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Detection and modeling of slow slip events as creep instabilities beneath major fault zones

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Detection and modeling of slow slip events as creep instabilities beneath major fault zones

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Content Detection and modeling of slow slip events as creep instabilities beneath major fault zones by Rachel Lippoldt Dissertation presented to the Faculty of the Graduate School University of Southern California for the degree of Doctor of Philosophy (GEOLOGY) August, 2018 2 Table of Contents Abstract 4 Introduction 5 Chapter 1: Relating transient seismicity to episodes of deep creep at Parkfield, CA 10 a) Temporal fluctuations in on-fault seismicity before the 2004 Event..................................................... 20 b) Temporal fluctuations in the periods of repeating earthquakes before the 2004 Event........................ 22 c) Temporal fluctuations in off-fault seismicity before the 2004 Event .................................................... 24 d) Increases in seismicity rate - real or data artifacts? ............................................................................. 26 e) Temporal fluctuations in non-volcanic tremor before the 2004 Event ................................................. 27 f) Temporal fluctuations in seismicity after the 2004 Event .................................................................... 28 a) Observations ...................................................................................................................................... 31 b) Methods and model Setup.................................................................................................................. 34 c) Natural Constraints: Regional Stress, and topography ......................................................................... 38 d) Results ............................................................................................................................................... 39 Chapter 2: Relating seismicity to the velocity structure of the San Andreas Fault near Parkfield, CA 45 a) Phase and Group Velocity Maps ......................................................................................................... 58 b) Sections across the SAF ...................................................................................................................... 60 c) Sections parallel to the SAF ................................................................................................................. 62 Chapter 3: A Spring-Mass-Dashpot Model for Slow Earthquakes on a Viscous Fault 67 a) Equations of motion ........................................................................................................................... 72 b) Initial conditions ................................................................................................................................. 73 a) Elastic Parameters .............................................................................................................................. 75 b) Anelastic Parameter ........................................................................................................................... 75 c) Asperity strength ................................................................................................................................ 76 d) Time step ........................................................................................................................................... 77 e) Equations of motion in terms of model parameters ............................................................................ 77 3 f) Relative strength of nucleating asperity .............................................................................................. 77 g) Actual speed of a slow slip event ........................................................................................................ 80 a) Dependence of propagation speed on the ratio of asperity strengths and the damping parameter...... 81 b) Individual LFEs .................................................................................................................................... 85 Conclusions 93 References 94 4 Abstract A dislocation model has been used to interpret the spatial distribution and focal mechanisms of deep off-fault seismicity adjacent to the southern terminus of the creeping section of the San Andreas Fault in Central California, near Parkfield. The most significant feature of the spatial distribution is a prominent seismic lineation that intersects the fault near the SAFOD borehole northwest of Parkfield and strikes southeast making a 20 degree angle with the trace of the San Andreas Fault. This feature can be explained by the termination of a creeping dislocation beneath the seismogenic layer which deepens to the southeast. The stress field corresponding to this dislocation is consistent with surface topography and the focal mechanisms of small off-fault earthquakes. A shear wave velocity model obtained using ambient noise tomography supports this inferred geometry of a deepening dislocation. Low-frequency earthquakes are associated with a low- velocity structure that deepens to the southeast of Parkfield along strike. This plunging low shear velocity structure can be interpreted as representing weaker materials or the presence of fluids and elevated pore pressures and is consistent with materials more prone to creep. This suggests that there may be a structural or rheological control on the occurrence of creep at depth. In order to investigate how creep events propagate in the brittle-ductile regime, a one-dimensional finite-difference spring-mass-dashpot model was used to show that a viscous fault plane pinned by an array of brittle asperities can produce slow slip propagation speeds in the observed range of kilometer per hour to kilometer per day. For physically reasonable values of wall rock elasticity, viscosity, and fault zone width, the model is able to produce propagation speeds consistent with observed tremor migration in subduction zones and at the base of large strike-slip faults. 5 Introduction Non-volcanic tremor (NVT), also referred to as tectonic tremor or simply tremor, is a seismic phenomenon, first discovered in the Nankai Trough subduction zone in Japan (Obara, 2002). Non- volcanic tremor is a long duration seismic signal that can last for hours or even weeks (Beroza and Ide, 2011). Although it occurs mainly in subduction zones, NVT is also observed in strike-slip settings such as on the San Andreas Fault (SAF) California (Nadeau and Dolenc, 2005) and on the Alpine Fault, New Zealand (Wech et al., 2012). Tremor occurs on the deep extension of the fault zone at depths between 20 and 40 km, well below the seismogenic zone (see review by Beroza and Ide (2011) and references therein). Tremor is thought to be composed of overlapping low- frequency earthquakes (LFE) and Ide et al. (2007) showed that LFE focal mechanisms in Japan are consistent with corresponding shear slip on the subduction interface (Ide et al., 2007; Shelly et al., 2007). In contrast to standard earthquakes of comparable magnitude, LFEs are depleted in higher frequencies. In both Cascadia (Rogers and Dragert, 2003) and Japan (Hirose and Obara, 2005), tremor is often associated with geodetically observed large-scale slow slip events (SSE). The combined observation of SSE and tremor, known as episodic tremor and slip (ETS) (Rogers and Dragert, 2003), suggests that tremor is associated with shear slip at depth. Since slow slip and tremor have been documented shortly before larger earthquakes (Kato et al., 2012; Uchida et al., 2016), a better understanding of these phenomena may play an important role in assessing seismic hazard. However, unlike in subduction zones, observations of tremor at the base of strike-slip faults has never been directly correlated with geodetically measured slip. This thesis uses the spatial distribution and focal mechanisms of deep off-fault seismicity adjacent to the San Andreas in Central California to provide evidence for such a correlation. 6 Individual LFEs, which compose tremor, represent families of repeating events and these events tend to be preceded or followed by nearby sources. These interactions define migration rates. In subduction zones, tremor migrates at velocities of 5 to 15 km/day along strike, comparable to geodetically observed slow slip events, which propagate at speeds on the order of 10 km/day (Dragert et al., 2001; Obara, 2002; Schmidt and Gao, 2010). LFEs have been observed to migrate at about 25 to 200 km/h both up and down-dip (Ghosh et al., 2012; Shelly et al., 2007). Similar migration speeds are observed for more complex propagation patterns of LFEs such as reversals away from the main front (Houston et al., 2011) and secondary tremor fronts (Bletery et al., 2017). Beneath the strike-slip SAF, Shelly (2015) has documented migration rates on the order of 50 to 150 km/h, similar to the up and down-dip LFE migration in subduction zones. SSE, NVT and ETS provide a unique opportunity to understand deformation of fault roots at depth. As these phenomena occur on the deep extension of faults within the transition from the brittle upper crust to ductile deformation at depth, their mechanisms are still poorly understood. Geodetic observations of SSE that are spatially correlated with tremor in ETS events suggest an association with shear slip. Ide et al. (2007) showed that LFE focal mechanisms (that comprises tremor) in Japan are consistent with corresponding shear slip on the subduction interface determined geodetically (Ide et al., 2007; Shelly et al., 2007). Similarly, beneath the SAF, LFEs occur in a narrow zone on the downward projection of the fault suggesting the fault root remains relatively localized to Moho depths (Shelly and Hardebeck, 2010). A key question in understanding the propagation of SSEs and the migration of LFEs is what controls the propagation velocity within the shear zone. Observed migration speeds in the range of kilometer per hour to kilometer per day are more than an order of magnitude slower than the propagation speeds of normal fractures of frictional slip in the seismogenic zone. The question 7 becomes: what slows propagation in the brittle-ductile regime? Frictional mechanisms have been proposed that invoke stick-slip instabilities where the rupture speeds are either slowed by the interaction with fluids, which causes slip-weakening behavior (Ikari et al., 2013) or are impeded by dilatant strengthening (Segall et al., 2010; Shelly, 2015). In fact, high vp/vs ratios in subduction zones (Audet et al., 2009), interpreted as evidence of high fluid pressure from the dewatering down-going slab, have been invoked as these events are sensitive to small stress perturbations due to tidal triggering (Thomas et al., 2009) and passing seismic waves (Hill et al., 2013). Although there is no clear consensus, models proposed tend to involve a frictional fault with low effective pressures and heterogeneous material properties. This thesis explores the possibility that slow propagation is achieved by an array of brittle asperities that pin motion on a viscous fault. The overarching theme of this study is to understand the rheological instability associated with slow slip and tremor. This dissertation is organized around two main topics. The first seeks to determine the geometry of transient slip on the deep extent of the SAF. The second explores the possibility that SSEs and the associated seismicity can be modeled as viscous creep on the deep fault plane that is constrained by brittle asperities. Chapter 1 models transient creep events beneath the seismogenic zone on the Parkfield section of the SAF that are revealed by transients in off-fault seismicity. Although tremor is observed at Parkfield, there has been no geodetic observation of corresponding slow slip (Smith and Gomberg, 2009). This is unusual since tremor is commonly correlated both spatially and temporally with measureable slow slip events in subduction zone settings (Hirose and Obara, 2005; Rogers and Dragert, 2003). It is possible that tremor at Parkfield is a different phenomenon not associated with transient creep, or that as discussed in Smith and Gomberg (2009), the displacements associated with the tremor at Parkfield are below the detection threshold of current geodetic instrumentation. 8 In this chapter, I investigate the possibility that the observations of transient off-fault seismicity can be taken as evidence of a deep creep event that preceded the 2004 Parkfield M6.0 earthquake. Coulomb stress modeling was used to show that the focal mechanisms and spatial pattern of off- fault seismicity are consistent with a deep creep event on the deep extent of the SAF, which deepens along strike to the south of Parkfield. In Chapter 2, ambient noise tomography is used to explain the observation developed in Chapter 1 that creep on the SAF deepens to the south of Parkfield. An outstanding question to understanding the mechanisms behind tremor is what controls the occurrence and depth of these events. Tremor events in subduction zones and strike-slip settings occur well beneath the seismogenic zone, at 20 to 45 km depth, yet the seismogenic nature of tremor indicates that it must involve a brittle component of deformation. The dislocation model described in Chapter 1, delineated by the LFE family locations, suggests the potential for geological structural control on the occurrence of tremor. Two ideas have been posited for how tremor can occur at such depths. One hypothesis is that as SSEs tend to occur near Moho depths they may be related to contrasts in strength at the crust to mantle boundary (Chen et al., 2012). The other hypothesis ties tremor locations to weaker local material properties more prone to creep and high fluid pressures as observed in subduction zones (Shelly et al., 2006). Thus, the goal of this chapter is to investigate whether there is evidence for tremor at Parkfield associated with an increase in strength at the Moho or if it is more likely associated with weaker materials and fluids. The shear wave velocity model obtained using ambient noise tomography, maps out the seismic structure along the creeping section of the SAF south of Parkfield. The model shows that LFE events tend to occur within a low seismic velocity structure which deepens to the north and to the south along strike of the SAF 9 suggesting that they may be associated to fluids or weaker rheologies rather than an increase in strength. In Chapter 3, an asperity model is formulated with the aim of understanding slow propagation observed in SSE events and LFE migration. In this model LFEs are seen to represent asperities, or stuck patches, that are loaded by surrounding creep. Although tremor migrates at very different rates perpendicular to and along strike in subduction zones, the focus here is on understanding the along strike migration of both SSEs (at rates of km/day) and the faster LFE migration in both subduction zones and strike-slip faults (at rates of km/hour). One question is whether asperities play an active role in limiting the propagation or whether they are a passive indication of slip that has been slowed by another mechanism. The model developed here tests the hypothesis that asperities may limit the slip speed of slow slip events. To investigate this idea, SSE are modeled as an advancing slip front slowed by delays at pinning asperities in a viscous fault. Using a one- dimensional spring-slider finite-difference model to investigate slow slip propagation in a ductile shear zone pinned by an array of stuck asperities, based on geologically sound parameters, the model is able to produce observed SSE propagation speeds. The first two chapters have been published in Bulletin of the Seismological Society of America and Geophysical Journal International respectively. The third chapter is in preparation for publication. 1) Sammis, C. G., Smith, S. W., Nadeau, R. M., & Lippoldt, R. (2016). Relating transient seismicity to episodes of deep creep at Parkfield, California. Bulletin of the Seismological Society of America, 106(4), 1887-1899. 2) Lippoldt, Rachel, Robert W. Porritt, and Charles G. Sammis. "Relating seismicity to the velocity structure of the San Andreas Fault near Parkfield, CA." Geophysical Journal International 209.3 (2017): 1740-1745. 3) Lippoldt, Rachel, Charles G. Sammis “A Simple Spring-Mass-Dashpot Model for Slow Earthquakes on a Viscous Fault” in prep. 10 Chapter 1 Relating transient seismicity to episodes of deep creep at Parkfield, California We establish a causal relation between tremor, deep creep and off-fault seismicity on the San Andreas Fault at Parkfield, CA by analyzing spatiotemporal seismicity data and using Coulomb stress modeling. The 2004 M6.0 earthquake was preceded by a four-year period of anomalously high seismicity adjacent to, but not on, the San Andreas Fault (SAF). The rate of small events (Mw<3) at distances between 1.5 and 20 km from the fault plane and at depths greater than 8 km increased from six events per year prior to 2000 to 20 events per year between 2000 and the 2004 earthquake. This increase in the rate of seismicity coincided with an increase in the occurrence of non-volcanic tremor, which suggests that creep may have driven the enhanced seismicity. Using Coulomb stress modeling, an observed southeast-striking lineation of enhanced seismicity is shown to be a direct consequence of a deepening brittle-ductile transition southeast of Parkfield, as evidenced by a deepening of the tremor and low-frequency earthquakes. Other evidence for a causal link between deep creep and off-fault seismicity is the observation that off-fault seismicity before and after the 2004 earthquake occurred in the same location. This is expected if the foreshocks are driven by an episode of deep creep and the aftershocks are driven by after-slip, both occurring on the same deep extension of the fault plane. Finally, a transient increase in off-fault seismicity at Parkfield was observed to follow the 2010 Maule and the 2011 Tohuku earthquakes. The seismic waves from these events were observed to trigger tremor at Parkfield, which is further evidence for a causal link between deep creep and off-fault seismicity, particularly since the increase in off-fault seismicity was limited to deep events having the same spatial pattern as those 11 that preceded the 2004 earthquakes. A similar anomaly in on-fault seismicity between 1990 and 1994 did not show any evidence of anomalous off-fault seismicity and did not culminate in a M6.0 earthquake. Introduction The stretch of the San Andreas Fault (SAF) that runs past Parkfield in central California is one of the most intensely studied fault segments in the world (Figure 1). Lying at the southern terminus of the creeping section of the San Andreas, this segment has produced a series of seven intermediate earthquakes with magnitudes near 6 between 1857 and 2004. Because the recurrence interval between successive events had been fairly constant (between 18 and 32 years) from 1857 to 1966, another M6.0 event was expected with a high probability between 1983 and 1988 (Bakun and McEvilly, 1984). Consequently, Parkfield became an international laboratory for the study of a wide variety of physical precursors that were hypothesized to precede intermediate and large earthquakes. When the expected M6.0 earthquake finally arrived on 28 September 2004 (20 years late) none of the anticipated short-term physical precursors were observed on a time scale of seconds to days before the event (Harris and Arrowsmith, 2006). There are, however, observations which suggest that the 2004 Parkfield event was preceded by a transient episode of deep creep, detected by the borehole High Resolution Seismic Network (HRSN) at Parkfield, California (Nadeau and Dolenc, 2005). Although there was no geodetically detected acceleration of surface creep prior to the 2004 earthquake, tremor beneath the San Andreas increased during the three months prior to that event and was tentatively attributed to accelerating creep beneath the eventual earthquake epicenter (Shelly, 2009). Non-volcanic tremor (NVT) has been observed in both subduction zones and in transpressional 12 regimes yet, the mechanism is poorly understood. NVT was first discovered in the subduction zone off the coast of Japan (Obara, 2002) and has since been observed prevalently throughout other subduction zones such as in Cascadia and Mexico (Dragert et al., 2001; Lowry et al., 2001) as well as on the transform plate boundary of the SAF near the Parkfield region (Nadeau and Dolenc, 2005). NVT in subduction zones has been linked to slow slip events (SSE) through geodetic observations of displacements in both Cascadia and Japan (see review by Beroza and Ide (2011) and references therein). The mechanisms responsible for NVT are still poorly understood but SSE have been proposed to be related to a material instability such as rate-state friction in combination with fluid effects (see summaries in (Peng and Gomberg, 2010; Rubinstein et al., 2009) or shear failure involving a cascade of small earthquakes (Ben-Zion, 2012). In analogy to the subduction zone tremor, slip has been proposed for the LFEs near Parkfield (Guilhem and Nadeau, 2012), but no slip has been observed geodetically on the San Andreas. It is also uncertain whether the same mechanism for NVT is operating at Parkfield since the San Andreas Fault system has not had active subduction for the past 30 Ma (Atwater, 1970), i.e. since the subduction of the Farallon plate. If the tremor were tied to fluids as proposed for subduction zones, then their source must be different for the SAF (Fagereng and Diener, 2011). Shelly et al. (2009) noted that the LFEs locations occur on a linear planar feature, interpreted to represent the deep San Andreas fault root with implications for shear slip and localized deformation up to 10 km deeper than the seismogenic zone, as opposed to along a slab interface as in in subduction zones. NVT has been observed to respond to low values of tidally induced shear stress in both subduction zones (Rubinstein et al., 2009) and on the SAF (Thomas et al., 2009), which suggests that the plate interface is a weak and nearly critically stressed fault. It is important to understand the mechanics 13 of tremor since the link between NVT, slow slip and seismicity will inform our understanding of deformation mechanisms on the deeper structure of fault roots, which, in turn, affect the timing of large earthquakes (Sammis and Smith, 2013). More specifically, the coincidence of tremor with slow-slip events in Cascadia and Japan suggests that shear slip is closely related to low-frequency earthquakes (LFE) through Tremor and Slip (ETS) (Rogers and Dragert, 2003). Tectonic tremor is clearly an important component of fault mechanics but remains poorly understood. If in fact tremor is indicative of deep fault slip that cannot be detected by surface geodetic instruments, then it may provide a useful tool in time-dependent forecasts in certain regions (Shelly, 2009). In addition, documented ETS events in Cascadia and Japan (Hirose and Obara, 2005; Rogers and Dragert, 2003; Shelly, 2009; Zigone et al., 2012) support a link between slow slip and tremor, but there is still some debate as to whether episodes of tremor are driven by significant slow slip or are a cascade of triggered isolated asperities with no significant overall fault displacement (Ben-Zion, 2012). NVT and LFEs have been observed and located on the transition zone of the creeping section of the SAF, south of Parkfield (Shelly and Hardebeck, 2010). Our study focuses on the relationship between the deeper off-fault seismicity (8 to 15 km depth) and the NVT observed in the Parkfield area of the SAF. This off-fault seismicity was observed to have increased during a four-year period leading up to the 2004 M6.0 Parkfield earthquake. The increase occurred along a linear trend that begins near the San Andreas Fault Observatory at Depth (SAFOD) site and is oriented at an angle of approximately 20° to the northeast of the strike of the SAF. The LFEs of this section of the SAF are observed to occur along a linear planar feature corresponding to the deep extension of the SAF, which supports the hypothesis that LFEs represent shear slip on the deep extent of the SAF(Shelly, 2009). 