Geophysical Journal International

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1 Geophysical Journal International Geophys. J. Int. (2012) 191, doi: /j X x Imaging the shallow crust with teleseismic receiver functions Garrett M. Leahy, Rebecca L. Saltzer and Jan Schmedes ExxonMobil Upstream Research Company, 3319 Mercer St., Houston, TX 77027, USA. Accepted 2012 July 16. Received 2012 July 8; in original form 2011 August 2 1 INTRODUCTION Controlled-source seismology is a standard tool for imaging the Earth s shallow crust. However, this technique can fail in complicated tectonic settings where conventional sources (such as dynamite or vibroseis trucks) have insufficient amplitude to overcome attenuation and scattering. Alternatively, earthquakes provide large, broad-band sources that can be passively recorded anywhere on the globe. However, attenuation of higher frequencies over long propagation paths is thought to limit the ultimate resolution of earthquake data. To assess the ability of earthquake data to constrain shallow structure, ExxonMobil funded the LaBarge Passive Seismic Experiment (LPSE) in collaboration with the University of Arizona. 63 broad-band seismometers (CMG-3Ts, Guralp Systems Ltd, Reading, UK) from the PASSCAL instrument pool were deployed in western Wyoming and continuously recorded at 100 Hz from 2008 November to 2009 June. The deployment included a dense array, with 250 m station spacing that permits direct assessment of the spatial resolution of earthquake analysis techniques (Fig. 1). This station spacing is two orders of magnitude smaller than that used in typical academic studies (tens to hundreds of kilometres). The data were archived with IRIS and are available to the public. A full description of the deployment including station installation and servicing was presented by Saltzer et al. (2011). The LPSE array has three branches. The northwest branch is angled towards the Aleutian Trench, and the southern branch is angled towards the Andean subduction zone. These orientations help to improve ray coverage for use in tomographic studies (see SUMMARY Teleseismic receiver functions (RFs) represent an estimate of the site-response to incoming seismic energy. This technique has long been a staple of the global earthquake community, as RFs are sensitive to impedance contrasts associated with major discontinuities in the crust and upper mantle. However, there is substantial debate in the community concerning the lateral and vertical resolution limits possible using these methods due to limitations resulting from ambient noise and non-uniform spatial sampling of finite-frequency wave kernels. Here, we take advantage of data from the LaBarge Passive Seismic Experiment to examine these questions in more detail. We find (1) that RFs can provide a robust image of the near-surface (<5 km) structure; (2) that vertical resolution may exceed 500 m and (3) that our results compare favourably to nearby wells. These results indicate that RF analysis can provide highresolution images of the shallow crust, which has potential value for hydrocarbon exploration. Key words: Body waves; Coda waves; Continental tectonics: compressional; Crustal structure; North America. Schmedes et al. 2012). The east west branch of the array is oriented to be perpendicular to the major local structural feature, the Hogsback thrust. The surface expression of this fault runs through the centre of the array, just to the east of Cretaceous Mountain (Fig. 1). The thrust fault placed about 1 2 km of Palaeozoic carbonates onto late Mesozoic clastics (e.g. Coogan 1992; Royse 1993). This yields a shallow, high-velocity wedge in addition to the more homogeneous basin structure, both of which can be used to assess resolution and value of earthquake imaging techniques. Because the P wave and coda retain the highest frequency components remaining in earthquake waves, we hypothesized that teleseismic receiver functions (RFs) would be a suitable technique to resolve structure in the shallow crust. RFs represent S waves scattered by the P-wave arrival as it interacts with interfaces below