Source mechanics for monochromatic icequakes produced during iceberg calving at Columbia Glacier, AK

Authors


Abstract

[1] Seismograms recorded during iceberg calving contain information pertaining to source processes during calving events. However, locally variable material properties may cause signal distortions, known as site and path effects, which must be eliminated prior to commenting on source mechanics. We applied the technique of horizontal/vertical spectral ratios to passive seismic data collected at Columbia Glacier, AK, and found no dominant site or path effects. Rather, monochromatic waveforms generated by calving appear to result from source processes. We hypothesize that a fluid-filled crack source model offers a potential mechanism for observed seismograms produced by calving, and fracture-processes preceding calving.

1. Introduction

[2] Rapid calving retreats are underway at tidewater glaciers in Alaska, including LeConte and Columbia Glaciers [Motyka et al., 2003; O'Neel et al., 2005], and have recently begun at several outlet glaciers in Greenland [e.g., Rignot and Kanagaratnam, 2006]. Largely due to unforeseen and unsustainably large ice and calving fluxes during these retreats, both the magnitude and timing of current sea level rise predictions may be severely underestimated [e.g., Intergovernmental Panel on Climate Change, 2007].

[3] Our focus is the mechanics of iceberg calving, a process that forms a substantial knowledge gap in the understanding of marine glacier retreat. Direct comparison with visual observations shows that iceberg calving produces emergent, monochromatic (narrow-band may be more descriptive, but we follow literature precedent calling these events monochromatic), often long-duration seismic waveforms (Figure 1, inset) with average recurrence times of about 10 minutes at Columbia Glacier. Spectral power is focused in a narrow pass band (1–3 Hz) regardless of event size (Figure 2a); thus these seismograms bear little resemblance to tectonic earthquakes, but strongly resemble long period volcanic events [e.g., Chouet, 1996]. In this paper, we build on results presented by O'Neel et al. [2007], who demonstrated that calving-generated seismicity is separable from the total recorded seismicity, through an examination of how variable material properties beneath the seismic network may skew interpretations of recorded seismograms.

Figure 1.

Vertical air photo mosaic of lower Columbia Glacier, July 2005. Rock-based seismic stations are indicated with stars, and ice-based stations with diamonds. Stations used in the H/V analysis are colored green and are located 1.6, 5.2 and 11.4 km from the terminus centerline. The upper inset gives the location of the glacier relative to the state of Alaska, and the lower inset shows the unfiltered vertical seismogram for a ∼10 second calving event observed on June 12, 2005 at 15:54 UTC as recorded at BBB. Field notes describe a small subaerial event lasting a few seconds.

Figure 2.

(a) Vertical component waveform data for two observed calving events. A subaerial event, lasting 25 seconds, is shown in red, and a 350 second submarine event is shown in black. (b) Normalized power spectrum for the events in Figure 2a. The short event has a peak frequency of 2.06 Hz, while the longer event is dominated by 1.96 Hz energy. (c–f) Log-log spectral ratios for both ambient vibrations (Figures 2a, 2c, and 2e) and events (bottom panels). Ice-based stations are on the right, rock-based BBB on the left. The solid line gives the mean value for each frequency and dashed lines indicate ±1 standard deviation. The vertical line and associated shaded region for BBB indicates a site effect at ∼5 Hz, probably related to the station's location atop a convex knoll. The lack of a clear peak at either ice-based station indicates the monochromatic character of seismic energy released during calving is not the result of a site effect.

[4] Two explanations for the time domain character of these waveforms were introduced during the mid-1980s; Wolf and Davies [1986] suggested the monochromatic nature of calving seismograms resulted from harmonic resonance of glaciers following a variety of source impulses (i.e. a site effect), while Qamar [1988] believed they were a result of source processes. To better understand the origin of the waveforms, we represent each component of ground motion u, as recorded by a seismometer, as the convolution of four time series: the source-time function (s), the path (p), the site (x), and the instrument response (i),

equation image

which can be written in the frequency domain to allow each term to be analyzed separately. Through such an unraveling of the signal, it is possible to determine whether the waveforms are best explained by site or path effects, or alternatively, if the spectral signature of calving-generated seismograms is a result of source processes.