14 To better understand the relationship between the spatial distribution of the observed seismicity and the processes on the deep extension of the San Andreas Fault we use Coulomb stress modeling. Using the Coulomb 3.4 program, we investigate whether or not a progressively deepening creep event, constrained by Parkfield tremor locations, could produce the observed spatial pattern in seismicity with increases in seismicity primarily associated with compression and reverse faulting. Gaining insight into the deformational processes at depth, we will be able to better inform our understanding of strain accumulation on the seismogenic crust above. In this study we show that the spatial and temporal patterns of seismicity adjacent to (but not on) the Parkfield segment of the SAF support a close connection between tremor and deep creep. We show that the spatial pattern of off-fault seismicity is consistent with slip on a deep extension of the fault, which, like the tremor and slow slip events, deepens from the SAFOD drill site in the northwest toward the southeast terminus of the Parkfield segment. This seismicity pattern remains unchanged following the 2004 event, even though the seismic activity jumps up and then decreases according to Omori’s law. Superimposed on the Omori law decrease in off-fault seismicity, we observe transients that coincide with documented episodes of tremor that were triggered by the seismic waves from distant large earthquakes. Similar transients in off-fault seismicity also occurred during a well-documented 1990 surface creep event and during the four years preceding the 2004 earthquake. We show that this four-year transient in off-fault seismicity was accompanied by a four-year increase in the level of tremor, the last three months of which were observed in the more detailed study by Shelly (2009). These observations suggest that off-fault “background” seismicity may be very sensitive to small stress changes associated with episodes of transient creep at the base of the seismogenic zone and may thus offer a new tool to monitor the transient loading of large faults. 15 Data and methods We use the Double-Difference Catalog from the Northern California Earthquake Data Center (NCEDC) over the time interval from 1984 through 2014. Our study is limited to the dashed rectangle in Figure 1, which contains 18,548 events. The width of the zone was chosen as ±18 km to minimize contamination from the aftershocks of the 1983 Coalinga and 2003 San Simeon earthquakes. Choice of the northwest and southeast boundaries was based on the seismicity in Figure 1 and the measured surface creep shown in Figure 2a. The northwest boundary was set 65 km north of the SAFOD site (near the Bitterwater geodetic site) where the creep rate on-fault begins to decrease significantly and seismicity pattern broadens further to the northwest. The southeast boundary was set 46 km south of SAFOD (near the Highway 46 crossing) where the surface creep ends and there is a break in the seismicity. 16 Figure 1: Seismicity on and near the Parkfield segment of the San Andreas Fault. The blue rectangle indicates the selected study area. The northwest boundary was chosen near the Bitterwater creep station since the creep rate decreases significantly further to the northwest. The southeast boundary was chosen at the termination of surface creep near the Highway 46 intersection. The northeast boundary was chosen to avoid aftershock clusters associated with the 1983 Coalinga earthquakes. The southwest boundary was chosen to avoid aftershocks of the 2003 San Simeon earthquake and the cluster associated with a secondary fault. Major fault traces are indicated in red. Epicenters are from an updated version (NCAeqDD.v200912.1) of the catalog originally published by Waldhause and Schaff (2008). 17 Figure 2: Panel a shows the creep rate from Cholame (Hw 46) at the south to San Juan Bautista (SJB) at the north. The open box symbols are from Lisowski and Prescott (1981), the dashed line is a summary of all measurement between 100 m and 1 km from the fault axis from Titus et al. (2006). Note that the creep rate is a maximum between Slack Canyon (SLC) and Bitterwater (BWT). Also labeled are Parkfield (PKF) and the epicenters of the 1966 and 2004 M6.0 earthquakes. Distances are measured north of SAFOD as indicated with geodetic stations for reference. Panel b shows the surface slip in the 1966 and 2004 events from Lienkaemper et al. (2006) superimposed on the creep data between Hwy46 and BWT. Surface creep in our study area is shown in Figure 2a, and is compared with the surface slip distributions in the 1966 and 2004 M6.0 earthquakes in Figure 2b. Note that the surface creep begins a sharp decrease near the Slack Canyon geodetic site (SLC) 20 km north of SAFOD. This is generally ascribed to the presence of a large asperity that fails quasi-periodically to generate the sequence of M6.0 events. Bilham and King (1989) presented topographic evidence that the Parkfield asperity has a geometrical origin. They demonstrated that uplifts at Middle Mountain and Gold Hill are consistent with changes in the fault direction at those locations. These fault bends produce barriers to slip that pin the segment in between. The M6.0 earthquakes tend to nucleate at one or the other 18 of these two barriers and rupture the pinned segment in between. The 1933 and 1966 events nucleated at the northern barrier near Middle Mountain and propagated southeast (Bakun and McEvilly, 1984) while the 2004 event nucleated at the southern barrier near Gold Hill and propagated to the northwest. Even though the 1966 and 2004 events nucleated at opposite ends of the pinned segment (nearly 20 km apart) and propagated in opposite directions, they had very similar slip functions (Figure 2b). The fault-normal event density profile in Figure 3 was calculated as in Powers and Jordan (2010) but has been updated to include events through 2014. Powers and Jordan (2010) interpreted their profile in terms of the fractal fault model proposed by Dieterich and Smith (2009). In this model the fractal roughness in the fault zone produces an off-fault stress field that decreases as a power law of distance from the fault, where the power is related to the fractal dimension of the roughness. This power law decrease in stress is assumed to produce the observed power-law decrease in seismicity. Dieterich and Smith (2009) show that the slope of the seismicity is approximately equal to the fractal dimension D of the fault roughness. The three hundred meters or so of constant activity near the axis is identified as the fault zone half-width d over which the roughness is developed. It is consistent with the fault zone dimension sampled by the SAFOD borehole Zoback et al. (2011) and the width of highly damaged fault zone rock observed in many exhumed fault zones (see Ben-Zion and Sammis (2003) and references therein). 19 Figure 3: Fault normal seismicity density distribution across the Parkfield segment of the San Andreas Fault. The flat portion within 300 m of the fault axis is interpreted as the fault zone. The power law fall-off between 300 m and 1.5 km is interpreted as a consequence of stress concentrations on a fractal fault surface where the power is related to the fractal dimension of the roughness. All events farther than 1.5 km from the fault axis (where the power law distribution reaches background) are termed off- fault events. Based on Figure 3, we divide the seismicity into on-fault events and off-fault events. On-fault events include those events in the fault zone and those in the power law region. Events within the power law region are combined with those in the fault zone because, being driven by fault roughness, they are expected to reflect changes in slip within the adjacent fault zone. Off-fault events include all seismicity between the distances at which the power law decrease reaches the background level and the ±18 km boundaries of our study area. As indicated in Figure 3, the transition from on-fault to off-fault seismicity occurs at a distance of about x=d*=1.5 km from the fault axis. 20 Temporal Relationship a) Temporal fluctuations in on-fault seismicity before the 2004 Event Figure 4 shows the cumulative on-fault seismicity (x< 1.5 km from the fault plane) as a function of time from the beginning of the catalog up to the 2004 M6.0 earthquake. The lower curve shows activity on the creeping segment to the north of Slack Canyon while the upper curve shows activity on the transitional segment to the south. The event rate on the creeping segment is very nearly constant over the entire time interval. In contrast, the event rate on the transitional segment south of Slack Canyon shows significant changes in slope. The event rates are relatively high from 1990 to 1995 and from 2001 to the 2004 earthquake. Rates are significantly lower between 1985 and 1990 and between 1996 and 2001. Roelofts and Langbein (1994) discuss the period of high seismicity beginning in 1990 and its possible relation to episodes of transient creep and the magnitude 4.7 earthquake in October 1992, which triggered the first and only A-level alert at Parkfield. Roelofts (2001) points out that it is difficult to correlate transient creep with seismic activity since seasonal temperature fluctuations and rainfall also produce apparent creep transients. No significant surface strain transients were observed before the 2004 event (Johnston et al., 2006). In Figure 5, the cumulative curve for on-fault events south of Slack Canyon, in the Southern Transition Zone from Figure 4, has been divided into shallow events with hypocenters shallower than 8 km and deep events with hypocenters deeper than 8 km. The boundary between shallow and deep events was arbitrarily set at 8 km guided by the distribution of seismicity as a function of depth shown as an inset in Figure 5 and Figure 9. Note that rate changes in the upper curve in Figure 4 are caused largely by changes in the shallow seismicity. The rate of deep events shows a short transient increase in 1993 and another between 2003 and the 2004 earthquake. 21 Figure 4: Cumulative number of on-fault events as a function of time from the beginning of the catalog to the 2004 earthquake (9/28/2004). The lower curve shows events on the creeping segment north of Slack Canyon. The upper curve shows events on the transitional segment south of Slack Canyon. Figure 5: Cumulative number of on-fault events in the transition zone south of Slack Canyon as a function of time from the beginning of the catalog to the 2004 earthquake. The upper curve shows events that have hypocenters above 8 km while the lower curve is for events that are deeper than 8 km. The inset shows the depth distribution of on-fault events south of Slack Canyon. 22 b) Temporal fluctuations in the periods of repeating earthquakes before the 2004 Event The Parkfield segment of the SAF is the site of many repeating earthquakes, each of which can be used to give a point measurement of the slip rate. Nadeau and Johnson (1998) measured the scalar moments of 221 on-fault micro-earthquakes in the transition segment south of Slack Canyon. These events comprised 53 repeating sequences of 2 to 13 nearly identical events with a nearly uniform repeat time T. Magnitudes were in the range -0.7<M<1.4. Their analysis also included repeating sequences of larger events (3.5<M<4.9) from the Stone Canyon segment of the SAF to the north and the 6 M6.0 Parkfield events since 1857. They found that the repeat time of a sequence scaled with the scalar moment M0 of its constituent events as !≈#$ % &/( (1) Johnson and Nadeau (2002) showed that the scaling is consistent with the assumption that repeating earthquakes are stuck patches (asperities) that are continuously loaded by creep on the surrounding fault plane. Known in fracture mechanics as an annular crack, it can be used to model the slip accommodated by each event in a sequence, which, together with the repeat time, can be used to calculate the slip rate at the asperity. Figure 6 shows the slip-rates calculated for 65 repeating sequences as a function of position along the fault. Note that this estimate agrees with surface slip-rate measurements in Figure 2. The implication is that the entire seismogenic zone slips at the rate measured at the surface. 23 Figure 6: Average slip-rates accommodated by repeating events between 1984 and the 2004 earthquake as a function of position along the fault. The top panel used a moving window smoothed over 12 adjacent sequences and stepped every one sequence. The sequences are shown in cross section in the central panel and map-view in the lower panel. The dashed line is the rate from surface geodesy (Figure 2a). The along-fault coordinates are the same as in Figure 2 with 0 at SAFOD. In Figure 7, the average cumulative slip accommodated by the repeating earthquakes is plotted as a function of time leading up to the 2004 earthquake. Note that the transient increase in seismicity between about 1991 and 1994 in Figure 5 is also seen by the repeating events. However, the small transient in on-fault seismicity in the few years before the 2004 earthquake was not seen by the repeating events. The implication is that the increases in on-fault events just before the 2004 earthquake (most of which are shallow) are not caused by an increase in on-fault slip rate within the seismogenic zone. 24 Figure 7: Cumulative slip at Parkfield from repeating events. c) Temporal fluctuations in off-fault seismicity before the 2004 Event Figure 8 shows the cumulative off-fault seismicity (x>1.5 km from the fault plane) as a function of time from the beginning of the catalog up to the 2004 M6.0 earthquake. The lower curve showing off-fault activity adjacent to the creeping segment north of Slack Canyon is characterized by an Omori-like deceleration to a fairly steady state rate with an acceleration beginning about one year before the 2004 earthquake. The lower curve showing activity adjacent to the transition section south of Slack Canyon shows a relatively constant event rate between 1986 and 2000 broken only by a small increase in activity in 1990 followed by a decrease back to the background rate that persists to 2000. An increase in event rate beginning in 2000 is followed by the onset of a significantly higher event rate in 2002 that persists up to the 2004 earthquake. Comparison with Figure 4 shows that the rate of on-fault seismicity south of Slack Canyon also increases in 2002. 25 Figure 8: Cumulative number of off-fault events as a function of time from the beginning of the catalog to the 2004 earthquake. The upper curve shows events adjacent to the transitional segment south of Slack Canyon. The lower curve shows events adjacent to the creeping segment north of Slack Canyon. Figure 9: Cumulative number of off-fault events adjacent to the transition zone south of Slack Canyon as a function of time from the beginning of the catalog to the 2004 earthquake. The upper curve shows events that have hypocenters deeper than 8 km while the lower curve is for events that are shallower than 8 km. The inset shows the depth distribution of off-fault events south of Slack Canyon. 26 In Figure 9, the off-fault seismicity south of Slack Canyon in Figure 8 has been divided into shallow events above 8 km and deep event with hypocenters below 8 km. The boundary between shallow and deep events was again arbitrarily set at 8 km guided by the distribution of off-fault seismicity as a function of depth shown as an inset. Note that almost all of the seismicity that produces the transient from 2000 to the 2004 have hypocenters below 8 km. d) Increases in seismicity rate - real or data artifacts? Before beginning our analysis, we first eliminate some obvious possible causes of the sudden increase in the off-fault seismicity rate south of Slack Canyon that begins in 2000 (Figure 8 and Figure 9). One possibility is that the detection threshold improved in 2000 such that more small events were recorded in subsequent years. We can eliminate this possibility by comparing the completeness of the first 16 years of the NCEDC Double-Difference catalog that we are using with the final four years of accelerated activity before the 2004 event. We made this comparison using the maximum likelihood method implemented in the ZMAP software. These results are summarized in Table 1. Table 1: Comparison of Catalog Completeness Before and After 2000 Time Interval No. of events M ≥ Mc a-value (annual) b-value Mc 1/3/1984 -9/28/2000 2866 3.22 .894 1.1 9/28/2000-9/28/2004 1130 3.46 .982 1.1 Note that the minimum magnitude of completeness is Mc = 1.1 for all time intervals. It is interesting that the b-value increases significantly during the last four years before the 2004 event. 27 This appears to be due to the increase in off-fault seismicity, which is comprised largely of small events. It is also possible that the increased seismicity rate after 2000 is caused by aftershocks of nearby intermediate and large events. For this to be the case, an event would have had to occur at the time of the change in slope, which, as accurately as we can tell, occurred during 2000 (see Figure 5). There were no intermediate or large earthquakes in central California during this time period. Finally, the observation in Figure 9 that the increase in activity between 2000 and the 2004 earthquake is limited to deep events also argues against an improvement in detection threshold. e) Temporal fluctuations in non-volcanic tremor before the 2004 Event Periods of NVT can be identified at the base of the Parkfield segment of the SAF as far back as 1994, although the records are not good enough to locate the individual constituent events as in Shelly et al. (2009). Figure 10 shows the cumulative number of minutes of NVT beginning in late 1993 and ending at the 2004 earthquake. Note that there was a small change in slope in 1997 and a much larger change that began during the void between mid 2000 and mid 2001 where the slope more than doubled from 760 minutes per year to 1830 minutes per year. If NVT is a proxy for creep, then the creep rate beneath the seismogenic zone at Parkfield more than doubled between 2001 and 2003, and remained somewhat elevated between 2003 and the 2004 earthquake. There was no change in off-fault or on-fault seismicity corresponding to the smaller rate change in 1997. However, the increase in off-fault seismicity between 2001 and the 2004 earthquake in Figure 8 and Figure 9 corresponds in timing and shape to the change in tremor rate during this time period. 