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Corresponding author: J. P. Richardson, Department of Geological and Mining Engineering and Sciences, Michigan Technological University, Houghton, MI 49931, USA. (email@example.com)
 The complex source processes associated with both glacier calving and the breakup of icebergs, combined with commonly heterogeneous periglacial seismic velocity structure, can result in complicated seismic records. Key features of the waveforms, which are typically characterized by low-amplitude or emergent first-arrivals and long-duration, narrow-band codas, have been attributed to either source processes or propagation path effects. This uncertainty must be addressed in order for seismic data to be effective for studying the calving process as it relates to terminus dynamics. In this study, we use sets of 3-element arrays of 3-component geophones and infrasound sensors to locate calving and iceberg breakup events and isolate path effects in the seismic records obtained near the Bering Glacier terminus in the summer of 2010. Using waveform correlation, we treat each array as an antenna and determine the direction to the source and apparent velocity of the wavefield across the array. The initial few (∼3) cycles ofPwaves recorded from an array, beam formed to identify coherent arrivals for each event, are useful for deriving a propagation azimuth and apparent velocity, allowing for location of events using a small number of similar arrays. We locate 125 calving and iceberg breakup events near the terminus with this method. We also demonstrate that the longer-lived narrow-band coda is not coherent across individual arrays, suggesting that the narrow-band coda observed at the Bering Glacier is attributable to a path effect rather than to the source process. The large number of iceberg breakup events that we located has important implications for other calving glaciers where icebergs are present, and calving rates may be erroneously overestimated from the seismic data if their contribution is not taken into account.
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 In recent years, studies of seismicity and infrasound generated by glaciers and ice shelves have proliferated as the significance of ice sheet mass loss due to calving is better understood. Icequakes have been observed on a teleseismic scale [e.g., Ekström et al., 2003; Joughin et al., 2008; Nettles and Ekström, 2010], from a regional scale [O'Neel et al., 2010], and on a local scale [e.g., Qamar, 1988; O'Neel and Pfeffer, 2007; Richardson et al., 2010; Walter et al., 2010]. While seismic signals associated with calving have been observed at teleseismic distances with periods greater than 30 s [Nettles and Ekström, 2010], local scale deployments have reported dominant and lengthy signals near 1–3 Hz at Columbia Glacier [Qamar, 1988; O'Neel et al., 2007], Jakobshavn ice stream [Rial et al., 2009], and Bering Glacier [Richardson et al., 2010] among others. While a number of source-related models have been proposed for the emergent (non-impulsive), long-duration, narrow-band signal observed at calving margins around the world, there is no consensus on a common seismic source process for calving events observed locally (∼1–3 Hz); additional evidence is needed to link these signals with either a long duration source or a propagation effect. It is critical to accurately understand the role of source generation, coupling, and propagation as they relate to observed signals in order to effectively use these signals to improve knowledge of processes related to terminus retreat and mass discharge.
 Small-aperture antenna arrays, in which sensors are placed relatively close together with respect to the wavelength of interest, are commonly used to identify emergent arrivals or discrete signals embedded within background noise. Wavefield features that are coherent across the array are identified through a measure of similarity such as semblance or cross-correlation [see, e.g.,Neidell and Taner, 1971]. The relative arrival times at the array stations yield the azimuth to the source and the apparent velocity of the wavefield with respect to the plane containing the array. Arrays of infrasound (also referred to as acoustic or microphone) sensors have been used for measurements of phenomena such as volcanic eruptions [e.g., Johnson and Ripepe, 2011] and bolide propagation and bursting [Walker et al., 2010]. With multiple arrays located in the far field from the calving source, Richardson et al. demonstrated that arrays of infrasound sensors could be used to locate icequakes. Arrays of seismometers have been used to identify sources lacking high-amplitude or impulsive body wave phases, and are frequently employed to identify and locate low-level earthquake signals [e.g.,Birtill and Whiteway, 1965; Rost and Thomas, 2002] as well as volcanic tremor signals [e.g., Chouet, 1996]. Seismic arrays can also be used for investigating both emergent first arrivals and long-duration codas from icequakes, the subject of this paper.