2. Methods and Data

[5] Several methods are used to evaluate the roles of site and path effects in the calving signal. Path effects are resolved qualitatively; we verify that variable source impulses do not result in similar seismograms at a given station. We study signal distortions with increasing distance from a known source [e.g., Chouet et al., 1994], and note that seismogram durations closely match those of visual observations. We assess the site response (harmonic resonance) using spectral ratio analysis [Nakamura, 1989], where site effects, X(f), can be evaluated independently of equation (1) by calculating the ratio of the geometric average of the horizontal amplitude spectra, to that of the vertical spectrum,

equation image

[6] Here the Fourier transform of ground motion is represented as U(f), with N and E representing horizontal motion components north and east, and Z vertical motion. Similar to receiver function analysis [Langston, 1979], this method assumes that vertical motion is unaffected by impedance contrasts at layer boundaries beneath the site. However, horizontal components of motion will be perturbed by such changes in material properties, thereby allowing detection of site effects. Local maxima in the H/V ratio identify frequencies of natural resonance, f0. A narrow peak, where H/V > 2 between f0 ± f0/4, is indicative of a site effect in the neighborhood of the sensor [Marcellini et al., 2004]. Although a theoretical basis for this assumption is still being pursued, observations [Nakamura, 1989] and modeling [Lermo and Chavez-Garcia, 1993; Konno and Ohmachi, 1998] support its validity. In theory, analysis of spectral ratios should resolve the natural resonance frequency as well as the magnitude of amplification, but in practice H/V ratios cannot accurately quantify the amplitude of site effects [Pratt and Brocher, 2006].

[7] Data come from instruments deployed at Columbia Glacier during 2005 (Figure 1). We primarily rely on a rock-based Guralp 40T broadband seismometer (BBB; flat from 30 sec to 40 Hz; 100 Hz sampling) installed near the glacier terminus [O'Neel et al., 2007], and two temporary stations (BR10, BR5) deployed 5.2 and 11.4 km upstream from the terminus, although other station data were used to evaluate path effects. BR10 and BR5 consisted of three mutually orthogonal L-28 geophones (4.5 Hz natural frequency) shallowly buried (<1m) in the glacier. Experimental loggers recorded L-28 data at 200 Hz with only relative timing (R. Fatland, personal communication, 2005). To match the sampling interval of the 40T, geophone data were decimated to 100 Hz using a FIR filter. Due to limited bandwidth of the L-28 sensors, we limited analyses to frequencies exceeding 1 Hz.

[8] Our analysis first excluded all events and considered only ambient vibrations. In a second analysis, we considered data segments centered on monochromatic events. As no calving observations were made during the short recording periods of ice-based sensors BR5 and BR10, we cannot guarantee that our set of events includes only calving events; some may be monochromatic icequakes of unknown origin (several authors describe such waveforms at non-calving glaciers [e.g., Métaxian et al., 2003; Stuart et al., 2005]).

[9] Pre-processing followed recommendations of the European science initiative SESAME (Site EffectS assessment using AMbient Excitations) [Marcellini et al., 2004]. We satisfied their minimum sampling requirements, averaging results from between 16 and 151 twenty-second data segments for each analysis. All analyses of ambient vibration contain more than 80 data segments, and during analysis of events between 16 and 80 events were processed. Data availability at BR5 constrains the event analysis to 16 segments. Each manually selected data segment was detrended and cosine tapered by 5% to reduce spectral leakage. After calculating the FFT for each segment, but before computing the spectral ratio, we averaged each channel's spectra for all segments. Finally, we applied Konno and Ohmachi [1998] smoothing, as its logarithmic kernel accounts for undersampling at low frequencies. We used the SESAME recommended dimensionless smoothing coefficient of 40, which yields intermediate smoothing.