the recording station (Langston 1979). Previous attempts to use RFs to obtain shallow crustal structure (e.g. Leahy & Park 2005; Zevallos et al. 2009; Leahy et al. 2010) report high frequency results (RFs containing information in excess of 3 Hz), but with stations that are essentially in geological isolation (spaced greater than 1 km apart). In this study, we take advantage of the close station spacing of the LPSE array to examine the ability of teleseismic RFs to resolve structure in the shallow crust. We examined the frequency dependence of shallow converters at each station in the array, and compared imaged structure at nearby stations. Our results indicate that RFs do contain signal attributable to the shallow crust: in fact we are able to image the base of the LaBarge thrust with resolution exceeding 500 m. A key finding of our study is that these results can be obtained with currently available methods and software (see methods) with little or no modification. Furthermore, these GJI Seismology C 2012 ExxonMobil Upstream Research Company 627

2 628 G.M. Leahy, R.L. Saltzer and J. Schmedes measurements compare favourably with sonic logs from nearby hydrocarbon wells. Combined, these results indicate that earthquake analysis techniques may provide an alternative pathway for nearsurface imaging in tectonically complex regions. 2 GEOLOGICAL CONTEXT Major features of the LaBarge field were formed by compressional deformation during the Laramide orogeny (Coogan 1992; Royse 1993; Law 1995). Hydrocarbon reservoirs have been discovered in Cambrian through Tertiary formations. Classic reservoirs in the vicinity of the LaBarge anticline include the Madison Limestone (Mississippian), Nugget Standstone (Jurassic) and the Mesaverde Group (Cretaceous) among others (Law 1995), likely sourced from the Phosphoria formation (Permian) or the older limestone sequences. See Powers (1995) for a detailed stratigraphic column. In particular, the LPSE array crosses the Hogsback thrust, a lowangle fault associated with eastward motion beginning in the late Jurassic and proceeding to the Eocene (Powers 1995). Potential hydrocarbon plays are located in both the hangingwall (e.g. Darby Formation and Madison Group), and Cretaceous reservoirs (predominantly sandstones and shales) in the footwall (Powers 1995). The carbonates in the hangingwall present a challenge to active source seismic imaging, as their generally heterogeneous structure scatters seismic energy. However, the emplacement of the high seismic velocity carbonates above the sandstones and shales results in a large impedance contrast that we show here can be detected using natural source seismicity. 3 D ATA A N D M E T H O D S The LPSE resulted in the collection of individual seismograms of teleseismic events of magnitude 5 and greater (Fig. 2) with epicentral distances between 30 and 90. RFs rely on correlations between recorded components at different frequencies, requiring careful event screening to eliminate events with correlated noise or low signal-to-noise ratio (SNR). The screening criteria used were as follows: (i) Determine the presence of a P-wave arrival near (±5 s) the predicted time via visual inspection of the seismogram: we used different frequency bands (unfiltered, f < 0.5 Hz, 0.5 < f < 5 Hz), noting that the minimum distinguishable SNR is generally greater than two. (ii) Determine whether the event has a stable multitaper cross-correlation (MTC) single-event RF (see below for details): we looked for the presence of a positive amplitude pulse at t = 0 using cut-off frequencies ranging from 1 to the frequency of interest, and controlled for Figure 2. Selected teleseismic earthquakes and their ray paths recorded at the LPSE array. C 2012 ExxonMobil Upstream Research Company, GJI, 191, C 2012 RAS Geophysical Journal International Figure 1. A map of the LaBarge Passive Seismic Experiment dense array. Stations (red circles) are spaced roughly 250 m apart, and the east west axis crosses the Hogsback thrust (approximate, after Oriel & Platt 1980). Highway 235 and a gas pumping station are a large source of cultural noise.

