Seismic interferometry using non-volcanic tremor in Cascadia



[1] Seismic interferometry to date has focussed on surface waves, due to paucity of deep, high-frequency noise sources. Here, we investigate use of non-volcanic tremor on the Cascadia subduction zone as a noise source to recover scattered body-wave contributions to the Green's function. Tremor data for 2004–2005 recorded at Polaris-BC stations TWKB, MGCB and LZB were filtered and cross-correlated. TWKB and MGCB correlations generate a highly reproducible arrival at 4.5 s for combinations of vertical with radial or transverse components. TWKB and LZB correlations are less reproducible, but yield a strong arrival at 3.5 s for 2005. Upon consideration of source/receiver geometry, polarity and timing, we interpret these arrivals to represent reflection-conversions. Arrival times imply that these signals originate at depths between 9 and 12 km, coincident with an interval of strong reflectivity imaged in the 1987 Lithoprobe Southern Cordillera transect.

1. Introduction

[2] Determination of an accurate Green's function from recordings of scattered seismic waves has been the subject of much research over the years, and various means have been developed to accomplish this task. For example, reflection seismology often makes use of Vibroseis© technology to impart elastic energy in the form of a frequency sweep into the ground. Since the source is known to a good approximation, an accurate reflection impulse response can be obtained through deconvolution or matched filtering. Use of anthropogenic sources place limits, however, on the depth of investigation. In global seismology, powerful natural sources, earthquakes, are used to probe structure to greater depths. In this case, the “receiver function” approximation [Vinnik, 1977] is made to remove the effect of the source, thereby introducing some degree of error, in particular regarding scattered P-waves [Mercier et al., 2006]. Moreover, since the distribution of earthquakes tends to be concentrated along plate boundaries, there are geometrical constraints placed on the imaging of subsurface structure. A third and independent approach to extracting scattered wave Green's functions was presented in a 1968 paper by Claerbout, who demonstrated that the 1-D subsurface reflection profile could be recovered through cross-correlation of seismic noise recorded at the surface from noise sources at depth. This work has been subsequently extended to 3-D [see e.g., Wapenaar and Fokkema, 2006]. Motivation for this approach resides in the fact that no source estimate is required, as cross-correlation largely eliminates the source signature. Practical demonstration of this concept has been accomplished in various settings (and frequency bands) including helioseismology [Duvall et al., 1993], ultrasonics [Lobkis and Weaver, 2001], and solid earth seismology [Campillo and Paul 2003; Shapiro et al., 2005; Roux et al., 2005]. Most solid earth applications have involved surface waves since the dominant noise sources are located close to the surface, and surface waves suffer less geometric loss than body waves. The work of Roux et al. [2005] represents an exception in that these authors identified the directly transmitted P-wave from correlations at seismic stations near Parkfield California. To-date, however, there has been little practical demonstration that weaker, scattered body-wave phases can be recovered from cross-correlations. In this paper we investigate the feasibility of using the recently documented non-volcanic Episodic Tremor and Slip (ETS) events [Rogers and Dragert, 2003] as a novel, deep-seated noise source to recover the scattered body wave Green's function within an active subduction zone through cross-correlation.

2. Data

[3] The map in Figure 1 displays the epicentral distribution of ETS in northern Cascadia for episodes in July 2004 and September 2005, as determined by Kao et al. [2005] (H. Kao, personal communication, 2005). ETS episodes occur every 13 to 16 months, and last from 10 days to a month as tremor moves from the south-east in northern Washington to the north-west along southern Vancouver Island [Rogers and Dragert, 2003; Kao et al., 2005]. The precise mechanism of ETS is not yet understood, and tremor depths can vary from 10 to 60 km. Tremor data satisfy several key requirements for recovery of scattered body wave Green's functions using seismic interferometry, namely: (1) a quasi-random source signature with near constant power spectrum in the frequency band of interest (1.5–10 Hz), (2) a source distribution that extends to depths below the target levels of interest, and (3) a wavenumber spectrum that is dominated by body wave energy [La Rocca et al., 2005]. We employ 3 stations of the Polaris-BC array [Nicholson et al., 2005] on Vancouver Island to recover tremor data for these two episodes. All high-amplitude tremor bursts (see Rogers and Dragert [2003] for examples) within the near vicinity of Polaris-BC stations LZB, MGCB, and TWKB were identified from epicenter compilations (see Figure 2) and corresponding seismograms were accessed using the Geological Survey of Canada automated server. On the basis of factors discussed in section 4, this station-event geometry was judged to afford the best likelihood of revealing structural signals using seismic interferometry. The final selection resulted in 24 and 44 hours of waveform data from the July 2004 and September 2005 episodes, respectively.