28 Figure 10: Cumulative minutes of non-volcanic tremor beneath Parkfield. Grey areas denote times of no data. Note sharp increase in rate that began during the data void between 2000 and 2001. f) Temporal fluctuations in seismicity after the 2004 Event Figure 11 shows the cumulative number of on-fault events (x<1.5 km) from the 2004 earthquake through 2014. In the creeping section to the north of Slack Canyon, the average event rate was nearly linear at about 50 events per year, compared with about 37 events per year background rate before the 2004 event (see Figure 4). The implication is that the aftershock rate has not yet reached background. In the transition zone south of Slack Canyon a vigorous aftershock sequence lasting about 2 years was followed by a steady event rate of about 390 events per year, compared with the background rate of about 324 events before the event. The times of the 2010 Maule, Chile, the 2011 Tohoku, Japan and the 2012 Aceh, Indonesia events are also indicated. Although the seismic waves from the first two of these large events were observed to trigger tremor on the deep extension of the San Andreas Fault (Hill et al., 2013; Peng et al., 2010) there is no evidence that 29 the rate of on-fault events on either the northern or southern section was affected by these large events. Figure 11: Cumulative number of on-fault events as a function of time from the 2004 earthquake through the end of 2014. The upper curve shows events on the southern transitional segment while the lower curve shows events on the creeping segment north of Slack Canyon. The open circles show an Omori 1/t aftershock sequence superimposed on a steady rate of 1.25 events/day, comparable to the rate before the 2004 event. Figure 12 shows the cumulative off-fault seismicity following the 2004 earthquake. After about three years of Omori-like decay, the activity adjacent to the northern creeping zone returns to its pre-earthquake level of about 6 events per year (Figure 8). Activity adjacent to the southern transition zone remains at 28 events per year to the end of the catalog. This rate is comparable to that during the four-year pre-earthquake transient in Figure 9. Note that an increase in activity adjacent to the southern transition zone coincided with the three largest global earthquakes during 30 the time of our study: the 2010 M8 event in Maule Chile, the 2011 M9 event in Tohoku Japan, and the 2012 M8 event in Aceh Indonesia. The seismic waves from the first two were observed to trigger tremor below the Parkfield segment (Peng et al., 2010; Hill et al., 2013). Figure 13 shows the activity south of Slack Canyon sorted into shallow events (hypocenters above 8 km) and deep events (hypocenters below 8 km). The increase in activity preceding the 2004 earthquake is due mainly to an increase in the rate of occurrence of deeper events. Following the 2004 event, shallow activity follows an Omori-like decay to a new rate higher than that before the event and comparable to the elevated rate of the deep events. Figure 12: Cumulative number of off-fault events as a function of time from the 2004 earthquake through 2014. The lower curve shows events adjacent to the creeping segment north of Slack Canyon. The upper curve shows events adjacent to the transitional segment south of Slack Canyon where the surface creep decreases from about 30 mm/year at Slack Canyon to zero, where the fault becomes locked to the SE. 31 Figure 13: Cumulative number of off-fault events south of Slack Canyon as a function of time from the 2004 earthquake through 2014. The lower curve shows deep events below 8 km while the upper curve shows shallow events above 8 km. Spatial Relationship a) Observations Earthquake ruptures cause displacement and stress transfer in the lithosphere that can trigger aftershocks as well as other events. After an earthquake rupture, coseismic stress changes cause seismicity rates to increase in areas of stress increase and decrease in areas where the stress drops (King et al., 1994). Coulomb stress quantifies the stress transfer from a discrete dislocation to the surrounding region, for a given set of assumed material properties (e.g., pore fluid pressure, coefficient of friction). King et al. (1994) observe that by modeling a fault as a dislocation in an elastic half space, triggered seismicity and aftershocks tend to occur within the modeled spatial patterns of increase in Coulomb stress as low as 1bar. Studies agree that a change in Coulomb stress of the order of 1-3 bars is sufficient to encourage or suppress seismicity in a region (Freed, 2005; King et al., 1994). 32 For the elastic rebound model, in a homogeneous elastic medium, the stress pattern leading to rupture has lobes of highest Coulomb stress change between 30° and 60° from the main fault trace. These areas of increased Coulomb stress correspond to areas with an increase in foreshock seismicity, whereas the areas perpendicular and parallel to the strike of the fault are in areas of stress shadow with reduced foreshock activity. After rupture, the pattern inverts. Areas previously in the stress shadow have high Coulomb stress and increased aftershock seismicity (King and Bowman, 2003). In contrast to the pattern inversion predicted by elastic rebound theory, the foreshocks and aftershocks of the 2004 M6.0 Parkfield earthquake differ from the elastic model’s predictions as both occur in the same pattern. The areas with increased seismicity rates both before and after the 2004 rupture correspond to events that occurred primarily deeper than 8 km and occur along a linear trend that begins near the SAFOD site and continues at an angle of approximately 20° with the strike of the San Andreas Fault (Figure 14). 33 Figure 14: Map view of off-fault seismicity south of Slack Canyon, rotated about SAFOD for the y- axis to align with SAF surface trace strike. The red circles are epicenters of events that preceded the 2004 earthquake while the blue circles are epicenters of events that occurred after the 2004 event up to the end of our catalog. The left panel shows all events while the right panel only shows events with hypocenters deeper than 8 km. The triangle indicates the location of the SAFOD borehole. The trend is highlighted by the dashed line. In order to explain this discrepancy with the elastic rebound model’s predictions, we propose that the increased seismicity was primarily associated with faulting that was driven by a transient creep event below the seismogenic zone that began to the north of Parkfield and terminated at progressively increasing depths to the South. The steepness of the progressively increasing depths of termination would therefore control the angle of the linear trend from the SAF, with steeper deepening widening the angle of the seismicity to the SAF. An increasing termination depth is consistent if foreshocks are driven by an episode of deep creep and the aftershocks are driven by after slip, both occurring on the same deep extension of the fault plane. In fact, LFEs are observed x[km] -20 -10 0 10 20 y[km] -50 -40 -30 -20 -10 0 10 20 All Off-Fault Events x[km] -20 -10 0 10 20 y[km] -50 -40 -30 -20 -10 0 10 20 Off-Fault Events >8km depth Events before the 2004 M6 EQ Events after the 2004 M6 EQ SAFOD 34 to progressively deepen from 18 km to 30 km depth from SAFOD to Highway 46 (geodetic station) for 75 km along the strike of the SAF (Guilhem and Nadeau, 2012; Shelly, 2009). b) Methods and model Setup The tremor level was elevated for four years prior to the 2004 event as shown in Figure 10 and Shelly (2009) observed increased tremor during a three-month period before the 2004 event. If tremor is a proxy for creep, then the 2004 M6.0 event was preceded by a four-year episode of enhanced deep creep. Off-fault seismicity was observed to increase during a four-year period leading up to the 2004 M6.0 Parkfield earthquake (Figure 8 and Figure 9). The increase in off- fault seismicity occurred along a linear trend that begins near the SAFOD site, making an angle of about 20° with the strike of the SAF (Figure 14). Based on the spatial pattern, our hypothesis is that the increased seismicity was primarily associated with thrust faulting, driven by a transient creep event below the seismogenic zone that began to the north of Parkfield and terminated at progressively increasing depths to the south. An increasing termination depth is consistent with the observed deepening of the tremor south of Parkfield. We use the Coulomb 3.4 program to further test our hypothesis that the precursory seismicity is related to a transient event on the ductile extension of the SAF fault plane. We model the deep extent of the SAF as a buried dislocation using the program Coulomb 3.4. This program, based on the King et al. 1994 model, implements the Okada solutions (Okada, 1992) for a buried dislocation in an elastic half space in three-dimensions. This model uses the imposed displacement from the initial dislocation to calculate three-dimensional strains and both normal and shear stresses using the elastic stiffness of the material. From these initial outputs and given material parameters such as friction and Poisson’s ratio we then calculate the change in Coulomb stress, or the Coulomb Failure Function (CFF) on an assigned fault plane in the half space. The 35 CFF parameter describes the likelihood of failure on a given plane orientation. When the CFF is reached, failure will occur on that plane. Coulomb 3.4 calculates changes in Coulomb stress based on an initial displacement on a dislocation model of a fault as: ∆s CF =∆t+µ ∆s n where ∆s CF is the change in Coulomb stress on the plane of failure, ∆t is the change in shear stress and ∆s n is the change in normal stress on the failure plane, and µ is the effective coefficient of friction. ∆t is positive in the direction of receiver fault slip and ∆s n is positive for tension, i.e., when the receiver fault is unclamped. The failure planes can be assigned a priori or can be calculated accounting for the interaction between the two stress fields, as well as taking in to account regional stress. On a given fault orientation, positive changes in Coulomb stress represent bringing the fault closer to failure whereas negative changes indicate that it is less likely to fail given the initial displacements. We model the fault geometry constrained by the locations of the LFE locations that occur beneath the creeping and transition zones of the SAF, detected by Shelly and Hardebeck (2010). Specifically in the southern transition zone and in the locked section, the LFEs deepen progressively from 18 to 30 km from Slack Canyon to HWY46, and further to the southeast. We know that the four-year off-fault transient seismicity was not caused by an acceleration of shallow creep since no creep transient was observed at the surface trace of the transition segment and no decrease was observed in the period of repeating events. As there is no change in seismicity rate or creep in the seismogenic zone, we are only interested in the effect of accelerated creep at depth. To show that the LFEs correspond to slip on the deep extension of the fault plane, we model the slip pattern to match the locations of the LFEs that progressively deepen to the south (Figure 15). 36 The deep slip is modeled as eight faults that taper from 15 km to 30 km depth over 60 km along strike. Our aim is to investigate whether a plausible creep distribution produces Coulomb stress changes that are consistent with the enhanced seismicity. Figure 15: Cross-section along strike of the SAF showing the dislocation geometry. The LFE locations are taken from Guilhem and Nadeau (2012). The rectangles represent the imposed slip geometry due to the SSE at depth. The rest of the seismogenic zone is not modeled as no increases in slip rate were observed over the time frame of the transient. As the deep displacement due to creep is not observed geodetically, we do not have constraints on its magnitude. However, we have constraints on surface creep and the slip rates form repeating earthquakes. We assume that the 30 mm/yr slip rate observed in the creeping section continues through the seismogenic zone in the transition zone and does not vary, as shown by the repeating earthquakes. We choose an arbitrary amount of slip on the source dislocation of 1 meter to represent the slip caused by the increase in tremor. As we are specifically interested in changes in rates of seismicity and not generating new faults, we focus on the change in Coulomb stress and not the magnitude of the change. 37 38 Figure 16: Focal mechanisms for a subset of the events in Fig. 14 superimposed on the topography. The upper panel shows the focal mechanisms shaded to indicate the depth of each event. P and T axes are indicated by the black and white dots on each mechanism. The lower panel shows the locations of the focal mechanisms in the upper panel and are color-coded to indicate whether they are on the east or west side of the fault. The compressive poles (blue) and tensile poles (red) for focal mechanisms on the east side of the fault are summarized in the inset at the upper right. Compressive and tensile poles for events on the west side of the fault are summarized in the inset in the lower left. Note that mechanisms on the east have compressive poles that are consistent with the N15W orientation of the regional stress while the tensile poles are mostly vertical indicative of thrust faulting. Most mechanisms to the west also have compressive poles aligned with the regional stress field, but the tensile poles are close to horizontal indicating strike-slip faulting. A few compressive poles are vertical, which, together with the tensile orientations indicates normal faulting on plane that strike at a high angle to the SAF. c) Natural Constraints: Regional Stress, and topography In this model, coulomb failure stress accounts for both the increased likelihood of failure due to either an increase in the shear stress and a decrease in the normal stress. Regional stress is constant and affects only the orientation of the faults optimally oriented for failure, whereas the Coulomb stress change on a specified fault depends only on the fault geometry, the coefficient of friction, and slip on the source fault, but is independent of regional stress (King et al., 1994). We choose target faults orientations based on regional stress and topography. Structural geology indicates that the elevated topography on the northeast side of the SAF corresponds to several anticlines and thrust faults (Miller, 1998) oriented 90˚ from the maximum horizontal principal stress (s 1 ). This is also in agreement with the general trend of the focal mechanisms for events of M0.5-3 in the study area (Figure 16, focal mechanism data provided from R. Nadeau). All focal mechanisms have an oblique sense of slip with the P-axis oriented perpendicularly to the trend in seismicity. In addition, both of these observations are in agreement with the regional stress orientation estimates for the area. Townend and Zoback (2000) report s 1 is oriented about 70˚ from the strike of the SAF. 39 d) Results We observe the effects of slip generated by displacement on the deep extent of the fault as modeled by a dislocation in an elastic half space. The slip on the source fault generates elastic displacement. The slope of the progressive deepening of the source fault termination controls the angle of the increase patterns to the fault in both uplift and Coulomb stress changes. The displacement on the source fault generates a pattern of positive displacement to the northeast and negative displacement to the southwest. This pattern corresponds to the patterns in deep off-fault seismicity, where the linear trend the off-fault seismicity to the southeast of the SAF corresponds to the lobe of maximum vertical displacement and the negative vertical displacement corresponds to an area with nearly no signal in seismicity (Figure 17). In addition, this corresponds extremely well to the topography of the area. The northeast side of the fault anticlines and higher topography than the southwest side. (see Figure 18, data from USGS NED) The off-fault seismicity south of Slack Canyon occurs primarily on the east side of the fault and is associated with topographic uplift. This is the expected result where the deepening right lateral deep creep produces compression on the east side which enhances regional seismicity and tension on the west side which suppresses it. We test whether LFEs generated by slip on the deep extent of the fault can generate a positive Coulomb stress change corresponding to the spatial distribution of the observed seismicity transient. In addition to the topography being asymmetric about the fault, the focal mechanisms and the structural features suggest the northeast side of the fault generally is in a compressive reverse faulting environment to accommodate the vertical uplift as previously discussed (Figure 15 lower panel). The moment tensors calculated for the events on the linear trend correspond to compressive reverse faulting and oblique faulting mechanisms on the northeast side of the fault. In addition, off-fault seismicity is more sensitive to regional stress orientations than amplitude 40 variations (King et al., 1994). Given the assigned right-lateral slip at depth, we therefore choose to look at corresponding Coulomb stress changes on thrust faults oriented parallel to the observed compressive features. We find that slip on the deep extension of the fault is consistent with the linear feature (Figure 17) as both the patterns in the uplift and Coulomb stress changes match the strike of the linear trend in seismicity. Figure 17: Both panels represent results from 1 meter of right lateral slip at depth. The left panel shows vertical displacement in meters. The right panel shows the maximum change in Coulomb stress between 8 and 13 km depth on thrust faults with strike orthogonal to the regional stress field. Note the fault trace is offset 3 km from the x-axis zero (surface trace) since the LFE locations indicate that the deep fault is slightly offset (Shelly, 2015). 41 To test the validity of the results, we add regional stress to the model. We run the same model without assigning any a priori fault and define the regional stress orientation in accordance to the Zoback papers (SHmax@70˚ from SAF). We successfully replicate the general trend in faulting mechanisms observed by the moment tensors (Figure 18), where the southwest side displays predominantly strike-slip and normal faulting mechanisms whereas the northeast side displays oblique thrust faulting. This confirms our fault orientation choice from above, where the thrust pattern also matches the fault orientation assigned prior. Table 2: Summary of Temporal Fluctuations in Seismicity Before the 2004 Parkfield Earthquake. Times of Anomalously High Seismicity are Highlighted. Year 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 On-fault Shallow (events/yr) Figure 5 146 146 146 146 146 146 194 194 194 194 194 159 159 159 159 159 159 240 240 240 240 On-fault Deep (events/yr) Figure 5 32 32 32 32 32 32 32 80 80 80 32 32 32 32 32 32 32 32 32 32 32 Repeating Earthquakes (cm/yr) Figure 6 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 3.4 3.4 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 Off-fault Shallow (events/yr) Figure 9 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 Off-fault Deep (events/yr) Figure 9 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 20 20 20 20 20 NV Tremor (min/yr) Figure 10 -- -- -- -- -- -- -- -- -- -- 760 760 760 760 760 760 1830 1830 1830 1830 1830 42 Figure 18: Results for the maximum change in Coulomb stress between 8 to 13 km depth on optimally oriented normal, strike-slip and thrust faults respectively. The first two panels show that the southwest side of the fault is dominated by strike-slip and normal faulting whereas the northeast side of the fault only displays positive CFF for thrust faulting. This is consistent with the focal mechanisms and topography plotted in Figure 16. 43 Conclusion Temporal fluctuations in seismicity preceding the 2004 Parkfield earthquake are summarized in Table 2. Times of unusually high seismicity are highlighted. Two anomalous periods stand out: 1990 to 1994 and 2000 to 2004. The former triggered the only A-level alert at Parkfield but did not culminate in an earthquake. The latter did not trigger an alert but culminated in the 2004 M6.0 earthquake. The two anomalies are compared in Table 2. Both are characterized by increases in shallow on- fault seismicity, but the increase in deep on-fault seismicity observed during the 1990s anomaly did not occur before the 2004 earthquake. Likewise, a change in periods of repeating events (indicating a creep event in the seismogenic zone) observed in the period between 1993 and 1994 was not observed before the 2004 event. Conversely, the high rate of deep off-fault events observed before the 2004 earthquake was not observed during the 1990s. Unfortunately, the tremor record begins in 1994 but the lack of an increase in deep off-fault events implies that there was no anomalous deep creep on the fault plane during the 1990s anomaly. Hence, the primary difference between the two anomalous periods is that the first was a creep event in the seismogenic zone (as evidenced by the shortened period of the repeaters) with no evidence for deep creep, while the second was primarily a creep episode on the deep extension of the fault plane with no evidence of creep in the seismogenic zone (from the repeating earthquakes). Two plausible interpretations can explain this pattern: either a deep creep episode is a prerequisite for a Parkfield event or, the 1990s anomaly was a “failed earthquake” simply because the seismogenic layer was not “ready” for a big event. 44 Our observation that off-fault seismicity is sensitive to small stress perturbations associated with deep creep events may indicate that the brittle crust away from major faults is always critically stressed and near failure. Townend and Zoback (2000) discuss three independent lines of evidence that intraplate crust is in a state of failure equilibrium: (1) the occurrence of seismicity induced by either reservoir impoundment of fluid injection, (2) earthquakes triggered by other earthquakes, and (3) in situ stress measurements in deep wells and boreholes that find stress levels at the Coulomb threshold. On-fault seismicity, on the other hand, may not be as sensitive. The crust on and near major faults may display intermittent criticality moving in an out of the critical state between major events (Sammis and Smith, 1999; Sammis and Sornette, 2002). 