Final Technical Report

USGS-NEHRP Award Number #G11AP20015

Probabilistic evaluation of the effects of episodic aseismic slip events on the occurrence of great Cascadia earthquakes: A simulation-based approach

Principal Investigator – James H. Dieterich Department of Earth Sciences University of California, Riverside 454 Geology Bldg Riverside, CA 92521 Telephone 951-827-2976 Fax 951-827-4324, E-Mail [email protected]

Term covered by award – Dec 2010 – Nov 2011

1 ABSTRACT

This project investigates interactions between earthquakes and episodic tremor and slip (ETS) events along the Cascadia subduction zone interface. The primary goal of the project is to evaluate possible changes in probability of great earthquakes that result from ETS events. The research employs large-scale computer simulations of Cascadia subduction earthquakes using the recently developed earthquake simulation program RSQSim. The RSQSim simulations provide an integrated means for modeling earthquakes, aseismic slip events in ETS events, and continuous fault creep at different depth ranges of Cascadia subduction zone interface. To develop robust statistical characterizations of Cascadia earthquakes, and the extent of their correlation with ETS events, the simulations will generate long histories of slip that consisting of ≥105 slip events (earthquakes + aseismic slip events). From these statistics, long-term earthquake probabilities, and probability gains associated with ETS events will be generated.

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Introduction The discovery of episodic tremor and slip (ETS) events [Dragert and others, 2001; Miller and others, 2002; Rogers and Dragert, 2003] and detection of ETS along the length of the Cascadia subduction zone [Szeliga and others, 2004; Brudzinski and Allen, 2007] raise potentially important questions that are the focus of this project: How might the aseismic slip in ETS events interact with sliding processes along the seismogenic parts of the subduction interface, and to what extent do those interactions affect the time- dependent probabilities of Cascadia earthquakes? There appear to be at least two mechanisms by which the occurrence of an ETS event may change earthquake probabilities. The first arises because the aseismic slip in an ETS event transfers stresses to adjacent seismogenic sections of the megathrust, resulting in intervals of accelerated stressing, that shorten the time required for nucleation of a large earthquake. The second involves the possibility that aseismic slip during an ETS event could propagate a sufficient distance into the adjacent seismogenic zone to directly nucleate earthquake slip. In the following we use the generic term slow slip event (SSE) to designate the aseismic slip component an ETS event. In Cascadia, SSEs are accompanied by tremor, but this relationship may not be universal. In reference to the first mechanism, a variety of observations indicate that earthquake probabilities (as expressed by earthquake rates) indeed change with stressing conditions. These include static triggering of aftershocks by stress changes from mainshocks, aftershock-like bursts of seismicity following rapid magmatic intrusions [Dieterich and others, 2000], and subtle, but discernable, seismic response to tides [Cochran and others, 2004]. In Cascadia the subduction interface is currently seismically quiet, so direct empirical evidence for (or against) changes of earthquake probabilities based on changes of earthquake rates associated with SSEs has not been established. However, SSEs beneath the south flank of Kilauea volcano in Hawaii [Brooks and others, 2006; Segall and others, 2006] and the along the Hikurangi subduction zone of New Zealand [Delahaye and others, 2009] are associated with transient increases of seismicity rates in areas adjacent to SSEs. In Hawaii the SSEs have moments that are equivalent to M=5.5- 5.8 earthquakes [Brooks and others, 2006] while in Cascadia the events are significantly larger, with magnitudes up to M=6.5-6.8 [Melbourne and others, 2005; Chapman and Melbourne, 2009]. Mazotti and Adams [2004] and Beeler [2009] have developed conceptual models to calculate the change of earthquake probability that arises from accelerated stressing rates during ETS events. Mazzotti and Adams [2004] estimate that stressing rates in the seismogenic zone increase by a factor of ~50x during ETS episodes and assume initiation of earthquakes occurs immediately at a fixed stress threshold – this translates to a 50-fold gain in the conditional probability of great earthquakes during ETS events. However, the assumption of immediate triggering at a fixed stress threshold is open to question and alternatively Beeler [2009] uses a constitutive formulation for earthquake rates based on rate-state friction effects wherein triggering effects are both time and stress dependent. This formulation [Dieterich, 1994] has been widely applied to model a variety of earthquake rate effects including aftershocks [Stein and others, 1997], seismic response

