S12B-01 INVITED
Slow-Slip Propagation Speeds
Combined seismic and geodetic data from subduction zones and the Salton Trough have revealed slow slip events with reasonably well-defined propagation speeds. This in turn is suggestive of a more-or-less well- defined front separating nearly locked regions outside the slipping zone from interior regions that slide much more rapidly. Such crack-like nucleation fronts arise naturally in models of rate-and-state friction for lab-like values of a/b, where a and b are the coefficients of the velocity- and state-dependence of the frictional strength (with the surface being velocity-neutral for a/b=1). If the propagating front has a quasi-steady shape, the propagation and slip speeds are kinematically tied via the local slip gradient. Given a sufficiently sharp front, the slip gradient is given dimensionally by Δτp- r/μ', where Δτp-r is the peak-to-residual stress drop at the front and μ' the effective elastic shear modulus. Rate-and-state simulations indicate that Δτp-r is given reasonably accurately by bσ\ln(Vmaxθi/Dc), where σ is the effective normal stress, Vmax is the maximum slip speed behind the propagating front, θi is the the value of "state" ahead of the propagating front, and Dc is the characteristic slip distance for state evolution. Except for a coefficient of order unity, Δτp-r is independent of the evolution law. This leads to Vprop/Vmax ~μ'/[bσ\ln(Vmaxθi/Dc)]. For slip speeds a few orders of magnitude above background, \ln(Vmaxθi/Dc) can with reasonable accuracy be assigned some representative value (~4-5, for example). Subduction zone transients propagate on the order of 10 km/day or 10-1 m/s. Geodetic data constrain the average slip speed to be a few times smaller than 1 cm/day or 10-7 m/s. However, numerical models indicate that the maximum slip speed at the front may be several times larger than the average, over a length scale that is probably too small to resolve geodetically, so a representative value of Vprop/Vmax may be ~106. For μ'=40 GPa and a lab value of b of ~10-2, this implies a value of σ of order 1 MPa. While this is extremely low, it is broadly consistent with the observed periods of these events [Liu and Rice, JGR 2007], their very large dimensions (length scales are proportional to σ-1), and their low stress drops (of order 10-2 MPa). The 2005 Salton Trough event had a similar propagation speed but a stress drop and slip speed of order 100 times larger, broadly consistent with lab values of b and hydrostatic pore pressure. Another contrast, possibly related to the difference in effective stress, is that the subduction zone events are associated with tremor while the Salton Trough event was associated with more typical earthquakes.
S12B-02 INVITED
Thermal Pressurization is Significant During Earthquake Nucleation, Before Seismic Slip
Shear heating-induced thermal pressurization has long been invoked as a potential weakening mechanism during earthquakes. It is often assumed that thermal pressurization does not become important until earthquakes have reached a critical size. Segall and Rice [2006], however, suggested that thermal effects may become dominant during the quasi-static nucleation phase, well before inertial effects are significant. By neglecting the feedback between pore-pressure change and slip rate, they estimated that thermal pressurization dominates weakening at slip rates in excess of 10-5 to 10-3 m/s. We further explore this problem numerically assuming a planar fault in a 2D elastic medium and accounting for full thermo-mechanical coupling. We include one-dimensional thermal and pore pressure diffusion normal to a fault governed by rate-state friction. Stress rate and fault slip rate are related through a Hilbert transform in the Fourier domain, and the thermal diffusion is computed with an explicit finite difference formulation. For uniform thermal and hydraulic properties, the pore pressure and temperature on the fault are uniquely related [Rice, 2006, JGR], so only one finite difference grid is required in this limit. As the slip rate increases, the temperature gradient adjacent to the fault increases dramatically. We refine the finite difference grid when the error in the spatial derivative exceeds a specified threshold. The radiation damping approximation is used to simulate inertial effects. For a hydraulic diffusivity of 10-6 m2/s---consistent with permeability inferred for some active fault zones-- -we find that results with and without thermal coupling diverge at slip rates substantially less than those estimated by Segall and Rice [2006]. This reinforces the conclusion that thermal pressurization cannot be ignored in earthquake nucleation. For calculations with the aging form of the state evolution equation and a/b = 1/3, the nucleation zone contracts to a smaller size than Dieterich's [1992] result, which ignored thermal effects.
