We provide a new link between tectonic tremor propagation, tremor amplitude, and tidal stresses by analyzing high-resolution tremor locations and amplitudes determined by multibeam backprojection of data from an array of subarrays. For two Cascadia episodic tremor and slip events, we observe repeating, high-amplitude rapid tremor reversals (RTRs) and tremor streaks. They tend to occur when tremor amplitudes are highest and occur almost exclusively during periods of thrust-encouraging, tidally induced shear stress on the fault. We speculate that thrust-encouraging shear stress from tidal loading forces trigger RTRs and streaks that energetically rerupture the weakened fault behind the slow slip front. The high rate and amplitude of tremor during RTRs and streaks stands in contrast to the hypothesis that activity at the leading edge of the slow slip zone is the most energetic and loudest. This implies that the spatiotemportal pattern of slow earthquake slip migration is even more intricate than previously reported.
 Episodic tremor and slip (ETS) events, first discovered in Cascadia [Dragert et al., 2001; Rogers and Dragert, 2003] and Japan [Obara, 2002; Obara et al., 2004], are periodic slow earthquakes observed in many subduction zones worldwide in which tectonic tremor is thought to be a consequence of slow slip in the transition zone. ETS transfers stress updip from the stable sliding zone to the locked zone along portions of the subduction interface, thereby loading and potentially triggering megathrust earthquakes [Dragert et al., 2004; Mazzotti and Adams, 2004; Segall and Bradley, 2012]. Observations of ETS tremor in Cascadia and Japan have shown three main modes of tremor propagation: (1) the long-term migration, or migration front, which propagates up to hundreds of kilometers along strike at an average rate of 7 to 13 km/day [Wech et al., 2009; Obara and Sekine, 2009; Houston et al., 2011]; (2) rapid tremor reversals (RTRs) that move more quickly (200 to 400 km/day) in a reverse direction, opposite to the main migration front [Houston et al., 2011], and (3) streaks with even faster (600 to 5000 km/day) motion parallel to the plate convergence direction with components in both the dip and strike directions [Shelly et al., 2007; Ghosh et al., 2010a; Ghosh et al., 2010b]. These tremor modes may represent main rupture and accompanying subrupture propagation during ETS.
 Tremor can be triggered by passing surface waves from distant earthquakes, and its amplitude is modulated by the amplitude of the surface wave shear stress resolved in the assumed direction of slip on the plate interface [Miyazawa and Mori, 2006; Rubinstein et al., 2009]. Furthermore, tremor is influenced by even smaller tidal stresses, fluctuating at the principal lunar and lunisolar tidal periods [Rubinstein et al., 2008]. In addition, peak tremor rate corresponds with modeled values of maximum tidal shear stress resolved on the subduction interface, or up to one-quarter cycle preceding it [Lambert et al., 2009; Hawthorne and Rubin, 2010]. Interestingly, modeled values of tidal stresses are 105 times smaller than the lithostatic stress at the depth of tremor, and so their capability to influence tremor suggests that the fault is very weak [Rubinstein et al., 2008]. Although tidal stresses are known to modulate amplitude and occurrence of ETS tremor, their effect on tremor propagation patterns is unrecognized. Such an effect could provide insight into the mechanics of tremor and slow slip migrations. To test this idea, we used an array of seismic subarrays to capture ETS in the Cascadia subduction zone [Ghosh et al., 2012], achieving high-resolution tremor locations and amplitudes that allow for the investigation of fine-scale migrations in tremor. In this paper, we detail these migrations and compare them with tremor amplitudes and tidal stresses. We then discuss the potential for tidal triggering of certain tremor propagation patterns and speculate as to why they are high amplitude in nature.