3 to tidal stresses [Cochran and others, 2004], and earthquake probabilities [Toda and others, 1998; Parsons and others, 2000; Hardebeck, 2004; Parsons, 2005]. Beeler [2009] obtains quite low estimates of the probability gains (1.5 or less) using same 50x stressing factor employed by Mazzotti and Adams [2004]. The analyses by Mazzotti and Adams [2004] and Beeler [2009] illustrate how accelerated stressing rates might affect earthquake probabilities, and demonstrate the sensitivity of probabilistic models to assumptions of fault constitutive properties. However, those analyses rely on point-characterizations of inherently position-dependent physical properties and stressing conditions, which introduces large uncertainties into the estimates of probability gain. For example, to determine the stress interaction factor, how does one select a location for the ETS event relative to the unknown location of the point where the next great earthquake nucleates? If the nucleation point is hundreds of kilometers away from the ETS event, the interactions that alter stressing-rates essentially disappear and the probability gain will be zero. Conversely, if the nucleation point for a great earthquake happens to occur where stresses are highly concentrated immediately adjacent to the crack tip of aseismic slip event, then the stress interaction factor and probability gain can be arbitrarily large. This suggests that a comprehensive investigation of probability gains should explicitly account for effects, and because the nucleation point of a great earthquake is not known a priori, the analysis should allow for interactions over a range of distances. The second way in which an ETS event may increase the probability of a great earthquake is based the possibility that the aseismic slip in ETS events may evolve into the earthquake nucleation process for a great earthquake. Because ETS events occur in the transition zone between the creeping section and the locked seismogenic sections of the subduction interface [Dragert and others, 2001; Miller and others, 2002], and because penetration stresses increase with every ETS cycle this scenario appears quite plausible. An earthquake will immediately nucleate if a propagating aseismic slip event is able to penetrate a sufficient distance into the locked portion of the megathrust. The critical penetration distance for initiating unstable slip, scales by the minimum length of for nucleation of unstable slip

G"Dc Lc = (1) #$ where G is the elastic shear modulus, s is effective normal stress, Dc is the critical slip distance appearing in rate-state friction formulations, x is a function of rate-state constitutive parameters a and b, (outlined below), and h is a dimensionless parameter ! with values near 1 [Dieterich, 1992, 2007]. There is also some observational evidence for the second scenario. Large-scale deformations, interpreted to represent aseismic slip events along the megathrust interface, may have occurred in association with the 1960 [M9.5] Chile earthquake, and the 2001 (M8.4) Peru earthquake. In the case of the 1960 Chile earthquake, Kanamori and Cipar [1974] report a large strain anomaly with a seismic moment Mo=~3.5 1030dyne-cm, associated with a M6.8 foreshock 15 minutes prior to the mainshock. Because the moment of the strain signal far exceeds the moment of the foreshock, they interpret the strain signal as originating from a large aseismic slip event originating down dip from the foreshock and mainshock. In the case of the 2001 Peru earthquake, no precursory strain

4 signal was reported for the mainshock, but a large strain transient appears to have been associated with a M7.6 aftershock [Melbourne and Webb, 2002]. The strain signal began 18 hours before the aftershock. Melbourne and Webb [2002] infer that the aftershock grew out of the aseismic slip event.

Method of Analysis In view of the possible complex interactions between SSEs and great earthquakes, comprehensive evaluation of SSE-driven probability gains must account for 1) the different ways in which SSEs may interact with earthquakes, 2) the effects of the unknown location of the point of earthquake nucleation with respect to the location of an SSE, and 3) the time- and stress-dependent characteristics of earthquake nucleation. In this context the use of standard approaches to estimate earthquake probabilities would appear to be quite difficult to implement, and would yield rather unreliable results. Ideally, one would like to have a long record through hundreds of cycles of great earthquakes (and perhaps tens of thousands of SSEs to have a statistical basis on which to derive probabilities. However, this is not possible with our miniscule historical record of SSE observations. Our approach is to implement numerical simulations of the Cascadia mega-thrust to generate synthetic physics-based statistical distributions of earthquakes and SSEs for probabilistic estimation. In this project we have developed an integrated simulation capability for large-scale computer simulations of Cascadia subduction zone processes that including earthquakes, slip in ETS events, and deep fault creep. The simulations incorporate rate-state friction effects and generate synthetic earthquake catalogs with 105- 106 slip events (aseismic slip events + earthquakes). The simulation method we are using for generating earthquake sequences has been validated with comparisons using detailed dynamic rupture propagation codes [Dieterich and Richards-Dinger, 2010] and tested against a wide range of observational and statistical characteristics of earthquakes. The primary implementation challenge to carry out this research is 1) development the simulation capability for SSE, and 2) test and validation of the SSE simulations against available observations. For the report period, we developed a simulation capacity for modeling slow slip events (in addition to the existing capacity for earthquake simulations and continuous fault creep) and conducted numerous simulations of SSEs to begin testing against observational data for SSEs. The simulation method employs the earthquake simulation code RSQSim [Dieterich and Richards-Dinger, 2010]. The simulations are employ rate-state constitutive properties to model the various sliding phenomena, and fully implement 3D stress interactions. To develop robust statistical characterizations of Cascadia earthquakes, and the extent of their correlation with SSEs events, the simulations incorporate interactions between the locked, transitional, and creeping sections of the megathrust and generate long histories consisting of 105 - 106 interface slip events (earthquakes + aseismic slip events). From these statistics, earthquake probabilities associated with ETS events will be generated. Repeated simulations will be used to explore the sensitivity of the results to model parameters. Rate- and state-dependent constitutive laws for friction and fault slip have been used