3 Shallow crustal imaging with RFs 629 Figure 3. Number of events screened and accepted at each station in the LPSE array. Low event yields are typically correlated with the presence of local noise sources, such as roads and drilling rigs. correlated noise or structural resonances. These effects are typically evident by monochromatic ringing in the RF trace in both the causal and acausal portions. Ringing in RF traces derives from coherent seismic energy reverberated in near-surface layers that can obscure the recovered structure. Because this resonance can be excited by ambient noise, the presence of ringing in the RF before the arrival of the P wave is a clear diagnostic tool. Though a stable RF may still be obtainable using a properly designed filter, this adds uncertainty and was ultimately unnecessary given the large number of high-quality events. After screening, we obtained 5853 total acceptable events, an average of slightly over 100 per station. Fig. 3 shows events screened and accepted at each station in the array. Event screening and single-station analysis shows that low event yield correlates with proximity to known sources of field noise in a variety of frequency bands. Key examples of this include the primary access road passing through the valley, resulting in low yields near stations 29 30, and Furthermore, active drilling contributed to low yields near stations 35 37, and pumping activity to low yields near stations 06 and Structure in the top 5 km of the crust results in Ps converted waves arriving in the first 1 2 s of the P coda. This requires that the RF computation provides robust results at frequencies exceeding those typically used in academic studies (3 5 Hz, see Leahy & Collins 2009). We therefore use a multitaper cross-correlation technique following Park & Levin (2000). This method is a noisedamped frequency domain operator that computes independent RF estimates at all frequencies present in the time-series. Furthermore, this method permits the computation of frequency-dependent signal variance (Park & Levin 2000), which provides an estimate of the reliability of a given signal. Visually, RFs are essentially plots of the Earth s impedance structure, with the time axis representing the relative delay time between the direct P arrival and the arrival of the scattered S wave from a material contrast. For the purposes of this study, frequency content of the RFs is parametrized via the corner frequency f (3 db down point) using a filter with cosine-squared roll-off (eq. 1, Leahy & Collins 2009). Subsequent references to frequency reflect choice of this parameter. The maximum frequency content in this formulation is given as 4 3 f. To image the shallow structure, we need to compute RFs with increasingly higher frequency. When RFs are computed in the Radial Transverse Vertical coordinate system (as here), a large, positive correlation is present at t = 0, representing correlated parti- Figure 4. Amplitude spectra of the vertical components of earthquakes (red) and pre-event noise (blue) at station L01. Mean amplitudes are plotted, as well as the total amplitude range (shaded) over the entire data set. cle motion on the radial and vertical components due to non-vertical ray incidence. This primary arrival may overprint subsequent conversions. This can be mitigated by rotation to the P-Sv-Sh coordinate system, but that requires an accurate estimate of the local velocity model. Instead, higher frequencies can be used, as they shrink the width of the correlation pulse at t = 0. Higher frequencies also act to reduce the length-scale at which two converters can be distinguished, because at least a quarter period of conversion separation is required to isolate an arriving conversion (Widess 1973). However, in addition to its benefits, high-frequency analysis has several drawbacks. First, the peak signal-to-noise ratio for teleseismic P waves is at approximately 1 Hz (Fig. 4). This implies that as we increase the frequency content of the RFs above this value we increasingly risk misinterpreting random correlations in the ambient noise background as subsurface structure. Secondly, increasing frequency results in a need to interpret an increasing number of possible converting interfaces. For stations in isolation, the interpreter may have difficulty identifying anything but the most obvious conversions in the P coda. Because Fig. 4 shows the presence of energy with signal-to-noise ratios between two and 10 at frequencies above 10 Hz, this may lead to an underutilization of the data. The method we use here addresses both of these concerns. The method downweights RF traces with high noise content, leading to relative weighting of a given frequency component shared between events, thereby extracting only the most robust high-frequency portion of the signal. We stack multiple events occurring over a long