 Small-aperture seismic arrays can facilitate source location when the signals are emergent, and also provide insight into the development and propagation of the characteristic 1–3 Hz signal, or ‘calving band’ [Walter et al., 2010]. This method can also demonstrate the similarity or differences in the waveform as it propagates the short distance between array elements. At each element in an array, the codas should be nearly identical if they are due to a source process or near-source path affect. On the other hand, if the arrivals across the array are incoherent, the waves must be affected by something in the portion of the path that is close to or within the array. In other words, we can investigate the influence of path effects by examining the coherency of the codas.
 Based on earlier observations of recordings of higher-frequency acoustic waves and seismic signals generated both by calving and iceberg breakup at the Bering Glacier [Richardson et al., 2010] and at Jakobshavn Isbræ [Amundson et al., 2010], seismic arrays appeared to be appropriate for the characterization and location of the source of compressional body waves (traveling through the ground and water), as well as for a detailed study of the narrow-band coda. Acoustic arrays in 2008 provided reasonable source location estimations for calving and iceberg breakup events, but the lack of co-located seismic arrays prevented analysis of the coherency and characteristics of the seismic wavefield from these sources [Richardson et al., 2010]. Based on the conclusions and inferences from the previous study, we designed an experiment using seismic arrays to provide a longer-term record of submarine and subaerial calving and iceberg breakup events that could be used to quantitatively track variations in the state of the terminus, without relying on all events to be acoustically loud enough to detect and locate with microphones.
 We find in the current study that seismic arrays deployed near the glacier terminus provide data for a robust, semi-automatic location technique for icequakes possessing low-amplitudePwave phases. We further conclude that the narrow-band signals at the Bering glacier can be readily produced by iceberg breakup, and not just calving; it is likely that many of the narrow-band coda signals observed at calving glaciers worldwide are also be produced by iceberg breakup. This result is significant for passive seismic monitoring surveys of calving margins, as amplitude and frequency detection thresholds may be exceeded by iceberg breakup, and are not necessarily indicative of mass loss or terminus retreat from the calving margin itself. In addition, observations of poor intra-array coherency in this narrow-band signal suggest that the signal is dominated by path effects, rather than the result of a long-lived source mechanism. This finding was detrimental to the original purpose of the experiment to study terminus dynamics, but did shed light on the propagation of seismic waves from the icequake sources to the receivers.
2. Observations and Data
 In late May 2010, 12 Sercel/Mark Products L22 3-component geophones (2 Hz corner frequency) and one Guralp ESPC 3-component seismometer (60 s corner period) were deployed at the Bering Glacier. Each seismograph station was equipped with a RefTek 130 data acquisition system and a GPS clock for digitizer time correction, and recorded at 100 samples per second. The 12 short-period geophones were deployed in four 3-element, equilateral triangular arrays, with ∼200 m between elements. Three seismic arrays were deployed south of the terminus on islands within Vitus Lake, one array was deployed in the Grindle Hills (SA4), and the single broadband station was deployed on rock just south of the Grindle Hills (Figure 1). The southernmost element of array SA2, site SA2C, was also outfitted with a small equilateral triangle array of All Sensors infrasound sensors (0.05–20 Hz) [Johnson et al., 2004], with 30.5 m between elements (on the maps, this infrasound array is shown as a single-point location due to its small footprint). The primary purpose for installing infrasound sensor arrays in this experiment was to ensure that the broadband impulsive arrivals observed on the seismograms were actually produced by the ground coupling of air-waves from calving and iceberg breakup, and not to some other unidentified seismic process that was not observable during the previous study in 2008. After several months of operation, one geophone from array SA4 on the Grindle Hills was dismantled, co-located with a 3-element acoustic array, and re-deployed on the glacier as station 6 to observe calving events from the ice. All originally deployed stations ran simultaneously for 30 days, with some stations operating continuously through instrument recovery in early August; termination of data recording was primarily the result of power disconnection due to animal disturbance. We found that the low-amplitude signals observed near the sources were generally not recorded by the more distant stations on the Grindle Hills (SA4 and station 5), so we focus on the three seismic arrays on islands south of the terminus, including the infrasound sensor array.