2 Data and Method
 Seismic data from the Earthscope Array of Arrays experiment is used in this work. Eight seismic arrays, composed of 10 to 30 sensors each, recorded the portions of the 2010 and 2011 ETS events occurring beneath the northern Olympic Peninsula, Washington State (Figure 1). The 2010 ETS event was Mw ~6.8 in size and occurred from 8 August to 8 September 2010, and the 2011 event was Mw ~6.6 and occurred from 23 July to 4 September 2011. We analyze 1 min time windows of vertical channel data, bandpassed to the tremor frequency band of 5 to 9 Hz energy. Tremor hypocenters were located by a multibeam-backprojection (MBBP) algorithm that determines the best slowness vector at each array, then backprojects through a local velocity model to pinpoint tremor with high resolution [Ghosh et al., 2012]. We observe that near-array tremor locations are distributed more tightly in space and delineate features in higher resolution than tremor locations farther from the arrays, and therefore limit our analysis to approximately 3 day periods (17–19 August 2010 and 16–18 August 2011) when 2010 and 2011 ETS tremor was near to the array.
 Figure 2 compares tremor locations, tremor amplitudes, and a time series of tidally induced shear stress. Tremor epicenters are projected strike parallel along the fault for a clear view of migration-front propagation and RTRs, with the potential to show streaks as well due to their along-strike component in this region. The tremor amplitudes are averaged values over 1 min time windows and are derived from the MBBP method, which produces the beam amplitude of the tremor signal corrected for geometrical spreading. To compute amplitude, tremor beams are normalized by the peak value recorded at each array during the ETS event, then averaged for all arrays. Tidal stress loads are computed at a point within a homogeneous elastic half-space using the method of Hawthorne and Rubin , which modifies the ocean-tide loading software SPOTL [Agnew, 1997] to compute stresses at depth due to Earth tide loads and ocean loads from less than 5° away. The method resolves normal stress and the component of shear stress in the direction of relative plate motion onto the dipping plate boundary determined by McCrory et al. . We compute these stresses at 1 min intervals for the time periods under investigation, and compare them with tremor locations and amplitudes to assess relationships. Additionally, we compare tremor epicenters from different time windows in map view (Figures 3 and S1 in the supporting information) to track the evolution of high-activity areas through time.
 We observe four clear and prominent RTRs in 2011 and one in 2010, as well as seven prominent streaks in 2010 (Figures 2, 3, and S1). To distinguish between these smaller-scale propagation patterns within an ETS event, we consider the typical characteristics of these phenomena as observed in previous ETS events [Houston et al., 2011; Ghosh et al., 2010a; Ghosh et al., 2010b], noting that their durations and velocities are not entirely distinct [Houston et al., 2011; Obara et al., 2012]. The RTRs have durations ranging from 1.5 to 4 h, lengths of 20 to 40 km, and velocities ranging from 7 to 15 km/hr. They migrate southeast (opposite the long-term migration direction) and are mostly confined to the updip portion of the ETS zone. In addition, they propagate slightly updip as they migrate, consistent with Houston et al. . Streaks propagate more closely parallel to the plate convergence direction, with durations ranging from 0.5 to 1.5 h, lengths of about 40 km, and velocities from 27 to 80 km/hr. One streak propagates downdip, the others updip. The RTRs from both 2010 and 2011 ETS are nearly colocated and propagate along a similar path. They initiate near the tremor migration front and propagate south/southeast, covering an area averaging about 25 km (strike parallel) by 15 km (strike perpendicular) within the updip portion of the ETS zone. The streaks from 2010 ETS are nearly colocated as well, but cover a more elongate area averaging about 40 km by 10 km and oriented roughly 10°N to 15°N of convergence parallel. All areas of RTR and streak activity experience tremor in the form of the long-term migration front prior to RTRs and streaks (Figures 3 and S1), with no portion of RTRs and streaks occurring outside of this previously ruptured area. Additionally, RTRs and streaks appear to overlap with the tremor patches imaged by previous studies [Ghosh et al., 2009, 2012]. Interestingly, some time intervals between major RTRs and streaks appear to exhibit streak-like activity on a smaller scale in length and time than the major RTRs and streaks (Figure 2). An analysis of these would be beyond the scope of this paper and perhaps beyond the resolution of our dataset.
