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Polar Science Center, University of Washington, Seattle, Washington, USA

Corresponding author: J. D. Carmichael, Polar Science Center, University of Washington, 4000 15th Ave. NE, Seattle, WA 98195-1310, USA. (joshuadc@u.washington.edu)

Corresponding author: J. D. Carmichael, Polar Science Center, University of Washington, 4000 15th Ave. NE, Seattle, WA 98195-1310, USA. (joshuadc@u.washington.edu)

Abstract

[1] Meltwater input often triggers a seismic response from glaciers and ice sheets. It is difficult, however, to measure melt production on glaciers directly, while subglacial water storage is not directly observable. Therefore, we document temporal changes in seismicity from a dry-based polar glacier (Taylor Glacier, Antarctica) during a melt season using a synthesis of seismic observation and melt modeling. We record icequakes using a dense six-receiver network of three-component geophones and compare this with melt input generated from a calibrated surface energy balance model. In the absence of modeled surface melt, we find that seismicity is well-described by a diurnal signal composed of microseismic events in lake and glacial ice. During melt events, the diurnal signal is suppressed and seismicity is instead characterized by large glacial icequakes. We perform network-based correlation and clustering analyses of seismic record sections and determine that 18% of melt-season icequakes are repetitive (multiplets). The epicentral locations for these multiplets suggest that they are triggered by meltwater produced near a brine seep known as Blood Falls. Our observations of the correspondingp-wave first motions are consistent with volumetric source mechanisms. We suggest that surface melt enables a persistent pathway through this cold ice to an englacial fracture system that is responsible for brine release episodes from the Blood Falls seep. The scalar moments for these events suggest that the volumetric increase at the source region can be explained by melt input.

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[2] Seismic monitoring has been successfully applied to the detection and interpretation of melt-triggered icequakes in both glaciers and ice sheets. This success is largely due to high sample rates that seismic instruments provide for observing brittle ice deformation that cannot be obtained with other instrumentation. In particular, seismic networks provide improved detection thresholds over single seismometers and the necessary spatial coverage for estimating observables such as icequake hypocenters and focal mechanisms. This capability is important for characterizing the response of glacial ice to meltwater. This is because meltwater is observed to trigger glacial faulting [Walter et al., 2010], basal stick-slip sliding [Weaver and Malone, 1979], and rapid fracture events [Roux et al., 2010; Das et al., 2008] from coincident releases of microseismic energy. However, direct comparison between meltwater availability and seismic observations presents challenges, especially at near-freezing or sub-freezing temperatures. These challenges include quantifying water storage in firn [Fountain and Walder, 1998], observing subsurface melt [Liston et al., 1999], and discriminating between sublimation and surface melt [Hoffman et al., 2008]. We suggest that improving our ability to quantify meltwater production is necessary to bound the influence it has on ice deformation. In this work, we therefore study a glacial regime (Taylor Glacier, ANT) in which no firn is present, meltwater can be confidently modeled, and seismic monitoring is available to estimate icequake activity and characteristics. We present evidence that even very small melt rates on cold glaciers (≤1.2 mm hr^{−1}) produce a response that is qualitatively distinct from melt-free conditions, and may trigger relatively large englacial fracture events where liquid water was not expected to exist. Our results follow from a novel network-based processing methodology that we have developed for detecting repeating icequakes and describe here.

2. Background

[3] Cold glaciers and temperate glaciers are distinguished by their temperature profiles. In cold glaciers, interior ice is uniformly below its pressure melting point (PMP), whereas temperate glaciers are composed of ice at or very near the PMP throughout. Cold and temperate glaciers also differ in both the hydrological forcing they receive from their environments and their response to this forcing. In temperate glaciers, englacial and subglacial water pathways that transmit water are transient in morphology and persistence due to frictional melting from variable water flow. Variable water input can also produce subglacial pressure pulses that accelerate basal sliding and cause rapid creep opening or closure of subglacial cavities that generate icequakes [Roux et al., 2010; Walter et al., 2008; Stuart et al., 2005]. Comparatively, deformation rates in cold ice are significantly lower. Below −10°C, the activation energy for creep decreases by more than half, and interstitial water that facilitates grain-boundary sliding is less abundant [Cuffy and Paterson, 2010]. In cold glaciers, lower water availability and ice flow rates result in suppressed basal sliding and lower crevasse density compared with temperate glaciers [Irvine-Fynn et al., 2011]. Thus, hydrological forcing may be absent except during brief periods in the melt season when hydrologically driven ice fracture may permit some surface-to-englacial water input [Boon and Sharp, 2003].