4 630 G.M. Leahy, R.L. Saltzer and J. Schmedes period of time to ensure that we sample a variety of ambient noise conditions, leading to enhanced signal by cancellation of noise. Finally, we exploit the close station spacing of the LaBarge array to enhance confidence in the signal. Stacks of events at adjacent stations should sample similar geological structure, and therefore we do not expect to see substantial variations in the computed RFs. Apart from these precautions, and the use of higher frequencies in the algorithms, no additional processing is required to obtain high-resolution images. Therefore, we found that commonly available software and existing techniques can be used to image shallow structure without modification. As a further control, we compute jackknife uncertainties (Leahy & Collins 2009). For each stacked average RF trace, this technique computes an ensemble of stacked RF traces by resampling events present in the stack. The variability in the ensemble is interpreted as an estimate of uncertainty in the final stack. RF amplitude exceeding one standard deviation from zero is considered robust, helping the analyst to distinguish between primary conversions (that stack coherently) and uncorrelated random noise (which typically does not stack coherently) or reverberated phases that tend to have higher Figure 5. Stacked receiver functions at 2 Hz. The direct arrival is indicated at 0 s, as well as a basement reverberation and a candidate Moho converter. Positive (blue) amplitude represents increasing impedance with depth. uncertainties due to more complicated ray paths and higher order effects (such as dipping layers or velocity perturbations). Each of these products is then carefully examined to determine whether or not amplitude on the RF trace is generated from a genuine Ps conversion in the crust. 4 RESULTS The first test of the acquired data set and our processing method is to identify the Ps conversion from the Moho discontinuity. This interface can occur over length-scales varying from hundreds of metres to several kilometres, depending on the tectonic setting. For LaBarge, we expect the continental setting may result in a broader transition, and therefore perform our analysis at 2 Hz yielding an approximate vertical resolution of 5 km. This represents the approximate thickness of a layer sampled in 0.5 s of Ps delay time for crustal velocities (eq. 4, Leahy & Collins 2009). For each station, all events are stacked together assuming moveouts are small relative to the 2 Hz frequency content of the RF traces. Our results (Fig. 5) indicate the presence of a candidate Ps conversion arriving at approximately 6 s for all stations. The similarity of the measurement between stations is as expected: the array aperture is about 7 km, and we do not expect the deep crustal structure to change dramatically on this length-scale. We estimate the depth of this conversion to be approximately km by using a seismic velocity reference model (IASP, Kennett & Engdahl 1991) to migrate the arrival to depth. This value is broadly consistent with other regional studies (e.g. Gans et al. 2011). Not surprisingly, our results using the 2 Hz filter do not suggest much shallow structure. Because the direct P arrival contains energy on both the horizontal and vertical component of the seismogram, RFs have a large correlation pulse centred at zero time. With a large-wavelength spatial filter, this pulse may be up to several seconds wide, effectively hiding near-surface conversions. This problem can be mitigated by rotating the arriving wave into the P- Sv-Sh frame, but this requires an approximate velocity model and is not necessarily indicative of primary structure. We then apply the RF technique at increasingly higher frequencies. This narrows the direct P arrival, revealing possiblepsconversions from the near-surface. Fig. 6 shows a suite of RFs computed from events recorded at station L01. The RFs, binned by epicentral distance, are plotted in time versus epicentral distance (offset) in Figure 6. Epicentral distance stacks of receiver functions for station L01. Increasing the frequency content of the receiver functions increases the resolution of geological structure and helps to determine which conversions are real. Positive (blue) amplitude represents increasing impedance with depth.