S12B-03
Quasistatic Fault slip on an Interface Separating Poroelastic Media With Different Diffusivity
It is now widely believed that high-pressure fluid plays some role in the occurrence of slow earthquake rupture. Positive feedback between fluid pressure change and fault slip is required for the occurrence of such rupture as noted by Yamashita (2007). He theoretically studied the quasistatic fault slip on an interface separating dissimilar poroelastic media. He assumed difference only in the values of drained and undrained Poissonfs ratios and their effects were examined. Although not clearly stated, he assumed that k/v is equal in the two media, where k is the permeability and v is the viscosity of fluid. We now theoretically study the effect of difference in the diffusivity. In other words, we assume that only the diffusivity is different in the two media. The fault behavior is studied using the boundary integral equation method (BIEM). We find that the fundamental solution is written in terms of single integrals of known functions, so that the numerical calculation can be carried out easily based on BIEM; here, the fundamental solution means the response from unit displacement discontinuity gradient. We first calculate the stress perturbation due to the sudden introduction of a finite 2-D in-plane fault. As observed in Yamashita (2007), the Coulomb failure stress begins to increase with time only at one of the fault tips, which may trigger unilateral quasistatic fault tip extension. The fault tends to extend in the direction of slip in the medium with higher diffusivity. This is largely due to the fluid flow enhanced near the fault tip. Although the increase in the Coulomb failure stress is larger for higher contrast in the diffusivity, there seems to exist an upper bound for the increase of the Coulomb failure stress. The increase in the Coulomb failure stress found in this study is generally larger than observed in the paper of Yamashita (2007). This suggests that spatial variation of diffusivity is more important for quasistatic fault slip due to fluid flow. The quasistatic fault extension is also simulated assuming the critical threshold value for the Coulomb stress.
S12B-04
Effects of the Metamorphic Dehydration Reactions on Long-term Slow Slip Events: Implications of two Dimensional Numerical Simulations
To clarify the mechanism of aseismic slow slip events at subduction zones, numerical model calculations using laboratory-derived rate- and state- dependent friction laws have been done heretofore. However, no studies have focused on effects of the metamorphic dehydration reactions in the oceanic crust, which is expected to change pore pressure on the plate interface. Therefore, we execute 2D model calculations taking into account pore pressure conditions reflecting the metamorphic dehydration reactions, which are considered to occur in the deep portion of seismogenic zone close to the transition region from unstable to stable sliding ones. Because the implication of the metamorphic dehydration reactions for pore pressure conditions remains unknown yet, we simply set two contradictory models: (1) the dehydration reactions increase the pore pressure and strengthen the overpressurization, (2) the dehydration reactions decrease the pore pressure and release the overpressurization. As a result of calculation, model (2) is more favorable for causing the aseismic slip events. We can interpret our result that small nucleation is needed to cause aseismic slip events. In addition, our result shows the possibility of a relaxation of overpressurization owing to the dehydration reactions via some factors such as the increasing permeability, or a transition of the frictional parameters to unstable slip regimes.
