Plate tectonics drives the slip budget available for deformation across a plate boundary. Within the upper crust, tectonic deformation is accommodated through a combination of frictional slip on faults and distributed deformation in the surrounding rock volume. Large earthquakes accommodate the majority of the slip budget. However, because faults are non-planar and have finite lengths, ruptures must breach zones of geometrical complexity along faults, or the spacing between neighboring faults, to continue growing. Geometrical complexity forces slip on the fault to taper and trade off with the surrounding volume, through a combination of elastic and permanent deformation. How these modes of deformation -localized frictional slip and distributed deformation of the bulk- operate together plays a fundamental role in the distribution of earthquake magnitude and locations across a fault system and the evolution of the physical properties of the crustal volume. This dissertation explores the mechanics of slip transfer through zones of geometrical complexity and the generation of permanent off-fault deformation over multiple earthquake cycles.
Chapters 1 and 2 in this dissertation are concerned with earthquake gates. Zones of geometrical complexity, or earthquake gates, can act as barriers to rupture propagation conditional on the fault geometry, rupture directivity effects, crustal properties, and prior stress history. In the first chapter, I focus on the geometrical aspect of the earthquake gate problem. I map step-overs, bends, gaps, splays, and strands from the surface ruptures of 31 strike-slip earthquakes at 1:50,000 scale, classifying each population into breached and unbreached groups. Based on these classifications, I calculate passing probability as a function of geometry for each group. Step-overs, gaps, and single bends halt ruptures more effectively than double bends, and <20% of the ruptures stopped on straight segments. Based on the modeled probabilities, I estimate event likelihood as the joint passing probabilities of breached gates and straight segments along an event's rupture length. Event likelihood decreases with magnitude, where the size and spacing of earthquake gates along ruptures support a barrier model for controlling earthquake magnitude. Through a simple mechanical model rooted in linear elastic fracture mechanics, I find that ruptures seldom renucleate on receiver faults across step-overs with Coulomb stress change below a critical threshold of 20% of the stress drop.
Complex stress distributions resulting from an integrated history of continuing and halting ruptures, as well as rheological heterogeneity, also act as earthquake gates, but their influence in the passing probability of a barrier are much harder to quantify observationally. By looking at the integrated history of events at an earthquake gate, comparing the number of events that halted versus those that made it past, it is possible to implicitly account for the effects of these harder to observe variables. In the second chapter of this dissertation, I combine a paleoseismic investigation with finite element modeling of secondary slip on a minor fault to determine the frequency and mechanics of earthquakes that co-rupture the San Andreas and the San Jacinto faults in southern California, with rupture transfer across the Cajon Pass releasing step-over. I find evidence that multi-fault events through Cajon Pass have occurred 3 times in the past 2000 years, where 20-23% of the events on the San Andreas and the San Jacinto faults are co-ruptures.
Chapters 3, 4, and 5 of this dissertation are concerned with how distributed deformation around faults is created and evolves over multiple earthquake cycles. Some of the distributed deformation around faults exceeds the yield stress the rock mass can support, resulting in the creation of permanent deformation that is accommodated by a suite of dissipative mechanisms, including fracture, granular flow, warping, and block rotations. In chapter 3, I combine fracture, aftershock, and strain maps from the 2019 Ridgecrest earthquakes to quantify the distribution of inelastic deformation in the surrounding volume of the rupturing faults. I find the decay of inelastic deformation with distance from the fault is well described by an inverse power law, consistent across datasets, and continuous without breaks in scaling, suggesting that a single mechanism dominates yielding.
Widespread distributed fracturing, such as that characterized in chapter 3, threatens infrastructure and lifelines. In chapter 4, I use high-resolution rupture maps from the five major surface-rupturing strike-slip earthquakes in southern California and northern Mexico since 1992 to incorporate the displacements produced by distributed ruptures into a probabilistic displacement hazard analysis framework. Through analysis of the spatial distribution of mapped ruptures and displacements for each of these events, I develop a magnitude-dependent expression for the probability per unit area of finding a distributed rupture that accommodates a displacement that exceeds a user-defined threshold at a given distance from the principal fault.
In chapter 5, I shift focus to the question of how permanent deformation accumulates over multiple earthquake cycles. Using lidar and field observations, I measure coseismic and cumulative folding from five locales in western North America. The observations link coseismic to cumulative deformation and show that folding amplitude accumulates over multiple slip cycles, scaling as the square root of fault throw. The distribution of folding strains is well described by the decay of elastic stress surrounding a crack tip, though the strains exceed the elastic limit of rock by over an order of magnitude. The field observations suggest that pre-existing fabrics in the rock mass help accommodate the large folding strains while maintaining the elastically created shape. The lidar and field observations can be explained by a simple model where the rock mass deforms linearly with stress, though the shear modulus that defines the rate of change in deformation decreases once the yield stress of the rock mass is reached.
Through the use of high-resolution topography, aerial imagery, earthquake catalogs and field observations, this dissertation contributes to the increasingly detailed picture of how tectonic strain is transferred and accommodated across the upper crust over different spatiotemporal scales. This work also contributes outstanding questions to this growing understanding: How much of the complexity and damage mapped at the surface persists at depth? Why do step-overs appear to require very high (~20% of the stress drop) Coulomb stress changes for rupture to renucleate yet widespread fracturing and aftershocks are easily triggered and populate a very large crustal volume following earthquakes? Fracturing and folding contribute to large reductions in the compliance around faults, even coseismically, how much of this reduction is recovered post- or interseismically through healing mechanisms? These questions will guide future data collection and modeling efforts addressing the mechanics of strain accumulation and release in the crust.