 The Bering Glacier terminus was stationary or slowly retreating during our study. In this state of passive calving, second-order processes of local stress fracture propagation and melt undercutting were likely the dominant processes [Benn et al., 2007]; although upstream reaches near the Grindle Hills exhibited severe fracturing, indicative of pre-surge activity [Molnia, 2008]. Average GPS-derived ice velocities near the terminus from May 24 through July 30 of 14 cm/day (K. A. Endsley, MTRI, unpublished data, 2011) were considered insignificant for active calving, which would be driven by lateral variations in surface ice velocity across the toe. The observed apparent calving rate was very low, consistent with the low terminus ice velocity, and the fact that Vitus Lake salinity ranges from fresh to brackish water. Fresh water calving rates are typically an order of magnitude lower than their marine analogs [Skvarca et al., 2002], perhaps due to the higher ice melting point in fresh water and isolation from damaging wave and tidal cycles. Although a number of icebergs were observed to be floating within Vitus Lake (Figure 1), as well as grounded near the Seal River outlet (Figure 2), both floating and grounded icebergs within Vitus Lake were generally not in contact with each other. Only in Tashlich Arm, just west of SA3, were icebergs in close enough contact to be considered an ice mélange; source locations from Tashlich Arm could not be accurately constrained because the three arrays were all to the east.
3. Icequake Analyses and Characteristics
3.1. Event Locations
 We developed an array-based processing scheme to detect emergent seismic signals and correlate them across the three 3-element seismic arrays that improves on the beam-forming technique that had been performed on the acoustic array data collected in 2008 [Richardson et al., 2010]. In the 2010 experiment discussed here, we had several months of data, which necessitated an automated picking scheme to efficiently search the data. In addition to the quantity of data, the often emergent seismic signals were difficult to discern visually, compared to the impulsive acoustic signals recorded in 2008, so a consistent automated method was needed to provide an unbiased analysis of the entire data set.
 The arrival identification scheme was based on waveform similarity. The initial coarse event identification scheme was adapted from frequency-slowness methods with signal coherence measured using semblance [seeNeidell and Taner, 1971, equation 11]. After filtering the data from 1 to 10 Hz in order the capture the highest amplitude of icequake P wave signals [see, e.g., Richardson et al., 2010], we searched through the entire vertical component data set of the elements within each array using 2.5 s windows overlapping by 0.5 s. In each window we performed a grid search over east (Sx) and north (Sy) slowness (the inverse of apparent velocity) combinations, using 0.02 s/km intervals from 0 up to +/−0.8 s/km, yielding vector slowness and associated semblance values. If a particular Sx-Sy combination resulted in a normalized semblance greater than 70%, we marked the event for further processing as described below.
 After our coarse grid identification, we sought association of events identified on one of the arrays with those on the other arrays: if the first-picks for each event from each array fell within 6 s (maximumP wave travel time through water between the furthest stations), an event was cataloged. This resulted in a catalog of events that were identified on all three arrays.
 Having identified events that were recorded by multiple arrays, we subjected the associated time series to a fine-scale location method in order to improve upon the initial coarse search. The waveforms were up-sampled from the native sampling rate of 100 sps to 500 sps, preserving the original data with a low-pass interpolation algorithm. The up-sampling procedure did not distort or add to the data in any way, but rather allowed a smoother search result over slowness space in which uncertainties were calculated. We then refined the detection search algorithm to 0.01 s/km increments, with windows of length 2.5 s and 0.1 s overlap, redefining the full event window for each array more precisely (seeFigures 3 and 4). This provided a time window of high vertical component waveform similarity at each array, which we call the correlation window, generally around 5 s long. The correlation window was comprised of the total time that consecutive 2.5 s windows exhibited an apparent velocity between 1.5 and 9.0 km/s (slownesses between 0.11 and 0.67 s/km), as well as an apparent velocity within 0.2 km/s of the mean apparent velocity for the event; this tended to remove spurious correlated signals that were unrelated to the selected icequake arrivals. The constraint imposed to only include windows with 0.2 km/s deviations from the mean apparent velocity was implemented to reduce the effect of frequent small near-receiver events, recorded only on one array, from lengthening the correlation window of signal from the selected larger, more distant event seen on multiple arrays. As a result of using only 3-element arrays, weaker local maxima at azimuths and velocities other than those from the source exist in the semblance plots (seeFigures 3 and 4), but these would be suppressed for arrays with greater numbers of elements.