S12B-05
Micro- Nano- and Picoearthquakes at SAFOD: Implications for Earthquake Rupture and Fault Mechanics
Seismometers in the main borehole of the San Andreas Fault Observatory at Depth (SAFOD) recorded a recurrence of the Mw 1.8 "Hawaii" repeating earthquake at 100 m range on August 11, 2006. We did not observe a Slow Initial Phase within the bandwidth of the seismometer (15 – 1600 Hz velocity response). The possible presence of a Seismic Nucleation Phase could not be determined due to the rapid clipping of the P wave on the recording system. Despite the clipping, a dynamic stress drop of 4 - 7 MPa during the first 0.5 - 1.0 ms of rupture could be measured using the Kostrov solution for a dynamically growing circular crack. This is comparable to the average stress drop for the entire event of 10 MPa determined with seismograms from nearby PASO surface and HRSN shallow borehole stations. An aftershock sequence of extremely small events was also observed in the SAFOD main hole, but went undetected in the SAFOD pilot hole, and at the HRSN and PASO stations. The first detected aftershock was noted as soon as the seismograms returned on scale at +2.5 s, and the activity rate declined following Omori's Law. Aftershock moment magnitudes range from M -1.9 (nanoearthquake) to below M -3.5 (picoearthquake). Because their corner frequencies lie above the pass band of the recording system, other source parameters could not be measured. Aftershock locations determined using the P-wave polarizations and S-P intervals (16 - 23 ms) define a northwest trending zone located 100 m below the borehole crossing at a depth of 2.7 km. Their very narrow depth range suggests that they define a "streak" as has been commonly observed along creeping faults in California. The aftershocks coincide with shallower of the two faults that have deformed the casing in the SAFOD main hole at 3190 m and 3300 m, measured depth. The 3190 m fault forms the southwest boundary of a 200-m- wide low velocity, low resistivity zone centered on the 3300 m fault. The "Hawaii" mainshock and its aftershocks behave like any normal crustal earthquake sequence occurring on a mature fault. They are just extremely small. The stress drop in the mainshock, beginning with the initiation of rupture, agrees well with measurements of neary earthquakes. By the time the rupture was no more than 1-2 m in length the dynamic stress release was nearly equal to the total average stress drop, suggesting crack-like behavior throughout the rupture process. Although source parameters of the picoearthquakes in the aftershock sequence could not be measured directly, their small moments and the 1600 Hz bound on corner frequency require that the smallest involve no more than a fraction of a mm of displacement. There appears to be nothing in these seismograms that contradicts laboratory-derived values for fault strength or slip-weakening distance.
S12B-06
Numerical Studies of Small Repeating Earthquakes and Their Source Parameters Using Laboratory-derived Friction Laws
Small repeating earthquakes have short recurrence times and known locations, and hence they present a rare predictable opportunity for detailed observation and insights into earthquake physics. That has been exploited in the San Andreas Fault Observatory at Depth (SAFOD) drilling project. It is important to establish realistic models for their occurrence, to provide a framework for proper interpretation of SAFOD data and other studies. One of the intriguing observation about repeating earthquakes is the scaling of their repeat time T and seismic moment M0 as T\propto M00.17 (Nadeau and Johnson, 1998). The scaling is abnormal compared to T\propto M01/3, the typical scaling that results from a simple conceptual model of circular ruptures with stress drop independent of the seismic moment and slip proportional to the repeat time. Several explanations for the discrepancy in scaling have been proposed, including high stress drop (Nadeau and Johnson, 1998), shading asperity (Sammis and Rice, 2001), and aseismic slip (Beeler et al., 2001). Our studies show that a model based on Dieterich-Ruina rate and state friction laws reproduces the observed abnormal scaling. In our 3D model, a small patch with rate-weakening friction is surrounded by a much larger region with rate-strengthening friction. Our simulations use the 3D methodology of Liu and Lapusta (AGU, 2006) that fully resolves all aspects of seismic and aseismic behavior of the fault. For a set of laboratory-based friction parameters, we can reproduce the observed scaling simply by varying the size of the rate-weakening patch. When the patch size is smaller than the nucleation size implied by the underlying rate and state formulation, the patch has fully aseismic slip. For larger patch sizes, small repeating events start to occur, with slip rates of order of 1 m/s and sharp stress drops. The events are accompanied by significant aseismic slip on the patch, providing a physical explanation for the idea of Beeler et al. (2001). Our recent and current work pursues several directions. We have studied properties of individual small events and found that their static stress drop, averaged over the zone of seismic slip, is in the typical range, although the stress drop is quite heterogeneous in space. We will use our simulations to investigate how well the average value of stress drop on the interface corresponds to the one determined from near-field seismograms. We have found a trade-off between values of frictional parameters and plate loading rate in determining the repeat time and moment of seismic events, and we will report on our current efforts to quantify it. Simulations in 2D models, needed to study a wider range of formulations, produce the same scaling, although individual small earthquakes have much larger moment and repeat time in 2D than in 3D. Our preliminary simulations with Ruina-Dieterich version of rate and state friction have results qualitatively similar to those with Dieterich-Ruina formulation. We are also exploring models that combine rate and state friction with dynamic weakening in the form of flash heating.