[4] Consequently, the deformation processes that are triggered by persistent englacial water passage and storage that produce seismic emissions in temperate glaciers may not be present in cold glaciers. Our interest here is to determine which processes areobserved during the introduction of water to an initially dry, cold glacier by interpreting icequake emissions produced during a brief melt season. We propose that it is necessary to study a setting where meltwater and basal sliding are initially absent, and subsequent surface melt can be adequately estimated. The melt-induced seismic response of the glacier from dry initial conditions will then provide a sensitivity test of exposure to surface melt. This test would address two primary questions: First, “are there initially absent seismic processes that are triggered by melt input?”, and second “are these events indicative of significant changes in the glacier's dynamics?”

2.1. Study Area

[5] Glaciers in the McMurdo Dry Valleys are representative of an extreme case of cold, polar glaciers due to the desert environment that they occupy [Fountain et al., 2006]. Among these is Taylor Glacier, which enters Taylor Valley as an outlet from the East Antarctic Ice sheet and terminates at the western lobe of the perennially ice-covered Lake Bonney (Figure 1). The mean annual and summer temperatures (respectively −17°C and −3°C) are consistent with a cold environment with limited meltwater input that we require for a study site. Ice thicknesses in the terminal 2 km range from ∼30 m at the terminus ice cliffs, to ∼200 m along the centerline. Prominent features of the glacier include a pair of meltwater channels that form 7 km upstream and deepen along flow, reaching ∼25 m near the terminus. During the summer months, micro-climatic conditions within these channels favor melt over sublimation, and cause supraglacial water flow [Johnston et al., 2005]. Observed melt is also produced from calving ice cliffs 20–35 m high at the ablation zone terminus.

[6] Basal ice temperatures recorded near the terminus (−17°C) suggest that Taylor Glacier is frozen to its substrate, and most of its motion is accommodated by internal creep in the ice and a debris-rich basal ice layer a few meters above the bedrock [Whorton et al., 2008; Samyn et al., 2008]. A force balance conducted several kilometers up glacier [Kavanaugh and Cuffey, 2009] further suggests that no basal motion is required to explain surface speeds.

[7] Taylor Glacier is the site of Blood Falls, an anomalous iron-rich seep that flows episodically from the northern end of the terminus. The seep originates from a cyroconcentrated pocket of brine that became isolated during a coupled recession of the Ross Sea Embayment and uplift of Taylor Valley and has probably been trapped since the last major advance of Taylor Glacier into the valley 1.5 My ago [Mikucki et al., 2009]. Despite ice flow rates of 3–5 ma^{−1}at the terminus, the seep location has remained stationary with respect to bedrock, emerging from a set of long cracks. The primary crack present during December 2006 was surveyed with GPS (T. Nylen, personal communication, 2007) and measured ∼80 m in extent, with strike ≅45° East of North. The maximum crack depth is unknown, but exceeds 15 m at some points. The separation distance between the crack faces increases with distance up ice, with a maximum of 6 m near the crack tip. Other surface cracks upstream of the primary crack run approximately parallel to it and catch summer melt that refreezes as blue ice. The brine emerges near the primary crack as an artesian well, indicating that the brine is pressurized at depth. For our purposes, the seep of Blood Falls is important as a surface-to-englacial pathway for meltwater.

2.2. Data Collection

[8] The data were collected using PASSCAL-supplied geophones, three UNAVCO-supplied GPS receivers, three time-lapsed cameras, and a meteorological station (Figure 1). The cameras were mounted on the valley floor and recorded daily images of the northern ice cliffs from early December 2005 through late March 2006 to document calving events. The meteorological station (−77.70°, 162.13°) recorded 15 min averages of meteorological conditions that provide the data for surface energy-balance modeling [Hoffman, 2011].

[9] Two continuous GPS stations were deployed on the ice, and a base station was deployed on a nearby benchmark. Data were collected at 30 sec sample rates during the summer for 24 hr per day, which was reduced to 1 hr during winter.

[10] The seismic network was deployed at the terminus region of Taylor Glacier from 2004–2006. The data acquisition system (DAS) consisted of six triaxial, 4.5 Hz L-28 geophones equipped with Quanterra Q330 digitizers and solid state data loggers. Three geophones were installed on-glacier in 1 m pits, and the remaining three receivers were coupled to large rocks on the valley floor. Ground velocity was sampled at 200 Hz in continuous recording mode and stored on the data loggers, which were retrieved in November, 2006. For analyses that require displacement records, we deconvolve the cumulative instrument response from these data using a 10^{−12} m water level regularization. Because these DAS time tag data to compensate for linear phase shifts caused by internal filters (Federation of digital seismograph networks: Standard for the exchange of earthquake data, SEED Format Version 2.4, unpublished reference manual, 2010, http://www.iris.edu/manuals/), we found no need to correct for the acausality of the anti-alaising filter as described elsewhere [Deichmann et al., 2000].