3. Results and Discussion

[10] Figure 2a shows examples of vertical component calving event waveform data. The event plotted in red was observed in the field as a subaerial event lasting ∼25 seconds, while the black line represents a large submarine failure observed for over 350 seconds. Panel b shows their power spectra, normalized for comparison. The spectra are extremely peaked, with frequencies of 2.06 and 1.96 Hz dominating the short and long event, respectively.

3.1. Path Effects

[11] We qualitatively examined several waveforms recorded during calving events to determine the magnitude of path effects, and found no systematic variation of spectral content with increasing distance from the source. Rather, spectral composition depends on the event considered, not the sensor location. Additionally, we recorded broadband earthquakes, high-frequency explosions, and low-frequency icequakes with similar time domain signatures at both ice- and rock-based stations. These observations suggest that seismic energy is not subject to strong path effects during travel through the ice, dismissing path effects as a possible explanation for the peaked spectrum observed during calving.

3.2. Site Effects

[12] We show the H/V ratio as a function of frequency (1 < f < 40) for ambient vibrations (Figures 2c and 2e) and monochromatic events (Figures 2d and 2f) at all three stations. Solid lines show the mean value of the spectral ratio, and dashed lines give ±1 standard deviation. Potential site effects are highlighted with a vertical line surrounded by shading spanning ±1 standard deviation. Our results are similar for both events and ambient vibrations at all stations, and display reasonable levels of solution variance. As expected, variance is greater for the event analysis due to data limitations. No anthropogenic sources (industry, human activity) are located near the glacier, and we can immediately rule them out of any interpretation. At the rock-based station BBB, a clear peak exists at ∼5Hz. Ice-based stations BR10 and BR5 display no clear peaks over the resolvable frequency range, including a flat response at 5 Hz where the BBB ratio is peaked. The events solution at BR5 suggests a weak, one-sided peak at ∼1.2 Hz. Due to lack of lower frequency data, this is not a robust result.

[13] Site effects have two primary origins, strong impedance contrasts at layer boundaries, as are common in sedimentary basins [e.g., Pratt and Brocher, 2006], and complicated or irregular topography [e.g., Bard, 1982]. An impedance contrast greater than ∼4 is required to produce non-topographic site effects [Marcellini et al., 2004]. We estimate the range of the impedance contrast at the bed of the glacier by considering the densities and S-wave velocities of ice and greywacke (900 kg m−3; 1.8 ± 0.2 km s−1 and 2650 kg m−3; 3.4 ± 0.5 km s−1, respectively). We prescribe large uncertainties because local seismic velocities are poorly constrained. The resulting impedance contrast ranges from 4.3 to 8.2, suggesting that site effects may manifest in glacier-generated seismicity.

[14] Because irregular surface topography may also cause site effects, spectral ratio methods are most useful when strong impedance contrasts exist beneath a seismometer located in flat topography [e.g., Pratt and Brocher, 2006]. Our ice-based sensors were deployed along the glacier centerline, which presents a simple geometry with a gently dipping, surface-parallel basal interface. Although instrument positioning reduces the likelihood for topographic site effects at the ice-based stations, we suspect a topographic site effect explains the 5 Hz H/V peak at the rock site, which was located atop a convex bedrock knoll.

[15] Given the potential for site effects, we estimate a frequency range for the expected resonance. The natural resonance frequency, f0, depends on ice thickness, H, the S-wave speed in ice, Vs, and the number of free surfaces (top only or both top and bottom),

equation image

where N is 4 for a single free surface and 2 for two free surfaces [Wolf and Davies, 1986]. Although the ice thickness at BR10 is unknown, we constrain ice thicknesses to ∼600 m in the terminus region [O'Neel et al., 2005] and at ∼400 m at BR5 [Mayo et al., 1979]. Given the uncertainties for parameters in equation (3), a range of natural resonant frequencies 0.6 ≤ f0 ≤ 2.5 Hz is plausible. Our preferred value at the terminus is f0 ≈ 0.80 Hz, resulting from a shear wave speed of 1.8 km s−1 [Deichmann et al., 2000] and a single free surface. Considering the thickness at BR5 we obtain f0 ≈ 1.1 Hz. Both values differ significantly from the ∼2.0 Hz peak we found to dominate the iceberg calving spectrum by stacking vertical component spectra for 80 observed events at the rock site BBB. Only with unrealistically fast S-wave speeds (>2 km/s) can we match the observed characteristic frequency of calving seismograms.

