We use 3-D waveform modeling of LFEs (low-frequency earthquakes) to investigate their relation to plate boundary structure along a linear transect in northern Cascadia. To account for crustal velocity heterogeneity, a smoothed 3-D model of subduction zone structure is assembled that incorporates constraints from regional tomographic and plate boundary models. Scattered phases within LFE waveforms are identified based on synthetic predictions that incorporate thrust mechanisms aligned parallel to a dipping plate boundary atop a high-Vp/Vs low-velocity zone (LVZ). Scattering for near-vertical paths is dominated by S-to-P/S-to-S reflections/conversions from the LVZ. The modeling suggests that LFEs lie at or very close to the plate boundary and that the LVZ structure is laterally heterogeneous but broadly consistent with results from teleseismic analysis.
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 Improvements in resolution of subduction zone structure are essential for better understanding the mechanisms of plate tectonics and to assess seismic hazard, in particular, in the Pacific Northwest. The discovery of tremor and constituent low-frequency earthquakes (LFEs) in Cascadia [Rogers and Dragert, 2003; La Rocca et al., 2009; Bostock et al., 2012], a region with generally low levels of regular seismicity, has afforded a new source of seismic energy with which to interrogate plate boundary structure. We review constraints on plate boundary structure of the Cascadia subduction zone and previous work on the detection and location of LFEs in northern Cascadia. We then perform waveform modeling of LFE waveforms to investigate the subduction zone structure and constrain the location of LFEs relative to the plate boundary.
2 Cascadia Low-Velocity Zone (LVZ) and LFEs
 The seismic signature of the Cascadia forearc at depths between 20 and 40 km is dominated by a thin (~3–4 km thick) zone of low S velocity (~2–3 km/s), high Poisson's ratio (~0.4), and high seismic reflectivity (hereafter referred to as the LVZ) that extends from northern California to northern Vancouver Island, and from some tens of kilometers seaward of the coast to depths in excess of 40–50 km beneath the fore-arc lowlands [Hyndman, 1988; Nedimovic et al., 2003; Audet et al., 2010]. The nature of this feature has been a matter of debate, and interpretations have included oceanic crust [Green et al., 1986; Langston, 1981; Nicholson et al., 2005), underplated sediments (Calvert and Clowes, 1990], and free fluids trapped at a metamorphic phase boundary in the overlying plate [Hyndman, 1988]. Recently, Hansen et al.  provided arguments supporting identification of the LVZ with upper oceanic crust, that is, as pillow basalts and sheeted dykes possibly including overlying sediments that have been pervasively hydrated at the mid-ocean ridge and outer rise. The extreme elastic properties characterizing the LVZ result from dehydration reactions that occur as the subducting oceanic crust encounters higher temperatures and pressures, producing fluids at lithostatic pressures that appear to be maintained by an impermeable plate boundary [Audet et al., 2009].
 At similar depths, displacement on the plate boundary occurs at 10–14 month intervals in the form of “slow slip” earthquakes with equivalent magnitudes of ~M6.5 [Dragert et al., 2001; Miller et al., 2002; Brudzinski and Allen, 2007; Wech and Creager, 2011; Ghosh et al., 2010]. The slow slip events are accompanied in time and space by a tectonic tremor signal that is dominated by energy in the 1–10 Hz band [Rogers and Dragert, 2003]. Similar observations have been made in southwestern Japan [Obara, 2002; Obara et al., 2004]. The physical conditions that lead to combined “episodic tremor and slip” (ETS) are of considerable interest not least because their elucidation could lead to significant improvements in seismic hazard assessment [Chapman and Melbourne, 2009]. Current models for slow slip genesis invoke high pore fluid pressures and dilatancy strengthening as key ingredients [e.g., Segall et al., 2010], consistent with the seismic observations.
 Tectonic tremor is characterized by a waveform envelope that rises and ebbs in amplitude over periods of minutes to hours and is composed in large part of many repeating LFEs. Some authors contend that tremor in Cascadia is distributed over a broad depth interval [Kao et al., 2005]; however, there is mounting evidence that tremor and LFEs in Cascadia [La Rocca et al., 2009; Bostock et al., 2012], like those in Japan [Shelly et al., 2006], locate near the plate boundary. Although the study of LFEs to date has focused primarily on their direct role in the ETS process, their origin near the plate boundary suggests that they could provide a useful complement to deeper intraplate events in efforts to resolve finer-scale plate boundary structure using passive sources.