 To characterize uncertainties in source azimuths, we used a bootstrapping method [e.g., Efron and Tibshirani, 1993]. A precursory noise window, randomly circularly shifted over the time window and convolved with Gaussian white noise, was added [Sandvol and Hearn, 1994] to the full event window. This procedure was repeated 500 times per event, which produced distributions in both azimuth and velocity space that were approximately Gaussian, and allowed for calculation of the mean and standard deviation of back-azimuth [Sandvol and Hearn, 1994]. To remove erroneous results due to cycle skipping in the semblance domain, apparent velocities less than 1.5 km/s were removed along with their associated azimuths. We assume that 3 standard deviations in either direction of the mean azimuth represents 99.7% confidence in back-azimuth to create “wedges” of most-likely back-azimuth, and we use the polygon resulting from the intersecting wedges from each array to define the icequake location confidence interval, with the center of the polygon corresponding to the “best” source location [e.g.,Almendros et al., 2001; Richardson et al., 2010]. In order to allow for consistent locating of events, including those where the intersection of three very narrow uncertainty wedges (from well correlated signals) failed to intersect, an additional five-degree band was added to each wedge in either direction of the mean. This relatively arbitrary constant was not only added as an upper error bound to represent some uncertain error which varies as a function of azimuth and unknown lateral heterogeneity, but also to allow for a consistent method to locate events where the intersection of very narrow uncertainty wedges (well correlated signal) fail to intersect solely due to these errors.
 We identified 151 events from the total number of detections, after manually removing events mislocated due to noise and teleseismic arrivals, which often exceeded the detection threshold. During this process, we found that a significant source of noise was late coda arrivals or air-waves from a prior event (or events), superimposed on thePwaves of the current event; the amplitude of this coherent noise generally dwarfed the new first-arrival amplitudes. For a number of events occurring near the terminus, the coda immediately or quickly followed thePwave first-arrivals (seeFigure 5), so semblance calculated for these windows was very low, despite visually correct time shifts. While we located all 151 events, only 125 events were used for analysis; these are shown in Figure 6. The remaining events had location uncertainties considered too high, and their uncertainty polygons covered unreasonably large areas. Although these rejected events could not be precisely located, the back-azimuth determination was adequate to discern between iceberg-breakup versus terminus-calving events; very few icebergs were located near the glacier terminus at the time of the study, which made classification easier (seeFigure 6 for locations of icebergs in Vitus Lake, relative to the glacier terminus).
 We found that most of the event locations were away from the glacier terminus. Based on these locations, only seven events could be attributed to terminus calving, while the remaining 118 plotted events can be attributed to iceberg breakup (Figure 6). Most of the iceberg breakup events were sourced within the grounded iceberg field near the Seal River outlet of Vitus Lake leading to the Gulf of Alaska (Figure 2). Although some of the “land” shown in the satellite images is actually an ice-rock mixture covered with rock and rock flour, events plotted on this land are almost certainly due to errors in location, and these errors generally increase with distance from the stations, as expected. The short time window available for correlation, prior to later arrivals, reduced the accuracy of the calving event locations. This interference greatly impaired not only the location of terminus calving events but also their detection; calving events are probably under-sampled in our study as a result. The significance of the number of events generated by icebergs is discussed in the following section.
3.2. Waveform Characteristics
 We classify two types of events based on the icequake locations: iceberg breakup events and glacial terminus calving events. The two types have somewhat different waveform characteristics as recorded by seismic stations around Vitus Lake, primarily in frequency content and the nature of the coda.
 Typical arrivals for iceberg breakup events were characterized by 1) a high-frequency (1–13+ Hz) onset with coherent arrivals within an array for ∼5 s, followed by 2) a ground-coupled air-wave arrival, which is the P-P coupling of air-waves generated by the source into the ground at the geophone location [Mooney and Kaasa, 1962], and 3) a 1 Hz coda, which usually exceeded five seconds in duration (Figure 7). The coda signals from icebergs often continue for more than 40 s. As seen in Figure 7, the 1 Hz coda was observable only at arrays SA1 and SA2 for many events, while this lower amplitude coda signal is more difficult to observe in the spectrogram of SA3 for this particular event. This iceberg-breakup event was located in the region plotted inFigure 8a.
 Terminus-calving events also exhibit a coda, but for these events it immediately follows the detection window onset, and is broader band than the corresponding iceberg breakup signal. Typical terminus-calving events were characterized by 1) a similar high-frequency onset (∼5 s duration), followed immediately by 2) 1–5 Hz narrow-band signal, and later by 3) the ground-coupled air-wave (Figure 5); Figure 8bshows the location of this calving event. Compared to most terminus-calving events, most iceberg events have higher-amplitude, narrower-band ∼1 Hz coda arrivals that occur later in the signal, with envelopes usually peaking after the arrival of the ground-coupled air-wave. In order to demonstrate the variability in icequake signals, a selection of seismograms for 21 events is plotted inFigure 9, using a subset of events from SA2C with the highest signal-to-noise ratios. Note that many iceberg breakup signals have higher amplitude codas than terminus-calving events, despite the icebergs having smaller to comparable vertical dimensions as compared to the ice of the calving terminus. This may indicate that the role of seismic coupling is as important in the amplitude of the recorded coda signal as the size of the source.