 RTRs and streaks are accompanied by high-tremor amplitudes and occur nearly exclusively during times of positive, thrust-encouraging tidal shear stress on the subduction interface (Figure 2). High amplitudes with varying peak levels are sustained throughout RTRs and streaks and generally taper toward the end of them. Additionally, the timing of RTR and streak initiation tends to coincide with increased amplitude, though high amplitudes also appear independent of RTRs and streaks at a few times. Of all RTRs and streaks observed, only two streaks (2010 ETS) do not coincide with an amplitude increase. Furthermore, all the RTRs and streaks mostly occur during periods of positive, thrust-encouraging tidal shear stress, with the mean shear stress during RTRs and streaks ranging from 0.28 to 0.99 kPa and 0.27 to 1.02 kPa, respectively (Figure 4). All but two of the RTRs/streaks initiate during positive tidal shear stress. The first RTR in 2011 and the single RTR in 2010 initiate during negative and fast-increasing shear stress, in each case, only about 10 min before shear stress becomes positive. However, the shear stress is positive throughout the majority of each time window containing these RTRs, with positive mean values of 0.35 and 0.39 kPa, respectively. All RTRs and streaks terminate while tidal shear stress is still positive.
 The tidal shear stress time series used in our analysis is computed on the plate interface at the average location of all tremors occurring during RTRs and streaks in each of the two separate ETS events. The phase of maximum tidal shear stress at the computation point is approximately in-phase with those of the eastern, western, and southern extents of RTRs and streaks but leads the phase at the far northern extent by a range of about 20 to 180 min (Figure S2). This variation is likely linked to the greater influence of local tidal variations in the Straight of Juan de Fuca on this northern computation point. A precise quantification of the stress regime at the start and end of RTRs and streaks is complicated by this tidal stress phase variation towards the north and even more so by our resolution of tremor locations, and so we limit our reporting to the mean tidal shear stress during each RTR/streak, which gives a broader characterization of stress conditions that have less dependence on these complications. Also, tidally induced normal stress is roughly twice the amplitude of the positive tidal shear stress in our study area, causing the coulomb stress to be heavily dependent on the normal stress. We find that positive, slip-favoring coulomb stress closely follows positive (tensional) normal stress and generally lags times of positive shear stress by ~3.3 h and shows no clear association with RTRs and streaks.
 The association of RTRs/streaks, high amplitudes, and tidal shear stress is not entirely clear. One idea is that the passing of the main rupture front causes the fault to become mechanically weaker, as asperities broken by the slip front have not had time to heal. The higher tremor amplitude in a given time increment could come either from a greater area slipping at once or more slip per unit area (which implies a higher slip rate or speed). We favor the former because RTRs and streaks seem to involve a large area due to their relatively large propagation velocities, but we cannot distinguish the possibilities at this point. It appears that the breakage causes the yield strength to drop more than the stress drops in the main slip front because the RTRs and streaks are notably sensitive to tidal stress changes.
 The high frequency of streaks detected in previous work [Shelly et al., 2007; Ghosh et al., 2010a, 2010b] precludes that every streak is triggered by tidal shear stress, but in our analysis, every prominent streak with high amplitude does occur during periods of positive shear stressing, which indicates that streaks large in both size and amplitude may be tidally triggered. We also find two prominent streaks that, although associated with positive tidal shear stress, do not coincide with high amplitudes. This indicates that large streaks occurring during slip-favoring stressing are not necessarily high energy in nature. In addition, due to the limited timespan of our analysis window, we cannot demonstrate over a long baseline period of time that all RTRs are tidally associated, but we show in Figure 4 that mean tidal shear stress is positive during the eight RTRs observed by Houston et al.  during the 2005 and 2007–2009 ETS events, as we would expect given our findings. Further, if times of high-amplitude ETS tremor can be considered as times of high tremor activity, and if these high-activity times manifest as large RTRs and streaks as found here, then the linkage between tremor activity and positive tidal shear stress shown by Lambert et al.  and Hawthorne and Rubin  would suggest a pervasive tidal coupling of these phenomena. Also, because RTRs and streaks are likely both subprocesses of long-term migration, in many cases, only slightly different in speed and direction, the chance increases that if one of these can be tidally triggered, the other can be as well.