5 previously to model SSEs. Those studies largely focus on possible mechanisms that quench the acceleration of slip before earthquake slip speeds are attained during the slip nucleation process. Shibazaki and Iio [2003] employ a variant of rate-state friction giving rate-weakening steady-state slip at slow slip speed and rate strengthening at high slip speeds. Rubin [2008] shows that aseismic slip events can arise under a narrow range of system conditions very close to the boundary between stable and unstable sliding. Similarly, Liu and Rice [2005, 2007] employ 2D and 3D numerical models in which aseismic slip events originate spontaneously in the transition zone at the down-dip edge of the seismogenic zone, where the rate-weakening friction is too large for steady continuous fault creep, but too small to support acceleration of slip to instability. Segall and others [2010] propose that dilatant strengthening halts the acceleration of slip before seismic slip speeds are reached. In the absence of direct observations of laboratory or natural faults during SSEs definitive understanding of the quenching mechanism that establishes the slip speed of SSEs may remain rather uncertain. Our simulations employ a model of SSEs based on the mechanism proposed by Shibazaki and Iio [2003] wherein the slip speed during an SSE is controlled by a transition from rate-weakening to rate-strengthening behavior. The transition slip speed is therefore set by the frictional properties of the fault. In our simulations the we set the slip speed during SSEs at the transition slip speed. The simulations are fully deterministic in the nucleation, propagation speed, event duration, and final distribution of slip. In general, we are guided by Liu and Rice (2005) in both the Cascadia model framework (arrangement of creeping, transitional and seismic sections of the megathrust) and model parameters (effective normal stress and rate-state constitutive parameters).

2.3 RSQSim modeling approach The wide range of length scales to be modeled, and the need to repeatedly simulate long histories of earthquakes and SSEs, point to the importance of computational efficiency together with quantitative integrity. To achieve the computation efficiency required for these applications RSQSim employs analytic solutions and large-scale approximations of sliding processes [Dieterich, 1995; Dieterich and Richards-Dinger, 2010]. For quantitative integrity an important component of the RSQSim development has been, and continues to be, evaluation of errors arising from the approximations incorporated in RSQSim, and model tuning. We are actively participating in the Southern California Earthquake Center (SCEC) earthquake simulator evaluation project led by Terry Tullis (Richards-Dinger is coordinating model comparisons), and we are carrying out independent tests to calibrate the fast simulations against detailed fully dynamic large-scale rupture simulations. Examples that compare RSQSim with fully dynamic 3D finite element models are described below. The current single-processor version of the code can accommodate up to ~50,000 fault elements. Simulations of 500,000 slip events (earthquakes and SSEs) typically require less than 24 hours on a single computer node. The parallelized version of the code on our local cluster can accept ~90,000 elements. RSQSim is based on a boundary element formulation whereby interactions among the fault elements are represented by an array of 3D elastic dislocations, and stresses acting on elements are

(2)

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where i and j run from 1 to N, the total number of fault elements; τi and σi are the shear stress in the direction of slip and fault-normal stress on the ith element, respectively; the two Kij are interaction matrices derived from elastic dislocation solutions; δj is slip of tect tect fault element j ; " i and " i are the externally applied (tectonic) stresses at fault element i; and the summation convention applies to repeated indices. The code uses rectangular [Okada, 1992] or triangular [Meade, 2007] fault elements to represent stress interactions on faults systems with geometric complexities. ! ! The simulations employ rate- and state-dependent formulation for sliding resistance [Dieterich, 1979, 1981; Ruina, 1983; Rice, 1983]