3. Methodology

3.1. Quantifying Seismicity

[11] To estimate the emission rate of icequakes (seismicity), we establish a criterion for counting icequakes that is based upon their observability. We first identify seismic events on each station using a standard detection methodology [Roux et al., 2008] in which we compute the ratio between a short-term average (0.5 sec) front window and long-term average (2.5 sec) back window of the squared-ground velocity (STA/LTA). When this STA/LTA ratio exceeds a threshold of 3.2, we declare a seismic event and retain a 10 second window centered on the pick time to prevent redundant event detections. We chose these picking parameters based upon a training procedure in which we compared the detector-generated picks with manual picks of waveforms from a subset of the data.

[12] To count these events, we define a weighted scoring method that assigns a scalar to each seismic event according to its size, as determined by its detectability at each receiver. A large event should produce observable ground motion at each receiver and closely timed picks, whereas a small event might only be observable by a pair of receivers near the source. If the difference in detector pick times between any pair of receivers is less than or equal to the maximum expected s-wave travel time Δt (0.5 sec), we assign the event a count score C≤ 1 that depends upon the square-distance between those receivers. This agrees with empirical relationships between detectability and square-distance observed elsewhere [Kijko and Sciocatti, 1995]. Quantitatively, we define this count score using:

Here r_{j} is the position of receiver j, β is the s-wave speed in ice, andI_{kn} is the indicator function that is one if receivers k and n both detect an event within Δt, and zero otherwise. The weight function a_{kn} is illustrated with its dependence on network geometry in Figure 2. Events observed at every receiver are given a maximum count score of one, and events observed at only one receiver are discarded. For an N receiver network, this scoring provides 2^{N} − (N + 1) possible combinations of receivers and event size (bins) that represent a distinct sub-network. Each event is counted only once. We assign each event in the observation period a valueC(Δt) and average the count scores by hour to obtain a time series of seismicity for each bin. The cumulative seismicity detected by any sub-network is computed by summing over the respective sub-network bins.Figures 3a and 3b illustrate the total seismicity summed over all bins and compared with modeled surface and subsurface melt.

3.2. Icequake Hypocentral Inversion

[13] To estimate hypocenters (source locations) for seismic events, we minimize the error between observed seismic wave arrival times and those computed using a geophysical model. We first measure waveform arrival times by manually picking phases for a subset of maximum count-score events (C(Δt) = 1). Waveforms which we include in our phase-picking procedure are constrained in two respects. First, the amplitude and energy of the waveform data limit the number of events for which we can pick first arrivals within acceptable certainty above channel noise. Second, we do not pick first arrivals for those events that give sources exterior to the glacial ice, as determined by the relative order that thep-wave arrivals are first observed at the receivers. This quality control removes all but ≅150 events recorded during the melt season between mid December and mid January. From these, we manually select thep-wave ands-wave arrival times, their polarity, and the coda wave duration time for each waveform.

[14] To construct a velocity model of the terminus region of Taylor Glacier, we use a publicly available 2 m resolution DEM (http://usarc.usgs.gov/lidar/_dload.shtml) and manually digitized the terminus outline. Our velocity model uses seismic wave speeds of 3850 m sec^{−1} for p-waves, 1950 m sec^{−1} for s-waves in the glacial ice and 4800 m sec^{−1} for p-waves, 2900 m sec^{−1} for s-waves in the valley substrate, based partially upon a seismic survey conducted in Beacon Valley [Shean et al., 2007]. Because precise bed topography information is unavailable, the forward model is two dimensional (2-D) and does not include vertical velocity gradients as would be present at the ice-bedrock interface.

[15] To produce each hypocenter estimate, we first perform a 2-D search over an epicentral grid 30 m below the local topography and minimize the error between the predictedp-wave arrival timesT^{P} and observed p-wave arrival timest^{obs}over this grid. We choose 30 m because it is consistent with the depth of the near-terminus ice and usedp-wave arrivals because ours-wave pick times are too uncertain to provide adequate constraint for locations. We then use these locations to initialize an inversion for hypocentersx_{0} using a centered, scaled version of Newton's method. At each iteration, an update for the hypocenter Δx_{0} is computed:

r=GS−1Δx0,

where the centered residual and centered Jacobian matrix components are:

rk=tkobs−tobs−TkP−TP,Gkn=∂TkP∂x0n−∂TkP∂x0n

and the scaling matrix is:

S=diagG1,G2,G3.

