Coupled interactions between the seismogenic zone and the ductile root of faults : earthquake cycle simulations with rate-and-state friction and nonlinear viscoelasticity

This thesis focuses on understanding the interaction between the seismogenic zone of strike-slip faults and their ductile roots, and resulting implications for the structure and dynamics of the continental lithosphere in which they are embedded. A wide range of observations highlight the significance of this interaction, including the time- and depth-dependence of transient postseismic deformation (both frictional afterslip and bulk viscous flow), the triggering of aftershocks by viscous flow, the spatiotemporal distribution of microseismicity, and microstructural data from exhumed faults. Furthermore, the depth-extent of large strike-slip earthquakes appears to be limited to the mid-crust, resulting from a transition in deformation style or material properties in the middle and to lower crust. Previous work has demonstrated by increasing temperature with depth in the crust causes two significant transitions: a transition in frictional properties on the fault from velocity-weakening (VW) to velocity-strengthening (VS), and a transition in off-fault deformation from brittle deformation to crystal-plastic creep (the brittle-ductile transition, or BDT). Both of these transitions are estimated to occur roughly at 10-20~km depth, and therefore both are candidates for control over the nucleation depth of large earthquakes and their downdip propagation limit, and therefore control over an upper bound on the largest earthquake possible on a strike-slip fault. As both transitions are temperature-dependent, the effects of heat generation through frictional and viscous shear heating will impact the structure and dynamics of the system, possibly producing a shallow BDT and smaller earthquakes. This work is performed in the context of earthquake cycle simulations, in which all phases of the earthquake cycle are modeled. In the interseismic period, slow tectonic loading causes a stress concentration to build up on the fault, which spontaneously nucleates each earthquake. The propagation of the rupture up and down the fault is then simulated, and finally the postseismic period is simulated as well. These simulations allow the slip, stress drop, and recurrence interval of each earthquake to develop in a way that is self-consistent with the history of earthquakes and postseismic deformation. Previous earthquake cycle work has generally focused on either the frictional transition on the fault or the transition from brittle to ductile deformation. Simulations which take the first approach simulate rate-and-state friction on the fault, representing the off-fault material as linear elastic, and are able to explore a rich variety of event types and sizes, including large and small earthquakes and slow slip events. They are also able to reproduce a number of observations, including: the general time scale of each phase of the earthquake cycle, the depth-extent of the seismogenic zone, and the signature of frictional afterslip in surface deformation. Other work, which takes the second approach, models the off-fault material with a thermally activated creep law, but kinematically imposes the earthquakes. These studies are able to explore the structure of the shear zones beneath faults, the time-dependence of the effective viscosity, and the effects of viscous shear heating. A few recent studies have included both transitions simultaneously, and have been able to reproduce observations of elevated bulk viscous flow in the postseismic period and the existence of a region of both coseismic slip and bulk viscous flow. My work fits into this last category, and I focus on the interaction between rate-and-state friction and viscoelastic material in the lower crust and upper mantle. In this thesis, I develop a thermomechanical finite difference code which is able to simulate earthquake cycles with the fault described by rate-and-state friction and viscoelastic off-fault material represented with a nonlinear power-law rheology, including both frictional and viscous shear heating. The primary focus is on representing the BDT as a broad transition zone whose depth is not imposed a priori, but rather results from the solution of the system of governing equations. The philosophy is to start with the simplest case that combines spontaneously nucleating earthquakes with bulk viscous flow. As a result these simulations are performed in antiplane strain in two-dimensions, with a vertical strike-slip fault. I also use the quasidynamic approximation in the first two chapters, an approximation which makes the development of the numerical method simpler by neglecting wave-mediated stress transfer. In the first chapter of the thesis, I perform viscoelastic cycle simulations. I consider a range of background geotherms, and find that this produces qualitatively different deformation styles in the lower crust and upper mantle, ranging from significant fault creep at depth in the coolest model to purely bulk viscous flow in the warmest model. The simulations presented in this study encompass the range of effective viscosity estimates for the Wester US from deformation studies, indicating that the effective viscosity estimates imply a great deal of uncertainty in the predominant deformation mechanism of the lower crust. Later in the thesis, I incorporate a method for the simulation of fully dynamic ruptures in the coseismic period into the viscoelastic cycle simulation code. I also explore criteria for switching from the quasidynamic method in the interseismic period to the fully dynamic method in the coseismic period and back, based on the magnitude of the radiation damping term relative to the quasi-static shear stress. In the next part of the thesis, I extend this work to include frictional and viscous shear heating, which produces elevated temperature (or thermal anomaly relative to the background geotherm) near the fault. This reduces the effective viscosity in this region, resulting in a shallower BDT and, in some parts of parameter space, reducing the depth of earthquake nucleation and the downdip limit of coseismic slip. One significant finding of this work is that frictional and viscous shear heating both contribute roughly equally to this thermal anomaly. Part of this work was the development of a steady-state approximation to the system, in which the viscous strain rates and slip velocity are constant. I find that this steady-state approximation well-characterizes the depth of the BDT and magnitude of the cycle-average thermal anomaly.

Keywords: Geophysics.
Advisor: Dunham Eric 
Klemperer Simon 
Segall Paul