Bostock et al.  implemented network correlation detectors [Brown et al., 2008] within an iterative stacking/detection procedure to data recorded on southern Vancouver Island for ETS episodes since 2003 to assemble a set of 140 LFE waveform templates. This procedure removes variability in source signature across individual repeating LFEs to produce what is effectively a record of empirical Green's functions. The corresponding locations, like those of LFEs in SW Japan, are spatially complementary to intraplate events. In particular, the LFE locations are confined to a zone that coincides closely with the 25–40 km contours of the subducting plate and are demonstrably shallower in depth than intraplate events occurring in the same epicentral region. Precise location of LFEs relative to the plate boundary (here assumed to be the top of the LVZ) using standard procedures is complicated by absolute depth errors that approach the LVZ thickness (3–4 km). Here we employ 3-D waveform modeling to examine scattered waveforms within LFE templates with higher sensitivity to LFE location relative to the LVZ.
3 Waveform Modeling of LFE Events
 Our data set comprises LFE templates for a subset of the stations (TWBB, TSJB, LZB, TWKB, MGCB, and KELB) employed by Bostock et al.  that form an approximately linear transect across southern Vancouver Island (Figure 1). A regional 3-D velocity model was assembled by smoothing the Vp tomographic model of Ramachandran et al.  and incorporating Vp/Vs constraints from Ramachandran and Hyndman . The smoothed model was resampled to 8 km in the lateral coordinate and employs a variable, vertical grid spacing from 2 to −100 km in depth. A laterally varying LVZ was then imbedded within the velocity model using the plate boundary model of Audet et al. . The plate boundary location is a variable subject to the constraints of the LFE data and was shifted downward by 3.4 km to better align with the average trajectory formed by the template LFE locations and to account for any remaining unmodeled crustal velocity structure. Model discontinuities include a 3.3 km thick LVZ at the top of the subducting plate underlain by a second 4.5 km thick layer with more modest negative velocity contrast [hereafter referred to as LOC, Hansen et al., 2012]. The resulting 3-D model is depicted in Figure 2a.
 From shear-wave splitting analysis of tremor on southern Vancouver Island, Bostock and Christensen  inferred split times of up to 0.3 s and E-W fast directions to result from anisotropic phyllites and schists of the Leech River Complex. Figure S1 in the supporting information displays the east and north components of selected template waveforms revealing minimal splitting distortion owing to their orientation with respect to the fast direction. Hence, synthetic waveform modeling is performed using the vertical and east components of the LFE data with the 3-D modeling package CRT [Červený et al., 1988] assuming isotropic media. An example of the 3-D ray tracing is shown in Figure 2b for LFE template 14 located at the top LVZ.
 Full-band ray theoretical Green's functions corresponding to a thrust source aligned parallel to the plate boundary are shown in Figure 3 for template 37 (see epicentral location in Figure 1) and 2 depths: the top of LVZ in Figure 3a and 1 km beneath the top of the LVZ in Figure 3b. Although the analysis of polarities by Bostock et al.  had suggested a mixture of thrust and strike slip faulting, more recent moment tensor modeling of both and waveforms by Royer and Bostock  consistently requires pure thrust mechanisms. The LVZ is modeled with a Vp of 4.6 km/s, a Vp/Vs of 2.36, and a density of 2700 kg/m3. Note that a 90° phase rotation has been applied to the waveforms to transform the arrivals on particle velocity seismograms due to a double-couple source into zero-phase spikes. The geometry of the source produces nodal planes parallel and perpendicular to the gently dipping slab with the result that direct S waves dominate seismograms for near-vertical paths. Scattering from the LVZ is also dominated by S interactions where the P coda registers strong reflection-conversions on the Z component, as well as transmission-conversions for an event within the LVZ shown in Figure 3b. The pure S-to-S reflection is the strongest scattered signal in the S coda on the E component. Converted phase amplitudes roughly track the amplitude of direct as a function of epicentral location, due again to the source orientation. Scattered phases from the lower boundary of the LOC layer are relatively insignificant.
 The timing of the scattered phases is sensitive to LFE location within the LVZ and to LVZ velocities. In particular, note that the time lag of the prominent conversions with respect to will vary from 0 s to ~1.0 s as the LFE position shifts from top to bottom of the LVZ [using representative velocities from Hansen et al, 2012]. Thus, LFEs located significantly below the top of LVZ should produce pulse broadening and distortion of on band-limited (1–8 Hz) LFE templates.
