ruina, A. Slip instability and state variable friction laws. J. Geophys. Res. 88, 10359–10370 (1983).

    ADS  Google Scholar 

  52. Noda, H. Frictional constitutive law at intermediate slip rates accounting for flash heating and thermally activated slip process. J. Geophys. Res. Solid Earth 113, B09302 (2008).

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Acknowledgements

This study was supported by the US National Science Foundation (NSF) (grants EAR 1142183 and 1520907), the US Geological Survey (grant G19AP00059) and the Southern California Earthquake Center (SCEC), contribution no. 10085. SCEC is funded by NSF Cooperative Agreement EAR 1033462 and US Geological Survey Cooperative Agreement G12AC20038. Numerical simulations for this study were carried out on the High Performance Computing Center cluster of the California Institute of Technology. We thank H. Kanamori, T. Heaton, J.-P. Avouac, V. Tsai and Z. Zhan for discussions and comments.

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Contributions

V.L and N.L contributed to developing the main ideas, interpreting the results and producing the manuscript. S.P. performed preliminary simulations comparing crack-like ruptures and self-healing pulses. V.L. designed, carried out and analysed the numerical experiments described in the paper.

Corresponding author

Correspondence to Valère Lambert.

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Peer review information Nature thanks Jeffrey J. McGuire, Peter Shearer and Alice-Agnes Gabriel for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

This file contains Supplementary Methods, Supplementary Text, Supplementary Figures 1–23, Supplementary Tables 1–6, legends for Supplementary Videos 1–3, and Supplementary References.

Supplementary Video 1

Evolution of shear stress during a self-healing pulse-like rupture on a quasi-statically strong but dynamically weak fault. Evolution of shear stress (black line) along the fault during a self-healing pulse-like rupture on a quasi-statically strong but dynamically weak fault (H1). The video illustrates the changes in shear stress with respect to the initial (grey) and final (blue) shear stresses, as well as the quasi-static strength (red). The initial stress on the majority of the fault is far below the quasi-static strength, except for the region in which the rupture nucleates, which is small compared to the total rupture area. As the rupture front crosses the seismogenic (VW) region, each point experiences a large dynamic stress increase towards ~100 MPa and then drops to low levels below 10 MPa. Only a small portion of the fault slips at a given time as the shear resistance heals behind the rupture front and the fault relocks, resulting in higher final stress levels than the level of shear resistance at which most of the slip occurred.

Supplementary Video 2

Evolution of shear stress during a crack-like rupture on a persistently weak fault. Evolution of shear stress (black line) along the fault during a mild crack-like rupture on a persistently weak fault (H2). The initial shear stress over the entire rupture region is within 1–2 times the static stress drop (7.3 MPa) away from the quasi-static strength. Slip continues within the regions behind the rupture front until the rupture front is arrested in the VS region on the other side of the seismogenic (VW) region, and healing waves redistribute stress and arrest slip. All conventions follow Supplementary Video 1.

Supplementary Video 3

Scaled evolution of shear stress during a crack-like rupture rupture on a persistently weak fault. Evolution of shear stress (black line) along the fault for the same mild crack-like rupture as shown in Supplementary Video 2, however with the shear stress axis rescaled to emphasize the dynamic stress changes during the rupture. Slip continues within the regions behind the rupture front until the rupture front is arrested in the VS region on the other side of the seismogenic (VW) region, and healing waves redistribute stress and arrest slip, resulting in a dynamic overshoot throughout most of the ruptured region. All conventions follow Supplementary Videos 1 and 2.

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Lambert, V., Lapusta, N. & Perry, S. Propagation of large earthquakes as self-healing pulses or mild cracks. Nature 591, 252–258 (2021). https://doi.org/10.1038/s41586-021-03248-1

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