〈•〉 denotes averaging a column vector over its rows, x_{0n} is the nth hypocentral parameter, and ∥G_{i}∥ is norm of the ith column of Jacobian matrix G. The centering (subtraction of the mean from the linearized equations) removes the source origin time as an inversion parameter, while scaling by S^{−1} normalizes the columns of the Jacobian matrix, thereby reduces it's rank, and improves the problems' conditioning [Gibowicz and Kijko, 1994, section 4.1]. The epicentral locations obtained from the inversion are illustrated in Figure 5. To compute the confidence region associated with a particular hypocenter x_{0}, we perform ∼5 · 10^{3} Monte Carlo inversions using 0 sec mean, (0.01 sec)^{2}variance Gaussian noise added to the predicted travel time for each receiver. The resulting inversions provide a sequence of misfit vectors. The squared-norm of these misfit vectors form an empirical probability density function for the uncertainty in the squared travel time that we then normalize and integrate to obtain a cumulative density function (Φ) for the squared residual. Φ^{−1}(0.95) then provides the 95% confidence region R(x_{0}) for the hypocenter x_{0}:

Rx0=x0+δx0:TP−tobs2≤Φ−10.95.

3.3. Multiplet Event Detection and Clustering

[16] Multiplets are distinct, repeating seismic events that produce nearly identical records of ground motion. They provide an observation of repeated stress release from the same source region and from similar source mechanisms [Harris, 1991]. To quantify the similarity between multiplet icequake waveforms, we implement a network-based measure for correlation between events that uses ground motion recorded by all receivers simultaneously. This approach is advantageous for identifying pre-processed multiplet waveforms with small time-bandwidth products (low degrees of freedom) because of the potential for increased detection capability [Weichecki-Vergara et al., 2001]. A sample of ground velocity v(t) from an N-receiver network is provided by a3N channel record section that we define as:

Here v_{kl}(t) symbolizes the ground velocity for receiver k in geographical direction l, sampled over time window T. In practice these are samples of ground velocity recorded over T seconds, arranged as 3N column vectors in a matrix so that v_{kl}(t) symbolizes col[v_{kl}(t_{0}), v_{kl}(t_{1}) ⋯, v_{kl}(T)]. Inoperable rows (channels) are down-weighted or deleted from the matrix. Ifv(t) and w(t) are each distinct T second record sections observed at the network, we define their normalized cross correlation to be:

Equation (5) assigns a functional on a product space [Stark and Yang, 1998, pp. 78], where •,•F and ∥•∥_{F} respectively denote the Frobenius inner product and norm. ρ is bounded by ±1 and is equivalent to the mean channel correlation. If two sources are separated in distance but are otherwise identical, the differential arrival times between the N receivers cause misalignment between the record sections v(t) and w(t) so that |ρ| < 1. Thus, ρnear +1 requires similar waveforms and source locations, but does not require intra-receiver coherence [Gibbons and Ringdal, 2006]. An explicit relationship between separation distances of multiplet sources and their displacement field cross-correlation is provided elsewhere [Snieder and Vrijlandt, 2005].

[17] To detect multiplets, we design an unsupervised, partition-based clustering algorithm that groups similar record sections usingequation (5)with null-weighted horizontal channels. This algorithm operates in two stages. First, it identifies multiplets from an icequake detection catalog (stage 1), and then builds template record sections from these multiplets to search a larger catalog (“database”) of record sections for additional events (stage 2). In stage 1, a group of two or more record sections is assigned to a setS (cluster) if the correlation between every possible pair of record sections within S and that group exceeds a threshold of ρ_{0} = 0.65. This threshold value was found to give negligible false alarm probabilities for waveforms with small time-band-width products [Harris, 1989]. Because high correlation requires similar source mechanisms and hypocenters, the cluster sets S are therefore populated with record sections that come from multiplet events. The record sections within each cluster Sare then coherently aligned (to subsample precision) and stacked to form record section templates. In stage 2, each catalog template is correlated with record sections in the database as a match-filtering operation. Additional record sections are then added to the pre-existing clusters if they correlate aboveρ_{0} = 0.65 with a template. During both stages, ρis computed in the frequency domain to sub-sample precision using the Fourier shifting-property. Stage 1 of our algorithm differs from typical complete-link clustering methods in that proximity between clusters is computed over all possible pairs. Stage 2 of our method differs from other clustering algorithms in seismology [e.g.,Thelen et al., 2010] in two important respects. First, we process record sections as the signals rather than the single traces as the signals; second, the templates are built automatically from mutually correlated sets, so no observer bias is introduced through manual template selection. We provide quantitative details of our methodology in the Appendix.

