S13D-01
Fault strength loss, slip velocity, and near-fault particle velocity during dynamic rupture propagation.
Near-fault particle velocity depends on the total energy released minus the portion of this energy that is dissipated and stored within the earthquake source. In earthquake source models without rupture propagation and where shear strength loss is instantaneous, the peak particle velocity is proportional to the shear strength loss (effective stress) and the wave speed [e.g., Brune, 1970]. In models incorporating dynamic rupture propagation, the propagation speed of the rupture front, rather than the wave speed, and changes in stress components other than shear stress, determine the peak particle velocity. To test these models from theoretical seismology, and to establish empirical relations amongst fault slip rate, off- fault particle velocity, fault strength loss and stress state, laboratory measurements were made during dynamic rupture propagation on a 2 m x 0.4 m fault surface between granite blocks. At multiple locations along strike and at small distances normal to strike, shear stress, particle velocity and acceleration were recorded at a sampling rate of 1 MHz. Fault slip was also recorded at multiple locations along strike. In these experiments the fault strength loss is not abrupt, because of significant on-fault fracture energy. As a consequence, in the early stages the rupture front accelerates slowly. Despite these complications, preliminary results show clear proportionality between the spatially averaged stress drop and local peak or average slip rates. The relations between local stress drop, local slip rate, rupture propagation speed and off-fault particle velocity are, as yet, not entirely clear. Instrumentation is currently being added to record changes in the tensor stress components to characterize the complete local stress state at multiple locations during propagation and arrest. We anticipate that analysis of this more comprehensive data set will clarify the relationships between the various rupture parameters.
S13D-02
Insights on the Physics of Earthquakes from Laboratory Stick-Slip Friction in Conjunction with a Dynamic Rupture Model
Comparing laboratory friction results to corresponding parameters measured for earthquakes can yield key insights concerning the question of whether the physics of large and small earthquakes differ. Measurements made during large-scale, biaxial stick-slip friction measurements in the laboratory are effective for predicting many earthquake source parameters including the maximum slips and maximum slip rates within the fault zone of major earthquakes, as well as apparent stress. To relate the laboratory measurements to their earthquake counterparts, the laboratory results are multiplied by two adjustment factors, one for stress and the other for stiffness. The stress adjustment accounts for the difference between loading stresses in the laboratory and those at seismogenic depths in the crust. The stiffness adjustment involves replacing the laboratory fault with an equivalent-stiffness buried circular crack. These adjustments render the laboratory measurements in agreement, within a factor of two, of those determined using slip models of large earthquakes. Using the dynamic rupture model developed by Madariaga (1976) and Boatwright (1980), additional comparisons of seismic rupture processes between laboratory events and earthquakes can be drawn. Laboratory estimates of fracture energy density, typically of the order of several J/m2, can be extrapolated up to those of major earthquakes, approximately 1 MJ/m2. Similarly, this dynamic rupture model can be applied to the laboratory data to investigate several aspects of the energy changes that take place during earthquakes. First, the rupture model indicates that the seismic energy flux adjacent to an earthquake fault surface consists of the seismic energy radiated into the far-field plus the energy change associated with the static stress drop; the ratio of these two energies depends only on the rupture speed. Second, the laboratory results can be used in conjunction with the rupture model to estimate the components of the energy budget of an earthquake. (Released energy=radiated energy+fracture energy+frictional energy) It turns out that of the released elastic strain energy, the vast majority is consumed in overcoming friction. Returning to the question of whether small and large earthquakes differ in terms of their rupture physics, the well-defined relationships between the parameters of laboratory events and their earthquake counterparts suggest that the source processes of small and large earthquakes are much the same as those in laboratory friction experiments. If so, then the strength of the seismogenic zone plays the key role in determining the peak slip rate and the apparent stress.
S13D-03
The Effect of Vibration on Stick-slip Behavior in Sheared Granular Media: Implications for Earthquake Recurrence and Triggering
Dynamic earthquake triggering remains a compelling mystery: how do transient seismic waves with strains of order 10-6 trigger earthquakes, often with failure occurring long after the waves have passed? To better understand the physics of dynamic triggering, we conducted laboratory studies of stick-slip in granular media and its response to applied acoustic vibration. Glass beads were used to simulate granular fault zone wear material, sheared in a double-direct configuration under constant normal stress, while subject to transient or continuous perturbation by acoustic waves. Here we show that small magnitude failure events, corresponding to triggered aftershocks in the glass bead layers, occur when applied sound-wave amplitudes exceed several microstrain, in accord with a nonlinear mechanism proposed previously (Nature, 473 871-874 (2005). The acoustic waves also cause large slip events to be delayed significantly relative to those observed without wave perturbation. Remarkably, the effects are observed for several major-event cycles after the termination of the acoustic signal, indicating a strain memory in the granular material despite the severe material reset that takes place during a large stick-slip event. The material memory looks suspiciously like the nonlinear slow dynamics observed in rock, granular media, some sintered metals and nearly all damaged solids.
