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


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 ( 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.


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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.

Author information

Authors and Affiliations



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.

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Correspondence to Valère Lambert.

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The authors declare no competing interests.

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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).

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