Spectral-element modeling of spontaneous earthquake rupture on rate and state faults: Effect of velocity-strengthening friction at shallow depths

Abstract

We develop a spectral-element methodology (SEM) for simulating dynamic rupture on rate and state faults and use it to study how the rupture is affected by a shallow fault region of steady-state velocity-strengthening friction. Our comparison of the developed SEM and a spectral boundary-integral method (BIM) for an anti-plane (two-dimensional) test problem shows that the two methods produce virtually identical solutions for the finest resolution we use and that the convergence with grid reduction of the developed SEM methodology is comparable to that of BIM. We also use the test problem to compare numerical resolution required for different state evolution laws and for linear slip-weakening friction. Using our three-dimensional implementation of the methodology, we find that a shallow velocity-strengthening fault region can significantly alter dynamic rupture and ground motion. The velocity-strengthening region suppresses supershear propagation at the free surface occurring in the absence of such region, which could explain the lack of universally observed supershear rupture near the free surface. In addition, the velocity-strengthening region promotes faster fall-off of slip velocity behind the rupture front and decreases final slip throughout the entire fault, causing a smaller average stress drop. The slip decrease is largest in the shallow parts of the fault, resulting in the depth profile of slip qualitatively consistent with observations of shallow co-seismic slip deficit. The shallow velocity-strengthening region also reduces the amplification of strong ground motion due to a low-velocity bulk structure.