45 Chapter 2 Relating seismicity to the velocity structure of the San Andreas Fault near Parkfield, California The central section of the San Andreas Fault (SAF) displays a range of seismic phenomena including normal earthquakes, low-frequency earthquakes (LFE), repeating micro-earthquakes (REQ), and aseismic creep. Although many lines of evidence suggest that LFEs are tied to the presence of fluids, their geologic setting is still poorly understood. Here, we map the seismic velocity structures associated with LFEs beneath the central SAF using surface wave tomography from ambient seismic noise in order to provide constraints on the physical conditions that control LFE occurrence. Fault perpendicular sections show that the SAF, as revealed by lateral contrasts in relative velocities, is contiguous to depths of 50 km and appears to be relatively localized at depths between about 15 to 30 km. This relative localization is consistent with the hypothesis that LFEs are shear-slip events on a deep extension of the SAF. We find that along strike variations in seismic behavior correspond to changes in the seismic structure, which support proposed connections between fluids and seismicity. LFEs occur within low velocity structures, suggesting that the presence of fluids, weaker minerals, or hydrous phase minerals may play an important role in the generation of slow-slip phenomena on the SAF. 46 1) Introduction: LFEs in both subduction zones and beneath the SAF are sensitive to tidal stress and have been attributed to conditions of near-lithostatic fluid pressures (Fagereng and Diener, 2011; Ide and Tanaka, 2014; Ozacar and Zandt, 2009; Shelly et al., 2006; Thomas et al., 2009). LFEs beneath the SAF are inferred to represent shear slip (Shelly et al., 2009), although no geodetic signal has been observed (Smith and Gomberg, 2009). Petrologic studies suggest that LFEs occur at pressures and temperatures that may coincide with metamorphic dehydration reactions that release fluids(Fagereng and Diener, 2011), which is consistent with both observed high vp/vs ratios (Ozacar and Zandt, 2009) and low electrical resistivity measurements (Becken et al., 2011). Frictional mechanisms have been proposed that invoke stick slip instabilities where the rupture speeds are slowed by the interaction with fluids causing slip-weakening behavior (Ikari et al., 2013) or are impeded by dilatant strengthening (Shelly, 2015). Correlations between seismic waves speeds and LFE locations can provide insight into (and constraints on) the physical mechanics that produce LFEs and REQs. Studies have suggested that LFE locations may be controlled by pressure and temperature conditions (Fagereng and Diener, 2011), anisotropic fabric (Audet, 2015) or contrasts in material strength at the Moho (Chen et al., 2012). For the SAF, LFE and REQ locations along strike also coincide with segments of surface creep which have been tentatively ascribed to the presence of talc, a mineral resulting from hydrothermal fluids interacting with serpentinite (Moore and Rymer, 2007). This has been taken as further evidence that LFEs may be closely related to a fluid supply in the central rapidly creeping section (Becken et al., 2011; Zeng et al., 2016). The presence of fluids may also explain REQs’ sensitivity to triggering by neighboring earthquakes (Chen et al., 2013). 47 Along strike variation in seismic phenomena in the central portion of the SAF defines three sub- sections (Figure 19). The creeping section to the north of SAFOD (Titus et al., 2006) hosts standard earthquakes and REQs (Turner et al., 2015). To the south, the Parkfield section is characterized by decreasing surface creep which transitions to the locked section near Cholame (Titus et al., 2006). The Parkfield section also hosts standard earthquakes, REQs, and LFEs (Shelly and Hardebeck, 2010) whereas the locked segment south of Cholame supports LFEs, but is characterized by a significant reduction in normal seismicity and REQs (Figure 19). REQs occur within the fault zone core at depths between 2 and 8 km (Nadeau and McEvilly, 2004; Turner et al., 2015) and are observed to be directly related to creep within the seismogenic zone and are not observed in the transition and locked portions of the SAF to the south of Parkfield. LFEs are observed along the southern 100 km of the creeping section and extend 50 km south of Parkfield beneath the locked portion of the SAF. The shallowest LFEs occur about 15 km beneath SAFOD and progressively deepen to the north and south, reaching depths of about 30 km (Shelly and Hardebeck, 2010). 2) Methods We map the regional shear wave velocity structure for central California using surface wave ambient noise tomography (ANT) and investigate its spatial relation to seismicity on and near the SAF. Although other local velocity models exist (Zeng et al., 2016) and ANT investigations of seismic structure have described the broad trends of the western United States (Lin et al., 2008; Shapiro et al., 2005), the aim of this study is to present a higher resolution model using the ANT for the central SAF region by supplementing the regional data set published in Porritt et al. (2011), with local network coverage. We derive a model of shear velocities in the crust and uppermost mantle from data recorded between 2003 and 2015 by the USArray, the Parkfield Hi-Resolution Seismic Network (HRSN), and other regional networks. 48 Figure 19: Map of the central portion of the SAF showing: local stations (black triangles), Northern California Earthquake Data Center Earthquakes (white dots), REQs (green dots)(Turner et al., 2015), LFEs (large magenta dots)(Shelly and Hardebeck, 2010). Fault traces are shown in red lines. Reference locations are marked with white stars. The SAF’s segments are labeled according to its surface creep rates (Titus et al., 2006) as the creeping segment, the Parkfield segment (Pkd Seg) and the Locked Segment. The top right inset shows location of map within California in the red box and the stations used. To outline the method, the ANT method approximates the Green’s function between stations by cross correlating seismic noise between station pairs. Rayleigh wave group and phase velocity maps are constructed from these cross correlations and then inverted to depth to build a three- dimensional model of shear wave velocity. The key advantage of this method is that it provides 49 resolution that is independent of local seismicity since we measure empirical Green’s functions between every available station pair. We are therefore able to resolve structures along strike of the SAF despite sparse station coverage in some areas. However, the depth resolution of the ANT model is based on Rayleigh waves’ period dependent sensitivity kernels and this causes the resolution to decrease with depth as the sensitivity kernel of each period broadens with increasing period. The total dataset used is composed of continuous vertical component data from a combination of the correlations from Porritt et al. (2011), between 1554 broadband stations from July 2007 through September 2010, supplemented with additional data from BK, BP, CI, PB networks (2004- 2015), which provide greater resolution along the SAF from Parkfield to SAFOD. For our model, we use data recorded at a total of 350 stations deployed across the western United States shown in Figure 19. The raw seismic waveform data is processed by applying the methods described in Bensen et al. (2007). The first steps are to remove the instrument response, remove the mean, remove the trend and then band-pass filter the raw data between 5 and 150 seconds and then cut the data to one day- long segments. We then apply time-domain normalization using the running mean normalization method and then apply a frequency domain whitening process to eliminate earthquake signals and instrumental irregularities that may obscure ambient noise (Bensen et al., 2007). Cross-correlations between station pairs are performed for each day of data and stacked over the available time periods. We then calculate symmetric cross-correlations by averaging the causal and acausal parts of the two-sided signal to obtain empirical Green’s functions for each inter-station pair (Bensen et al., 2007). Two examples of cross-correlations stacked over the available time periods, the corresponding symmetric cross correlation and dispersion curves are shown in Figure 20. 50 Figure 20: Example of cross correlations between station CVS-RAMR (a) and RAMR-KCC (b) and their corresponding symmetric stack (c-d). e-f show corresponding dispersion curves for group and phase velocity for the corresponding cross correlations shown above. From these empirical Green’s functions, we obtain group and phase dispersion measurements (example in Figure 20) using Frequency Time Analysis (Dziewonski et al., 1969) between periods of 8 to 35seconds in one-second increments. These measurements are quality controlled by requiring a minimum signal to noise ratio of 20 and an interstation path length of 1.5 wavelengths, as well as filtering the results to fall within minimum and maximum velocities of 1.2 km/s and 4.5 km/s. The final numbers of cross-correlations measured and used for each period are listed in Table 3. Rayleigh wave phase and group velocity maps are then calculated from the dispersion curves using a grid spacing of 0.25˚ at periods of 8 to 35 seconds in one-second increments according to the methods of Barmin et al., (2001). According to their parameterization, we set the damping parameter of 10, a smoothing penalty function of 500 and the radius of smoothing to about the -500 0 500 Time - s -20 -10 0 10 CVS - RAMR 0 100 200 300 400 500 Time - s -20 -10 0 10 0 10 20 30 40 Period - s 2.5 3 3.5 4 Velocity - km/s Group Velocity Phase Velocity -500 0 500 Time - s -20 -10 0 10 20 RAMR - KCC 0 100 200 300 400 500 Time - s -20 -10 0 10 5 10 15 20 25 30 35 Period - s 1.5 2 2.5 3 3.5 4 Velocity - km/s Group Velocity Phase Velocity a) c) e) Figure S1: Example of cross correlation between station CVS-RAMR (a) and RAMR-KCC (b) and their corresponding symmetric stack (c,d) . e) and f ) show corresponding dispersion curves for group and phase velocity for the corresponding cross correlations shown above. b) d) f) 51 wavelength of each respective period. Figure 21 and Figure 22, described in the Results section below, show respectively group and phase velocity maps for periods of 8s, 10s, 15s, 20s, 25s, 30s, and 35s. Table 3: Number of correlations measured per selected per period Period Group Phase 8 17766 17950 9 21895 22106 10 24287 24532 11 26140 26386 12 27709 27956 13 28896 29190 14 30021 30303 15 30852 31093 16 31359 31603 17 31575 31826 18 31754 32002 19 31765 32031 20 31717 31958 21 31375 31617 22 30902 31144 23 30268 30526 24 29544 29834 25 28686 28997 26 27641 27995 27 26571 26954 28 25465 25831 29 24262 24606 30 23072 23445 31 21722 22083 32 20651 21086 33 19659 20212 34 18585 19353 35 17431 18397 52 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 8s 10s 15s 20s 35s 30s 25s Figure 21: Group Velocity Maps. Rayleigh wave group velocity maps in km/s for periods of 8s, 10s, 15s, 20s, 25s, 30s and 35s. Stations are plotted in black triangles, reference locations are marked with white stars and fault traces are shown in red lines. 53 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 −122˚00' −121˚30' −121˚00' −120˚30' −120˚00' −119˚30' −119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 8s 10s 15s 20s 35s 30s 25s Figure 22: Phase Velocity Maps. Rayleigh wave phase velocity maps in km/s for periods of 8s, 10s, 15s, 20s, 25s, 30s and 35s. Stations are plotted in black triangles, reference locations are marked with white stars and fault traces are shown in red line 54 We extract one-dimensional velocity profiles curves on a 0.1x0.1 degree grid, from the two- dimensional phase and group velocity maps, which are then inverted for depth with the code surf96 (Herrmann, 2013) to obtain one-dimensional shear wave velocity profiles at each grid-point which are then combined to obtain a three-dimensional volume. This method uses a linearized inversion scheme over a 45-layer model of increasing thickness with depth where the shallowest 25 layers are 2 km thick, the next 10 layers are 5 km thick and the deepest 10 layers are 10 km thick. Our initial velocity model is the continental ak135 model. These shear wave velocity results are shown in the cross sections in the Results section. One of the main assets of this method is the density of coverage. Using noise cross-correlated between station pairs, we circumvent the limited ray-path coverage of earthquake source locations and increase our ray-path coverage to all possible interstation pairs. This ensures good ray-path density and azimuthal coverage (Figure 23a-f). Although non-uniform noise sources may result in asymmetric Green’s functions and the main noise source for our data are ocean weather systems and deep ocean storms from the Pacific (Porritt et al., 2011), we mitigate this by using the symmetric version of the correlations. This, in combination with stacking over up to 12 years of data both help to improve the signal to noise ratio. To assess the resolution of ANT data, Figure 24 shows a resolution estimated as a measure of the quality of these velocity maps. The resolution distance plotted here is defined in Barmin et al. (2001) as a measure of the minimum distance at which two delta functions can be resolved on tomographic maps. Additionally, we assess the quality of our resolution with checkerboard tests for phase velocity at the periods of 8 seconds, 15 seconds and 30 seconds (Figure 23g-i). We are able to recover our input grid of checkers with size 0.5˚ x 0.5˚, confirming the quality of coverage for the entirety of the SAF and inland continent. Resolution quality is lost to the west of the fault 55 on the Pacific plate within about ~50 km of the coast. This is due to our land-based station coverage. The best resolution is obtained, for all periods, near the HRSN stations, which provide higher resolution in the Parkfield and SAFOD region of the fault. Figure 23: Resolution tests for 8s, 15s and 30s periods. In (a-c) yellow lines represent ray paths between station pairs. For (d-f) each cell is colored by ray path density. (g-h) show checkerboard tests. The input checkers are 0.5˚ x 0.5˚ and correspond to a perturbation of ±10% relative to the mean of 5 km/s. Stations are plotted in black triangles, reference locations are marked with the white stars and fault traces are shown in the red lines. 56 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 −122˚00'−121˚30'−121˚00'−120˚30'−120˚00'−119˚30'−119˚00' 35˚00' 35˚30' 36˚00' 36˚30' 37˚00' SAFOD SAO Cholame Parkfield 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 8s 10s 15s 20s 35s 30s 25s Figure 24: Resolution maps of group speed maps in kilometers for periods of 8s, 10s, 15s, 20s, 25s, 30s and 35s for Rayleigh waves estimated with the resolution test described in Barmin et al. (2001). Warmer colors indicate better resolutions. 57 The depth resolution of the ANT model is based on Rayleigh waves’ period dependent sensitivity kernels. This causes the resolution to decrease with depth as the sensitivity kernel of each period broadens with increasing period (Figure 25). We assess the ability of our model to resolve a lower velocity structure in the middle and lower crust using a synthetic test shown in Figure 26. We invert synthetic data for cases with a lower velocity layer of thickness varying from 5 km, 10 km and 15 km thickness and cases varying in depth with a top boundary at 15 km, 20 km and 25 km depth. Although our model is unable to resolve the shallowest structures, it performs best in resolving a low velocity structure layer at least 10 km thick in the middle to lower crust which gives us confidence that our observed feature is resolvable within our ~10 km resolution. Figure 25: Sensitivity Kernels for Rayleigh wave group and phase velocity as a function of depths calculated for 8s,10s, 15s, 20s, 25s, 30s and 35s periods. -0.05 0 0.05 0.1 0.15 0.2 Normalized dU/db 0 5 10 15 20 25 30 35 40 45 50 Depth in km 8s 10s 15s 20s 25s 30s 35s -0.05 0 0.05 0.1 Normalized dc/db 0 5 10 15 20 25 30 35 40 45 50 Depth in km 8s 10s 15s 20s 25s 30s 35s Figure S5: Sensitivity Kernels: Group and phase velocity sensitivity kernels for Rayleigh waves to shear velocity with depth calculated for 8s, 10s, 15s, 20s, 25s, 30s and 35s periods. 58 Figure 26: Inversion to depth test for alternating layers of high and low velocity structure. The input models tested vary in the mid crustal low velocity structure depth and thickness, shown in red, and the recovered model are shown in blue. Tests use the same set of periods (8s-35s) and both group and phase velocity as in the three-dimension model inversion. 3) Results a) Phase and Group Velocity Maps Rayleigh wave group and phase velocity maps for 8s, 10s, 15s, 20s, 25s, 30s and 35s periods are shown in Figure 21 and Figure 22. Our 8s and 10s maps are generally consistent with the surface geology (Jennings, 2010) and other published velocity models for the region (Shapiro et al., 2005; Zeng et al., 2016). The 8s, 10s and 15s waves are more sensitive to shallow and mid-crustal 34 Vs km/s 0 10 20 30 40 50 depth [km] 34 Vs [km/s] 0 10 20 30 40 50 depth [km] 34 Vs [km/s] 0 10 20 30 40 50 depth [km] 34 Vs [km/s] 0 10 20 30 40 50 depth [km] 34 Vs [km/s] 0 10 20 30 40 50 depth [km] 34 Vs [km/s] 0 10 20 30 40 50 depth [km] 34 Vs [km/s] 0 10 20 30 40 50 depth [km] 34 Vs [km/s] 0 10 20 30 40 50 depth [km] 34 Vs [km/s] 0 10 20 30 40 50 depth [km] 34 Vs [km/s] 0 10 20 30 40 50 depth [km] Figure S6: Inversion to depth tests: Inversion to depth test for alternating layers of faster and lower velocity structure. The input models tested vary in the mid-crustal low velocity structure depth and thickness shown in red and the recovered models are in blue. Tests use the same set of periods (8-35 seconds) and both group and phase velocity as in the 3D model inversion. 59 structures. The most prominent feature of the 8s and 10s map are the large NW-SE trending low velocity body parallel to the SAF that coincides with the sedimentary basin of the Central Valley. A high velocity body coinciding with the Sierra Nevada Mountain range bounds this feature on the northeastern side. To the west of the SAF, near SAFOD, another region of higher velocities extends along the Pacific coast coincident with the Coast Ranges. At the 15s period, phase maps are most sensitive to mid-crustal features. The low velocity features observed at shorter periods are still present but less prominent. A striking low velocity body appears beneath the SAF from the San Andreas Geophysical Observatory (SAO) south to SAFOD. This is similar to the low velocity layer observed by Zeng et al. (2016) in their three-dimensional v p and vs model in which they suggest high v p/v s ratios are responsible. The 25s, 30s and 35s phase maps represent a broader section of the lower crust and uppermost mantle due to the broader sensitivity kernel of the 25s, 30s and 35s Rayleigh waves (Figure 25). The low velocity feature observed at 15s persists, but it is slightly smaller in its spatial extent. The 30s low velocity structure is strongest in two regions: just north of SAFOD and just south of SAO. At 30s, the low velocity basin to the east of the SAF, bottoms out and is dominated by faster velocity structures that are bounded by slightly lower velocities to the northeast. Refraction surveys taken across SAO, further north indicate a mafic basement beneath the Central Valley (Fuis and Mooney, 1990), which is consistent with our observations of a 10% higher phase velocity in this region. This may also be interpreted as the Great Valley ophiolite (Cox et al., 2016), which would under-plate the sedimentary basin. 60 b) Sections across the SAF In Figure 27, the SAF is localized to depths of 50 km. No major velocity structure crosses the SAF in any of the sections south of San Andreas Observatory (SAO) (Figure 27a). In the shallow crust, the strongest lateral velocity contrast is delineated by repeating events within the fault zone (Figure 27b). This section also displays a lateral velocity contrast in the lower crust. These lateral discontinuities support the hypothesis that a relatively shear zone is maintained at depth across the SAF. Although the resolution of ANT decreases with depth due to the properties of the Rayleigh wave sensitivity kernels (Figure 25), this velocity contrast between the east and west side of the fault observed in the upper and lower crust, weakens but persists along strike south of Cholame. These observations support models based on mantle xenolith fabrics from the deep SAF (Titus et al., 2007) as well as lithosphere-asthenosphere steps (Ford et al., 2014) suggesting the SAF extends through the lithosphere. The lateral discontinuity we observe in the lower crust (Figure 27b and d) coincides with the locations of the LFEs that occur on the interface, supporting the idea that the LFEs represent shear slip on the relatively localized fault root of the deep extent of the SAF (Shelly et al., 2009). LFEs plot on a downward projection of the crustal fault and they occur at the transition between a low velocity structure (about 3.25 km/s) belonging to the Pacific plate and a higher velocity structure of the North American plate (about 3.75 km/s). In the cross-section near Cholame (Figure 27d), the LFEs occur predominantly on the SAF interface on the edge of the lower relative velocity structure of the Pacific plate. Near SAFOD (Figure 27c), although the LFEs are still in the downward projection of the fault, they are located in a broader region of low velocity material. In contrast, no LFEs are observed to the north (Figure 27a), and this is highlighted by a more homogenous lower crust and uppermost mantle across the plate boundary beneath the SAF. This 61 suggests that the LFEs occur within the fault zone in an interface of contrasting material types and are associated with a low velocity structure. Figure 27: Shear Velocity Perpendicular to Strike. The top right map shows the locations of the cross- sections shown in Figure 27 and Figure 28. Panels a-d show cross-sections taken from across strike. Surface trace of the SAF is marked by the red inverted triangles. NCEDC Earthquakes (white dots), REQs (green dots)(Turner et al., 2015),LFEs (large magenta dots)(Shelly and Hardebeck, 2010), within 5 km of each section are projected onto the cross-section’s plane. 