Intellectual Merit

Prior to this project, numerical models of earthquake rupture propagation and slip have almost exclusively used frictional formulations for which the frictional stress is proportional to the normal stress such that the constant of proportionality may be slip, sliprate, and/or statedependent, but normal stressindependent. Such an assumption implies that a rapid change in normal stress is immediately manifested as a rapid change in shear (frictional) stress on the fault. As noted in the context of bimaterial interfaces [Cochard and Rice, 2000], such a formulation can lead to an illposed problem, and griddependent numerical results. Furthermore, laboratory research [Linker and Dieterich, 1992; Prakash, 1998] shows that the response of shear stress to normal stress changes is not (entirely) immediate: there is a significant lag time after the change in normal stress over which the shear stress evolves. This timedependence is mathematically represented as a frictional coefficient that is normalstress dependent. Our work helps to show how normalstressdependent frictional coefficients may influence the propagation of rupture and slip on nonplanar fault segments, where seismic waves cause the normal stress to be time dependent. Our basic result implies that the strong effects of fault geometry on the earthquake are most likely somewhat more moderate in the real world than numerical models have implied up until now. In particular, the extreme ground motion amplification of thrust faults relative to normal faults seen in numerical models [e.g., Oglesby et al., 1998] may not be quite as strong as had been thought (Figure 1). Similarly, compressional and dilational stepovers may not be as distinct from each other as had been previously thought [e.g., Harris et al., 1991] (Figure 2). 
Broader Impacts

The incorporation of a normal stressdependent constitutive friction law into dynamic rupture models will improve understanding of the coseismic frictional behavior of faults. Using this constitutive law will allow models to properly include the types of complexities in the rupture that appear in inversions of ruptures on complex fault systems, most notably, the changes in rupture velocity in the vicinity of geometrical complexities, and any time delays the rupture may experience in negotiating those complexities. The details of fault behavior associated with these normal stress changes have implications for rupture size on individual fault segments, probability of multifault rupture, slip distribution across individual faults and systems, and ground motion. We anticipate that our results will be particularly important with regards to SCEC research priorities 3c (modeling fault resistance mechanisms for seismic radiation and rupture propagation, using constitutive laws that incorporate fault properties) and 3e (rupture modeling to constrain stress levels on faults, and to address fault weakening and healing mechanisms). We also address priority 3a (laboratory experiments on fault materials) in that our constitutive law is based on results of laboratory work by the current PIs that was funded by previous SCEC grants. 