5 Shallow crustal imaging with RFs 631 degrees. Examining how features sharpen with increasing frequency resolution provides a strong indication as to the reliability of the signal. For example, in Fig. 6, a positive conversion (blue) is seen at approximately 0.8 s of Ps delay time. As frequency content increases (left to right) the pulse sharpens but remains essentially stationary in time. Lack of significant focusing beyond 10 Hz suggests that the converting interface is actually a transitional gradient spanning approximately 0.1 s of the time sequence. In contrast, the negative (red) arrival imaged at low frequency at approximately 0.4 s of Ps delay time breaks down into a series of pulses at higher and higher frequencies, with only the arrival at 0.5 s remaining robust beyond 10 Hz. This analysis helps to build confidence in the potential resolving power of the data at higher frequencies, but further tests are required. A major benefit of the LPSE with regards to RF imaging is the tight station spacing of 250 m. At peak frequency (1 Hz), this width approximates the wave s Fresnel zone (sampling kernel), implying that two adjacent stations essentially see the same structure. Further increase in the frequency content of the RFs includes more and more information that is unique to the particular recording station. On the other hand, we also expect varying length-scales to be present in the geological structure: the Moho may be uniform over the entire array; basement structure may change over several hundreds of metres; or local faulting may cause changes over several tens of metres. These two considerations suggest that the RFs should image smoothly varying structure from station to station. As an example, Fig. 5 shows that at low-frequency stations L25 L28 show identical structure. At high frequency (Fig. 7), the structure remains similar but has developed small changes due to local structure or noise conditions. Visual inspection demonstrates that correlation between stations decreases with increasing separation, though quantification of this effect remains elusive due to the ambiguity between spatial coherence of ambient noise and structural coherence. These effects are inseparable without external constraints. Further analysis can be performed to distinguish primary conversions from layer multiples (e.g. PpPs, PpSs, or PsPs, see Zhu & Kanamori 2000; Leahy & Park 2005, for ray diagrams). Primary conversions arrive earlier in the time-series as the epicentral distance of the source increases. This is because the waves propagate with increasingly vertical incidence angle as they approach the recording C 2012 ExxonMobil Upstream Research Company, GJI, 191, C 2012 RAS Geophysical Journal International station. Conversely, multiples arrive later with increasing epicentral distance. The difference in slope therefore allows the analyst to distinguish primary arrivals (negative slope) from multiples (positive slope) in RF trace plots. In Fig. 8, we show how a conversion at 0.8 s has a negative slope and is therefore primary, while a later arriving conversion at 2.0 s has a positive slope and is therefore likely a multiple. This hypothesis is supported by similar analyses performed at all stations in the array (see Supporting Information for epicentral stacks at all stations at 15 Hz). Additional confidence can be gained by examining the computed RF uncertainties. Fig. 8 shows an epicentral distance stack from station L40 compared to an identical stack with RF uncertainties applied. In the second frame, only amplitude exceeding one standard deviation from zero is plotted. Several primary conversions ( 0.8 s) are seen to sharpen when this filter is applied, whereas the multiples ( 2 s) tend to be eliminated as they have higher uncertainties due to complex ray paths and other higher order effects. In an alternative interpretation, Gans et al. (2011) propose the presence of a mid-crustal interface with Ps conversions arriving with the basement multiples. The authors found that reverberations from this proposed interface interfered destructively with the Moho signal underneath the array, explaining the weak amplitudes identified in Fig. 5. Our analysis of statistically significant RF amplitude cannot definitively rule out the presence of such an interface, but suggests it is either highly variable from station to station and event to event, or perhaps not required by the data. An RF image along the array is presented in Fig. 9, where each individual trace represents a summation of all data from a given station. In this figure, we plot only the first 4 s of the RF trace, as this captures both shallow structure as well as later arriving multiples. We see several notable features. The feature that dominates the section is the positive (blue) arrival at approximately 0.8 s, and is present at every station examined in the array. This arrival is shallowest underneath stations L09 L14, and grows gradually deeper (to 0.9 s) to the east. The changes in arrival time for this pulse are very gradual from station to station. Secondly, two negative (red) arrivals appear in the western portion of the array (stations 1 17). These arrivals shoal and converge near station 11. Because a negative arrival indicates decreasing velocity with increasing depth, these signals are indicative of a possible highvelocity lid. The decrease in arrival time for eastern stations relative to western stations is indicative of a possible dipping interface. Figure 7. Epicentral distance stacks of receiver functions for stations L25 L28. Adjacent stations show similar, smoothly varying structure at 10 Hz. Positive (blue) amplitude represents increasing impedance with depth.