0 5 10 15 20 25 30 35 40 45 50 025 50 75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 km/s 0 5 10 15 20 25 30 35 40 45 50 25 50 75 100 3.25 3.5 3.75 4 4.25 4.5 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 km/s 0 5 10 15 20 25 30 35 40 45 50 0 25 50 75 100 125 2.5 2.75 3 3.25 3.5 3.75 3.75 4 4 4.25 4.5 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 km/s 0 5 10 15 20 25 30 35 40 45 50 025 50 75 100 125 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 km/s Depth (km) Depth (km) Depth (km) Depth (km) Distance (km) −122˚ −121˚ −120˚ −119˚ 35˚ 36˚ 37˚ a b d e f c a b c d SAF SAF SAF SAF SAF SAF SAF SAF 62 c) Sections parallel to the SAF The low velocity structure observed near SAFOD in the lower crust and uppermost mantle, highlighted by the dip in the 4.25 km/s contour line 35 km deep, beneath the SAF trace (Figure 27c), is consistent with the presence of fluids and weaker mineral phases and a deeper fluid source (Becken et al., 2011). This interpretation is consistent with observations of talc in the surface geology, which provides evidence for hydrothermal fluids interacting with serpentinite at depth (Moore and Rymer, 2007; Solum et al., 2006). The along strike extent of the low velocity structure in the lower crust and uppermost mantle, extending 50 km north of SAFOD along the SAF (Figure 28f) is similar in extent and coincides with the SAF’s section’s highest creep rate (Moore and Rymer, 2007; Titus et al., 2006). Becken et al. (2011) also support this interpretation showing a large anomalously low resistivity area with similar extent to the low velocity structure in the lower crust and uppermost mantle. This is also corroborated by Zeng et al. (2016) who a show a lower velocity zone at mid-crustal depths to the west of the SAF in the same region. Above this deeper low velocity structure, another low velocity structure extends horizontally along strike at depths from 15 to 25 km (Figure 27b-d). The low velocity structure, located west of the SAF, is strongest to the north of SAFOD (Figure 27b) and extends to the south (Figure 27d) and beyond Cholame. Near SAFOD, a low velocity structure at 15 to 25 km depth is present on both sides of the fault but is stronger on the east side of the fault, shown by a slight deepening of the 3.75 and 4 km/s contour lines across the fault (Figure 27c). Along strike, this low velocity structure gently dips to the north from SAFOD and to the south toward Cholame, following the 3.75 km/s contour on the west side of the fault, shown in Figure 28f. Near SAFOD, it is highlighted by the 3.75 km/s contour on the east side of the fault shown in Figure 28e, extending for about 50 km north of SAFOD between 20 km to 25 km depth. The LFEs are shallowest beneath SAFOD, which corresponds to the shallowest low velocity structure (Figure 28e). The LFEs deepen to the north 63 and to the south of that point, which follows the contours of the low velocity structures belonging to the west side of the fault (Figure 28f). Figure 28: Shear Velocity Parallel to Strike: Shear velocity from cross-sections e and f along strike of the SAF, as shown in the location map inset of Figure 27 where e) is a section through the North American Plate on the east side of the fault and f) the Pacific Plate on the west side of the SAF. Reference locations (white stars), REQs (green dots)(Turner et al., 2015),LFEs (large magenta dots)(Shelly and Hardebeck, 2010), within 5 km of each section are projected onto the cross-section’s plane. 3) Discussion and conclusions Our observations of a low velocity structure 15 to 25 km deep are consistent with regional velocity models (Zeng et al., 2016), local receiver function observations of a low velocity layer in the lower Salinian crust (Cox et al., 2016) near SAFOD, as well as high vP/vS ratios near Parkfield (Audet, 2015; Ozacar and Zandt, 2009). The uppermost mantle low velocity feature may be the deeper fluid source responsible for these lower velocity layers within the lower crust. In combination with a higher permeability in the lower Salinian crust relative to the lower crust across the fault (Becken Distance (km) Depth (km) Depth (km) 0 5 10 15 20 25 30 35 40 45 50 025 50 75 100 125 150 175 200 2.75 3 3.25 3.25 3.5 3.5 3.75 3.75 3.75 4 4 4.25 4.5 4.5 4.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 km/s f 0 5 10 15 20 25 30 35 40 45 50 025 50 75 100 125 150 175 200 2.25 2.5 2.75 2.75 3 3 3.25 3.25 3.5 3.5 3.75 3.75 4 4 4.25 4.25 4.5 4.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 km/s e SAFOD Parkfield Cholame SAFOD Parkfield Cholame 64 et al., 2011), this could explain both the along fault extent of the low velocity layer as well as the strong velocity contrast across the fault in the lower crust (Figure 27b). There is evidence that geologic structure controls the depth of LFEs along strike. Using receiver functions, Audet (2015) found that the LFEs are located within an anisotropic layer of weak minerals potentially related to serpentinization of the lower crust. Many authors have pointed out that LFE are located near Moho depths (Beroza and Ide, 2011), and Chen et al. (2012), argue that LFE locations may be related to the increase in strength at the Moho where the compositional contrast leads to a change from the more ductile lower crustal rock to the more brittle rheology of olivine rich uppermost mantle rocks. This interpretation is supported by observations that the crust thickens from 25 to 35 km along the Cholame segment (Fuis and Mooney, 1990; Levander and Miller, 2012) in concert with the increase in depth of the LFEs. Our findings support the interpretations that the LFEs are located within a low velocity layer distinctly above the Moho. Although the Moho deepens in the Cholame segment with a similar trend to the LFE locations, our along-strike cross-sections find that the low velocity layer shown by the dip in the 3.75 km/s contour in Figure 28f also deepens to the north and to the south away from SAFOD. Our observation that LFEs occur in relatively low velocity materials suggests that weaker minerals and/or high fluid pressures, and not an increase in strength at the Moho, are mechanistically important. Similarities can be found between LFEs and REQs as they correspond to families of events that rupture the same location repeatedly. Additionally, small low stress-drop repeating events, so much so that they are detected with similar methods (Nadeau and McEvilly, 2004; Shelly et al., 2009). REQs have been shown to be small asperities, which rupture repeatedly and occur within 65 the seismogenic crust driven by aseismic creep. They are thought to be either annular cracks loaded by creep on the surrounding fault plane (Nadeau and Johnson, 1998) or thought to represent weak patches at the edges of stronger fault asperities (Sammis and Rice, 2001), both of which are loaded by surrounding creep. We observe that REQs occur near the boundary between a shallow low velocity layer and a deeper higher velocity layer, as in Figure 28f. We also note that LFEs occur within the low velocity layer that underlies this same higher velocity structure. This observation raises the possibility that LFEs may also be related to creep within weaker layers, possibly weak patches at the edges of stronger fault asperities. The observation that LFEs are located in low velocity structures and are probably occurring in a material that is more prone to creeping behavior is consistent with several independent lines of evidence. By modeling spatial and temporal fluctuations of off-fault seismicity, Sammis et al. (2016) derived a fault creep model similar to that derived here from ANT in Figure 28. Additionally, we note similarities between our lower relative velocity structures and those found from InSAR and GPS inversions (Jolivet et al., 2015). Jolivet et al. (2015) show a sustained higher creep rate that generally matches the LFE locations that deepen to the south of Parkfield. In addition, the spatial correlation of the locked portion above the low velocity structure in the transition zone and the higher velocities was also observed by Thurber et al., 2006. Our higher relative velocity mid-crustal structures to the north and to the south of SAFOD correspond to areas that are geodetically inferred to be locked asperities or have lower creep rates. The southern-most REQs occur in a region of lower relative velocity structure, which in their study is also ascribed to creep. The similarity of the locations of our observed lower relative velocity structure near SAFOD, that deepens to the south in the Cholame segment and to the north of SAFOD, matches the locations of the LFEs, as well as inferred higher creep rates. This suggests a compositional or 66 rheological explanation due to the fluid source at depth for the LFE as well as the higher creeping rates in these sections. 67 Chapter 3 A Spring-Mass-Dashpot Model for Slow Earthquakes on a Viscous Fault A one-dimensional spring-mass-dashpot model is used to simulate the propagation of slow events in a viscous fault zone that is pinned by an array of asperities. The asperities fail at prescribed stress thresholds to produce low-frequency events and tremor. Slow slip propagation speed in this model is caused by a “waiting time” at each asperity, which is controlled mainly by the ratio of fault-zone viscosity to fault zone thickness and to a lesser extent by the range of asperity strengths. For physically reasonable values of wall-rock elasticity we can simulate observed propagation velocities of slow slip events (in the range of 5 to 15 km/day) using values of (viscosity)/(shear zone width) in the range of 10 #$ to 10 #% Pas/m and over a three order of magnitude range in threshold strengths. While the propagation of slow slip events reflects the bulk mechanical properties of the shear zone at depth, the more rapid propagation of low-frequency events and rapid tremor reversals during a slow slip event may require local heterogeneity and asperity weakening behind the main slip front. 68 Introduction Seismic and geodetic studies have recently found transient slip phenomena including non-volcanic tremor, slow slip events (SSE), low-frequency earthquakes (LFE). All occur in major fault zones at depths below the seismogenic zone where normally seismicity ends. Non-volcanic tremor is a continuous seismic signal that can last for hours or even weeks. It was first observed in Japan’s subduction zone (Obara, 2002). Although tremor is most commonly observed in subduction zones (Beroza and Ide, 2011), it has also been observed at depth on the downward projection of large transform faults. The first example of non-volcanic tremor on a strike-slip fault was observed on the creeping section of the SAF near Parkfield CA (Nadeau and Dolenc, 2005) and subsequently observed on the Alpine fault (Wech et al., 2012). Non-volcanic tremor is sensitive to small stress perturbations associated with solid earth tides and seismic waves from large earthquakes (Thomas et al., 2009). Non-volcanic tremor is composed of overlapping LFEs (Shelly et al., 2007). LFEs are small events (generally M<4) having seismic spectra that are depleted in high frequencies relative to comparable small earthquakes that occur above the brittle-ductile transition. Individual LFEs commonly occur as families of repeating events that tend to be preceded or followed by nearby sources. These interactions define migration speeds of about 25 to 150 km/h and in both directions along strike of the SAF (Shelly, 2015). Similar migration speeds are observed for up and down- dip migration of LFEs in subduction zones (Ghosh et al., 2009; Shelly et al., 2007). One possibility is that each LFE corresponds to a small brittle displacement on a stuck asperity. Ando et al. (2010) proposed a composite asperity to explain the unusual seismic spectra produced by LFEs. SSEs were first identified geodetically in subduction zones (Dragert et al., 2001; Hirose et al., 1999), and were subsequently observed to be correlated both in space and time with tremor (Obara, 69 2002; Rogers and Dragert, 2003) that propagates along strike at velocities on the order of 5 to 15 km/day. The combined observation of SSEs and tremor, known as episodic tremor and slip (ETS) (Rogers and Dragert, 2003) suggests that tremor is consistent with shear slip. Although SSEs have been inferred beneath the Parkfield segment of the San Andreas Fault (SAF) (Guilhem and Nadeau, 2012; Sammis et al., 2016), direct geodetic observations have been limited to subduction zones. Current observations of tremor, LFEs, and SSEs and their physical characteristics are summarized in Table 4. Note that the propagation speed of SSE and ETS events is more than an order of magnitude slower than the propagation speed of LFE and rapid tremor reversal (RTR) events. Table 4: Observations of Slow Slip Events and Low Frequency Earthquakes Event Type Duration Slip Slip Speed Propagation speed Selected References SSE 1 week 3cm 40mm/yr 5-15 km/day (Ohta et al., 2006) (Hirose and Obara, 2005) (Schmidt and Gao, 2010) ETS 1-3 weeks 2cm 1-2mm/day 7-12 km/day (Rogers and Dragert, 2003) (Wech and Bartlow, 2014) RTR 10 hours 3 mm 1.1 mm/h 3-40 km/h (Bletery et al., 2017) (Houston et al., 2011) LFE 0.2 seconds 0.05 mm 0.24mm/s 20-150 km/h (Shelly et al., 2007) (Thomas et al., 2016) Because slow-slip events load the shallower seismogenic part of the fault above, they could play a role in the timing of large earthquakes (Beroza and Ide, 2011; Peng and Gomberg, 2010), possibly providing useful precursors to pending events toward the end of a seismic cycle (Shelly, 2009; Uchida et al., 2016). To better assess their role in the seismic cycle, it is important to identify 70 the mechanisms. Since the propagation speed of SSEs and the migration speed of LFEs are orders of magnitude slower than either a shear rupture of friction-limited slip on a fault, a central question is what exactly slows the propagation. The question also arises as to whether LFEs are an active or passive component of slow slip propagation. Several proposed mechanisms for SSEs modify the rate and state friction model to achieve low slip velocities. Some models use friction laws with a velocity cutoff, where the interplay between velocity weakening and velocity strengthening slows the ruptures and prevents earthquake nucleation (see review by Beroza and Ide (2011) and Peng and Gomberg (2010)). Other models invoke fluid motion and pressure changes to slow propagation. Friction mechanisms have been proposed that invoke stick slip instabilities where the rupture speeds are slowed by the interaction with fluids either by slip-weakening behavior (Ikari et al., 2013) or through dilatant strengthening at the rupture tip (Segall et al., 2010; Shelly, 2015). These models are consistent with seismic observations of high vp/vs ratios (Audet et al., 2009; Matsubara et al., 2009) and tidal triggering (Hawthorne and Rubin, 2010; Thomas et al., 2009). In contrast explanations based on rate- and state-dependent friction, Hayman and Lavier (2014) suggest that the shear deformation which produces SSEs and LFEs may include distinct brittle and ductile components. Faults exhumed from depths below the seismogenic zone exhibit a mixture of brittle and ductile structures that have been attributed to slow slip and tremor (Behr et al., 2018; Fagereng and Diener, 2011). Simple mechanical models using a mixture of brittle and ductile sliding have been used to explain LFE repeat times on the SAF (Daub et al., 2011). 71 Ide (2010) proposed that tremor is produced by slow slip on a surface pinned by asperities. In this view, the LFEs that comprise the migrating tremor correspond to the progressive failure of the asperities. The question arises: what in this model controls the migration speed of the tremor? In this paper we use a simple one-dimensional spring-mass-dashpot model to simulate a ductile fault that is pinned by an array of asperities. We find that we can simulate the observed displacement and migration speed of both SSEs and LFEs using physically reasonable values of fault zone width, effective viscosity, asperity strength, asperity spacing, and wall rock elasticity. In addition to providing a mechanism to slow rupture speeds, asperity models also may provide a simple mechanism for LFEs. A one-dimensional asperity model for slow slip events We use a variant of the Burridge and Knopoff (1967) spring-block model shown in Fig. 1. Each member of an array of Nm blocks, indexed i=1 to i=Nm, has mass mi and is linked to its two nearest neighbors by coil springs with constant K2. An upper plate moves with constant velocity v0 driving the individual masses through leaf springs with constant K1. The motion of each free mass is resisted by a force proportional to its velocity represented by the dashpots, where c is the damping parameter. 72 Figure 29: Linear mass-spring-dashpot model used to simulate slow earthquakes. Note that the central mass is an asperity. It cannot move until the force from the springs exceeds a specified threshold strength & ' ( ∗. We assume that Na equally spaced asperities do not move during loading. Each asperity is has a threshold element that fails at a prescribed force * + , ∗. Once an asperity fails its threshold element is removed and subsequent motion is resisted by its viscous element. The spacing L between asperities is specified and sets the length scale of the problem. If there are Ns coil springs between each pair of asperities, then the total number of masses is - . = - 0 - 1 . For symmetry, Ns is chosen to be even. An event nucleates when the displacement of the upper plate reaches a slip d equal to the maximum slip on the fault plane consistent with geodetic observations. a) Equations of motion Let a be the spacing between the masses. Let 2 , 3 be the displacement of the i th mass at the j th time step following nucleation. Let d be the displacement of the driving plate at nucleation. Since a slip- event propagates much faster than the loading velocity v0, the driving plate is held stationary during an event and d remains constant. The force on the i th mass at the j th time step is (positive to the right). * , 3 = 4 5 67 89: ; <7 8 ; = > +4 5 67 8@: ; <7 8 ; = > + A : B C DE<7 8 ; F G − I B C 2̇ , 3 (1) F i* $ 73 Note that the displacements are expressed as strains so the spring constants have units of force. The strain associated with each leaf spring is assumed to extend to a fault-normal distance H, which, guided by St. Venant’s principal, is taken to be larger than the distance L between fixed asperities. Also, the leaf-spring constant K1 acting on each mass is scaled by the number of masses Ns per unit length L, as is the damping constant c, thus assuring that the displacements between stuck asperities are independent of the choice of Ns. Writing equation (1) in terms of accelerations and using finite differences centered on time j, equation (1) can be written 67 8 ;9: <57 8 ; K7 8 ;@: = L M = A M .> N2 ,K# 3 −22 , 3 +2 ,<# 3 P+ A : B C .G QR−2 , 3 S− I B C . 67 8 ;9: <7 8 ;@: = 5L (2) where t is the time-step. Equation (2) can be solved for the displacements at time step j+1 in terms of those at earlier time steps j and j-1. 2 , 3K# = 61+ IL 5B C . = <# D L M .> 4 5 N2 ,K# 3 −22 , 3 +2 ,<# 3 P+ L M B C .G 4 # QR−2 , 3 S+6 IL 5B C . −1=2 , 3<# +22 , 3 F (3) Boundary conditions at the ends of the array are ignored since events are nucleated at the central asperity and calculations are stopped before the asperities fail at the ends of the chain. b) Initial conditions A subset of initially stuck masses (asperities) are identified by subscripts i*. These masses T , ∗ do not move during loading and hence accumulate a monotonically increasing slip deficit d. Rather than specify the strength of the weakest asperity (which we don’t know), we specify the maximum slip that occurs during a slow-slip event, d*, which we know from seismic and geodetic measurements (Dragert et al., 2001; Hirose and Obara, 2005; Schmidt and Gao, 2010). The initial displacements can be found using the equations of motion equation (1). Since the viscous force and acceleration can be ignored during tectonic loading, the system is in static equilibrium at nucleation described by the equations 74 * , U V ,, ∗ = 4 5 N2 ,K# 3 −22 , 3 +2 ,<# 3 P W + 1 - 1 4 # QR−2 , 3 S X (4) where V ,, ∗ is the Kroniker delta and * , ∗ U is the force on an asperity that opposes the net forces of the attached springs such that 2 , ∗ U = 0. We find the initial displacements and * , ∗ U by focusing on a subset of (- 1 −1 ) masses between any two asperities. We index members of this subset n, where 1 ≤] ≤ (- 1 −1). For ^ ≠ ^ ∗ the net force on a mass at nucleation is zero and equation (4) becomes 0= - ` 4 5 4 # X W N2 ,K# U −22 , U +2 ,<# U P+QR−2 , U S (5) Equation (5) can be put in matrix form 4 a 2 U bbbb⃑ = −R ⃑ and solved for the initial displacements 2 d U of the free masses. Once the 2 d U have been determined, * , ∗ U can be found as the net force on any asperity in the initial state using equation (4). * , ∗ U = 24 5 W 2 , ∗ K# U + 4 # - 1 X R (6) The value of * , ∗ U is the strength of the asperity that will nucleate an event with the specified maximum displacement d. We denote the strength of the nucleating asperity as * + , e ∗ = * , ∗ U and place it in the center of the array. We make all the other asperities slightly stronger by specifying ∆g + 8 ∗ g + 8 e ∗ = g + 8 ∗<g + 8 e ∗ g + 8 e ∗ . The relative strength of the other asperities will be discussed in the next section. Figure 30 shows the displacements of the masses at the onset of an event. 75 Model Parameters a) Elastic Parameters For a standard linear mass-spring chain the force is h 5 2 and the compressional wave speed is i j = Wk l M . , where a is the distance between masses. However, we defined force in terms of strain as 4 5 7 > in eqn. (1), so h 5 = 4 5 /W and the compressional wave speed in our system is i j = k A M (. />) . , where m/a is the linear density of the chain. We take the shear wave velocity to be i ` = k A : (. />) . If Poisson’s ratio is n = #/% (typical of most rock), then i j = √3i ` and A M A : = q r M q s M = 3. b) Anelastic Parameter The equation of motion for a single spring-mass-dashpot is Tẗ = −h 5 t−vṫ . The natural frequency is w U = k l M . and the damping parameter is defined as x = I 5y. l M . No oscillations occur at or above critical damping when x ≥1. Again, because we defined K2 as a force in equation (1), the natural frequency is w U = k A M >. and the damping parameter is x = I 5y(. />)A M . Although our system also includes leaf springs, we use this simpler definition of the damping parameter to write v T = 2y(T/W)4 5 T x = x 2 W | 4 5 (T/W) = 2i j W x (7) and limit our calculation to x ≫1. In order to relate viscosity in the shear zone to ζ, consider the case of steady state motion with velocity v0 in a system with no asperities. The net force on any mass is zero. The forces associated with the coil springs on any mass cancel, and the equilibrium equation for any mass becomes 76 * , = v2 ~ ̇ (8) Since the forces from the coil springs cancel, Fi is the net force supplied by the leaf springs. Equation (8) may be written * , = vℎÄ 2 ~ ̇ ℎ Å= vℎÇ̇= 2y(T/W)4 5 xℎÇ̇= 2 T , W | 4 5 (T/W) xℎÇ̇= 2 T , W i j xℎÇ̇ (9) where h is the thickness of the shear zone. Since viscosity h is defined by the equation É = 2ÑÇ̇, we write equation (9) in the form * , Ö = 2T , i j WÖ xℎÇ̇ (10) and identify Ñ = 2Üi j xℎ (11) where Ö = W 5 and the density is Ü= . 