, % $˙ ( % + (/ ! $! " = #. µ0 + a ln' * + b ln' *1 , where d! = dt " d# " d% (3) ˙ * & * ) -. & $ ) + 01 Dc b%

where µ0 , a, and b are experimentally determined constants; "˙ is sliding speed, θ is a * * ! state variable that evolves with time and slip and normal stress history; and "˙ and θ are normalizing constants. The evolution of θ takes place over a characteristic sliding distance D and at steady-state ˙ . In the simulations fault strength is fully c "ss = Dc /# ! coupled to normal stress changes through the coefficient of friction! and through θ, which evolves with changes of normal stress as given by Linker and Dieterich [1992]. See Marone [1998] and Dieterich [2007] for detailed reviews of rate- and state-dependent friction and discussion of! applications. Fault elements may slip either by continuous fault creep, or intermittently in earthquakes or SSEs, where the mode of slip for each fault element is set by input parameters. For continuously creeping elements we assume steady-state rate- strengthening friction (a>b in equation 3) and update slip speed as stress acting on an element evolves. The simulations of earthquakes and SSEs, employ analytic solutions and event- driven computational steps as opposed to time stepping at closely spaced intervals. This approach, which avoids the computationally intensive solution of systems of equations at closely spaced time intervals, results in immense gains in computational efficiency. Computation time for a slip event of some fixed size embedded in a model with n fault elements scales approximately by n1. SSEs are modeled simply as slow earthquakes having a fixed slip speed that is set as an input parameter. The acceleration of slip during the nucleation of earthquakes and SSEs is calculated using the rate-state nucleation solutions of Dieterich [1992] modified to take into account normal stress changes [Dieterich, 2007, Fang et al, 2010]. Slip speed during earthquakes is based on first-order rupture dynamics using the relationship for elastic shear wave impedance together with the local dynamic driving stress. Slip speed during SSEs is an input constant that can be adjusted to fit observations of SSE rupture propagation speed and SSE duration. Rupture propagation speeds (earthquakes and SSEs) are an outcome of the simulations and are controlled by stress interactions, slip speed, and rate-state nucleation solutions.

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2.4 Model characteristics A central feature of RSQSim is the capability to repeatedly generate large catalogs of earthquakes and SSE to characterize effects fault interactions, test the sensitivity of catalog statistics to input parameters, and to provide a physical basis for extrapolating statistical data to conditions where observations are not available (e.g. large earthquakes over long time intervals). Key performance measures for such applications are the accuracies with which the calculations represent a) nucleation processes that determine the time and place of a slip event, b) the spatial extent of earthquake (or SSE) rupture given a stress state at the initiation of the event, and c) the slip distribution in that event, which determines the details of the stress state following the event (and therefore the subsequent history). The analytic nucleation solutions used in RSQSim are used for both SSEs and earthquakes, and have been validated by the laboratory observations of nucleation [Dieterich and Kilgore, 1996] and by detailed models with rate-state friction [Dieterich, 1992; Fang and others, 2010]. To address items b) and c) we have undertaken a program of tests with our colleague David Oglesby that compare single-event RSQSim earthquake simulations with detailed fully dynamic finite element calculations (see Dieterich and Richards-Dinger [2010] for additional comparisons). Figure 1 shows an example of a rather challenging comparison between RSQSim and DYNA3D, a fully dynamic 3D finite element code. This example is for a planar strike-slip fault that extends to the free surface, with idealized asperities consisting of eight patches with high normal stress compared to the background normal stress of 120 MPa. In this simulation a uniform initial shear stress is set just above the minimum value that results in rupture propagation across the entire fault surface for nucleation near the left end of the model (indicated by the + symbol). While some details of rupture propagation with RSQSim differ from results obtained with DYNA3D, the simulations are remarkably similar in most respects, including rupture complexity. The RSQSim computation time for this simulation is on the order 10-3 of that required by DYNA3D. That computational advantage rapidly increases as system size increases because of the n1 scaling of computation time in RSQSim. Because we model SSEs as slow earthquakes, the SSE simulations have comparable computational accuracies, subject to our assumption of constant slip speed during an event. Synthetic earthquake catalogs from multi-event simulations with RSQSim Simulations Synthetic earthquake catalogs replicate a range of characteristics found in real earthquake catalogs. These include moment-area scaling, magnitude frequency statistics and clustered seismicity (foreshocks, aftershocks and occasional clusters of large earthquakes). The simulations produce the Omori aftershock decay of aftershock rates by t−p with p ~ 0.8 [Dieterich, and Richards-Dinger, 2010]. Similarly, foreshocks in the simulations have Omori-like rate dependence by time before the mainshock with p ~ 0.9. Figure 2 compares inter-event waiting time statistics from the California earthquake catalog 1911-2009 with the a simulated catalog obtained using the all-California model, which spans about 20,000 years of seismicity. have been implemented with complex fault systems, including an all-California model (without Cascadia) of faults with slip rates ≥1mm/yr at 3km and 1.5km resolution.

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Figure 1. Comparison of rupture simulations using the fast simulator RSQSim and the detailed and fully dynamic finite element model DYNA3D. (a) Normal stress distribution on fault surface. (b) Rupture initiation time (the contours map the rupture front as a function of time). (c) Final stress (upper panel) and slip (lower panel) along a profile at depth of 4.25 km. Fault elements for this simulation are 500 m x 500 m. Times for ruptures to reach the end of model differ by about 2%.