S13D-04
Shear Strain Localization in Elastodynamic Rupture Simulations
We study how shear strain localization affects the propagation and dynamics of earthquake rupture. We model the fault as a layer of gouge governed by Shear Transformation Zone Theory, which provides a microscopic physical model for plastic deformation of the gouge, and a state variable for effective temperature. The effective temperature represents the local disorder in the gouge, and regions with higher effective temperature become more susceptible to plastic deformation. When strain is allowed to vary normal to the fault plane, a shear band instability permits sustained shear strain localization. We examine both homogeneous shear and localized shear in the spontaneous propagation of elastodynamic ruptures, and study how localization affects the stress dynamics, energy balance, and slip rate of earthquakes.
S13D-05
Variability of Slip Behavior in Simulations of Dynamic Rupture Interaction With Stronger Fault Patches Over Long-Term Deformation Histories
Heterogeneity in fault properties can have significant effect on dynamic rupture propagation and aseismic slip. It is often assumed that a fixed heterogeneity would have similar effect on fault slip throughout the slip history. We investigate dynamic rupture interaction with a fault patch of higher normal stress over several earthquake cycles in a three-dimensional model. We find that the influence of the heterogeneity on dynamic events has significant variation and depends on prior slip history. We consider a planar strike-slip fault governed by rate and state friction and driven by slow tectonic loading on deeper extension of the fault. The 30 km by 12 km velocity-weakening region, which is potentially seismogenic, is surrounded by steady-state velocity-strengthening region. The normal stress is constant over the fault, except in a circular patch of 2 km in diameter located in the seismogenic region, where normal stress is higher than on the rest of the fault. Our simulations employ the methodology developed by Lapusta and Liu (AGU, 2006), which is able to resolve both dynamic and quasi-static stages of spontaneous slip accumulation in a single computational procedure. The initial shear stress is constant on the fault, except in a small area where it is higher and where the first large dynamic event initiates. For patches with 20%, 40%, 60% higher normal stress, the first event has significant dynamic interaction with the patch, creating a rupture speed decrease followed by a supershear burst and larger slip around the patch. Hence, in the first event, the patch acts as a seismic asperity. For the case of 100% higher stress, the rupture is not able to break the patch in the first event. In subsequent dynamic events, the behavior depends on the strength of heterogeneity. For the patch with 20% higher normal stress, dynamic rupture in subsequent events propagates through the patch without any noticeable perturbation in rupture speed or slip. In particular, supershear propagation and additional slip accumulation around the patch are never repeated in the simulated history of the fault, and the patch stops manifesting itself as a seismic asperity. This is due to higher shear stress that is established at the patch after the first earthquake cycle. For patches with higher normal stress, shear stress redistribution also occurs, but it is less effective. The patches with 40% and 60% higher normal stress continue to affect rupture speed and fault slip in some of subsequent events, although the effect is much diminished with respect to the first event. For example, there are no supershear bursts. The patch with 100% higher normal stress is first broken in the second large event, and it retains significant influence on rupture speed and slip throughout the fault history, occasionally resulting in supershear bursts. Additional slip complexity emerges for patches with 40% and higher normal stress contrast. Since higher normal stress corresponds to a smaller nucleation size, nucleation of some events moves from the rheological transitions (where nucleation occurs in the cases with no stronger patch and with the patch of 20% higher normal stress) to the patches of higher normal stress. The patches nucleate both large, model-spanning, events, and small events that arrest soon after exiting the patch. Hence not every event that originates at the location of a potential seismic asperity is destined to be large, as its subsequent propagation is significantly influenced by the state of stress outside the patch.