8 > á . Hence, one of the physical parameters in our model is the ratio of viscosity to fault zone width Ñ ℎ = 2Üi j x (12) c) Asperity strength We picture an asperity as a brittle circular patch that is loaded on its circumference by slip on the adjacent fault plane. This structure is known as an annular crack or interior crack and has been used by Johnson and Nadeau (2002) to model repeating earthquakes at Parkfield, CA. In their model, each repeating source is represented as a cluster of smaller, closely spaced, interacting annular cracks. This configuration produces the weak dependence of repeat time T on moment M0, (à = â U # ä ⁄ ) which was observed by Nadeau and Johnson (1998). Ando et al. (2010) also used this cluster model to simulate the unusual scaling between moment and duration for LFEs and their unusual seismic spectra. For both repeating earthquakes and LFEs the composite asperity model 77 yields a weak dependence of displacement on rupture area since the failure strength is determined by the size of the smaller asperities at the edge of the cluster, which is only weakly dependent on the area of the cluster. These results suggest that we might expect a narrow range of asperity strengths in our model. d) Time step A slip event begins when the weakest asperity fails. The time step must be short enough that the compressional wave velocity times the time step is less than the spacing between masses, åk A M (. />) <W or, å< k .> A M . This may be written å = é k .> A M , where b<1. e) Equations of motion in terms of model parameters The equation of motion (4) can now be written in terms of the time-step parameter b and damping parameter x as 2 , 3K# = Ä1+ xé - 1 Å <# èé 5 N2 ,K# 3 −22 , 3 +2 ,<# 3 P+ é 5 W 3- 1 X QR−2 , 3 S+Ä xé - 1 −1Å2 , 3<# +22 , 3 ê (13) where we have used A M A : = 3, å = ë> q r , L M .> 4 5 = é 5 , L M B C .G 4 # = ë M > $B C G , and IL 5B C . = íë B C . f) Relative strength of nucleating asperity One model parameter is the difference in strength between the nucleating asperity and all the others. The weakest asperity is located at the center of the array and is given the scaled strength * , e ∗ U from eqn. (10), which assures that it will fail when the remote strain reaches the prescribed value d/H. The strength of all other asperities is increased by ∆* , ∗ = * , ∗ −* , e ∗ U . The choice of ∆* , ∗ is one factor that determines the speed of propagation of an event. A larger ∆* , ∗ results in slower propagation. If ∆* , ∗ is too large the event will not propagate. 78 We check at each time step to see if the next unbroken asperity has failed by calculating ∆* , ∗ 3K# = * , ∗ 3K# −* , ∗ U . Note that the next asperity to break remains fixed until the time it breaks. The only increase in force on an asperity leading up to its failure is due to a change in length of the coil spring in the direction from which the rupture is propagating. For the next asperity to break on the left, ∆* , ∗ 3K# = A M > N2 , ∗ K# 3K# −2 , ∗ K# U P. For the next asperity to break on the right, ∆* , ∗ 3K# = A M > N2 , ∗ <# 3K# −2 , ∗ <# U P. We specify the variation in asperity strength by the ratio ì ∆* , ∗ 3K# * , ∗ U ì= 3N2 , ∗ K# 3K# −2 , ∗ K# U P 62 , ∗ K# U + WR - 1 X (14) Figure 30 shows the evolution of the displacement field following nucleation for the choice of parameters given in the caption. All asperities except the nucleation site are fixed. In Figure 31 the scaled increase in force on an asperity next to the nucleation site is shown as a function of time for three values of the damping parameter z. Since the wait time is defined as the time it takes for the force on an asperity to reach a given threshold ∆*/* U , increases in z will increase the wait time at each asperity. 79 Figure 30: Time evolution of the scaled displacement following the failure of the nucleating asperity. All other asperities are fixed. The initial condition is shown for ï ̂=0. The dimensionless time ï ̂ = - ó å(i j /ò), (after N t time steps) is indicated for each curve. The parameters in this calculation were: L=1 km., d=3cm., v P=6 km/s, r=2900 kg/m 3 , N a=4, N s=100, ß=0.1, K 2/K 1= 3, z=10 5 . These parameters produce a propagation speed of 0.62 km/h, in the range of typical of SSEs propagation. Figure 31: Scaled force increase as a function of dimensionless time at the fixed asperities adjacent to the nucleating asperity shown in Figure 30 for a range of damping constants z. Note that slip events do not propagate for ∆g g ô >0.44 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Scaled Position x/L 0 1 2 3 4 5 Scaled Displacement u/L 10 -6 t=36000 t=18000 t=9000 t=1800 t=288000 t= 576000 t=144000 t=72000 t=0 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Dimensionless time t 10 5 0 0.1 0.2 0.3 0.4 0.5 Strength Ratio F/F 0 ˆ =10 3 =10 4 =10 5 80 g) Actual speed of a slow slip event In order to find the actual speed of a slow slip event we need to revert to dimensional variables. If a slip event takes - ó time steps to travel the distance L between nodes, then its propagation speed is i = ò - ó å = ò - ó éW/i j = Ä - 1 - ó é Åi j (15) Figure 32a shows the displacement at each node as a function of time while Figure 32b shows the speed of propagation of the disturbance as it spreads along the chain in both directions from the central point of nucleation. Figure 32: Panel (a) shows the displacements on the chain as a function of position plotted at the time each 10 th asperity breaks. Panel (b) shows the propagation speed of the rupture as a function of position along the chain. Note that the speed reaches a constant value after about 4 asperities have failed. Parameters are z= 10 5 , ∆F/F o=0.1. -50 -40 -30 -20 -10 0 10 20 30 40 50 Scaled Position x/L 0 0.5 1 1.5 2 2.5 3 Scaled Displacement u/L 10 -5 -50 -40 -30 -20 -10 0 10 20 30 40 50 Scaled Position x/L 0.57 0.58 0.59 0.6 0.61 0.62 0.63 Propagation speed [km/h] t=4 days t=8 days t=12 days t=16 days t=20 days t=0 days 81 Results a) Dependence of propagation speed on the ratio of asperity strengths and the damping parameter The central question is whether our model can produce slow slip events having a maximum slip on the order of 3 cm and a migration speed of 5 to 15 km/day using physically reasonable values of the model parameters. The P wave velocity, Poisson’s ratio, and density are fixed at typical mid- crustal values: vP = 6 km/s, n=1/4, and r=2900 kg/m 3 . Since the rupture speed does not depend on L or d (see AppendixA), the remaining parameters are the ratio of the viscosity to shear-zone width h/h, and the range of asperity strengths ∆*/* U . Our goal is to see what range of these parameters produce slow slip events with speeds in the observed range. We begin with a first guess model choosing d = 3cm consistent with observations of slow slip events and arbitrarily choosing L = 1km. Figure 33 shows the dependence of the propagation speed on the asperity strength ratio and damping parameter and illustrates the trade-off between viscosity and asperity strength at constant propagation speed. A larger asperity strength ratio corresponds to a larger difference between the strength of the nucleating asperity and all other asperities. As the asperity strength ratio increases, the other asperities are further from their failure strength when the event initiates, and it therefore, it takes longer for non-nucleating asperities to reach failure. The waiting time at each asperity is longer and the propagation is slower. As was noted in Figure 31, if ∆g g ô >0.44 the other asperities never reach failure and there is no propagation following nucleation. 82 The propagation speed depends most strongly on the damping parameter. As indicate in Figure 33 and highlighted in Figure 34, propagation speed is inversely proportional to the damping parameter. Since the wait time is defined as the time it takes for the force on an asperity to reach a given threshold, increases in z will proportionally increase the wait time and decrease the propagation speed. Figure 33: Contours of constant propagation speed (in km/h) as a function of the damping parameter and asperity strength ratio ∆F/F 0. The right y-axis shows values of viscosity/shear zone width (in Pas/m) corresponding to values of z on the left y-axis. -4 -3 -2 -1 10 10 0 1 2 5 10 25 50 100 200 0.1 km/h 0.2 0.5 SSE SSE 5 5 5 5 50 0 1 10 0 00 0 2 0 00 0 5 5 1 1 1 5 50 0 5 2 5 2 5 5 50 0 5 5 2 25 5 5 50 0 0 2 2 5 200 25 500 LFE LFE 10 2 10 3 10 4 10 5 10 4 10 10 10 10 10 11 10 12 10 13 10 14 Viscosity / shearzone width /h [Pas/m] Damping Parameter Asperity Strength Ratio F/F 83 Figure 34: Propagation speed as a function of h/h for different asperity strength ratios. For a given viscosity, smaller ∆F/F 0 result in shorter waiting times and faster propagation velocities. Figure 35: Viscosity as a function of fault zone width at for h/h values giving propagation speeds of SSEs and LFEs. Geologic observations provide constraints on ranges of shear zone widths(Fagereng et al., 2014; Fusseis et al., 2006; Hayman and Lavier, 2014). 10 10 10 11 10 12 10 13 10 14 /h 10 -2 10 -1 10 0 10 1 10 2 10 3 Propagation Velocity [km/h] F/Fo=0.0001 F/Fo=0.001 F/Fo=0.01 F/Fo=0.1 SSE SSE LFE LFE Viscosity / Shear Zone Width 10 0 10 1 10 2 10 3 10 4 Shear Zone Width h[m] 10 10 10 11 10 12 10 13 10 14 10 15 10 16 10 17 10 18 Viscosity [Pas] LFE LFE SSE SSE Platt et al. (in press) Hayman & Lavier, 2014 Fusseis et al., 2006 Fagereng et al., 2014 84 Figure 34 shows an inverse relationship between propagation speed and h/h. Note that h/h is between 5t10 #5 and 5t10 #$ Pas/m for velocities in the range of slow slip events (5 to 15km/day) and for a large range of strength ratios (0.001<∆*/* U < 0.48). For velocities typical of LFE and tremor migration (25 to 150 km/h), h/h is between 2t10 #U and 5t10 ## Pas/m. Figure 35 shows the trade-off between viscosity and shear zone width for the allowable h/h. The h/h parameters for an SSE are consistent with most estimates of both viscosities and shear zone widths in the literature. Strain localization in the ductile portion of the fault is still an area of active research, (Bürgmann and Dresen, 2008) and there is a wide range of estimates of both viscosity and shear zone width for ductile fault roots. Estimates of viscosity, stress and strain-rate are related and often require assumptions of shear zone width. Estimates from post seismic relaxation suggest effective viscosity is in the range of 10 18 to 10 19 Pas, but geodetic inversions have difficulty distinguishing between distributed deformation and localized deformation in a shear zone (Bürgmann and Dresen, 2008). In strike-slip settings, localized faults at depth are inferred from velocity structure discontinuities to be on the order of several km (Ford et al., 2014). Ductile fault zone widths between 1 and 5 km are consistent with thermomechanical models (Takeuchi and Fialko, 2012). Hearn and Thatcher (2015) assumed a weak fault in the lower crust and found h/h = 10 15 Pas/m is consistent post-seismic deformation. Note that this is still at least an order of magnitude larger than our estimate. Subduction zone interfaces widths are observed to be on the order of kilometers wide at tremor depths based on examples of exhumed faults (Fagereng, 2011; Hayman and Lavier, 2014), seismology (Eberhart-Phillips and Reyners, 1999) and numerical modeling (Zheng et al., 2016). 85 Assuming a constant stress, lower viscosities imply narrower shear zones. Narrow shear zones have been proposed in the middle crust for normal faults (Platt and Behr, 2011) and near the brittle- ductile transition (Fusseis et al., 2006). Localized ductile fault zones have been proposed beneath mature faults due to weakening attributed to mylonitic shear zone development at lower crustal depths (Montési, 2013) or locally interconnected weak phases such as phylosilicates (Fagereng et al., 2014). If the weak phases are responsible for the deformation, this could significantly lower the effective viscosity of shear zones and depending on rock types and rheologies, correspond to viscosities ~10 11 to 10 15 Pas as suggested by Lavier et al. (2013) and localized deformation observed geologically (Fagereng et al., 2014; Hayman and Lavier, 2014; Hearn and Thatcher, 2015). Fluids inferred to be present at LFE locations in subduction zones due to observations of high vP/vS (Audet et al., 2009) and from low resistivities in the SAF creeping section (Becken et al., 2011) would further weaken the ductile deforming materials (Karato, 2012). Our ranges of parameters for SSE are consistent with most observations of both viscosities and shear zone widths suggested by the literature although does not constrain the ranges of viscosities required. b) Individual LFEs To provide an additional constraint we investigate whether our estimates of h/h could generate seismic radiation. The failure of each asperity may represent a simplistic LFE source. Figure 36 shows the slip speed and cumulative displacement of an asperity as a function of time, following failure. The motion can be separated into two distinct phases: an initial high velocity with a peak speed and an extended low speed slip that decreases monotonically with time. The slip speeds and cumulative displacements are a function of asperity strength ratio ∆F/Fo, damping parameter z, as well as the asperity size, which we take to be a. Although this is only a simple one-dimensional 86 model we explore the range of parameters that produce slip velocities and displacements that are consistent with observed for seismic events. Figure 36: Velocity and cumulative displacement of an asperity as a function of time following failure. Note that failure is followed by a seismogenic event with velocity of 1 mm/s and displacement of about 0.05 mm followed by slow creep to the total displacement of 1 cm. For this calculation z = 1000, L=1000, ∆F/Fo=0.1 a=10 m. Figure 36 shows an example of an LFE that would radiate seismically using a h/h value consistent with LFE migration speeds. Daub et al. (2011) estimate that the slip speed on an LFE on the SAF must be above 0.1 mm/s if it is to generate seismic radiation. This is shown by the horizontal line in Figure 36 and is consistent with 0.24 mm/s estimated for LFEs observed by Thomas et al. (2016). The duration of the LFE in Figure 36 is taken as the time interval during which the velocity is above 0.1 mm/s which, in this case, is about 0.29 seconds. The cumulative displacement accrued during the seismic portion of the rupture is about 0.055 mm, which is comparable to slip estimates by Daub et al. (2011) and Thomas et al. (2016). However, this slip represents only 0.6% of the 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] 0 0.5 1 Slip Velocity [mm/s] 0 0.05 Displacement [mm] Cumulative Displacement Slip Velocity 0.1mm/s 0.1 Seismic Aseismic 87 maximum slip in an event and the rest is then accommodated by ductile creep in the purely viscous model. This model assumes that an asperity can fail only once and that the subsequent deformation is controlled by fault-zone viscosity. However, LFEs have been observed to repeat (Shelly et al., 2007) which implies that the asperities heal. A more plausible explanation is that the LFE is caused by frictional slip on an asperity that is loaded by viscous creep. Frictional failure could explain the repeating nature and healing of the asperities which, driven by the ductile deformation rupture multiple times. One possibility is that asperities fail by frictional slip where the strength falls from its static to its dynamic value upon rupture and then returns to the larger static value when slip is arrested. As long as the slip per event is less than the size of an asperity, asperities will persist. The small slip estimated for individual LFEs (less than one mm) suggest this is true. Figure 37 shows the peak slip velocity as a function of the anelastic parameter h/h and patch size a. Increasing patch size decreases the acceleration at the asperity due to inertial effects. Note that there is no seismic radiation when z > 10 4 or using (12) this corresponds to û ü = 3.5 t 10 ## Pas/m as plotted in Figure 37. These h/h values are consistent with LFE propagation velocities but at least two orders of magnitude less than the value of h/h required to produce the propagation velocities observed in slow slip events (see Figure 33). 88 Figure 37: Maximum slip velocity as a function of the anelastic parameter h/h and for asperity sizes of 20, 50 and 100m. Events would not radiate for h/h>10 11 . For the ranges of h/h which correspond to SSE propagation velocities, the asperities that limit the propagation do not radiate seismically. In contrast, ranges of h/h corresponding to LFE up and down-dip propagation velocities, can radiate seismically. LFE limiting propagation velocities for faster migration is consistent with fast propagation velocities as seen in Shelly 2015 however they do require very low viscosities. In our model, LFE migrations may be indicative of local heterogeneity in viscosities, potentially due to structural effects. These local heterogeneities could include dip parallel structure in the slab related to the subduction process (Ghosh et al., 2010; Ide, 2010) or local differences in permeability (Shelly, 2015). 10 9 10 10 10 11 10 12 /h (Pas/m) 10 -5 10 -4 10 -3 10 -2 Slip Velocity (m/s) =20m =50m =100m Thomas et al. 2016 Daub et al. 2011 89 Discussion and Conclusions The simple spring slider-block model developed here was able to generate events that propagate at speeds matching along-strike slow slip events (5 to 15 km/day) with geologically reasonable values of h/h (5t10 #5 to 5t10 #$ †°¢/T). However, the failure of an asperity under these conditions does not radiate seismic energy. Such along strike pinning asperities do not correspond to individual LFE sources, but maybe more consistent with structural or geometric pinning points like kinks and jogs which would pin SSE propagation. Tremor associated with SSE propagation would in that case be related to processes behind the slip front itself. In fact, there are observations that slow slip can occur without tremor (Wech and Bartlow, 2014). If LFEs sources are responsible for slowing the SSE propagation, another possibility is that the failure of an asperity is due to slip-weakening. In this model the asperities do not have a viscous element. Resistance drops from a static threshold value to a lower dynamic value over a slip distance Dc. When sliding stops resistance rises again to the static value. Because asperities lack a viscous element, their velocity and displacement may produce seismic radiation. The viscous elements on all the masses between asperities will again produce slow propagation. Repeated frictional failure can also produce repeating events as observed. LFE propagation and radiation can be explained without invoking friction at the asperities. Observed propagation speeds in the range 20 to150 km/h and seismic slip velocities >0.1 mm/s can both be produced by an asperity that fails at a threshold stress but retains its viscous resistance. LFEs propagate at speeds that are more than an order of magnitude faster than those of SSE. In our model, this means that the fault zone viscosity for an LFE is lower or the fault zone is thinner or both. If LFE migration occurs during an SSE, then LFE migration must represent local 90 heterogeneity. In subduction zones the slower SSEs propagate along strike while streaks of the LFEs tend to propagate up and down-dip at a faster speed in the direction of plate motion (Ide, 2010). These events may either correspond to differences in material properties in the up and down-dip directions such as local heterogeneity in rheology or a different process than the along strike propagation such as changes in fluid pressure (Ghosh et al., 2010), or changes in strength such as weakening behind the slip front (Houston et al., 2011). It has been suggested that such streaks are a geometrical effect of a non-vertical SSE slip front (Ando et al., 2010), but the observation of comparable migration speeds of LFEs on the SAF at Parkfield suggest differences on the fault plane. While the one-dimensional spring-block asperity model is useful in exploring the propagation speed of slow events, it cannot explain several important observations including repeating events, reverse propagation, the quasiperiodic occurrence of large SSE events, and scaling laws for the seismic moment. The fact that two different viscosities and/or fault zone widths may be needed to explain both SSE and LFE migration speeds is indicative of these limitations. In addition, a one- dimensional chain can only consider propagation in one direction whereas SSE and tremor propagation is much more complex along the two-dimensional interface of a subduction zone. It has been shown that a two-dimensional Burridge-Knopoff model can be formulated as a cellular automaton. Such a two-dimensional extension of our model may be required to explain fast LFE propagation velocities up and down-dip as well as observations of rapid tremor reversals (Houston et al., 2011) and multiple fast propagation velocities (Bletery et al., 2017; Ghosh et al., 2010). 91 Appendix A: Figure 38: Dependence of propagation speed on asperity spacing The steady-state propagation speed is independent of the asperity spacing. This is because we specify the total displacement in an event. As the asperity spacing increases their density decreases and each takes a larger share of the load. This increase in load compensates for the larger distance to the nearest unbroken asperity. 10 3 10 4 10 5 L in m 10 0 10 1 10 2 10 3 Propagation Velocity km/h =1e2 =1e3 =1e4 92 Figure 39: Dependence of propagation speed on maximum slip in an event The propagation speed is independent of the slip for a given dimensionless value of the asperity strength ∆F/F0. This is because F0 is set by the given maximum slip. A larger maximum slip corresponds to a larger F0 and hence a larger ∆F. The effect is that the propagation speed is independent of the displacement for a fixed value of ∆F/F0. 