Figure 2. Inter-event waiting time density distributions from the California earthquake catalog (1911 through 2010) and the All-California simulated catalog (spanning ~9x109years). The blue curves show the distribution for a Poisson distribution of event times. The power law fit to the data (red lines) reflects Omori-like clustering shorter inter-event times. Note at large inter-event times the distributions fit neither Poisson nor power law distributions.

Results We successfully modified RSQSim to simulate SSEs and continuous fault creep in addition to earthquake events. Compared to earthquakes SSEs are poorly understood and characterized. Hence, during the reporting period we necessarily focused on comparing our simulations to observations, and characterizing the processes and model parameters that control SSEs. Indeed, we were rather surprised by the complexity and richness of the slip phenomena that arose from the SSE simulations. Initial results are given in the paper Colella, Dieterich and Richards-Dinger, 2011). 12 full-scale simulations consisting of

9 ≥105 SSE events were carried out and analyzed by PhD student Harmony Colella, together with Dieterich and Richards-Dinger. The simulations of Cascadia employ simplified representations of the Cascadia megathrust illustrated in Figure 3. The initial SSE model has a straight subduction zone with an along-strike length of ~550km, along-dip width of ~350km, and convergence rate of 37mm/yr. The seismogenic section is held locked, but interactions with the deep creeping section are enabled. Small positive values of (b - a) are expected in the transition zone between the seismogenic and creeping sections; and low effective normal stresses (σ) from dehydration reactions are indicated by thermal modeling [Peacock et al., 2002] and seismological observations [Kodaira et al., 2004; Shelly et al., 2006]. Based on these considerations the simulations use σ = 4.5 MPa and (b – a) = 0.002, with uniform b- and a-values of 0.012 and 0.010, respectively, in the transition zone. The simulations use σ = 4.5 MPa and (b – a) = -0.002, with uniform b and a-values of 0.008 -5 and 0.010, respectively, in the continuous creep zone. Additionally we assign Dc = 10 m and Lame´ elastic parameters λ = µ = 30 GPa. The results reported here use a SSE slip speed of 1.25 x 10-6 m/s. This value, together with the assumed values of a, b and σ, yield SSEs that agree rather well with observations for Cascadia, including inferences of SSEs from tectonic tremor observations. Fault slip is driven by stressing-rate boundary conditions derived from the back-slip method [Savage, 1983; King and Bowman; 2003], with a tectonic slip rate of 37 mm/year. Slip does not occur outside the limits of the model. The simulations consist of 100,000 SSEs with moment magnitudes that range from ~Mw4.0 to ~Mw7.0. The simulations reach a statistical equilibrium following a run-up time of ~10 years (run-up data are excluded from reported results). Because SSEs may penetrate into and hence interact with the adjacent continuous creep zone, simulations both with and without a creeping zone are used to explore these effects.

Figure 3. Cascadia subduction zone. Left panel: The subduction interface is divided into three sections based on sliding behaviors: locked zone, transition zone, and continuous creep.

10 The locked zone corresponds to the seismogenic section of the megathrust that slips in large earthquakes. Geodetic and historic leveling data suggest the seismogenic zone extends to 25 km depth [Chapman and Melbourne, 2009; Burgette and others, 2009]. The transition zone corresponds to the section of the megathrust that participates in ETS events. Geodetic and seismic data constrain the depth range of ETS events between 25-45 km [Dragert and others, 2001; Miller and others, 2002; Wech and others, 2009]. Continuous creep occurs at depths greater than ~45 km. Contours represent depths to the subducting slab based on McCrory and others [2006]. Temperatures at 25km and 45km are approximately 430° and 525°C [Peacock, 2002]. Right panel: Simplified model used in initial simulations.

Figures 4 and 5 illustrate some features of simulated Cascadia SSE simulations. The largest simulated SSEs (Mw6.4-7.0) have mean slip of 2.5-3.5 cm compared to 2.3-4.0 cm for Cascadia, and durations of 10-30 days compared to 10-40 days, for Cascadia [Dragert et al., 2004]. Rupture propagation speeds are 9-20 km/day compared to 5-15 km/day reported by Dragert et al. [2004] (Figure 5b). Relationships for seismic moment vs. fault area and seismic moment vs. event duration for the largest events are also consistent with those observed along Cascadia and Nankai (Figure 4b, 4c). A short period of quiescence follows Mw > 6.4 SSEs, followed by a progressive increase in magnitude and frequency of SSEs prior to the next event (Figure 4a), which is analogous to the pattern of tremor swarms reported by Wech et al. [2010]. Simulated SSEs often occur simultaneously at several locations (Figure 5a) including large SSEs that occasionally coalesce. A similar effect of overlapping slip times is seen with large Cascadia SSEs [Boyarko and Brudzinski, 2010] and is quite evident in the space-time plots of tremor reported by Wech et al. [2010]. Finally, we note that the simulated SSEs lack the robust spatial and Omori- type temporal clustering characteristics of earthquakes – to date no we know of no reports for Omori-type clustering wof SSEs. In summary, the initial simulations broadly agree with SSE observations reported for Cascadia and provide a foundation for advancing to more comprehensive and more carefully tuned models.

