Variation of large elastodynamic earthquakes on complex fault systems

One of the biggest assumptions, and a source of some of the biggest uncertainties in earthquake hazard estimation is the role of fault segmentation in controlling large earthquake ruptures. Here we apply a new model which produces sequences of elastodynamic earthquake events on complex segmented fault systems, and use these simulations to quantify the variation of large events. We find a number of important systematic effects of segment geometry on the slip variation and the repeat time variation of large events, including an increase in variation at the ends of segments and a decrease in variation for the longest segments

Impact of Friction and Scale-Dependent Initial Stress on Radiated Energy-Moment Scaling

The radiated energy coming from an event depends on a number of factors, including the friction and, crucially, the initial stress. Thus we cannot deduce any scaling laws without considering initial stress. However, by simulating long sequences of events, where the system evolves to a statistically steady-state, we can obtain the appropriate distribution of initial stresses consistent with the dynamics and a given friction. We examine a variety of frictions, including power-law slip dependence, and explore a variety of scaling relations, with the aim of elucidating their radiated energy-moment scaling. We find, contrary to expectations, that apparent stress is not seen to increase with earthquake size for power-law weakening. For small and for large events, little change in apparent stress is seen with increasing rupture size, while intermediate sized events interpolate in between. We find the origin of this unexpected lack of size dependence in systematic changes of initial stress, with bigger events tending to sample regions of lower initial stress. To understand radiated energy-moment scaling, scale-dependent initial stress needs to be considered

Frictional weakening and slip complexity in earthquake faults

Previous work has shown that velocity-weakening friction produces slip complexity in simple dynamical models of earthquake faults (Carlson and Langer, 1989). Here I show that a different type of dynamical instability, caused by slip-weakening friction, also produces slip complexity. The deterministically chaotic slip complexity produced by slip-weakening friction in a simple one dimensional model is studied and the scaling of the distribution of sizes of events with the parameters in the model examined. In addition, a possible physical origin of frictional weakening is examined, through a very simplified mathematical representation of a physical process proposed by Sibson (1973), whereby frictional heating causes an increase in pore fluid temperature and pressure, thereby reducing the effective normal stress and friction. The two different types of frictional weakening are derived from two opposing limits, with slip weakening occurring when the dissipation of heating is slow compared to the rupture timescale, as Lachenbruch (1980) has shown, while velocity weakening is shown to occur when the dissipation is fast compared to the rupture timescale. Since both end-member cases of frictional weakening are seen to produce slip complexity, slip complexity is argued to be a generic feature of frictional weakening and elastodynamics on a fault

Complexity in a spatially uniform continuum fault model

Recently, Rice [1993] pointed out that, up to now, the self-organizing models which have produced complex nonperiodic sequences of events have all been sensitive to the spatial discretization used, and thus did not have a well defined continuum limit. He went on the suggest that spatial nonuniformity or “inherent discreteness” may be a necessary ingredient in allowing the complexity to develop in these systems. In this paper, I present a counterexample to this suggestion: a spatially uniform model with a well defined continuum limit is shown to give rise to complex nonperiodic sequences. The complexity arises in the deterministic model from inertial dynamics with a velocity-weakening frictional instability, with the instability being stabilized at short lengthscales by a viscous term. The numerical results are shown to be independent of the spatial discretization for discretizations small compared to the viscous lengthscale. Furthermore, the qualitative features of the complexity produced are seen to be invariant with respect to two very different types of small scale cutoffs, implying a universality of the results with respect to the details of the small scale cutoff

Earthquake Surface Slip-Length Data is Fit by Constant Stress Drop and is Useful for Seismic Hazard Analysis

We present a new method to use directly observable surface-slip measurements in seismic hazard estimates.We present measures of scaling-relation fits to slip length data. These fits show sublinear scaling, a slowing in the rate of slip increase for the longest ruptures, so that L scaling—scaling with the length of the rupture—does not hold out to very large aspect ratio events. We find the best fitting for a constant stress drop model, followed next by a square root of length model. The constant stress-drop model, newly introduced here, provides a geometrical explanation for a long-standing puzzle of why slip only begins to saturate at large aspect ratios. The good fit of the constant stress-drop model to the slip-length data lends further support to the observations of constant stress-drop scaling across the whole range of magnitudes of earthquakes, from small to great earthquakes. The good fit of the constant stress-drop model is also reflected by the low variability about the mean, with an average of less than a factor-of-2 variability in stress drop about the mean observed. Converting magnitude-area scaling into implied slip-length scaling, we determine qualitative consistency in the functional forms, but a quantitative difference of, on average, about 30 percent more slip estimated from magnitude area compared with slip length