[16] Although not shown in Figure 2, we extended the spectral ratio analysis to frequencies lower than 1 Hz at the broadband station BBB. We obtained no clear low frequency peaks when considering ambient vibrations, but a weak peak was observed at 0.65 Hz for event inputs. This suggests that calving may induce a weak resonance of the ice, but not at the frequencies that characterize calving waveforms. None of the stations show site amplifications between 1 and 3 Hz, the characteristic frequencies for calving waveforms, implying that site effects do not dominate the monochromatic seismograms.

[17] A comparison with historical observations offers additional validation that site and path effects are negligible. We consider terminus ice thicknesses at Harvard (∼110 m), Yale (220 m) and pre-retreat Columbia Glaciers (∼250 m) presented by Brown et al. [1982] and spectral characteristics of calving-generated icequakes presented by Wolf and Davies [1986], Qamar [1988] and those recorded by us (with a broadband instrument). We assume that the ice thickness in a region within a few km of the terminus would dictate the observed resonant frequency, and due to lack up upstream thickness data, we must assume a flat bed in this region. Columbia Glacier's present near terminus ice thickness of ∼600 m is roughly twice as large as any historical value presented above, even given the drastic thinning through retreat. In contrast to predictions given by equation (3), however, the characteristic frequency of calving icequakes has increased, suggesting that harmonic resonance does not dominate the signals.

3.3. Source Processes

[18] Combined, spectral ratio analyses and historical data demonstrate that energy produced during calving results from source processes rather than site or path effects. Thus we seek a source capable of producing monochromatic 1–3 Hz waveforms. Pressure transients in fluid-filled voids can generate such signals. Englacial conduits were explored by St. Lawrence and Qamar [1979], but their models require both high water flux and conduit sizes on the order of 10 m in diameter and several hundred meters long. Because such conduit sizes are implausible over the range of glacier geometries where monochromatic waveforms have been observed, we draw from volcano-seismology, and examine the fluid-filled crack source model [e.g., Aki et al., 1977; Chouet, 1986]. The appeal of this model is that crack geometries have a longer resonance period than conduits, thus physically reasonable crack sizes can produce the signals we observe. Additionally, water-filled cracks have been observed in englacial environments [Harper and Humphrey, 1995; Fountain et al., 2005; Meierbachtol et al., 2006] where theory does not predict elastic failure. Under this model, two processes may generate the observed waveforms. Fluids may enlarge crack tips, thus changing the volume of the crack, or fluids may be forced through constrictions in an existing crack. Resonance of the crack walls develops from either process and propagates along the cracks length [e.g., Chouet, 1996; Métaxian et al., 2003; Stuart et al., 2005]. The crack-tip enlargement process provides a more likely source for the events, primarily due to the destructive nature of the events.

[19] The resonant properties of a fluid-filled crack depend on the crack geometry (length, L, thickness, d, and fixed width W = L/2), material properties of the fluid (acoustic velocity, a, bulk modulus b, and density, ρf) and the solid (compressional wave speed α, rigidity μ, and density, ρs), space-time variations in fluid pressure, and boundary conditions along the crack. A primary control on resonance frequency is the crack stiffness, C = equation image [Chouet, 1986]. Métaxian et al. [2003] give convincing evidence that the fluid is water, or bubbly water, rather than air. They also showed that cracks capable of producing low frequency monochromatic waveforms must have large length-to-thickness ratios, in agreement with borehole video observations of crack dimensions.