 Apparent velocities for the P wave onsets (arrivals within the correlation windows) from all 151 icequakes (calving and iceberg) were estimated at each array, with consistent mean apparent velocities of 3.43, 3.30, and 3.14 km/s for seismic arrays SA1, SA2, and SA3 respectively (Figure 10a). The lengths of the detection (or correlation) windows averaged 5.2, 5.0, and 5.1 s (Figure 10b). Peak detection frequencies for each window ranged from 1 to 13 Hz for all arrays, in contrast to the higher-amplitude, narrow-band signals in the coda, outside of the correlation window (Figure 10c). 97% of recorded icequakes also had observable ground-coupled air-wave arrivals, indicating that the sources of both the calving and iceberg events were well coupled to the atmosphere.
 By comparing waveforms from each of the three elements within individual arrays, we were able to obtain insight regarding the nature of the narrow-band coda observed from iceberg and calving events. Previous studies have reported a common coda frequency for signals from calving icequakes, which is referred to as the calving band (1–3 Hz) [e.g.,O'Neel and Pfeffer, 2007]. The cause of this waveform feature is not well known, but our seismic array data provides constraints on the mechanism. Energy in the calving band was common in the data recorded in the 2010 experiment reported here, although the amplitude varied from array to array. From our list of 151 icequakes, 71% had calving-band signal-to-noise ratios of two or greater as observed from SA2 (Figure 6), while only 50% of events met the threshold for SA1, and 27% for SA3.
Figure 11a shows the ∼1 Hz signal from each element of SA2 from an iceberg event observed 31 May 2010, 00:59:55 UTC (also used for Figure 7). We found that the signals observed from each element of the array, located only 200 m apart, display not only great differences in amplitudes, but also go in and out of phase with each other several times throughout the coda. Due to the variation in inter-element phase lag with time, it is impossible to match more than a few seconds of these signals, using time shifts corresponding to any velocity, without stretching the signals. Due to the inconsistent phase lag with time, neither body nor surface waves can be used to fit more than a few cycles in the entire coda wave train. InFigure 11b, a similar trend was observed for a calving event recorded 9 June 2010, 13:41:32 UTC (also used for Figure 5), although the peak frequency is ∼3 Hz, compared with ∼1 Hz for the iceberg event. Particle motion plots also confirm that within the coda, horizontal component polarities of adjacent array elements from an iceberg event can differ by as much as 90 degrees within any two second window (Figure 12). Assuming a P wave velocity through water of 1.5 km/s, the corresponding wavelengths, given the peak frequencies observed, would be 1.5 km for iceberg events and 0.5 km for calving events. We do not identify any P wave arrivals directly through the water, but use this value as a physical lower bound for wavelength. The aperture of each array is only 0.2 km, a fraction of the wavelength, so the lack of coda waveform correlation across each array suggests that the signal characteristics are due to local propagation effects, rather than to source properties.
4. Discussion and Implications of the Bering Icequake Data
4.1. The Importance of Accurate Event Locations
 The use of seismic arrays to provide locations of icequakes allowed us to discriminate between terminus calving events and iceberg breakup events. Near the Bering Glacier terminus in Vitus Lake, the breakup of icebergs, rather than glacial terminus calving, was the main source of recorded Pwave arrivals at all three 3-element seismograph arrays deployed in the summer of 2010. In addition, it was noticed that the “calving band” coda signal, identified at other glaciers (1–2 Hz [Qamar, 1988], 1–3 Hz [O'Neel et al., 2007; Walter et al., 2010], 1–10 Hz [Rial et al., 2009]), originated from icebergs within Vitus Lake in a large number of cases. Only seven of the 125 events that we located were related to terminus calving. Some calving events were necessarily missed from our detection algorithm due to the interference between closely timed arrivals, and the amplitude of the narrow-band coda signal from calving events was found to be consistently lower than the corresponding narrow-band signal from iceberg events. However, all of these events would likely have been listed as calving events by automated 1–3 Hz frequency-detection algorithms. We suggest that caution be used with automated frequency detection algorithms whenever icebergs are present, and suggest that these algorithms cannot be used as a direct measurement for calving rate. Indeed, in this study the rate of calving would have been significantly overestimated; the icebergs would presumably have been correctly observed as calving events when initially separating from the glacier, but as shown here, they would have been “counted” numerous additional times as they later broke up in the lake.