Figure 1.

Geographical setting. Black arrow indicates direction of ETS path progression across southern Vancouver Island. The locations of Lithoprobe lines 2 and 4 are indicated in the inset. Grey squares indicate tremor locations for 2004, white circles indicate tremor locations for 2005, and white triangles represent Polaris-BC stations. The dashed ellipses indicate the spatially clustered sources which contribute to reproducible arrivals for the two years.

Figure 2.

Schematic model involving a single, horizontal reflector between surface stations A and B with an underlying band of sources (stars). The solid line identifies the stationary ray path contributing to reflection on the causal portion of cross-correlation A*B. Sources on this line (black stars) illuminate this contribution. A second path on the right (dashed line) produces a comparable acausal contribution.

3. Data Processing

[4] The first task in preparing the data for analysis was to remove occasional, artificial high-amplitude transients resulting from instrumental noise sources using a standard despiking algorithm. The data were then divided into 30 minute segments, tapered, and filtered using a 1.5–10 Hz band-pass Butterworth filter to isolate the tremor signature. We detrended the filtered data, rotated them into a radial(R), transverse (T) and vertical (Z) coordinate system as defined by the station locations, and cross-correlated the results for all components of station pairs TWKB-MGCB and TWKB-LZB. Same-station, cross-component correlations and autocorrelations were also computed. We opted to always time-reverse components of station TWKB in the correlations. Correlated data were then amplitude normalized and stacked to investigate the presence of possible structural arrivals.

4. Geometrical Considerations

[5] Before proceeding to results, we consider a simplified problem geometry (Figure 2) and employ semi-intuitive arguments based on previous work [Snieder, 2004; Snieder et al., 2006] that will aid in our interpretation. A narrow horizontal reflector segment is located below and midway between 2 receivers at xA and xB on the free surface, within an otherwise homogeneous, acoustic medium. Within a depth interval underlying the reflector segment is a band of densely and uniformly distributed sources extending to infinity in both horizontal coordinates. These sources are uncorrelated when averaged over time and are recorded at the surface stations. The temporal correlation of wavefields recorded at the two receivers, denoted A*B (where * represents complex conjugation in frequency or reversal in time) can be represented as a volume integral. The integrand involves correlations of Green's functions propagating between source points x and receiver coordinates xA, xB convolved with the source autocorrelation (taken here as a delta function). We expect from the work of Snieder and coworkers that stationary phase evaluation of such an integral [Bleistein et al., 2000] will yield a two-sided (causal and acausal) quantity which is proportional to the Green's function for a source at one receiver recorded at the other. The extent to which the Green's function is properly represented depends on whether sources are present for all possible stationary points of the oscillatory integrand that give rise to significant physical arrivals. In the specified geometry, absence of sources near the Earth's surface to either side of xA and xB precludes recovery of the direct wave. The band of sources at depth (i.e. tremors) will, however, illuminate stationary paths corresponding to reflections from the short reflector segment via free-surface reflection at either of the two station locations. Two sets of stationary paths exist for this arrival along lines emanating from xA, xB that satisfy Snell's law for the reflection. Each path contributes to a different side of the correlation, such that, e.g. the path on the left produces the causal arrival for A*B.

[6] We expect these same geometrical relations to hold for more complex structural models, i.e. that sources to the left/right will contribute to causal/acausal portions of the correlation. For elastic waves we face the added complexity of excitation/observation component directions. Since the source/receiver geometry defines both the portion (causal or acausal) of the correlation on which stationary arrivals will occur and the ray geometry, the polarization direction of the wavefield on both the up-going (receiver side) and down-going (source side) portions of the raypath can be readily inferred. With a more complete, two-sided distribution of sources at depth, we should expect a symmetric correlation function with both sides corresponding to the Green's function. This assertion is, however, dependent on sources uniformly exciting all modes (P, S), a condition that, if not met, will break the symmetry.

