Continuum of earthquake rupture speeds enabled by oblique slip


Earthquake rupture speed can affect ground shaking and therefore seismic hazard. Seismological observations show that large earthquakes span a continuum of rupture speeds, from slower than Rayleigh waves up to P-wave speed, and include speeds that are predicted to be unstable by two-dimensional theory. This discrepancy between observations and theory has not yet been reconciled by a quantitative model. Here we present numerical simulations that show that long ruptures with oblique slip (both strike-slip and dip-slip components) can propagate steadily at various speeds, including those previously suggested to be unstable. The obliqueness of slip and the ratio of fracture energy to static energy release rate primarily control the propagation speed of long ruptures. We find that the effects of these controls on rupture speed can be predicted by extending the three-dimensional theory of fracture mechanics to long ruptures with oblique slip. This model advances our ability to interpret supershear earthquakes, to constrain the energy ratio of faults based on observed rupture speed and rake angle, and to relate the potential rupture speed and size of future earthquakes to the observed slip deficit along faults.

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Fig. 1: Earthquake rupture propagation on a long fault with oblique slip.
Fig. 2: Rupture propagation controlled by energy ratio and rake angle.
Fig. 3: Comparison between observed and simulated speeds and synopsis of rupture behaviours.
Fig. 4: Conceptual implications for time-dependent seismic hazard assessment.

Data availability

The numerical data used for the figures in the main body and in the Extended Data are presented in the Source data. The theoretical data are presented in the Methods. Other data are previously published and available in the references explained in the figure captions. Source data are provided with this paper.

Code availability

The open-source software SPECFEM3D used in our 3D dynamic rupture simulations is available from the Computational Infrastructure for Geodynamics at


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This work was supported by the French government through the Investments in the Future project UCAJEDI (ANR-15-IDEX-01) managed by the French National Research Agency (ANR). We thank D. Molina for providing the central Andes coupling model in digital form.

Author information




H.W. designed and carried out the numerical experiments, and analysed the numerical results. H.W. and J.-P.A. developed the theoretical model, interpreted the results, and wrote the paper.

Corresponding author

Correspondence to Huihui Weng.

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Extended data

Extended Data Fig. 1 Horizontal rupture speed controlled by energy ratio and rake angle.

a, Normalized depth-averaged horizontal speed \({{\rm{v}}}_{{\rm{r}}}^{{\rm{hor}}}\) as a function of normalized rupture propagation distance L/W from the 3D dynamic rupture simulations with Gc/G0 = 0.63 and various rake angles (indicated by colors). b, Dependencies of normalized depth-averaged horizontal speed on energy ratio and rake angle. Source data

Extended Data Fig. 2 Rupture speed across depth.

a, Definitions of real speed (left) and apparent horizontal speed (right). b, Shape (left), real speed (middle) and horizontal speed (right) of steady rupture fronts as a function of depth. Colors indicate rake angle. Source data

Extended Data Fig. 3 Rupture properties of a kinematic rupture model with oblique slip.

a, Rupture contours of the kinematic model, extending as an elliptical front propagating at the P wave speed along its major axis and at the S wave speed along its minor axis. The rake angle is the angle between the major axis of the ellipse and the strike direction. Comparison between the kinematic and dynamic models with Gc/G0 = 0.63 of (b) depth-averaged real speed, (c) horizontal speed and (d) depth-averaged real speed angle as a function of rake angle. Source data

Extended Data Fig. 4 Sketches of friction laws.

Sketches of fracture energy Gc and static energy release rate G0 for (a) linear and (b) power-law slip-weakening friction laws.

Extended Data Fig. 5 Effects of nucleation speed on rupture evolution.

Normalized depth-averaged rupture speeds as a function of normalized distance L/W for two 3D dynamic rupture simulations with different nucleation speeds (vnuc). Source data

Source data

Source Data Fig. 2

Numerical simulation data: rupture behaviours, real rupture speed, steady rupture speed and real speed angle.

Source Data Extended Data Fig. 1

Numerical simulation data: horizontal rupture speed.

Source Data Extended Data Fig. 2

Numerical simulation data: shape, real speed and horizontal speed of steady rupture fronts.

Source Data Extended Data Fig. 3

Numerical simulation data: kinematic models.

Source Data Extended Data Fig. 5

Numerical simulation data: rupture speeds for different nucleation speeds.

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Weng, H., Ampuero, JP. Continuum of earthquake rupture speeds enabled by oblique slip. Nat. Geosci. (2020).

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