3.4. Analysis of Icequake Moment

[18] Seismic moment tensors provide a description of the focal mechanism of icequakes and a measure of their strength. Physical sources like cracks or faults often are modeled as combinations of force-couples using the seismic moment tensorMwhich also governs the geometry of the far-field seismic displacement [Aki and Richards, 2002, equation 4.97]. The magnitude is characterized by the scalar moment which is defined by the moment norm, M0=12MF. In practice, M_{0} is estimated by contracting the displacement with the p-wave direction e^Pat the free-surface and integrating over time [Boatwright, 1980],

where t_{P} is the p-wave duration, ux,t is the observed displacement at the receiver, e^Px is the p-wave direction of displacement at the receiver,ris the source-to-receiver distance,F_{C}is the free-surface amplification,ϱ is medium density (ice or bedrock), x0 is the source position, x is the receiver position, α is p-wave speed, Γ^ is the vector pointing from the source to the receiver, and M^ is the normalized moment tensor. The integrated moment rate M˙0 gives the desired scalar moment M_{0}:

M0=4πrΩFCϱ(x)ϱ(x0)α(x)α5(x0)Γ^TM^Γ^

Here Ω is the area under the attenuation-correctedp-wave seismogram. Physically,M_{0} is proportional to either total slip along the crack face or local volume change from crack face opening. In the case of planar ice crack (fault) faces, M_{0} = μūA, where μ is the shear modulus of the faulting ice, ūis the fault-averaged net slip, andA is the faulted area. If the source is volumetric, the total confined volume change δV at the source region from an icequake is related to the scalar moment of that icequake according to Richards and Kim [2005, equation 1]:

M0=δVλ+2μ,

Elastic parameters for ice are λ ≅ 6.5 GPa, μ ≅ 3.5 GPa, at −16°C [Gammon et al., 1983]. An alternative expression M0=ΔVλ+2μ3 is frequently used in place of equation (8), where ΔV ≈ 2δV. However, ΔVgives the volume change in stress-free conditions, whereas confinement of buried source prevents the true strain from attaining a stress-free state [Aki and Richards, 2002]. We therefore use equation (8) to compute δV.

[19] The moment tensor may further be interpreted by decomposing it into a sum of independent tensors that are orthonormal under 12•,•F and represent different source types. The component of M attributable to source type “I” (such as tensile opening) with unit moment tensor M^I then has scalar moment defined by M0I=12M,M^IF.

3.5. Estimating Surface Melt Production

[20] It is difficult to measure surface meltwater production on glaciers directly. Total ablation can be measured over finite time periods, e.g. using ablation stakes, but this method includes contributions from both sublimation and melt. Although melt composes the majority of ablation on temperate glaciers, sublimation is a substantial fraction of ablation on Taylor Glacier [Johnston et al., 2005; Hoffman et al., 2008]. This makes ablation-stake measurements of melt inaccurate. Furthermore, melt can occur below the surface in the upper 50 cm through solar heating of the ice while the ice surface remains frozen, a process which cannot be detected with traditional ablation measurements [Hoffman, 2011]. Therefore, to estimate meltwater production from the surface of Taylor Glacier, we use a one-dimensional surface energy balance model that has been calibrated against ablation measurements and tested using ice temperature measurements in the upper meter [Hoffman et al., 2008; Liston et al., 1999]. The surface energy available for melt is computed as the residual from balances between net shortwave radiation, net longwave radiation, the turbulent heat fluxes of sensible and latent heat, and heat conducted into or out of the glacier. This surface energy balance is coupled with a one-dimensional heat transfer equation that is used to calculate the heat flux through the glacier surface and includes a source term for solar radiation absorbed beneath the surface. The distribution of solar radiation with depth is determined by a spectrally dependent extinction coefficient which is a function of the solar spectrum, ice surface albedo, ice density, and effective ice grain radius [Brandt and Warren, 1993; Liston et al., 1999]. The model's adjustable parameters include the aerodynamic surface roughness (which affects the magnitude of the turbulent heat fluxes, and therefore sublimation), the effective ice grain radius (which determines the distribution of net solar radiation with depth), and the thickness of the surface layer (which determines the fraction of net radiation included in the surface energy balance).

[21] We apply the model using an hourly time step with meteorological forcings of air temperature, relative humidity, wind speed, incoming solar radiation, surface albedo, incoming longwave radiation, and atmospheric pressure. Model outputs at the surface include ice surface temperature and the ablation components of sublimation and melt, and model outputs for the subsurface ice column include temperature, melt flux, and water fraction. The model is applied at a point (162.237°E, 77.726°S) and calibrated to 14 years of summer ablation measurements averaged from three ablation stakes located within 0.5 km [Fountain et al., 2006]. We consider this location representative of the near horizontal surface of the terminal 2 km of Taylor Glacier, exclusive of the large channels and ice cliffs, which have substantially higher melt rates [Johnston et al., 2005], and Blood Falls, which has substantially lower surface albedo and likely higher melt rates. Local meteorological forcings are obtained by applying the quasi-physically based meteorological distribution model MicroMet [Liston and Elder, 2006] from observations at Taylor Glacier and Lake Bonney meteorological stations. The calibration at the Taylor meterological station yielded an aerodynamic surface roughness of 0.2 mm, effective ice grain radius of 0.08 mm, and surface layer thickness of 1 cm, comparable to those at the Taylor Glacier meteorological station, 2 km upglacier [Hoffman et al., 2008]. We perform a visual test on surface melt production using the daily images obtained from the time-lapse camera system. During days surface melt occurs in the model, water is visible as a stream around the perimeter of the ice cliffs. Similarly, the stream volume diminishes during days modeled melt is absent. We therefore consider the model qualitatively representative of conditions near the ice cliffs as well. The time evolution of modeled melt is illustrated inFigure 3a.