[20] Using dispersion curves from Chouet et al. [1994], and considering fundamental mode frequencies between 1– 3 Hz, we have investigated the applicability of the crack geometry as a potential source for the observed monochromatic seismograms. This narrow characteristic frequency band is reproducible from a wide (infinite) variety of crack geometries, with L ranging from a few tens of meters to several hundred meters, and d < 2 m. Predicting crack geometries relies on the highly unconstrained value of C, but confining crack lengths to less than an ice thickness and d < 1 m results in C between 100 – 3000. Chouet et al.'s [1994] dispersion curves only extend to C = 500, but the dimensions of plausible cracks suggest higher values may be needed for a detailed application of this model. Nonetheless, a zeroth order implementation of the fluid-filled crack resonator fits our observations.

[21] Both subaerial and submarine calving events produce monochromatic waveforms with similar frequency content [O'Neel et al., 2007], which may imply the direct involvement of water in both styles of calving (alternatively, two source models could result in a similar waveform). At Columbia Glacier, water is available to force crack propagation for both subaerial and submarine events either from water-filled surface crevasses or from upward-propagating basal fractures forced by a highly pressurized basal hydraulic system. During winter when surface water is scarce, the number of calving events (especially small subaerial events) decreases [O'Neel, 2006], suggesting water may be important in many small events, and/or that multiple source processes are likely.

[22] Surface and englacial crack sizes are variable, and the fluid-filled crack model suggests that crack sizes may indeed span a wide range and still produce the observed seismograms. Upstream locations of monochromatic events unassociated with iceberg calving suggest that fluid-driven fracturing is also important in preparing the ice for calving (and potentially on non-calving glaciers). Fluid pressure transients and englacial crack enlargement provide a plausible explanation for seismicity without invoking large changes in basal motion or crevasse formation, and may instead indicate changes to the basal hydraulic system. Large calving events may result when unconnected fractures link during failure at the terminus; the extent of such a linkage governing the size of a calving event. This idea is consistent with the percolation theory model described by Bahr [1995], who suggested that the continual buildup of small cracks combine to form large features at the terminus and is supported by data presented by O'Neel [2006].

[23] Our qualitative suggestion of a source mechanism is by no means unique. Other possible source processes exist, including oscillations of the cliff face induced by release of bending moments during failure, or a single-force landslide model similar to that given by Brodsky et al. [2003]. Numerical modeling is an essential, yet currently lacking, component that will clarify the likelihood of possible source mechanisms.

4. Conclusions

[24] In this paper we investigated the prevalence of site and path effects in calving-generated seismograms, then speculated on possible source mechanisms for seismic energy produced during iceberg calving at Columbia Glacier. Spectral ratios and historical data analysis each indicate that monochromatic waveforms produced by glaciers are a source effect and are not a result of resonant properties of the glacier or alterations along the seismic ray path. A fluid-filled crack source model, where spectral content is governed by crack geometry rather than ice thickness, fits both the seismic data and observations of the water storage and transport systems thought to exist in temperate glaciers. Our observations suggest that water is critical in forcing fracture propagation, and that fractures begin to weaken the ice long before it arrives at the terminus. A critical fracture at the calving front may link pre-existing fractures, forming a broad range of event sizes via a common mechanism. In the future we will continue to investigate this possibility by frequency-magnitude distribution analyses. A physically based calving model would greatly improve future sea-level rise predictions, and our research suggests that inclusion of englacial water and basal hydraulics is important not only in developing any such model, but as a component of the calving mechanism and associated tidewater glacier retreat.

Acknowledgments

[25] This project was funded by NSF OPP 0327345 and was inspired by Tony Qamar's early work. Thanks to Dan McNamara for advice throughout this work. We thank IRIS/PASSCAL for providing seismic equipment and VPR for logistical support. Thanks to Thomas Hart for blasting, and Jan Gunderson (ERA Helicopters) for flying us. Comments from Andy Smith, Jeremy Bassis and anonymous reviewers greatly improved this manuscript.

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