 Figure 4 displays data (blue) and corresponding synthetics (red) for LFE templates 14 and 37 along the central part of the transect axis (Figure 1). Synthetics have been filtered to the passband of the data, and both signals have been phase rotated by 90° to produce zero-phase pulses. The most consistently observed phase is on the Z component whereas appears more intermittently on the east component. arrives approximately 2.2 s after on the Z component for templates 14 and 37. For template 160, arrives somewhat earlier suggesting lateral variability in the LVZ. The amplitudes of these scattered phases place further constraint on the LVZ and, in particular, require large contrasts in S velocity at its lower boundary.
 The simplicity of the direct P arrivals for these and other templates indicate that LFEs occur at or near the top of the LVZ structure. If the LFE sits immediately below the LVZ upper boundary, there is insufficient lag time accumulated between and to cause significant waveform distortion, whereas if the LFE occurs on the boundary, no phase is generated. Figures S2–S4 of the supporting information show similar waveform modeling for selected LFE templates but for source depths of 0.25, 0.5, and 1 km below the top of the LVZ. In addition to modeled and scattered phases that arrive too early, distortion and complexity of the modeled phase increases with increasing source depth as a result of the emergence of and is not observed in the data.
 The timing of and allows us to resolve some of the trade-off between P and S velocities in the LVZ and its thickness. The phase is expected to be the cleaner signal due to its timing within the P coda where signal generated noise levels will be low. In contrast, the signals occur in the S coda where noise levels, generated by a strong phase scattered from a near-surface structure, will be stronger. Nonetheless, the combined times are sensitive primarily to the Vp/Vs ratio and thickness-velocity quotient, with scattered phase amplitudes supplying further constraint on S impedance contrast at the LVZ lower boundary.
 In Figure 4, Vp, Vp/Vs, and thickness were constrained primarily through forward modeling; however, grid searches on waveform fits for individual templates were also performed. The Vp, Vs, and density of the underlying LOC were set at 7 km/s, 3.4 km/s, and 3000 kg/m3, respectively, whereas the density of the LVZ was specified to be 2700 kg/m3. For template 14, the LVZ was modeled by a Vp/Vs of 2.25, Vp of 4.8 km/s, and a thickness of 3.3 km. The LVZ for template 37 was modeled by a Vp/Vs of 2.36, Vp of 4.6 km/s, and thickness of 3.3 km. Comparable values were recovered for other LFEs along the central portion of the transect. The waveforms for template 160 located at the western end of the transect (Figure 4c) are best matched by similar Vp/Vs (2.25) but larger wave speeds (P velocity equal to 5.4 km/s) and a somewhat smaller thickness (3.1 km), suggesting again the presence of lateral variability in the LVZ. These results are broadly consistent with teleseismic estimates of average LVZ properties made by Audet et al.  and Hansen et al. , although Vp/Vs ratios are slightly lower and LVZ thicknesses slightly thinner.
 In this study, we have exploited a novel, passive seismic data source, namely, LFE templates, as empirical Green's functions to investigate the constraints that scattered waves in the coda of P and S place on an LFE location and structure near the plate boundary in northern Cascadia beneath southern Vancouver Island. The expression of scattering from the LVZ is influenced by the focal mechanisms and dominated by converted scattering in the coda of P and pure scattering in the S coda. The simplicity of the direct P arrivals and the modeling of the scattered phases indicate that the LFEs are situated at or very near the top of the LVZ. The modeling of the LFE waveforms yields estimates of LVZ thickness, velocity contrast, and Vp/Vs ratios that are broadly consistent with those from previous teleseismic analyses and with the interpretation of this structure as overpressured metabasalts in subducted upper oceanic crust.
 The authors would like to thank Luděk Klimeš, Petr Bulant, and Ivan Pšencík of the SW3D Consortium (http://sw3d.mff.cuni.cz/) for their early assistance with 3-D ray tracing and modeling. The authors also thank Kumar Ramachandran for providing access to his tomographic model for the Vancouver Island region. The first author thanks the University of British Columbia for hosting him for part of his sabbatical during 2012. The second author acknowledges the support of the Natural Sciences and Engineering Research Council of Canada through grant RGPIN 138004.
 The Editor thanks Allan Rubin and Teh-Ru Alex Song for their assistance in evaluating this paper.