6 632 G.M. Leahy, R.L. Saltzer and J. Schmedes Figure 8. Epicentral distance stacks for station L40 at 15 Hz cut-off frequency. Direct Ps conversions and PpPs multiples are identified based on their moveout. The left panel shows raw RF amplitude, whereas the right panel shows the 1σ significant amplitude, a process that mitigates noise-related correlations. Positive (blue) amplitude represents increasing impedance with depth. Epicentral stacks for all stations at 15 Hz are presented in the Supporting Information. Thirdly, a more disperse train of arrivals is seen at most stations, particularly in the eastern, uniform portion of the array. These conversions are first positive ( s) then negative ( s), with energy partitioned between multiple broad pulses. The arrival times for these conversions and positive moveout again suggest that these pulses correspond to reverberations in the shallow layer delineated by the 0.8 s conversion. Furthermore, the dispersed nature of the putative multiples is suggestive of the presence of a velocity gradient. 5 DISCUSSION These results are suggestive of possible structure. However, deriving a model of subsurface structure is challenging. RF amplitudes are sensitive to impedance contrasts at material interfaces, and multiples from shallow layers can easily interfere with later arriving phases resulting in converted amplitudes that do not represent true interface properties. The most straightforward, first-order interpretation can be achieved by simply forward modelling traveltimes for

7 Shallow crustal imaging with RFs 633 Figure 9. Receiver function image of the subsurface along the primary array axis. Each trace represents a weighted average of RFs from all earthquakes at a given station. Positive (blue) amplitude represents increasing impedance with depth. converted arrivals, but even this method involves some ambiguities as traveltimes are non-unique indicators of Vp, Vs and layer thickness h. Additional constraints are required to obtain an accurate subsurface model. One way to do this is to consider the predicted arrival times of multiples in addition to the direct arrival. This technique, developed by Zhu & Kanamori (2000) and Chevrot & van der Hilst (2000), uses multiples to constrain one additional parameter, namely the Vp/Vs ratio. The process examines a 2-D space of Vp/Vs and h, and for each point in that space computes the predicted arrival time for the direct conversion (Ps), and two classes of near-surface multiples (PpPs and PpSs). The amplitudes of the RF trace at these arrival times are then stacked, noting that the polarity of PpSs is predicted to be flipped relative to the other two arrivals. The location of the maximum value (and its uncertainty) is expected to be the preferred property model for the data. This analysis can be extended to incorporate the amplitudes of many individual RF traces sampling a given structure, which further constrains the model while reducing the impact of noise contamination. The application of this technique to shallow structure suffers from several drawbacks. First, the resolution is directly related to the frequency resolution of the RFs: low-frequency RFs have greater uncertainties than high-frequency RFs. This is particularly acute with shallow structure, where differences in delay times between multiples and direct arrivals as a function of layer thickness are small. Furthermore, higher frequency analysis provides more information to interpret, and deeper conversions are impacted by the velocity structure of shallow layers. Finally, multiple stacking can introduce ambiguity if the multiples are dispersed (as in this data set) rather than comprising a coherent arrival. Because of these considerations, we decided to focus this analysis on two stations, first on one from the eastern portion of the array (L40, with apparently uniform shallow structure) and second on one from the western portion of the array (L01, with the velocity inversion). In both cases, one free parameter remains, which is typically chosen to be Vp as this parameter is less sensitive than Vs to physical conditions or fluid content, and h is generally unknown. For the eastern station, we assumed an average sediment Vp of 4kms 1, and found this resulted in a Vp/Vs ratio of approximately two, and a candidate basement converter at approximately 3.5 km depth (Fig. 10, upper). For the western station (Fig. 10, lower), noting the likely velocity inversion, we assumed a Vp of 5 km s 1 based on presumed carbonate lithology of the Hogsback thrust (Coogan 1992), and examined the negative conversions instead of the positive conversions. This analysis yielded similar results for Vp/Vs ratio, but required a thinner layer (of approximately 1 km). Whereas Vp/Vs = 2 is high relative to typical crust and mantle lithologies, these values are routinely measured in sedimentary systems, and in fact values exceeding 10 are not uncommon in near-surface