Dynamic heterogeneities versus fixed heterogeneities in earthquake models

A debate has raged over whether fixed material and geometrical heterogeneities, or alternatively dynamic stress heterogeneities, arising through frictional instabilities dominate earthquake complexity. It may also be that both types of heterogeneities interact and are important. This paper makes a first step in examining this interaction, combining two previously separate lines of research. One line examined friction, which has attractors (the subset of the phase space that the system evolves towards in the long run) on homogeneous faults, which are simple, and then added fixed heterogeneities to the faults to obtain complex attractors. Another line examined frictions, which produced complex attractors on homogeneous faults. Here, we examine frictions, which produce complex attractors on homogeneous faults, and study them on heterogeneous faults, in order to study the interaction of dynamic stress heterogeneities and fixed fault heterogeneities. We consider two types of fixed heterogeneities: an additive noise and a multiplicative noise to the frictional strength of the fault. Because of the linearity of the bulk elastodynamics, the attractor is unaffected by additive fixed noise in the strength of the fault: adding an arbitrary function of space, fixed in time, to the friction leaves the resulting attractor unchanged. In contrast, multiplicative fixed noise multiplying the friction can have a profound effect on the resulting attractor. In the small multiplicative noise amplitude limit, the frictional weakening attractor is little perturbed; at finite amplitudes, fixed heterogeneities substantially alter the attractor. We see, as one consequence, a shift toward longer length events at larger amplitudes. Fixed heterogeneities are seen to reduce the irregularities created by the frictional instability we study, but by no means destroy them. We quantify this by examining a measure of variability of the importance in hazard estimates, the coefficient of variation of large event recurrence times. The coefficient of variation is seen to remain substantial even for large fixed heterogeneities. For friction that weakens with time, so the underlying uniform fault attractor is simple, fixed heterogeneities increase irregularity. For all frictions examined, at low fixed heterogeneity the stress concentrations left over by the ends of the large events dominate where most of the small events occur, while at higher heterogeneity the stress irregularities left over by fixed fault heterogeneities begin to dominate where the small events occur. This may be the strongest signature of fixed heterogeneities, and should be examined further in the Earth. Finally, in what may have important implications for more sophisticated estimates of earthquake hazard, we see a correlation of locations with lower strength drop having higher variation in large event repeat times

Probabilities for jumping fault segment stepovers

Seismic hazard analysis relies heavily on the segmentation of faults. The ability of ruptures to break multiple segments has a big impact on estimated hazard. Current practice for estimating multiple segment breakage relies on panels of experts voting on their opinions for each case. Here, we explore the probability of elastodynamic ruptures jumping segment stepovers in numerical simulations of segmented fault systems. We find a simple functional form for the probability of jumping a segment stepover as a function of stepover distance: an exponential falloff with distance. We suggest this simple parameterization of jumping probabilities, combined with sparse observational data to fix the length scale parameter, as a new approach to estimating multisegment earthquake hazard

Slip-length scaling in large earthquakes' Observations and theory and implications for earthquake physics

For twenty years there has been a dilemma in earthquake physics, because the observed scaling law for large earthquakes did not appear to be consistent with the stress-drop invariance of small earthquake scaling. Surprisingly, slip was seen to continue to increase with rupture length L even for events with lengths much longer than the event widths W (the brittle crust down-dip depth), whereas it might have been expected to saturate for lengths much beyond the width. If this implies that the physics of great earthquakes is somehow different from that of their smaller counterparts, this casts serious doubts on predicting the effects of the rare and damaging great events from observations of the more common smaller events. Here we bring together recently compiled observations of very large aspect ratio earthquakes with results of a 3 dimensional dynamic earthquake model to show that slip-length scaling observations are, in fact, consistent with a scale-invariant physics. Further, we discuss the origin of the large earthquake scaling in the model

Transition regimes for growing crack populations

Numerous observational papers on crack populations in the material and geological sciences suggest that cracks evolve in such a way as to organize in specific patterns. However, very little is known about how and why the self-organization comes about. We use a model of tensilelike cracks with friction in order to study the time and space evolution of normal faults. The premise of this spring-block analog is that one could model crustal deformation for long time scales assuming a brittle layer coupled to a ductile substrate. The long time-scale physics incorporated into the model are slip-weakening friction, strain-hardening rheology for coupling the two layers, and randomly distributed yield strength of the brittle layer. We investigate how the evolution of populations of cracks depends on these three effects, using linear stability analysis to calculate the stable regimes for the friction as well as numerical simulations to model the nonlinear interactions of the cracks. We find that we can scale the problem to reduce the relevant parameters to a single one, the slip weakening. We show that the distribution of lengths of active cracks makes a transition from an exponential at very low strains, where crack nucleation prevails, to a power law at low to intermediate strains, where crack growth prevails, to an exponential distribution of the largest cracks at higher strains, where coalescence dominates. There is evidence of these different length distributions in continental and oceanic normal faults. For continental deformation the strain is low, and the faults have power-law frequency-size distributions. For mid-ocean ridge flanks the strain is greater, up to an order of magnitude higher than the continental strain, and faults have exponential-like frequency-size distributions. No theory has been offered to explain this difference in the distributions of continental and mid-ocean faults. In this paper we argue that they are indicative of different stages of evolution. The former faults are at an early stage of relatively small deformation, while the latter are at a later stage of the evolution. For high strain the faults reach a saturation regime with system size cracks evenly spaced in proportion to the brittle layer thickness. We asymptotically approximate the time space evolution of faults as a long time-scale phenomenon, thereby avoiding modeling the short time-scale earthquakes. We show that this assumption is valid, which implies that the faults that creep and faults with earthquakes display the same time and space evolutions