Numerical simulations of dynamic earthquake rupture require an artificial initiation procedure, if they are not integrated in long-term earthquake cycle simulations. A widely applied procedure involves an 'overstressed asperity', a localized region stressed beyond the static frictional strength. The physical properties of the asperity (size, shape and overstress) may significantly impact rupture propagation. In particular, to induce a sustained rupture the asperity size needs to exceed a critical value. Although criteria for estimating the critical nucleation size under linear slip-weakening friction have been proposed for 2-D and 3-D problems based on simplifying assumptions, they do not provide general rules for designing 3-D numerical simulations. We conduct a parametric study to estimate parameters of the asperity that minimize numerical artefacts (e.g. changes of rupture shape and speed, artificial supershear transition, higher slip-rate amplitudes). We examine the critical size of square, circular and elliptical asperities as a function of asperity overstress and background (off-asperity) stress. For a given overstress, we find that asperity area controls rupture initiation while asperity shape is of lesser importance. The critical area obtained from our numerical results contrasts with published theoretical estimates when background stress is low. Therefore, we derive two new theoretical estimates of the critical size under low background stress while also accounting for overstress. Our numerical results suggest that setting the asperity overstress and area close to their critical values eliminates strong numerical artefacts even when the overstress is large. We also find that properly chosen asperity size or overstress may significantly shorten the duration of the initiation. Overall, our results provide guidelines for determining the size of the asperity and overstress to minimize the effects of the forced initiation on the subsequent spontaneous rupture propagation.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). CP was funded through the Emmy Noether-Programm (KA2281/2-1) of the Deutsche Forschungsgemeinschaft and by the Volkswagen Stiftung (ASCETE project). This work was supported in part by the Slovak Research and Development Agency under the contract number APVV-0271-11 (project MYGDONEMOTION). JPA was partially supported by NSF grant EAR-1151926. Part of the calculations were performed in the Computing Centre of the Slovak Academy of Sciences using the supercomputing infrastructure acquired in project ITMS 26230120002 and 26210120002 (Slovak infrastructure for high-performance computing) supported by the Research & Development Operational Programme funded by the ERDF. We also gratefully acknowledge the funding by the European Union through the Initial Training Network QUEST (Grant agreement number 238007), a Marie Curie Action under the People Programme. We appreciate useful reviews by Steve Day and an anonymous reviewer that helped us to improve the article.