 While iceberg events dominated the catalog of locations, their contribution to the total seismic energy release is uncertain, as the sources of many of the highest amplitude signals were not locatable; these large-amplitude arrivals resembled the narrow-band prolonged signals from both iceberg and calving events, but were not accompanied by identifiable precursory body wave phases. Even so, our results indicate that single seismic station monitoring of calving may be inaccurate in the presence of icebergs using a frequency domain detector [e.g.,O'Neel et al., 2007] because the iceberg breakup band can overlap with the calving band. This was observed in this experiment, and the same calving band has been reported by others at other glaciers. The role of icebergs in seismic energy partitioning is certain to be different at other glaciers and even during other cycles at the Bering Glacier, but we argue that their part in generating recorded signals cannot be ignored.
4.2. The Long-Lived Coda: A Source or Path Effect?
 We also consider the mechanism of iceberg “bobbing” [Schwerdtfeger, 1980] as a narrow-band source generator for iceberg events. Most icebergs located near the Seal River outlet are grounded, and destructive fracturing of part of the subaerial portion would enable flotation and subsequent oscillation back to equilibrium, regularly impacting the lake bottom. For the dominant ∼1 s period observed, the iceberg bobbing frequency would only be matched for icebergs with ∼0.28 m total thickness. Icebergs of this size are too small to contribute to the signals observed several kilometers away.
 While we cannot necessarily eliminate all of these source mechanisms as possible causes of the signal, our observations indicate that the narrow-band coda observed at the Bering Glacier is not solely a source effect, because the long wavelengths of the signal are poorly correlated within each array.
 To demonstrate this, we further examine the nature of the coda in the vertical velocity seismograms from a calving event, shown in Figure 13. This example was chosen because it occurred while station S6 was operating, allowing examination of a seismogram that was recorded on the glacier, rather than on an island in Vitus Lake. Vertical-component traces from stations S6, SA3E (which was the only station in array SA3 working at the time), and all three vertical-component elements of arrays SA1 and SA2 are plotted in order of increasing offset. Glacier station S6 recorded a ∼3 s long, high-amplitude arrival, presumed to be thePwave through the ice, but it did not record the narrow-band coda observed at the other stations. Each of the other stations recorded the long-lived, narrow-band coda, as well as the higher-amplitude air-wave arrival. Across arrays SA1 and SA2, the coda is poorly correlated, again suggesting that path differences from the calving event to each element of the array cause the differences in signal detail. This particular event, in addition to several others like it, provides evidence that the source time function is short (<5 s), but that the path across Vitus Lake provides a mechanism for generation of the long coda signal. The variation in frequency character, both within arrays and between arrays, can be examined from differences in the average, normalized spectra recorded during the deployment.Figure 14 demonstrates the variability in frequency content, suggesting that shallow structure differs enough near individual array elements to affect paths and alter the dominant background noise frequency. The background noise, with travel paths through either the lake water or till to arrive at each array element, demonstrates the subtle variability of the dominant recorded frequencies within arrays, and the larger differences in spectral content between arrays. Arrays SA1 and SA2 are dominated by background noise with spectral content similar to that of the icequake coda, probably from high occurrence rates of low amplitude ice and lake noise, while the spectral peak in SA3 corresponds to oceanic microseism. While we cannot entirely dismiss deviations in instrument response as a cause of some of these differences in spectra, the use of identical instruments, direct burial methods, and digitizing systems alleviates most of these concerns.