 Within the context of a proposed diffusive slip pulse model of tremor [Ando et al., 2010; Ide, 2010; Houston et al., 2011], the large RTRs and streaks we detect may each represent a slip pulse intensified by tidal stressing that propagates along structural striations or other fault heterogeneities [Ghosh et al., 2010b; Houston et al., 2011, Ide, 2010]. Additionally, the activity we see repeats over the same area (Figures 3 and S1), further suggesting that tremor is controlled by local striations or other structures on the plate interface here. Indeed, although RTRs occur in various locations along the entire Cascadia subduction zone, many of them are concentrated near the relatively tight bend in the subduction zone around the Strait of Juan de Fuca, where more structural complexity may be expected. This could explain why slip-encouraging tidal stressing is associated with backward-propagating slip in the form of loud RTRs rather than forward-moving slip, as RTRs may nucleate in regions where it is more difficult for the main ETS slip front to advance due to geometry or some other feature of the plate interface.
Hawthorne and Rubin  model slow slip events via a velocity weakening to velocity strengthening friction law that produces back-propagating slip fronts near the times of maximum tidal shear stress. In some key respects, their results are inconsistent with our observations of RTRs and streaks. The modeled fronts propagate backwards less than 10 km, whereas our observed RTRs and streaks all propagate 2 to 4 times farther than this. Hawthorne and Rubin also consider back-propagating fronts driven by stress recovery. Although these fronts can propagate much farther than 10 km, repeating fronts would likely propagate more slowly with each repetition [Hawthorne and Rubin, 2013], a phenomenon not witnessed in observed repeating RTRs and streaks. Additionally, the modeled fronts do not repeat over the same areas and in fact, cease propagation once they reach areas that previously hosted fronts, whereas we observe multiple RTRs and streaks repeating over the same area. Our observations likely require either modifications to the slip parameterization of Hawthorne and Rubin  or a different slip law altogether; both of which are discussed in their work.
 The evidence for smaller-scale background streaking behavior between larger RTRs and streaks (Figure 2) agrees with other work that shows streaking dominates tremor propagation on short timescales [Shelly et al., 2007; Ghosh et al., 2010a, 2010b; Obara et al., 2012]; thus the large, high-amplitude streaks found here, and perhaps the RTRs as well, could be less of a triggered phenomenon and more a continuous process accentuated and magnified by tidal stresses. Regarding amplitudes, the high amplitudes associated with RTRs and streaks are upwards of 10 times the average amplitude, suggesting large energy release. Based on this assertion, tidally triggered RTRs and streaks may represent a significant process of stress drop during ETS.
 We analyze high-resolution locations of ETS tremor in Cascadia and track tremor propagation and amplitude through time. We calculate tidal stresses and compare them to tremor propagations and amplitude to clarify their relationship. Large, high-amplitude RTRs and streaks occur in our analysis period and occur almost exclusively during times of positive, thrust-encouraging tidal shear stress on the plate interface. This observation suggests that tidal stresses may trigger or intensify large, high-amplitude RTRs and streaks, which themselves represent the backwards and updip propagation of slow slip rupture into previously ruptured and weakened zones on the fault. This interrelated pattern of tidal stress, tremor amplitude, and slip migration provides the most detailed observational picture yet of slow slip and should, by providing constraints for modeling, help uncover the mechanics of slow slip asperities and their relation to normal earthquakes and silent and steady fault motion.
 We thank NSF-EarthScope for funding this study, our designated reviewers for extremely helpful comments, and the multitude of individuals that helped with the necessary fieldwork.
 The Editor thanks Elizabeth Cochran and an anonymous reviewer for their assistance in evaluating this paper.