SCEC Award Number 16108 View PDF
Proposal Category Individual Proposal (Integration and Theory)
Proposal Title The effect of roughness on the rupture of small faults and the up-scaling of lab friction laws
Name Organization
Bradford Hager Massachusetts Institute of Technology
Other Participants Yuval Tal
SCEC Priorities 3c, 3d, 3f SCEC Groups FARM, Seismology
Report Due Date 03/15/2017 Date Report Submitted 11/14/2019
Project Abstract
Faults are rough at all scales. This deviation from planarity results in geometric asperities and a locally heterogeneous stress field, which affect the nucleation and propagation of shear rupture. We studied this effect numerically at the scale of small earthquakes. The numerical approach developed includes three main features. First, to enable slip that is large relative to the size of the elements near the fault, we implement slip-weakening and rate and state friction laws into the Mortar Finite Element Method. Second, the mesh near the fault is refined using hanging nodes to enable accurate representation of the fault geometry. Finally, to model the whole seismic cycle, , the method uses variable time stepping with quasi-static and fully dynamic implicit schemes. We then study the response of rough faults governed by rate and state friction to slow tectonic loading. With increasing roughness, there is a transition from seismic to aseismic slip behavior, with the stress released by more slip events with lower slip rate, seismic moment, and average static stress drop. We analyze nucleation and show that the roughness introduces barriers that complicate the nucleation process and result in asymmetric rupture, non-monotonic increases in the slip rates, and multiple slip pulses. The nucleation length generally increases with increasing roughness amplitude. However, there are large differences between first slip events in the sequences, where the initial conditions are homogenous, and later events, where the initial stress field and friction conditions are determined by the rupture growth and arrest in previous slip events.
Intellectual Merit Many of SCEC’s core science questions involve the extent to which slip on faults is seismic or aseismic. The prevalent treatment of fault friction is rate-state friction, which is governed by the parameters a, b, and Dc. For a smooth fault, whether a fault slips in a stable (aseismic) or unstable (seismic) manner depends primarily on the sign of (a - b), but also on Dc. Real faults are rough, not smooth, which raises the issue of how to extrapolate laboratory experiments on planar surfaces to faults in the field. This study addresses how, for a given a, b, and Dc, fault roughness effects slip, including nucleation, magnitude, and timing of events.
Broader Impacts This proposal provided partial support for then senior MIT graduate student Yuval Tal. Tal’s 2017 thesis, “The role of roughness in earthquake source physics,” addressed the problem of modeling the effect of roughness on the nucleation and propagation of shear rupture using a rate-state formulation of earthquake source dynamics. This work was presented at the 2016 SCEC Annual Meeting and led to 3 peer-reviewed publications. As a postdoc at Caltech, Tal continues to be actively involved in SCEC, with work presented at both the 2018 and 2019 Annual Meetings plus an additional peer-reviewed publication. He will start a faculty position in Ben-Gurion university (Israel) in the summer, strengthening SCEC’s ties internationally.
Exemplary Figure Report Figure 2, from Tal, Y., & Hager, B. H. (2018). The slip behavior and source parameters for spontaneous slip events on rough faults subjected to slow tectonic loading. Journal of Geophysical Research: Solid Earth, 123.

This figure shows the evolution of maximum slip rates (a, c, and e) and average shear traction (b, d, and f) obtained for three different representations off fault geometries for 5 values of the roughness multiplier. All calculations assume the same rate-state-friction law. Increasing roughness leads to less regularity in the earthquake "cycle," as well as an increasing fraction of the slip occurring seismically.