layers (Hamilton 1979). In principle, this analysis can be extended from single-layer property estimates to full velocity models by building a stack of layers recursively down from the surface. Furthermore, this technique could also be applied at every single station, yielding a full velocity model for every location in the array. For the purposes of this study, however, we used these results to help to guide the development of a regional velocity model that would then be applied at each of our stations, using synthetic RF trace modelling to derive station-specific velocity models. Synthetic seismograms were computed using an elastic propagator matrix method (Levin & Park 1997, 1998) that accounts for direct arrivals, mode conversions and their multiples. Using this information, we developed a generalized five-layer model (Fig. 11). At each station, we tested which of these five layers were present, and if present, what thickness is required in order for the RF traces to approximate the data. Layer properties were chosen based on the initial inspection of the data presented earlier. The layers, from deepest to shallowest are (i) typical granitic basement, (ii) a gradient from sediment velocities to basement velocities (representing the original carbonates preserved in the footwall), (iii) typical buried clastic sediments, (iv) the carbonate thrust sheet and finally (v) shallow, near-surface clastic sediments. During the modelling, the order of the layers does not change, merely their presence and thickness. Fits were assessed by visual comparison between observed and predicted station-stacks. Because the synthetic forward model operates on stacks of flat layers, gradients were represented by a sequence of layers of intermediate velocities. This assumption could cause problems if the layer thickness is large relative to the frequencies of interest. To control this, we performed tests of gradient representation using layer thicknesses ranging from 1 to 500 m. We found that gradients

8 634 G.M. Leahy, R.L. Saltzer and J. Schmedes Figure 10. Stacked RF amplitude using direct Ps conversions and multiples can constrain layer Vp/Vs ratio. The upper panel represents analysis for the sediment column at station L40, and the lower panel analysis for the carbonate overthrust. The stars indicate the maximum amplitude. represented as stacks of layers less than 200 m thick reproduced RFs from fine-scale representations (e.g. 10 m) at the frequencies of interest. Use of a simple model for the petrophysical properties substantially reduces the complexity of the modelling effort, but results in RF traces with amplitudes that may differ from those observed in the data. However, multiples, conversion interference and data noise also affect pulse amplitudes in complex ways that can introduce error to the resulting image; we therefore proceed with the knowledge that a more sophisticated effort will be necessary to image second-order structure. Furthermore, because of the trade-off between velocity and layer thickness, the synthetic modelling process tolerates some degree of non-uniqueness though it is somewhat mitigated by the control obtained on Vp/Vs. The synthetic model therefore speaks only as to whether the hypothetical structure is consistent with the data. We find that the synthetic model based on the simple-layered structure proposed earlier (Fig. 12) reproduces the major characteristics of the data. In particular, we demonstrate that a velocity inversion is necessary to reproduce the shallow structure in the western portion of the array, and that this structure tapers from west to east. In a detailed sense, the synthetics show that the two red pulses representing the velocity inversion are the direct conversion ( 0.2 s, 1 km depth) and the PpPs reverberation ( 0.5 s) in the carbonate layer. These two pulses converge as the structure shallows, and the reverberated time delay approaches the direct arrival time delay. This interpretation is consistent with the presence of the Hogsback thrust (Fig. 13), which emplaced high-velocity Palaeozoic carbonates onto lower velocity late Mesozoic clastic strata (e.g. Coogan 1992; Royse 1993). Beneath the thrust sheet, the synthetic model verifies the presence of the basement converter at roughly 3-4 km depth. In the eastern portion of the array, the data are consistent with a slowly dipping basement conversion, as well an intermittent shallow converter at 1 2 km depth which may correspond to the base of the Mesaverde formation. Careful consideration of the reverberations associated with the basement conversion support the hypothesis that a transitional layer with increasing velocity is required by the data just above the granitic half-space. Although distinct layers are not C 2012 ExxonMobil Upstream Research Company, GJI, 191, C 2012 RAS Geophysical Journal International Figure 11. A cartoon of the generalized velocity model used in the forward modelling step.

