Mechanical and Civil Engineering Seminar
Slip Patterns on Heterogeneous Frictional Interfaces
Ph.D. Thesis Defense
Understanding the implications of heterogeneity on frictional interfaces for the resulting slip patterns is a challenging, highly nonlinear and dynamic problem with special relevance to earthquake source processes. Natural fault surfaces are rarely homogeneous, and host a spectrum of slip behaviors in response to slow tectonic loading where slow steady slip and earthquake ruptures are just the end members. Understanding how heterogeneous frictional properties translate into different slip patterns would enable us to constrain the heterogeneity of natural faults and get an insight into processes that are difficult to observe in the field such as earthquake nucleation, with important implications for the assessment of seismic hazard.
In this thesis, we advance our understanding of fault heterogeneity and its effects by conducting numerical simulations of long-term slip histories on heterogeneous frictional interfaces. We first focus on how irregular fault geometry affects the variability in repeating sequences by investigating a specific example of the SF-LA repeaters in the Parkfield segment of the San Andreas Fault (SAF) in California. We then investigate the effect of increasing heterogeneity in the effective normal stress on earthquake nucleation processes, complexity of earthquake sequences, and features of larger-scale ruptures. In both cases, we incorporate the heterogeneity in physical properties into 2D planar faults governed by rate-and-state friction and embedded into 3D homogeneous elastic bulk. Fully dynamic simulations are used to numerically solve the resulting elastodynamic problems with friction as a nonlinear boundary condition.
Our models reproduce many observations about SF-LA repeating sequences, including their mean moment, mean recurrence times, stress drops, the observed non-trivial scaling between the seismic moment and recurrence times of the repeaters, the ranges of variability in moment and recurrence time, and the ranges of triggering times between the two sequences. Multiple models produce slip behaviors comparable to observations, indicating that the models cannot be uniquely constrained based on available observations. We also study how small-scale features of heterogeneity affect model response and find that smoothing the distribution over scales larger than governing length scales in the problem case modifies the response qualitatively.
Our study of the earthquake initiation processes on interfaces with normal stress heterogeneity reveals that systematic increase in heterogeneity induces a continuum of behaviors, ranging from purely fault-spanning events to persistent foreshock-like events interspersed between fault-spanning mainshocks. In models with strong heterogeneity, most smaller-scale and larger-scale events initiate from scales much smaller than the nucleation size estimates calculated for uniform interfaces with equivalent average properties. Our simulations show that several hypothesized scenarios of earthquake nucleation and foreshocks on natural faults may be viable and reflect different types and levels of heterogeneity on different faults the effects of which, in addition, vary as fault conditions evolve. For example, even with strong fault heterogeneity, some large-scale events have foreshocks and some do not, in the same simulation.
The increasing fault heterogeneity generally leads to increasing complexity of the resulting earthquake sequences and moment-rate release (also called source-time function) of large-scale, fault-spanning events. We find that, in the presence of significant normal-stress heterogeneity, source-time functions of many larger-scale events exhibit prolonged seismic initiation phases, similar to some observations. The source-time functions also reveal that larger-scale events in our models - that are arrested by velocity-strengthening barriers - have a more abrupt arrest phase than natural earthquakes, which places constraints on rupture-arresting mechanisms that should be used in modeling. The initial moment rates are similar for events of different eventual sizes on interfaces with strong heterogeneity, implying that, in those cases, large events are just small events that ran away.
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