4.3. A Waveguide Path Effect
 Vitus Lake is greater than 150 m deep in places and underlain by unconsolidated glacial mud that is at least 100 m thick based on active seismic data [Molnia et al., 1996]. In the case of a low-velocity layer sandwiched between higher velocity adjacent media, or a low-velocity layer bounded above by the free-surface, a waveguide condition may exist where certain frequencies (and wavelengths) will constructively interfere to propagate a narrow-band signal significant distances with very little dispersion, while other frequencies destructively interfere or leak out of the waveguide. For an efficient compressional or shear (SV) waveguide to exist, we consider situations where constructive interference occurs at reflected angles greater than the critical angle [seeSheriff and Geldart, 1995, section 13.3], as plotted in Figure 15for a reasonable range of velocity and water depth or mud-layer thickness. The minimal dispersion associated with a broad range of group velocities over a narrow frequency band provides a plausible mechanism for the observed long-lived, narrow-band signals in the absence of a prolonged source process during calving (Figure 13). While scattering alone could account for the signal elongation of an impulsive source at distant receivers, we find that the envelope of the coda signal does not decay in amplitude monotonically (Figure 9), which would be expected for a scattering only model. Scattering alone also cannot account for the preservation of certain frequencies in the coda in comparison to others found in the initial broadband impulse. Because deep-channeled sediment-filled structures are found throughout Vitus Lake, local variations in the group velocity curves would be expected for each path. A partially floating calving margin will be inefficient at transmitting energy into the ground, and early portions of the seismic wave path to islands will include transmission through deep water and unconsolidated rock flour; on the other hand, grounded icebergs have a direct and high velocity path to the receivers placed on till. The potential waveguides responsible are addressed in the following few paragraphs.
 A P waveguide can be formed by the soft unconsolidated sediment (Vp = 2200 m/s) underlying the lake's free surface (Figure 16). The channeled waves produced by calving events traveling to each element of an array could each encounter multiple waveguides, with differences in the individual paths to each element accounting for the dissimilarity of codas observed (see Figure 14). Simply placing adjacent array elements on different sides of an island may result in significant energy and frequency differences, because substantially different glacier scour channels could be encountered for each path through the lake. Glacially scoured channels of comparable dimensions to those found within Vitus Lake may account for the similar coda signals observed in other studies, as deep sediment-filled channels constitute a common feature for nearly all tidewater glaciers. Columbia Glacier bathymetry for example, was measured to have an elongated channel in excess of 300 m depth from a survey conducted from 1995 through 1997 [seeKrimmel, 2001, Figure 8], capable of supporting a similar waveguide condition.
 The coda for grounded iceberg events is also consistent with the model of a waveguide, but a P waveguide requires water three times as deep (∼450 m) at 1 Hz with a comparable velocity structure (see Figure 15a). Bathymetric mapping [Molnia et al., 1996] indicates that this is unreasonably deep, so we suggest that an SV waveguide could be responsible for the iceberg breakup coda signals (Figure 15b). A low velocity SV waveguide could consist of a ∼25 m thick unconsolidated mud layer (Vs = 100 m/s) bounded by water above (Vs = 0 m/s) and higher velocity till below (Vs = 1000 m/s), with approximate waveguide thickness inferred from the iceberg event coda frequency and those reasonable shear wave velocities. Unconsolidated mud thicknesses in this range are likely, as Molnia et al.  found thicknesses ranging up to ∼100 m. The slower apparent velocity of SV waves through a waveguide compared to a Pwaveguide is consistent with coda travel-time observations from iceberg events compared to calving events when aligned byP wave onset; the earliest possible waveguide arrivals would travel with velocities of 1000 m/s and 2200 m/s for iceberg (SV) and calving (P) waveguides respectively. Recognizing the inherent non-uniqueness, we propose that a Vitus Lake waveguide, with either glacial mud or the water layer serving as anSV or P waveguide respectively (see Figure 16), is the likely cause for the limited frequency content and long duration of the coda arrivals. Given the clear difference in the phase of the coda signals across each array, a path-effect model is needed, also suggesting a waveguide model.
4.4. Comparison With Previous Work Regarding Icequake Source, Path, and Site Effects
 Other prior studies have attempted to eliminate path and site effects as being possibilities for generation of the characteristic calving signal, attributing the signal to a prolonged source [O'Neel and Pfeffer, 2007]. In fact, the original goal of this experiment was designed to use array analysis of the long-duration calving signal, assumed to be generated at the source, to provide precise source locations for a temporal study of ice edge dynamics. Due to the contradictory nature of our conclusions of a path effect dominated signal to those made byO'Neel and Pfeffer , who concluded a long-duration resonant source, we replicate their methods in addressing the roles of source and path effect in our data.