Figure 4. Characteristics of simulated SSEs (Colella et al., submitted). a) SSE moment magnitudes vs. time (from a portion of a much longer simulation). The largest SSEs are followed by a short interval of relative quiescence, which in turn is followed by a progressive increase of SSE rate and magnitude. b) Duration vs. Moment. The durations of large SSEs in the simulations scale as Mo " t1.8±0.2 . For comparison event durations are shown for Cascadia (black rectangle) and Japan (magenta rectangle). c) Area vs. Moment with event stress drop contours.

!

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Figure 5. SSE characteristics. a) Slip distribution in a large SSE event from a simulation of 105 SSEs. Note penetration of slip into the continuously creeping section (only a portion of the continuously creeping zone in shown). b) Space-time plot of the event in panel Fig.4a. The color scale indicates the number of elements slipping at the indicated time and along-strike distance. The initiation and termination slip in large SSEs is often diffuse, but once an event is underway the propagation is highly coherent with well defined along-strike propagation speed. In addition, note the backward rupture propagation into previously slipping regions at higher speeds

A possible departure of simulated SSEs from observed SSEs is the seismic ~1.5 moment-duration scaling. The simulations yield M0 ∝ t for events Mw < 5.6, and M0 ∝ ~2 t for events Mw ≥ 5.6 (Figure 3b), while Ide et al. [2007] propose a linear scaling (M0 ∝ t) based on a synthesis of data from different regions. However, Peng and Gomberg [2010] conclude that the seismic moment-duration scaling relationship may not be as simple as originally proposed. This is supported by observations of Ide et al. [2008], which indicate the best-fit scaling for a set of slow earthquakes from Kii Peninsula in 1.5 western Japan that last 20-200s and are estimated to be Mw3-4, is M0 ∝ t and Gao et al. 1.1–1.7 [Gao et al., manuscript in preparation, 2011], which indicate M0 ∝ t based on geodetic observations for Cascadia SSEs with moment magnitudes that range from Mw6.4-6.9. Stress transfer during SSEs strongly affects stressing rates in the seismogenic zone (Figure 6) and may directly affect the occurrence of great subduction earthquakes [Mazzotti and Adams, 2004]. Our simulation approach provides a means to investigate the interactions between SSEs and adjacent sections of the subduction interface. The stressing rate near the base of the seismogenic zone is 0.005 MPa/yr in the interval

12 between SSEs compared to a maximum rate of ~0.67 MPa/yr during a large SSE. Over time this stress transfer results in elevated stress levels near the base of the seismogenic zone. We now plan to implement mega-thrust earthquakes in the simulations to investigate these questions.

Publications Colella, H. V., J. H. Dieterich, K. B. Richards‐Dinger, 2011, Multi‐event simulations of slow slip events for a Cascadia‐like subduction zone, Geophysical Research Letters (GRL), VOL. 38, L16312, doi:10.1029/2011GL048817.