S12B-07
Variation of repeating earthquake activities depending on their focal depths as inferred from 3-D numerical simulations
We investigated depth dependence of the slip velocity of small repeating earthquakes using 3-D numerical simulations for a subduction zone involving large and small asperities based on a rate- and state-dependent friction law. In this study, we examined slip at small asperity located at depth of 5, 10 and 15 km. Our results reveal that the postseismic slip of a large earthquake trigger gslowh slip (with slip velocity lower than that of the spontaneous rupture of the small asperity) rupture of the small asperity located at a depth of 15 km, whereas grapidh slip (with higher slip velocity) one at a depth of 5 km where the small asperity usually occur slow repeating earthquakes. In case of the small asperity at a depth of 10 km, all of events are seismic and recurrence intervals are temporally shorter in the passage of postseismic slip. Uchida et al. [2003; GRL] showed that the repeating earthquakes in the NE Japan subduction zones occur constantly, conforming with the rate of the plate convergence in the depth range of > ~40 km. On the other hand, shallow (< ~10 km) focus repeating earthquakes tend to be activated only in the postseismic period of nearby large interplate earthquakes and cumulative slip estimated from them is less than that expected from the plate convergence rate. In general, asperities in the shallower part are more stable than deeper ones because of low effective normal stress. Thus, most of the observed shallow repeating earthquakes may be grapidh slip events triggered by the postseismic slip of the neighboring large asperities, and the corresponding small asperities give rise to (aseismic) slow slip events usually.
S12B-08
Experimental observations of fault zone compaction during stick-slip sliding: implications for fault strength and stability
The conditions favoring stable (aseismic) or unstable (seismic) sliding on a fault depend on the interaction between the frictional properties of the sliding surface and the loading conditions of the surrounding rock. Rapid volumetric changes within a fault zone during unstable sliding can affect loading conditions, enhancing or diminishing instabilities if pore fluids are present. For example, if dilatancy occurs during rapid slip within a fault zone containing pore fluid pressure and fluid pressure cannot be maintained, then pore pressure will drop and the effective normal stress will increase (dilatancy hardening). Fault zone dilatancy will thus act to limit the magnitude of the instability. Previous experiments have shown that higher slip velocity promotes dilatancy, whereas a reduction in shear stress promotes compaction. Evaluating which of these competing effects dominates the volume change of the fault zone during unstable slip is important in understanding the magnitude of the instability that may occur. In order to evaluate these competing effects, we measured the mechanical behavior of 2 mm thick layers of quartz gouge and bare-surface Fontainebleau sandstone samples during large-displacement experiments in our rotary shear apparatus. The experiments were conducted at 25°C, normal stress on the fault surface ranging from 25 to 89 MPa, confining pressures ranging from 24 to 88 MPa, and pore fluid pressures ranging from 0.1 MPa to 79 MPa. We studied the interplay between volumetric strain, shear stress, sliding velocity, and effective normal stress during stable and unstable sliding. At the start of the experiments, prior to the onset of localization and stick-slip behavior, increases in sliding velocity are accompanied by dilatancy as found by previous workers. As the experiments proceed and stick-slip sliding is initiated, we observe the opposite phenomena: net compaction during rapid slip and stress drop. During unstable sliding it thus appears that the reduction in shear stress that causes compaction overcomes the tendency for increases in slip velocity to cause dilatancy. These results suggest that dilatancy-hardening effects may play a secondary role during unstable slip and earthquake nucleation.