10 -2 10 -1 10 0 10 1 d in cm 10 0 10 1 10 2 10 3 Propagation Velocity km/h =1e2 =1e3 =1e4 93 Conclusions In conclusion, although there is no geodetic observation of slip associated with tremor at the SAF, Coulomb stress models reveal that the spatial distribution of LFEs and off fault seismicity are both consistent with a right lateral slip at depth. Stress orientations in the Coulomb model are also consistent with surface topography and observed focal mechanisms for off-fault seismicity. This deepening pattern of the LFEs and geometry of the Coulomb stress model are consistent with the deepening trend of a low-velocity structure observed using ambient noise tomography which matches the locations of inferred higher creep rates. In combination with independent observations of high vP/vS, anisotropic fabric and low resistivity, the extent of the low velocity structure suggests a compositional or rheological explanation for the LFE as well as the higher creeping rates in these sections. SSE propagation slip speeds can be simulated using a simple one-dimensional spring-mass dashpot model with geologically reasonable parameters of (viscosity)/(shear zone width). These along- strike pinning asperities do not correspond to individual LFE sources as the asperities do not radiate seismically for model parameters producing SSE propagation speeds. Asperities slowing along strike SSE propagation may be more consistent with structural or material contrasts or geometric pinning points. The faster LFE propagation speeds require a much lower viscosity with this model. A two-dimensional model may be required to jointly explain both fast LFE propagation speeds up and down-dip in subduction zones and slow along strike slow slip propagation, as well as observations such as rapid tremor reversals and multiple fast propagation speeds. 94 References Ando, R., Nakata, R., and Hori, T., 2010, A slip pulse model with fault heterogeneity for low-frequency earthquakes and tremor along plate interfaces: Geophysical Research Letters, v. 37, no. 10. Atwater, T., 1970, Implications of plate tectonics for the Cenozoic tectonic evolution of western North America: Geological Society of America Bulletin, v. 81, no. 12, p. 3513-3536. Audet, P., 2015, Layered crustal anisotropy around the San Andreas fault near Parkfield, California: Journal of Geophysical Research: Solid Earth, v. 120, no. 5, p. 3527-3543. Audet, P., Bostock, M. G., Christensen, N. I., and Peacock, S. M., 2009, Seismic evidence for overpressured subducted oceanic crust and megathrust fault sealing: Nature, v. 457, no. 7225, p. 76. Bakun, W. H., and McEvilly, T. V., 1984, Recurrence models and Parkfield, California, earthquakes: Journal of Geophysical Research: Solid Earth, v. 89, no. B5, p. 3051-3058. Barmin, M., Ritzwoller, M., and Levshin, A., 2001, A fast and reliable method for surface wave tomography, Monitoring the Comprehensive Nuclear-Test-Ban Treaty: Surface Waves, Springer, p. 1351-1375. Becken, M., Ritter, O., Bedrosian, P. A., and Weckmann, U., 2011, Correlation between deep fluids, tremor and creep along the central San Andreas fault: Nature, v. 480, no. 7375, p. 87. Behr, W. M., Kotowski, A. J., and Ashley, K. T., 2018, Dehydration-induced rheological heterogeneity and the deep tremor source in warm subduction zones: Geology. Ben-Zion, Y., 2012, Episodic tremor and slip on a frictional interface with critical zero weakening in elastic solid: Geophysical Journal International, v. 189, no. 2, p. 1159-1168. Ben-Zion, Y., and Sammis, C. G., 2003, Characterization of fault zones: Pure and Applied Geophysics, v. 160, no. 3-4, p. 677-715. Bensen, G., Ritzwoller, M., Barmin, M., Levshin, A., Lin, F., Moschetti, M., Shapiro, N., and Yang, Y., 2007, Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements: Geophysical Journal International, v. 169, no. 3, p. 1239-1260. Beroza, G. C., and Ide, S., 2011, Slow earthquakes and nonvolcanic tremor: Annual review of Earth and planetary sciences, v. 39, p. 271-296. Bilham, R., and King, G., 1989, The morphology of strike-slip faults: Examples from the San Andreas Fault, California: Journal of Geophysical Research: Solid Earth, v. 94, no. B8, p. 10204-10216. Bletery, Q., Thomas, A. M., Hawthorne, J. C., Skarbek, R. M., Rempel, A. W., and Krogstad, R. D., 2017, Characteristics of secondary slip fronts associated with slow earthquakes in Cascadia: Earth and Planetary Science Letters, v. 463, p. 212-220. Burridge, R., and Knopoff, L., 1967, Model and theoretical seismicity: Bulletin of the seismological society of america, v. 57, no. 3, p. 341-371. 95 Bürgmann, R., and Dresen, G., 2008, Rheology of the lower crust and upper mantle: Evidence from rock mechanics, geodesy, and field observations: Annual Review of Earth and Planetary Sciences, v. 36. Chen, K. H., Bürgmann, R., and Nadeau, R. M., 2013, Do earthquakes talk to each other? Triggering and interaction of repeating sequences at Parkfield: Journal of Geophysical Research: Solid Earth, v. 118, no. 1, p. 165-182. Chen, W.-P., Hung, S.-H., Tseng, T.-L., Brudzinski, M., Yang, Z., and Nowack, R. L., 2012, Rheology of the continental lithosphere: progress and new perspectives: Gondwana research, v. 21, no. 1, p. 4- 18. Cox, P., Stubailo, I., and Davis, P., 2016, Receiver function and geometric tomography along the monterey microplate to test slab delamination or lithospheric drip models of the Isabella Anomaly, California: Bulletin of the Seismological Society of America, v. 106, no. 1, p. 267-280. Daub, E. G., Shelly, D. R., Guyer, R. A., and Johnson, P. A., 2011, Brittle and ductile friction and the physics of tectonic tremor: Geophysical Research Letters, v. 38, no. 10. Dieterich, J. H., and Smith, D. E., 2009, Nonplanar faults: Mechanics of slip and off-fault damage, Mechanics, structure and evolution of fault zones, Springer, p. 1799-1815. Dragert, H., Wang, K., and James, T. S., 2001, A silent slip event on the deeper Cascadia subduction interface: Science, v. 292, no. 5521, p. 1525-1528. Dziewonski, A., Bloch, S., and Landisman, M., 1969, A technique for the analysis of transient seismic signals: Bulletin of the seismological Society of America, v. 59, no. 1, p. 427-444. Eberhart-Phillips, D., and Reyners, M., 1999, Plate interface properties in the northeast Hikurangi subduction zone, New Zealand, from converted seismic waves: Geophysical Research Letters, v. 26, no. 16, p. 2565-2568. Fagereng, Å., 2011, Geology of the seismogenic subduction thrust interface: Geological Society, London, Special Publications, v. 359, no. 1, p. 55-76. Fagereng, Å., and Diener, J. F., 2011, San Andreas Fault tremor and retrograde metamorphism: Geophysical Research Letters, v. 38, no. 23. Fagereng, Å., Hillary, G. W., and Diener, J. F., 2014, Brittle-viscous deformation, slow slip, and tremor: Geophysical Research Letters, v. 41, no. 12, p. 4159-4167. Ford, H. A., Fischer, K. M., and Lekic, V., 2014, Localized shear in the deep lithosphere beneath the San Andreas fault system: Geology, v. 42, no. 4, p. 295-298. Freed, A. M., 2005, Earthquake triggering by static, dynamic, and postseismic stress transfer: Annu. Rev. Earth Planet. Sci., v. 33, p. 335-367. Fuis, G. S., and Mooney, W. D., 1990, Lithospheric structure and tectonics from seismic-refraction and other data: The San Andreas Fault System, California, v. 1515, p. 206-236. 96 Fusseis, F., Handy, M., and Schrank, C., 2006, Networking of shear zones at the brittle-to-viscous transition (Cap de Creus, NE Spain): Journal of Structural Geology, v. 28, no. 7, p. 1228-1243. Ghosh, A., Vidale, J. E., and Creager, K. C., 2012, Tremor asperities in the transition zone control evolution of slow earthquakes: Journal of Geophysical Research: Solid Earth, v. 117, no. B10. Ghosh, A., Vidale, J. E., Sweet, J. R., Creager, K. C., and Wech, A. G., 2009, Tremor patches in Cascadia revealed by seismic array analysis: Geophysical Research Letters, v. 36, no. 17. Ghosh, A., Vidale, J. E., Sweet, J. R., Creager, K. C., Wech, A. G., Houston, H., and Brodsky, E. E., 2010, Rapid, continuous streaking of tremor in Cascadia: Geochemistry, Geophysics, Geosystems, v. 11, no. 12. Guilhem, A., and Nadeau, R. M., 2012, Episodic tremors and deep slow-slip events in Central California: Earth and Planetary Science Letters, v. 357, p. 1-10. Harris, R. A., and Arrowsmith, J. R., 2006, Introduction to the special issue on the 2004 Parkfield earthquake and the Parkfield earthquake prediction experiment: Bulletin of the Seismological Society of America, v. 96, no. 4B, p. S1-S10. Hawthorne, J. C., and Rubin, A. M., 2010, Tidal modulation of slow slip in Cascadia: Journal of Geophysical Research: Solid Earth, v. 115, no. B9. Hayman, N. W., and Lavier, L. L., 2014, The geologic record of deep episodic tremor and slip: Geology, v. 42, no. 3, p. 195-198. Hearn, E. H., and Thatcher, W. R., 2015, Reconciling viscoelastic models of postseismic and interseismic deformation: Effects of viscous shear zones and finite length ruptures: Journal of Geophysical Research: Solid Earth, v. 120, no. 4, p. 2794-2819. Herrmann, R. B., 2013, Computer programs in seismology: An evolving tool for instruction and research: Seismological Research Letters, v. 84, no. 6, p. 1081-1088. Hill, D. P., Peng, Z., Shelly, D. R., and Aiken, C., 2013, S-wave triggering of tremor beneath the Parkfield, California, section of the San Andreas fault by the 2011 Tohoku, Japan, earthquake: Observations and theory: Bulletin of the Seismological Society of America, v. 103, no. 2B, p. 1541-1550. Hirose, H., Hirahara, K., Kimata, F., Fujii, N., and Miyazaki, S. i., 1999, A slow thrust slip event following the two 1996 Hyuganada earthquakes beneath the Bungo Channel, southwest Japan: Geophysical Research Letters, v. 26, no. 21, p. 3237-3240. Hirose, H., and Obara, K., 2005, Repeating short-and long-term slow slip events with deep tremor activity around the Bungo channel region, southwest Japan: Earth, planets and space, v. 57, no. 10, p. 961-972. Houston, H., Delbridge, B. G., Wech, A. G., and Creager, K. C., 2011, Rapid tremor reversals in Cascadia generated by a weakened plate interface: Nature Geoscience, v. 4, no. 6, p. 404. Ide, S., 2010, Striations, duration, migration and tidal response in deep tremor: Nature, v. 466, no. 7304, p. 356. 97 Ide, S., Shelly, D. R., and Beroza, G. C., 2007, Mechanism of deep low frequency earthquakes: Further evidence that deep non-volcanic tremor is generated by shear slip on the plate interface: Geophysical Research Letters, v. 34, no. 3. Ide, S., and Tanaka, Y., 2014, Controls on plate motion by oscillating tidal stress: Evidence from deep tremors in western Japan: Geophysical Research Letters, v. 41, no. 11, p. 3842-3850. Ikari, M. J., Marone, C., Saffer, D. M., and Kopf, A. J., 2013, Slip weakening as a mechanism for slow earthquakes: Nature geoscience, v. 6, no. 6, p. 468. Jennings, C. W., with modifications by Gutierrez, C., Bryant, W., Saucedo, G., and Wills, 2010, Geologic map of California : California Geological Survey, Geologic Data Map No. 2, scale 1:750,000. Johnson, L. R., and Nadeau, R. M., 2002, Asperity model of an earthquake: Static problem: Bulletin of the Seismological Society of America, v. 92, no. 2, p. 672-686. Johnston, M., Borcherdt, R., Linde, A., and Gladwin, M., 2006, Continuous borehole strain and pore pressure in the near field of the 28 September 2004 M 6.0 Parkfield, California, earthquake: Implications for nucleation, fault response, earthquake prediction, and tremor: Bulletin of the Seismological Society of America, v. 96, no. 4B, p. S56-S72. Jolivet, R., Simons, M., Agram, P., Duputel, Z., and Shen, Z. K., 2015, Aseismic slip and seismogenic coupling along the central San Andreas Fault: Geophysical Research Letters, v. 42, no. 2, p. 297- 306. Karato, S.-i., 2012, Deformation of earth materials: an introduction to the rheology of solid earth, Cambridge University Press. Kato, A., Obara, K., Igarashi, T., Tsuruoka, H., Nakagawa, S., and Hirata, N., 2012, Propagation of slow slip leading up to the 2011 Mw 9.0 Tohoku-Oki earthquake: Science, v. 335, no. 6069, p. 705- 708. King, G. C., and Bowman, D. D., 2003, The evolution of regional seismicity between large earthquakes: Journal of Geophysical Research: Solid Earth, v. 108, no. B2. King, G. C., Stein, R. S., and Lin, J., 1994, Static stress changes and the triggering of earthquakes: Bulletin of the Seismological Society of America, v. 84, no. 3, p. 935-953. Lavier, L. L., Bennett, R. A., and Duddu, R., 2013, Creep events at the brittle ductile transition: Geochemistry, Geophysics, Geosystems, v. 14, no. 9, p. 3334-3351. Levander, A., and Miller, M. S., 2012, Evolutionary aspects of lithosphere discontinuity structure in the western US: Geochemistry, Geophysics, Geosystems, v. 13, no. 7. Lin, F.-C., Moschetti, M. P., and Ritzwoller, M. H., 2008, Surface wave tomography of the western United States from ambient seismic noise: Rayleigh and Love wave phase velocity maps: Geophysical Journal International, v. 173, no. 1, p. 281-298. 98 Lisowski, M., and Prescott, W., 1981, Short-range distance measurements along the San Andreas fault system in central California, 1975 to 1979: Bulletin of the Seismological Society of America, v. 71, no. 5, p. 1607-1624. Lowry, A. R., Larson, K. M., Kostoglodov, V., and Bilham, R., 2001, Transient fault slip in Guerrero, southern Mexico: Geophysical Research Letters, v. 28, no. 19, p. 3753-3756. Matsubara, M., Obara, K., and Kasahara, K., 2009, High-VP/VS zone accompanying non-volcanic tremors and slow-slip events beneath southwestern Japan: Tectonophysics, v. 472, no. 1-4, p. 6- 17. Montési, L. G., 2013, Fabric development as the key for forming ductile shear zones and enabling plate tectonics: Journal of Structural Geology, v. 50, p. 254-266. Moore, D. E., and Rymer, M. J., 2007, Talc-bearing serpentinite and the creeping section of the San Andreas fault: Nature, v. 448, no. 7155, p. 795. Nadeau, R. M., and Dolenc, D., 2005, Nonvolcanic tremors deep beneath the San Andreas Fault: Science, v. 307, no. 5708, p. 389-389. Nadeau, R. M., and Johnson, L. R., 1998, Seismological studies at Parkfield VI: Moment release rates and estimates of source parameters for small repeating earthquakes: Bulletin of the Seismological Society of America, v. 88, no. 3, p. 790-814. Nadeau, R. M., and McEvilly, T. V., 2004, Periodic pulsing of characteristic microearthquakes on the San Andreas Fault: Science, v. 303, no. 5655, p. 220-222. Obara, K., 2002, Nonvolcanic deep tremor associated with subduction in southwest Japan: Science, v. 296, no. 5573, p. 1679-1681. Ohta, Y., Freymueller, J. T., Hreinsdóttir, S., and Suito, H., 2006, A large slow slip event and the depth of the seismogenic zone in the south central Alaska subduction zone: Earth and Planetary Science Letters, v. 247, no. 1-2, p. 108-116. Okada, Y., 1992, Internal deformation due to shear and tensile faults in a half-space: Bulletin of the Seismological Society of America, v. 82, no. 2, p. 1018-1040. Ozacar, A. A., and Zandt, G., 2009, Crustal structure and seismic anisotropy near the San Andreas Fault at Parkfield, California: Geophysical Journal International, v. 178, no. 2, p. 1098-1104. Peng, Z., and Gomberg, J., 2010, An integrated perspective of the continuum between earthquakes and slow-slip phenomena: Nature Geoscience, v. 3, no. 9, p. 599. Peng, Z., Hill, D. P., Shelly, D. R., and Aiken, C., 2010, Remotely triggered microearthquakes and tremor in central California following the 2010 Mw 8.8 Chile earthquake: Geophysical Research Letters, v. 37, no. 24. Platt, J., and Behr, W., 2011, Lithospheric shear zones as constant stress experiments: Geology, v. 39, no. 2, p. 127-130. 99 Porritt, R. W., Allen, R. M., Boyarko, D. C., and Brudzinski, M. R., 2011, Investigation of Cascadia segmentation with ambient noise tomography: Earth and Planetary Science Letters, v. 309, no. 1- 2, p. 67-76. Powers, P. M., and Jordan, T. H., 2010, Distribution of seismicity across strike-slip faults in California: Journal of Geophysical Research: Solid Earth, v. 115, no. B5. Roeloffs, E., and Langbein, J., 1994, The earthquake prediction experiment at Parkfield, California: Reviews of Geophysics, v. 32, no. 3, p. 315-336. Roeloffs, E. A., 2001, Creep rate changes at Parkfield, California 1966–1999: Seasonal, precipitation induced, and tectonic: Journal of Geophysical Research: Solid Earth, v. 106, no. B8, p. 16525- 16547. Rogers, G., and Dragert, H., 2003, Episodic tremor and slip on the Cascadia subduction zone: The chatter of silent slip: Science, v. 300, no. 5627, p. 1942-1943. Rubinstein, J. L., Shelly, D. R., and Ellsworth, W. L., 2009, Non-volcanic tremor: A window into the roots of fault zones, New Frontiers in Integrated Solid Earth Sciences, Springer, p. 287-314. Sammis, C. G., and Rice, J. R., 2001, Repeating earthquakes as low-stress-drop events at a border between locked and creeping fault patches: Bulletin of the Seismological Society of America, v. 91, no. 3, p. 532-537. Sammis, C. G., and Smith, S. W., 1999, Seismic cycles and the evolution of stress correlation in cellular automaton models of finite fault networks, Seismicity Patterns, their Statistical Significance and Physical Meaning, Springer, p. 307-334. -, 2013, Triggered tremor, phase-locking, and the global clustering of great earthquakes: Tectonophysics, v. 589, p. 167-171. Sammis, C. G., Smith, S. W., Nadeau, R. M., and Lippoldt, R., 2016, Relating transient seismicity to episodes of deep creep at Parkfield, California: Bulletin of the Seismological Society of America, v. 106, no. 4, p. 1887-1899. Sammis, C. G., and Sornette, D., 2002, Positive feedback, memory, and the predictability of earthquakes: Proceedings of the National Academy of Sciences, v. 99, no. suppl 1, p. 2501-2508. Schmidt, D., and Gao, H., 2010, Source parameters and time-dependent slip distributions of slow slip events on the Cascadia subduction zone from 1998 to 2008: Journal of Geophysical Research: Solid Earth, v. 115, no. B4. Segall, P., Rubin, A. M., Bradley, A. M., and Rice, J. R., 2010, Dilatant strengthening as a mechanism for slow slip events: Journal of Geophysical Research: Solid Earth, v. 115, no. B12. Shapiro, N. M., Campillo, M., Stehly, L., and Ritzwoller, M. H., 2005, High-resolution surface-wave tomography from ambient seismic noise: Science, v. 307, no. 5715, p. 1615-1618. Shelly, D. R., 2009, Possible deep fault slip preceding the 2004 Parkfield earthquake, inferred from detailed observations of tectonic tremor: Geophysical Research Letters, v. 36, no. 17. 100 -, 2015, Complexity of the deep San Andreas Fault zone defined by cascading tremor: Nature Geoscience, v. 8, no. 2, p. 145. Shelly, D. R., Beroza, G. C., and Ide, S., 2007, Non-volcanic tremor and low-frequency earthquake swarms: Nature, v. 446, no. 7133, p. 305. Shelly, D. R., Beroza, G. C., Ide, S., and Nakamula, S., 2006, Low-frequency earthquakes in Shikoku, Japan, and their relationship to episodic tremor and slip: Nature, v. 442, no. 7099, p. 188. Shelly, D. R., Ellsworth, W. L., Ryberg, T., Haberland, C., Fuis, G. S., Murphy, J., Nadeau, R. M., and Bürgmann, R., 2009, Precise location of San Andreas fault tremors near Cholame, California using seismometer clusters: Slip on the deep extension of the fault?: Geophysical research letters, v. 36, no. 1. Shelly, D. R., and Hardebeck, J. L., 2010, Precise tremor source locations and amplitude variations along the lower-crustal central San Andreas Fault: Geophysical Research Letters, v. 37, no. 14. Smith, E. F., and Gomberg, J., 2009, A search in strainmeter data for slow slip associated with triggered and ambient tremor near Parkfield, California: Journal of Geophysical Research: Solid Earth, v. 114, no. B12. Solum, J. G., Hickman, S. H., Lockner, D. A., Moore, D. E., van der Pluijm, B. A., Schleicher, A. M., and Evans, J. P., 2006, Mineralogical characterization of protolith and fault rocks from the SAFOD main hole: Geophysical Research Letters, v. 33, no. 21. Takeuchi, C. S., and Fialko, Y., 2012, Dynamic models of interseismic deformation and stress transfer from plate motion to continental transform faults: Journal of Geophysical Research: Solid Earth, v. 117, no. B5. Thomas, A. M., Beroza, G. C., and Shelly, D. R., 2016, Constraints on the source parameters of low- frequency earthquakes on the San Andreas Fault: Geophysical Research Letters, v. 43, no. 4, p. 1464-1471. Thomas, A. M., Nadeau, R. M., and Bürgmann, R., 2009, Tremor-tide correlations and near-lithostatic pore pressure on the deep San Andreas fault: Nature, v. 462, no. 7276, p. 1048. Titus, S. J., DeMets, C., and Tikoff, B., 2006, Thirty-five-year creep rates for the creeping segment of the San Andreas fault and the effects of the 2004 Parkfield earthquake: Constraints from alignment arrays, continuous global positioning system, and creepmeters: Bulletin of the Seismological Society of America, v. 96, no. 4B, p. S250-S268. Titus, S. J., Medaris Jr, L. G., Wang, H. F., and Tikoff, B., 2007, Continuation of the San Andreas fault system into the upper mantle: evidence from spinel peridotite xenoliths in the Coyote Lake basalt, central California: Tectonophysics, v. 429, no. 1-2, p. 1-20. Townend, J., and Zoback, M. D., 2000, How faulting keeps the crust strong: Geology, v. 28, no. 5, p. 399- 402. Turner, R. C., Shirzaei, M., Nadeau, R. M., and Bürgmann, R., 2015, Slow and Go: Pulsing slip rates on the creeping section of the San Andreas Fault: Journal of Geophysical Research: Solid Earth, v. 120, no. 8, p. 5940-5951. 101 Uchida, N., Iinuma, T., Nadeau, R. M., Bürgmann, R., and Hino, R., 2016, Periodic slow slip triggers megathrust zone earthquakes in northeastern Japan: Science, v. 351, no. 6272, p. 488-492. Wech, A., Boese, C., Stern, T., and Townend, J., 2012, Tectonic tremor and deep slow slip on the Alpine fault: Geophysical Research Letters, v. 39, no. 10. Wech, A. G., and Bartlow, N. M., 2014, Slip rate and tremor genesis in Cascadia: Geophysical Research Letters, v. 41, no. 2, p. 392-398. Zeng, X., Thurber, C. H., Shelly, D. R., Harrington, R. M., Cochran, E. S., Bennington, N. L., Peterson, D., Guo, B., and McClement, K., 2016, 3-DP-and S-wave velocity structure and low-frequency earthquake locations in the Parkfield, California region: Geophysical Journal International, v. 206, no. 3, p. 1574-1585. Zheng, L., May, D., Gerya, T., and Bostock, M., 2016, Fluid-assisted deformation of the subduction interface: Coupled and decoupled regimes from 2-D hydromechanical modeling: Journal of Geophysical Research: Solid Earth, v. 121, no. 8, p. 6132-6149. Zigone, D., Rivet, D., Radiguet, M., Campillo, M., Voisin, C., Cotte, N., Walpersdorf, A., Shapiro, N. M., Cougoulat, G., and Roux, P., 2012, Triggering of tremors and slow slip event in Guerrero, Mexico, by the 2010 Mw 8.8 Maule, Chile, earthquake: Journal of Geophysical Research: Solid Earth, v. 117, no. B9. Zoback, M., Hickman, S., and Ellsworth, W., 2011, Scientific drilling Into the San Andreas Fault Zone– an overview of SAFOD's first five years: Scientific Drilling, v. 11, p. 14-28.