References Ampuero, J. P. and A. M. Rubin, Earthquake nucleation on rate and state faults – Aging and slip laws, J. Geophys. Res., 113, B01302, doi:10.1029/2007JB005082, 2008. Beeler, N., Estimated effects of episodic slow-slip on the occurrence and probability of great earthquakes in Cascadia using lab-based failure relations, Seismol. Res. Lett., 80(2), 295, 2009. Beroza, G. C., and T. Mikumo, Short slip duration in dynamic rupture in the presence of heterogeneous fault properties, J. Geophys. Res., 101, 22,449–22,460, 1996. Brooks, B. A., J. H. Foster, M. Bevis, L. N. Fazer, C. J. Wolfe, and M. Behn, Periodic slow earthquakes on the flank of Kilauea volcano, Hawai’i, Earth Planet. Sci. Lett., 246, 205-216, 2006. Brudzinski, M. R., and R. M. Allen, Segmentation in episodic tremor and slip all along Cascadia, Geology, 35, 907-910, doi:10.1130/G23640A, 2007. Burgette, R. J., R. J. Weldon II, and D. A. Schmidt, Interseismic uplift rates from western Oregon and along –strike variations in locking on the Cascadia subduction zone, J. Geophys. Res., 114, B01408, doi: 10.1029/2008JB005679, 2009. Chapman, J. S., and T. I. Melbourne, Future Cascadia megathrust rupture delineated by episodic tremor and slip, Geopyhys. Res. Lett., 36, L22301, doi:10.1029/2009GL040465, 2009. Cochran, E. S., J. E. Vidale, and S. Tanaka, Earth tides can trigger shallow thrust fault earthquakes, Science, 306, 1164-6, 2004. Dieterich, J. H., Modeling of rock friction 1. Experimental results and constitutive equations, J. Geophys. Res., 84, 2161–2168, 1979. Dieterich, J., Constitutive properties of faults with simulated gouge, in Monograph 24, Mechanical Behavior of Crustal Rocks, edited by N. L. Carter, M. Friedman, J. M. Logan, and D. W. Sterns, pp. 103–120, American Geophysical Union, Washington, D.C., 1981. Dieterich, J. H., Earthquake nucleation on faults with rate- and state-dependent strength, Tectonophysics, 211, 115–134, 1992. Dieterich, J. H., A constitutive law for rate of earthquake production and its application to earthquake clustering, J. Geophys. Res., 99, 2601–2618, 1994. Dieterich, J. H., Earthquake simulations with time-dependent nucleation and long-range interactions, Journal of Nonlinear Processes in Geophysics, 2, 109–120, 1995. Dieterich, J., Applications of rate-and-state-dependent friction to models of fault slip and earthquake occurrence, in Treatise On Geophysics, Vol. 4, edited by G. Schubert, Elsevier, Oxford, 2007.

13 Dieterich, J. H., V. Cayol, and P. Okubo, The use of earthquake rate changes as a stress meter at Kilauea volcano, Nature, 408, 457-460, 2000. Dieterich, J. H., V. Cayol, and P. Okubo, Stress changes before and during the Pu’u O’o- Kupaianaha eruption, U.S.G.S. Prof. Pap. 1676, 187-201, 2003. Dieterich J. H., Kilgore B. Implications of Fault Constitutive Properties for Earthquake Prediction. Proceedings of the National Academy of Science 93:3787–3794, 1996. Dieterich, J. H., and K. Richards-Dinger, Earthquake recurrence in simulated fault systems, Pure Appl. Geophys., doi:10.1007/s00024-010-0094-0, 2010. Dragert, H., K. Wang, and T. S. James, A silent slip event on the deeper Cascadia subduction interface, Science, 292, 1525-1528, doi:10.1126/science.1060152, 2001. Fang, Z., J. H. Dieterich, and G. Xu, Effect of initial conditions and loading path on earthquake nucleation, J. Geophys. Res., 115, doi:10.1029/2009JB006558, in press. Goldfinger, C., Nelson, C.H., Morey, A., Johnson, J.E., Gutierrez-Pastor, J., Eriksson, A.T., Karabanov, E., Patton, J., Gracia, E., Enkin, R., Dallimore, A., Dunhill, G., and Vallier, T., 2010, Turbidite Event History: Methods and Implications for Holocene Paleoseismicity of the Cascadia Subduction Zone, USGS Professional Paper 1661-F, Reston, VA, U.S. Geological Survey, p. 178p, 64 Figures. (unformatted preprint available at http://activetectonics.coas.oregonstate.edu/Goldfinger_1661.zip), in press. Hardebeck , J. L., Stress triggering and earthquake probability estimates, J. Geophys. Res., 109, B04310, doi:10.1029/2003JB002437, 2004. Heaton, T. H., Evidence for and implications of self-healing pulses of slip in earthquake rupture, Phys. Earth Planet. Inter., 64, 1–20, 1990. Kanamori, H. and J. J. Cipar, Focal process of the great Chilean earthquake May 22, 1960, Phys. Earth Planet. Inter., 9, 128-136, 1974. Linker, M.F., and J.H. Dieterich, Effects of variable normal stress on rock friction – Observations and constitutive equations, J. Geophys. Res., 97, 4923-4940, 1992. Liu, Y., and J. R. Rice, Aseismic slip transients emerge spontaneously in three- dimensional rate and state modeling of subduction earthquake sequences, J. Geophys. Res., 110, B08307, doi:10.1029/2004JB003424, 2005. Liu, Y., and J. R. Rice, Spontaneous and triggered aseismic deformation transients in a subduction fault model, J. Geophys. Res., 112, B09404, doi:10.1029/2007JB004930, 2007. Marone, C., Laboratory-derived friction laws and their application to seismic faulting. Annual Rev. Earth Planet. Sci. 26, 643–696, doi:10.1146/annurev.earth.26.1.643, 1998. Mazzotti, S., and J. Adams, Variability of near-term probability for the next great earthquake on the Cascadia subduction, Bull. Seismol. Soc. Am., 94, 1954-1959, doi:10.1785/012004032. McCrory, P. A., J. L. Blair, D. H. Oppenheimer, and S. R. Walter, Depth to the Juan de Fuca slab beneath the Cascadia subduction margin: A 3-D model for sorting earthquakes, U.S.G.S. Data Series DS-91, 1 CD-ROM, version 1.2, 2006. Meade, B. J. (2007), Algorithms for the calculation of exact displacements, strains, and stresses for triangular dislocation elements in a uniform elastic half space, Comp. Geosci. 33, 1064–1075, doi:10.1016/j.cageo.2006.12.003, 2007. Melbourne, T. I. and F. H. Webb, Precursory transient slip during the 2001 Mw = 8.4 Peru earthquake sequence from continuous GPS, Geophys. Res. Lett., 20, 2032,