O'Neel and Pfeffer  addressed path effects by looking at systematic variations in frequency content at different stations for several event types of icequakes, concluding that no such variations were present within their data. We performed a similar analysis by plotting the spectra at all operational stations from 11 icequakes occurring while SA6C was operational (see Figure S1 in the auxiliary material). We identified the coda signal independently at each operational station, estimating the start time for each window after the Pwave arrival, if it was identified, and before the air-wave arrival. If no clearP waves were identified, the start of the coda window was chosen where the first hint of signal emerged from the noise. We then plot and compare the normalized spectra for each window from the instrument deconvolved data. While the coda signal is confined to a narrow band with most energy 1–5 Hz, the spectral peaks rarely coincide exactly within each array, and greater variations exist between arrays. While O'Neel and Pfeffer claimed no systematic variations existed in their spectra, the variations in both frequency content and coda duration within and between small-aperture arrays for our subset of events, as well as the large variations in signal shape between adjacent array elements, support a path effect model.
 Site amplification effects were also addressed by O'Neel and Pfeffer , utilizing an H/V method [Konno and Ohmachi, 1998] for both ambient vibrations and icequakes. In order to rule out site effects at the Bering Glacier stations, we apply a similar technique on continuous data from two time ranges, spanning Julian days 150–153 and 213–216, and on the subset of the 11 icequakes with spectra calculated in Figure S1. The results of the ambient vibration H/V ratios are shown in Figure S2. The first time range from days 150–153 (Figure S2a) shows no frequency dependent peaks at any station except for SA1E and SA2N, and these peaks are well outside of the calving band at ∼10 Hz. Figure S2b shows similar results over the second time range, with no frequency dependent peaks at any station except for SA2N, SA2E, and SA6C. Again the peaks in SA2N, SA2E, and SA6C occur above the frequency band of most icequake codas, so we again do not attribute the icequake coda signal to site effects at these three stations.
Figure S2c shows the average of 11 event H/V ratios, defined by the plot windows for each event shown in Figure S1. While these are much noisier than the ambient vibration plots due to the lack of contributing data, the global maxima appear well below 1 Hz for most stations, which is not within the icequake coda band. There are several peaks within the icequake coda band, so we cannot completely rule out the contribution of site effects for this subset of events, but generally observe a characteristically lower frequency coda signal for iceberg breakup events as compared to terminus-calving events (seeFigure 9). The peak coda frequencies are not constant between event types, so site effects cannot account for the observed signals entirely, as they would filter and amplify all signals uniformly into their respective site effect bands; a path process must be invoked to explain the differences in observed coda waveforms.
 Using 200-m equilateral-triangle seismic arrays, we correlatedPwaves from events by beam forming the traces to derive propagation azimuths and apparent velocities across each array. We located 125 events related to terminus calving and iceberg breakup during the summer of 2010, with 118 of these being attributed to iceberg breakup, and only seven events to calving, although our algorithm may result in an underestimate of calving events. In general, iceberg events may comprise a significant fraction of seismic-based calving monitoring studies, and if not properly accounted for, could yield inaccurate calving budgets. The use of only one properly spaced small-aperture seismic array and collocated microphone as a substitute for a single seismic station in calving studies can help to alleviate many of these uncertainties.
 Detailed analysis of the waveforms led to additional results concerning the nature of the icequake source. The low-amplitudePwaves were well correlated among elements of the arrays, but the higher amplitude, narrow-band coda signals were found to be dissimilar across each array as well as between arrays, suggesting that this signal is not necessarily due to a long-lived source process. In addition, a station on the glacier ice often did not observe the same narrow-band coda recorded by land-based stations, even though it was well-situated to record radiation from the same calving source (seeFigure 9 and Figure S1). Instead, wave-propagation phenomena appear to be the source of the long, narrow-band coda, where an impulse caused by calving or iceberg breakup would lead to a long-lived, narrow-band signal created by waveguides within Vitus Lake. While this model for generating signal differences as a result of path effects is non-unique, we believe that such a model could fit in the environment of Vitus Lake and at similar glacier margins with comparable channel dimensions, to produce the observed signals without the need for a prolonged source time function.
 The authors thank the Bureau of Land Management and the Michigan Tech Research Institute for logistical and financial support. The seismic instruments were provided by the Incorporated Research Institutions for Seismology (IRIS) through the PASSCAL Instrument Center at New Mexico Tech. Data collected 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-0552316, the NSF Office of Polar Programs, and the DOE National Nuclear Security Administration. The Michigan Tech Earth, Planetary, and Space Science Institute, the Michigan Tech Office of the Vice President for Research, and the Michigan Tech Fund generously provided financial support.