9 Shallow crustal imaging with RFs 635 Figure 12. Synthetic RFs generated using the estimated structural model (Fig. 13). Positive (blue) amplitude represents increasing impedance with depth. Figure 13. Cartoon of the Hogsback thrust (after Royse 1993), with structural model used to generate synthetic RFs (Fig. 12). resolved by direct conversions, the top of the gradient appears to be consistent with the Nugget formation at approximately 3 km depth. Several notable differences can be discerned between the real and synthetic data. First, the amplitudes of shallow conversions appear at times to be considerably different. As mentioned before, this is likely to result from both errors in the velocity model, as well as noise in the data. Secondly, in the eastern portion of the array we image coherent negative energy arriving after the basement converter between 1 and 2 s that is not captured by the synthetic model. The timing may be supportive of a PsPs reverberation in the Mesaverde formation, and the lack of support in the model may indicate that the velocity contrast is larger than expected from the direct conversion alone. Finally, there are indications that coherent Figure 14. Comparisons of RF velocity model to nearby well logs. Well locations are shown in Fig. 1. The top panel corresponds to the well near station L12, and the bottom panel corresponds to the well near station L19. pulses are arriving even after the sediment-layer reverberations. These may be more complicated multiples from shallow structure, or may represent features of the granitic basement, but further analysis is required to distinguish between these possibilities. A few deep wells drilled near the seismic array allow us to compare the model derived from RFs to logs from nearby wells (Fig. 14). Our results suggest that with no external constraints, the RF model succinctly captures the first-order structure of the wells. In particular, we image the high-velocity thrust sheet (not always present in well logs due to shallow casing), a velocity gradient, and the granitic basement. Of course, errors in the velocity model propagate through the section, resulting in inaccuracy in the exact basement depth, yet the accuracy is striking for such a simple model. 6 CONCLUSION RF analysis of the data collected during the LPSE strongly supports the use of earthquake data as a tool to image the shallow crust. The data indicate that geological structure can be resolved, including basement as well as a high-velocity thrust sheet. Conservative estimates of vertical resolution from synthetic modelling suggest that 500 m thick formations should generally be identifiable using this technique, whereas lateral resolution may exceed 250 m (the station spacing in this experiment). The ability of RFs to resolve structure at frequencies in excess of 10 Hz with the appropriate processing techniques suggests that other, more sophisticated analytic tools (such as anisotropic modelling) may also be successfully applied to this data set. Finally, these

10 636 G.M. Leahy, R.L. Saltzer and J. Schmedes results show that there is significant room for collaboration between the generally academic natural source seismology community and the generally energy-related controlled-source seismology community. This is particularly relevant in regions where controlled sources are insufficiently large to illuminate structure, or where other constraints (e.g. wildlife sensitivities, rugged terrain or infrastructure) render controlled sources impractical. ACKNOWLEDGMENTS We would like to thank Susan Beck, George Zandt and their groups at the University of Arizona for their efforts during the deployment; Tom Becker for discussions regarding the regional geological framework; Christine Gans for early technical discussions, and Vadim Levin and an anonymous reviewer for improvements to the final manuscript. The instruments used in the field program were provided by the PASSCAL facility of the Incorporated Research Institutions for Seismology (IRIS) through the PASSCAL Instrument Center at New Mexico Tech. Data collected during this experiment will be available through the IRIS Data Management Center. The facilities of the IRIS Consortium are supported by the National Science Foundation under Cooperative Agreement EAR and by the Department of Energy National Nuclear Security Administration. REFERENCES Chevrot, S. & van der Hilst, R., The Poisson s ratio of the Australian crust: geological and geophysical implications, Earth planet. Sci. Lett., 183, Coogan, J.C., Structural evolution of piggyback basins in the Wyoming Idaho-Utah thrust belt, in Regional Geology of Eastern Idaho and Western Wyoming, Geol. Soc. Am. Mem. 179, pp , eds Ling, P.K., Kuntz, M.A. & Platt, L.B., Geological Society of America, Boulder, CO. 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Res., 105(B2), SUPPORTING INFORMATION Additional Supporting Information may be found in the online version of this article: Supplement. Epicentral stacks for all stations at 15 Hz. Please note: Wiley-Blackwell are not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.