4. Observations

4.1. Seismicity

[22]Figure 3 documents a comparison between modeled melt and an hourly time series of the cumulative seismicity computed from equation (1). Surface melt was confined to brief, sub-daily events in December and January, with peak melt rates ≤1.2 mm hr^{−1}. Subsurface melt was also present within the ice column at shallow depths (≤50 cm) both December and January, with and without coincident surface melt (Figure 3a). We estimate that a fraction of the water produced in the subsurface over the season (≅1.8 cm) drained through intergranular veins or subsurface cracks, with drainage rates ≤0.5 mm hr^{−1}.

[23] Comparatively, the surface melt was abrupt in timing and resembles a binary process as represented in Figure 3b. The total seismicity was composed of two qualitatively distinct components that differ with the coincidence of modeled melt. The dominant features of the melt-absent seismicity include a diurnal component in timing and amplitude with minimum emission rates (background rates) that are near zero during the local daytime (Figure 4). The dominant features of the melt-coincident seismicity include a non-zero background rate that is superimposed on a reduced diurnal component with a lower overall average count rate (Figure 3b).

[24] We next compare the total seismicity with the seismic events that are sufficiently large to result in a unit-count score (Figure 3c). The unit-count score events are similar to the melt-coincident seismicity in both timing and localization. We then compare these signals with the subset of seismic events that are observed exclusively on ice-based stations (the ice sub-network) and the subset observed exclusively on land-based stations (the ground sub-network) inFigure 3d. The ice sub-network seismicity exhibits a coincidence with the unit-score seismicity, while the land sub-network seismicity exhibits a coincidence with the melt-absent component of the total seismicity.

[25] Thus the seismic events observed exclusively on the ice sub-network are active during the melt season, and the events observed exclusively on the ground sub-network are active from late January through the remainder of the observation period, with little overlap. We observed no change in GPS speed at any time.

4.2. Icequake Locations

[26] We implement the inversion scheme summarized in section 3.2 using travel times from our data set and assemble a catalog of the corresponding icequake hypocenters. The dominant feature present in this catalog is a concentration of epicenters within a “cloud” just west and nearly parallel to the Blood Falls crack (Figure 5a). The icequake depths are poorly constrained from the tight elevational coverage of the network and we do not interpret them. Using equation (3), we compute the 2D, 95% confidence region for a prescribed hypocenter x0 coincident with the Blood Falls crack tip 30 m below the surface of the ice (Figure 5b). Approximately ∼75% of all located events are interior to this confidence region. Additional icequakes were located near an actively calving cliff face East of receiver CINDY, and in the topographical depression of the Northern melt channel. In addition to the confidence region, we compute error ellipsoids for each inversion to estimate the individual location uncertainties and illustrate the distribution of the ellipsoid axes lengths in Figure 6.

4.3. Multiplet Clustering

[27] We identified multiplets from three distinct detection catalogs and database combinations.

[28] In the first case, we cluster record sections from the phase pick catalog that we used to locate icequakes. We determine that these events comprise 16 multiplet clusters of varying size containing a total of 85 muliplets. About ≥81% of these located multiplets are interior to the confidence region and are distinguished by colored epicentral markers in Figures 5a and 5b. The most populous of these multiplets is composed of 24 events (blue), the second and third most populous clusters are respectively composed of 15 and 9 events (red and green), and the remainder of the multiplet populations are composed of between 7 and 2 events (orange). A residual ∼30 events had no cluster membership in the phase pick catalog (pale gray). The velocity seismograms for the three most populous clusters are documented with the same color assignment in Figure 5c. Each waveform is <1 second in total duration, with poor intra-network waveform correlation on average (ρ∼ 0.5) relative to the intra-multiplet record section correlation (ρ ≥ 0.65). There issignificant intra-multiplet variance in the network-averaged root-mean square amplitude of the seismogram displacements that is shown in 5(e). We rotate the displacement seismograms for the most populous cluster into a local free-surface and refraction-corrected (non-orthogonal)p, sv, sh wave system and illustrate the p-wave component inFigure 5d. The p-wave first motions for each receiver are upward.Figure 7 demonstrates that p and swave separation on station JAN and GREG is more pronounced relative to the other receivers due to greater receiver-to-source distance, while channel malfunctions on station MARSH lead to an ambiguous rotation.