Abstract (if available)

Abstract A dislocation model has been used to interpret the spatial distribution and focal mechanisms of deep off-fault seismicity adjacent to the southern terminus of the creeping section of the San Andreas Fault in Central California, near Parkfield. The most significant feature of the spatial distribution is a prominent seismic lineation that intersects the fault near the SAFOD borehole northwest of Parkfield and strikes southeast making a 20 degree angle with the trace of the San Andreas Fault. This feature can be explained by the termination of a creeping dislocation beneath the seismogenic layer which deepens to the southeast. The stress field corresponding to this dislocation is consistent with surface topography and the focal mechanisms of small off-fault earthquakes. ❧ A shear wave velocity model obtained using ambient noise tomography supports this inferred geometry of a deepening dislocation. Low-frequency earthquakes are associated with a low- velocity structure that deepens to the southeast of Parkfield along strike. This plunging low shear velocity structure can be interpreted as representing weaker materials or the presence of fluids and elevated pore pressures and is consistent with materials more prone to creep. This suggests that there may be a structural or rheological control on the occurrence of creep at depth. ❧ In order to investigate how creep events propagate in the brittle-ductile regime, a one-dimensional finite-difference spring-mass-dashpot model was used to show that a viscous fault plane pinned by an array of brittle asperities can produce slow slip propagation speeds in the observed range of kilometer per hour to kilometer per day. For physically reasonable values of wall rock elasticity, viscosity, and fault zone width, the model is able to produce propagation speeds consistent with observed tremor migration in subduction zones and at the base of large strike-slip faults.

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Asset Metadata

Creator Lippoldt, Rachel (author)

Core Title Detection and modeling of slow slip events as creep instabilities beneath major fault zones

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Geological Sciences

Publication Date 07/23/2018

Defense Date 04/26/2018

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag OAI-PMH Harvest,Parkfield CA,San Andreas fault,slow slip,tremor

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Sammis, Charles (committee chair), Kassner, Michael (committee member), Platt, John (committee member)

Creator Email rachel.lippoldt@gmail.com,rlippold@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-21506

Unique identifier UC11671307

Identifier etd-LippoldtRa-6442.pdf (filename),usctheses-c89-21506 (legacy record id)

Legacy Identifier etd-LippoldtRa-6442.pdf

Dmrecord 21506

Document Type Dissertation

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Rights Lippoldt, Rachel

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Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

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