S13D-06
Effective Friction Resulting from the Presence of Heterogeneous Strength for Rupture Dynamics
Inversions of strong motion records can produce reliable descriptions of the evolution of the slip during an earthquake. However, the resolution of the kinematic parameters for these models is limited by the distribution of stations and by our knowledge of the details of the Earth structure. As a result, the rupture models we deduce are restricted to large length scales, typically larger than one kilometer. These models can be reproduced in dynamic simulations with simple friction laws and heterogeneities in friction parameters and initial stress. These simulations are used to constrain the values of friction parameter such as weakening rate, critical slip or fracture energy on actual faults. Indeed there are numerous arguments for the existence of fault heterogeneity at all scales. We investigate numerically the implication of neglecting small wavelength heterogeneity on faults by computing 3D finite element solutions of heterogeneous faulting under slip weakening friction. We show that the average properties of a spontaneous rupture (evolution of the rupture and amplitude of slip) on a fault with stationary heterogeneity are well reproduced when imposing an effective friction on a homogeneous fault. We deduce the properties of the effective friction from the elastic deformation in the bulk off the fault in a way similar to what was proposed for the 2D antiplane case on the basis of the mathematical analysis of the initiation phase. The effective friction law exhibits a nonlinear slip dependence with an initial weakening rate different from the one imposed on the heterogeneous fault. With strongly heterogeneous faults, the effective critical slip is larger than the actual one. This indicates that neglecting small-scale heterogeneity in the interpretation of kinematic rupture models likely leads to a misconstruction of actual friction properties of faults. We further investigate different types of heterogeneity to assess the validity of the concept of effective friction.
S13D-07
Dynamic Interface Rupture in Extremely Heterogeneous Media
Fracture experiments of monolithic brittle materials usually show the maximum speed of smooth rupture at some 30 % of the relevant shear wave speed. This experimental maximum rupture speed is by far lower than those predicted by theories and inferred from inversions of seismograms, and some seismic inversions (e.g., the 1979 Imperial Valley, 1992 Landers, 1999 Izmit, 2001 the central Kunlunshan and 2002 Denali earthquakes) even suggest the existence of supershear rupture speeds (i.e., rupture propagating faster than the relevant shear wave). Recently, Uenishi et al. ( SSJ Fall Meeting, 2004, 2005; AGU Fall Meeting, 2006) experimentally investigated dynamic fracture in monolithic hyperelastic materials under static mode-ƒ§ loading conditions with relatively high crack-parallel stresses. Using a high-speed digital video camera system, they showed that cracks may propagate supersonically even in homogeneous materials. However, the exact mechanism for rupture nucleation and the transition of a nucleated rupture from sub-Rayleigh to super-shear rupture speed has not been identified yet. In this contribution, we further develop our experimental system and investigate dynamic fracture in extremely heterogeneous media, consisting of thin fluid and solid films: Inside a wire frame (50mm high, 50mm wide), a flat soap film contacts a flat thin solid plastic film (20mm high, 20mm wide), under static tensile loading conditions. The rupture (crack), initiated at a point, propagates subsonically in the linear elastic fluid film (see e.g., Uenishi et al., SSJ Fall Meeting, 2006, for the dynamic rupture in monolithic fluid films). When the circular rupture front reaches the interface, the rupture advances along the interface and then it is "diffracted" at the two corners of the interface. We record the rupture propagation process utilizing our high-speed digital video camera at a frame rate of 20 μs (20×10-6s). The observed results show that interface rupture propagation may accelerate (or even decelerate) and the dynamic rupture behavior is very sensitive to the geometry of the interface between the two films: (1) When the subsonic rupture front reaches the first rectangular corner, it accelerates around the corner and then advances supersonically along the interface; and (2) when the supersonic interface rupture front approaches the second corner (obtuse with respect to the rupture front in fluid), it bifurcates for a short period (400 μs): the first branch unexpectedly expands rather straight into the bulk and the second one propagates along the interface at a lower speed; At a later stage, again unexpectedly, the first branched crack decelerates significantly in the bulk and the two cracks eventually merge into a single crack. The overall behavior is - in some sense - similar to that of the oblique shock and Prandtl- Meyer expansion waves in fluid mechanics, and it might give new insights not only into the question of high rupture speeds of natural earthquakes but also into the generation mechanism of tsunamis. http://www2.kobe- u.ac.jp/~uenishi/
S13D-08
A Test of Two Earthquake Modeling Methods
A primary challenge in earthquake modeling is to decide which fundamental mechanisms are required to accurately reproduce the earthquake process, and which are less important. With this in mind, we compared two modeling methods that incorporate different levels of approximation in the earthquake process. The first model, DYNA3D, solves the full dynamic equations of motion (including the frictional interaction on the fault and wave propagation) by the finite element method, but uses a simple slip-weakening friction law. The second model rapidly simulates large earthquake sequences by applying quasi-static approximations with rate- and state- dependent friction and long-range elastic interactions. We investigated how different aspects of the model (e.g. initial stress, and rupture location) affect different features of the simulated ruptures (e.g. slip and stress drop) and to what extent the models agreed with each other on the resulting properties. We found the quasi-static model can qualitatively reproduce the general slip and stress drop patterns of earthquake rupture given by the fully dynamic model as well as produce different modes of rupture (crack-like and rupture pulses). As expected, rupture velocity and the details of the slip rate function agreed the least.