[29] In the second case, we assemble templates from record section stacks in the phase pick catalog and cluster over all detected unit count-score events from the entire detection database over the observation period. This results in a 3.7-fold gain in the total multiplet population, with a peak multiplet emission rate of ∼45 events per day (Figure 8, top). The largest gain in detected multiplets comes from the most populous and third most populous cluster templates. We illustrate the detection history of these multiplets in Figure 8 (top) where we have maintained the color coding from Figure 5.

[30] In the final case, we assemble templates obtained from cluster catalogs that are computed on each separate day. We again cluster over the detection database for the entire observation period. This recovers an additional 936 events from 205 multiplet templates. These multiplets contain 22% of unit-count score detections, 18% of all unit-count score melt season detections, and an additional 5% gain in detections from outside the melt season period (188 new events). The detection history is illustrated inFigure 8 (bottom).

4.4. Moment Calculations

[31] We compute the scalar moment M_{0} for icequakes interior to the 95% confidence interval pictured in Figure 5b. We are confined to use station JAN exclusively to compute moment with equation (7) within the confidence we require, however. Differential arrival times between p- ands-waves are too small or uncertain, relative to the sample interval, to provide adequate measurements of Ω on other receivers. There are additional sources of uncertainty in our application ofequation (7) that are difficult to quantify; for example, the quality factors that we use for attenuation correction (∼10^{2}) are not well known, the p-wave pulse may include scattered arrivals that we unintentionally integrate with Ω, and Γ^ and F_{C}depend on uncertain hypocentral depths. We therefore compute icequake magnitudes using the moment-magnitude scale Mw=23log10M0−9.1 [Kanamori, 1977] to evaluate the reasonability of our M_{0} estimates. We find that −0.9 ≤ M_{w} ≤ +0.3, comparable to smaller stick-slip events on alpine glaciers [Weaver and Malone, 1979], and within expectation.

5. Interpretations

[32]Figures 3a and 3b document a transition in seismicity during melt input that suggests meltwater is the primary trigger for increasing background emission rates, while its absence seems to increase the diurnality of emissions and decrease background rates. We interpret the coincidence of the unit count score (large) seismic events with glacial icequakes in Figures 3c and 3d to indicate that the large events without inverted locations are also glacial in origin, and therefore reject the possibility that they are due to a source exterior to the glacier, such as lake ice. From the timing of melt relative to icequake response, we conclude that large icequakes are triggered by meltwater input. Figure 3dfurther suggests that there are at least two different mechanisms for triggering smaller seismic events that are detected only on these sub-networks. One set triggers glacial icequakes, and the other drives seismicity exterior to the glacier, such as lake ice.

[33] We next address the possibility that the diurnal signal is borne from noise that would mask waveforms and reduce detections. We estimate the statistics for 10^{3}, 30 sec noise sequences recorded on each receiver from dates uniformly distributed over the observation period and discard any within 30 sec of a known pick time. From these sequences, we observe that the noise is near-Gaussian and has no statistically significant fluctuation in variance that would reduce the STA of the detector. We conclude that observed seismicity is physical rather than a result of diurnal noise.

[34] We propose that the diurnally responsive icequake sources that are active without melt include fracture of lake ice (and glacial ice to a lesser extent) through generation of thermal bending moments. These occur in thick sea ice [Bazant, 1992] when thermal stresses near the surface induce bending moments that store significant strain energy. The release of that strain energy can cause large fracture events and microseismic emissions (M_{w} ∼ 0.2) that are recorded as icequakes (C. Thurber, personal communication, 2012). This is more effective at lengthening large seismogenic cracks in ice compared to thermal diffusion, which is restricted to penetration depths of ∼20 cm over a daily temperature cycle.

[35] To evaluate this interpretation, we estimate the magnitude of thermally generated moments in the ice as a result of temperature increases, using a sinusoidally heated half-space thermal stress model [Turcotte and Schubert, 2002, Equation 4–194]. This model does not include an advection term from interstitial water that may further warm the ice at depth. We compute the thermal bending moment by integrating the product the thermal stress and depth (moment arm) to a reasonable isothermal boundary [Bazant, 1992, equation 4]. Our parameters include a thermal skin depth of 0.17 m and an integration depth of 4 m for either the lake ice lower boundary or an isothermal depth for the glacial ice. The result gives M_{T} = 4.25 · 10^{6} Pa · m. We use data from Gagnon and Gammon [1995] and compute an upper bound on the bending strength for glacial ice of M_{T} = 3.0 kPa · m at −5°C for 10^{−5}sec^{−1} strain rates. We conclude that thermal bending moments are sufficient for triggering fractures through 4 m of ice.