[7] The main points to take from this simple analysis are: (1) true reflections within the Green's function will be built up from free surface reflections of transmitted waves created at depth from stationary points in the volume integral over source locations; (2) if the source distribution is dominantly to one side of the station pair, we expect to see meaningful contributions to the Green's function on only one side of the cross-correlation; and (3) the vectorial components of up and downgoing waves that constitute a particular scattered signal on the recovered Green's function can also be inferred from the source-receiver (transmission) geometry or, equivalently, from the portion (causal/acausal) of cross-component correlations on which that signal appears.

5. Results and Interpretation

[8] Figure 3 shows four panels of the first 10 s of cross-correlated 30 minute data segments prior to stacking. These examples display several coherent signals exhibiting little moveout as observed for most combinations of cross-correlations involving component Z with components R or T. Figure 4 shows examples of cross-correlations after stacking for which these same strong arrivals persist. A remarkable aspect of many correlations involving TWKB and MGCB is their reproducibility between the tremor events of 2004 and 2005 (Figures 4a and 4b). This observation, especially relevant for same-station correlations but also true for some cross-station correlations, strongly suggests that the tremor signature has been removed, and that we are left with some form of structural response. The most prominent later arrival for stations TWKB and MGCB occurs at 4.5 s, and is evident in both same-station and cross-station cross-correlations for combinations of component Z with components R or T. For cross-correlations between LZB and TWKB, (Figure 4c) an arrival occurs at 3.5 s and although not as reproducible between years as results from TWKB-MGCB, it appears on correlations of Z with both R and T for the 2005 sequence. For both station combinations in 2005, the strong arrivals emerge from spatially clustered tremor events to the northeast of the stations as shown in Figure 1. If the tremor source moves in a stable, steady fashion, we would expect strong arrivals exhibiting little moveout in the cross-correlations to correspond to stationary points of the integral discussed in section 4, and thus to represent physical signals, e.g. specular reflections [Van Manen et al., 2005; Snieder et al., 2006].

Figure 3.

Cross correlations for different combinations of stations and components displaying large coherent arrivals for the September 2005 ETS episode. Plot titles identify components and stations as described in the text. The labels −c and −a indicate whether the correlation is shown for positive or negative lags, respectively.

Figure 4.

(a, b) Grey lines represent correlations between TWKB and MGCB for the 2005 ETS event, whereas black lines represent correlated data for the 2004 ETS event. Labels −a or −c indicate whether the causal or acausal portion of the correlation is plotted. (c) Stacked data for correlations between stations TWKB and LZB for 2005. Grey lines display causal correlated data from 2005, black lines show acausal correlated data for 2005. Note 3.5 s arrival appearing on causal lags.

[9] To develop a physical interpretation for these signals we must examine their temporal, spatial and directional attributes. Consider first the 4.5 s arrival evident on correlations for TWKB and MGCB. Its presence on cross-component correlations suggests it represents a conversion-reflection mode. On cross-station correlations, the arrival is stronger for the 2005 tremor locations than the 2004 suite and is evident on causal portions of correlations Z*TRM and Z*TTM and acausal portions of correlations R*TZM and T*TZM, where subscripts T, M, L will denote stations TWKB, MGCB, LZB, respectively. The 2005 source locations are symmetrically disposed with respect to both stations, consistent with the appearance of coherent energy at both positive and negative lags. The 2004 sources lie to the SE of both stations and the signal appears strongest on R*TZM at negative lags, as expected. These observations combined with the fact that ETS generates dominantly S-waves [La Rocca et al., 2005], suggests the signal is composed of combinations of S reflection/conversion at the free surface followed by conversion at subsurface structure, that is an S-P-S ray path. The timing of the signal at 4.5 s places the likely depth of this structure near 10 km.

[10] As previously mentioned, the TWKB-LZB arrival at 3.5 s is less well defined. Here we note that the source/station geometry is rather different from that for TWKB-MGCB. The 2005 tremor sequence, for which the 3.5 s arrival is most pronounced, extends further to the NE than the 2004 sequence (which, in contrast, more closely parallels the NW–SE line joining TWKB and MGCB, see Figure 1). Sources further to the NE may be more suitably positioned therefore to produce stationary arrivals that are not represented in the 2004 tremor sequence. The 3.5 s arrival for the 2005 sequence is best defined on the causal portions of correlations Z*TRL, Z*TTL and a little less clearly on Z*TZL. This combination of components and source-receiver geometry again conforms with an interpretation as S-P-S. We also note that the greater distance between sources and stations, and the earlier arrival time (3.5 s versus 4.5 s) are both consistent with an origin from shallower structure.