14 doi:10.1029/2002GL015533, 2002. Melbourne, T. I., W. M. Szeliga, M. M. Miller, and V. M. Santillan, Extent and duration of the 2003 Cascadia slow earthquake, Geophys. Res. Lett., 32, L04301, doi: 10.1029/2004GL02790, 2005. Miller, M. M., T. Melbourne, D. J. Johnson, W. Q. Sumner, Periodic slow earthquakes from Cascadia Subduction Zone, Science, 295, 2423, 2002. Okada, Y., Internal deformation due to shear and tensile faults in a half-space, Bull. Seismol. Soc. Am., 82, 1018-1040, 1992. Parsons, T., Significance of stress transfer in time-dependent earthquake probability calculations, J. Geophys. Res., 110, B05S02, doi:10.1029/2004JB003190, 2005. Parsons, T., S. Toda, R. S. Stein, A. Barka, J. H. Dieterich, Heightened odds of large earthquakes near Istanbul: An interaction-based probability, Science, 661, doi:10.1126/science.288.5466.661, 2000. Peacock, S. M., K. Wang, and A. M. Machon, Thermal structure and metamorphism of the subducting oceanic crust: Insight into Cascadia intraslab earthquakes, in The Cascadia Subduction Zone and Related Subduction Systems: Seismic Structure, Intraslab Earthquakes and Processes, and Earthquake Hazards, edited by S. Kirby, K. Wang, and S. Dunlop, U.S. Geol. Surv. Open File Rep., 02-328, 123-126, 2002. Rice, J. R., Constitutive relations for fault slip and earthquake instabilities, Pure Appl. Geophys. 121, 443-475, doi:10.1007/BF02590151, 1983. Rogers, G., and H. Dragert, Episodic tremor and slip on the Cascadia subduction zone: The chatter of silent slip, Science, 300, 1942-1943, 2003. Rubin, A. M., Episodic slow slip events and rate-and-state friction, J. Geophys. Res., 113, B11414, doi:10.1029/2008JB005642, 2008. Ruina, A., Slip instability and state variable friction laws, J. Geophys. Res., 88, 10,359- 10,370, 1983. Segall, P., E. K. Desmarais, D. Shelley, A. Miklius, P. Cervelli, Earthquakes triggered by silent slip events on Kilauea volcano, Hawaii, Nature, 442, 71-74, doi:10.1038/nature04938, 2006. Segall, P., A. M. Rubin, A. M. Bradley, J. R. Rice, Dilatent Strengthening as a Mechanism for Slow Slip Events, J. Geophys. Res., 115: B00A27, 2010. Shibazaki, N., and Y. Iio, On the physical mechanism of silent slip events along the deeper part of the seismogenic zone, Geophys. Res. Lett., 30(9), 1489, doi:10.1029/2003GL017047, 2003. Stein, R. S., A. A. Barka, and J. H. Dieterich, Progressive failure on the North Anatolian fault since 1939 by earthquake stress triggering, Geophys. J. Int., 128, 594–604, 1997. Szeliga, W., T. I. Melbourne, M. M. Miller, V. M. Santillan, Southern Cascadia, Geophys. Res. Lett., 31, L16602, doi:10/1029/2004GL020824, 2004. Toda, S., R. S. Stein, P. A. Reasenberg, J. H. Dieterich, and A Yoshida, Stress transferred by the 1995 Mw=6.9 Kobe, Japan, shock: Effect on aftershocks and future earthquake probabilities, J. Geophys. Res., 103, 24543-24565, 1998. Zheng, G., and J. R. Rice, Conditions under which velocity-weakening friction allows a self healing versus a cracklike mode of rupture, Bull. Seismol. Soc. Am., 86 , 1466–1483, 1998. Wech, A. G., K. C. Creager, T. I. Melbourne, Seismic and geodetic constraints on Cascadia slow slip, J. Geophys. Res., 114, B10316, doi:10.1029/2008JB006090, 2009.

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