[11] For additional insight into the nature of subsurface structure responsible for these arrivals, we compared results with seismic reflection data collected as part of the Lithoprobe southern Cordillera transect [Clowes et al., 1987]. Seismic lines 2 and 4 are located a few km to the southeast and west of our station pairs LZB, TWKB, MGCB (see Figure 1) and the corresponding reflection profiles image a sequence of strong reflectors between 9 and 14 km depth that dip at approximately 20 degrees in a northerly direction. The timing of the 3.5 s and 4.5 s arrivals would be consistent with origins from the depth interval (9–12 km) corresponding to the B and C layers based on simple 1-D velocity models for the region [e.g., Nicholson et al., 2005]. The B layer coincides with the Leech River thrust fault that marks the juxtaposition of Eocene basalt terranes with continental rocks, whereas the C layer is interpreted as the top of the underplating subduction complex [Clowes et al., 1987]. The appearance of signals on correlations involving the transverse component implies the presence of lateral heterogeneity and/or anisotropy, both of which are documented for this region [Clowes et al., 1987; Cassidy and Bostock, 1996].

[12] To conclude our discussion we consider the limitations of the imperfect source distribution represented by the tremor events. We generally note short lag (i.e. [−0.5 s, 0.5 s]) large amplitude signals on the correlations for TWKB-MGCB for both 2004 and 2005, that probably signify the presence of uncancelled (i.e non-stationary) contributions from deep sources near stations. These signals are too early to correspond to the true, first arrival within the Green's function that should arrive near ±0.8 s based on a 4 km station separation and a near surface P-velocity of 5 km/s. Moreover, from the arguments made in section 4, we would expect the true first arrival to emerge from stationary contributions corresponding to shallow, near-surface sources on either side of the station pair. Another interesting point concerns the correlations for TWKB-LZB. The ETS distribution for 2005 from H. Kao (personal communication, 2005) places the sources dominantly to the NE of the station pair. As predicted for this geometry, the spatially clustered tremors for 2005 generate a large coherent arrival on the causal portions of correlations, while the acausal portions display mainly incoherent energy (Figure 4c).

6. Conclusions

[13] Stacked correlations of ETS tremor data from recordings at Polaris-BC stations TWKB and MGCB show remarkable consistency between ETS events in 2004 and 2005 for same station correlations and, to a lesser degree, cross-station correlations. This consistency suggests the emergence of a structural signal which is related to the Green's function that would be recorded at one station due to a point source at the other, as predicted from the theory of seismic interferometry [Wapenaar and Fokkema, 2006]. Cross-station correlations from stations TWKB and LZB are less reproducible but, for the 2005 ETS sequence, nicely demonstrate the predicted emergence of signal at positive lags for sources located to the northeast of the stations. Approximate knowledge of the source-receiver geometry allows us to interpret strong, structural arrivals observed at 4.5 s (TWKB-MGCB) and 3.5 s (TWKB-LZB) as dominantly S-to- P-to- S reflection-conversions. The timing of these arrivals places the scattering structure at depths between 9 and 12 km, which corresponds to the interval at which reflectors B and C were identified in seismic reflection profiles over the same region [Clowes et al., 1987]. If our interpretation proves correct, it would represent an important practical demonstration of the retrieval of scattered body wave contributions to the surface Green's function using seismic interferometry and deep, passive sources. Because ETS events occur at regular and frequent 14 month intervals, it may prove feasible to tailor future seismic experiments for the investigation of subsurface structure using this approach.


[14] We thank Honn Kao for supplying us with unpublished tremor locations for the 2005 sequence. We gratefully acknowledge the technical assistance of Issam Al-Khoubbi, Isa Asudeh and the Polaris technical team. Denoising of data was accomplished using the Wavelab wavelet transform package for Matlab. This work was supported by a Natural Sciences and Engineering Council of Canada Discovery Grant to MGB.