[36] To determine if seismic energy from these events can couple into the ground, we compute the required size for an event required to be detectable by the land sub-network receivers. We compute an ice-to-water-to-ground net amplitude transmission coefficient and multiply this by the displacement amplitude from the integrand ofequation (6), where we use a value for F_{C} that has been averaged over the focal sphere [Boore and Boatwright, 1984]. We find that a fracture area-crack opening displacement product of 2.2 m^{3} will produce peak displacements over a detection threshold of 10^{−9} m for the p-wave that we determine fromFigure 5e. These dimensions are consistent with physically abundant fracture features on Lake Bonney. In summary, we conclude that fracture of lake ice due to thermal bending moments may be observed at the ground based receivers.

[37] Conversely, surface melt apparently triggers seismic events that are not sensitive to diurnal forcing and produces more steady emissions of icequakes. We propose the presence of interstitial melt creates a heat source upon freezing that maintains a more uniform ice temperature, thereby suppressing thermal bending moments and resultant icequakes.

[38] We next evaluate the source of multiplet seismicity. Multiplets often result from repeated stress release within the same source region and produce high intra-multiplet record section correlation [Harris, 1989]. We quantify the prevalence of melt triggered sources for large icequakes as the number of multiplets temporally coincident with modeled surface melt. The epicentral locations for ≥75% of the multiplets that we identified in Figures 5a and 5b are spatially coincident with the confidence region centered on the Blood Falls crack tip. This spatial coincidence suggests that sources near the crack tip likely account for the most populous clusters from the phase pick catalog, with location variability due to typical pick errors. The detection history of multiplets that we obtained from clustering (Figure 8) demonstrates that additional icequakes (∼230) also belong to these multiplet sequences and therefore likely share the crack tip region. The total number of these multiplets constitute about 7% of all unit count score events observed with the STA/LTA detector.

[39] Waveforms from these multiplet sequences that are documented in Figures 5c, 5d, and 7have traits common of microseismic events: arrivals are impulsive, intra-receiver coherence is low, and coda waves dominate the latter portion of the wave train. This is consistent with a short duration source time function and strong scattering environment [Oye et al., 2005]. The motion of the direct p-wave is up and away from the source location at all receivers, as shown by the record sections inFigures 5d and 7. This uniform p-wave polarity is observed from other sources composed of volumetric or isotropic focal mechanisms [Walter et al., 2009; Julian et al., 2010]. One source consistent with these focal mechanisms that will generate the observed multiplet first motions is the tensile crack.

[40] While pure tensile cracking (mode I cracking) is sufficient for producing compressive p-wave displacements at the receiver locations, it is not necessary. A seismic source composed of a mix of fracture modes can also produce compressive first arrivals at the six receiver locations. To bound the possible modes leading to the observed polarities, we forward model thep-wave surface displacement resulting from a fracture source localized at the Blood Falls crack tip. We first compute motions using a description for whole space [Aki and Richards, 2002, equation 4.97] and a suite of crack face displacement vectors that combine tensile with mode II (slipping) and mode III (tearing) fracture. To estimate the surface motion polarity at each receiver, we then correct for ice-to-ground refraction, surface amplification, andp-wave inclination at the free surface. Some results of this modeling are illustrated inFigures 9 and 10. Crack face displacements oriented more than 68° from the crack face normal result in insufficient tensile cracking that produces downward first motions at some receivers, inconsistent with observations. The least-isotropic moment tensor consistent with observations has a projection onto a mode-I unit tensor of 0.66·MF≈12M,M^IF. This indicates that tensile cracking is the dominant mechanism for these icequakes, regardless of the possibility for other fracture modes. Figure 10 suggests that the crack face normal vector and displacement must be within 40° and 60° to match the observed relative seismogram amplitudes.

[41] A second kind of source that is capable of producing the observed first motions is the volumetric expansion of a pressurized source of brine at depth, analogous to what is often observed in volcanic or geothermal systems with inflationary sources [Julian et al., 2010]. The surface channels of Taylor carry meltwater off-glacier and into Lake Bonney, thereby unloading the glacial substrate. Peak melt rates of 1.2 mm hr^{−1} over the glacier surface produce spatially averaged peak unloading rates of m˙ϱWg≅12Pahr−1, where m˙ is the melt rate in dimensions of length per time per unit area, ϱ_{W} is water density, and g is gravitational acceleration. Johnston et al. [2005] report melt rates in the channels to be 4.5 times that of measured melt rates on the flat ice surface, giving an upper bound for the peak unloading rate of m˙ϱWg≅54Pahr−1. We compute comparable peak unloading rates of order 10 Pa hr^{−1}from atmospheric tide data supplied by the NSF McMurdo Dry Valley Long-term Ecological Research (LTER), during December through January. We therefore consider the tensile crack model more likely, because the alternative requires the brine source to respond to changes in overburden comparable to that produced by atmospheric tides. Our estimates do not consider the effect of pressure gradients caused by changes in ice surface topography from melting, because the energy balance model implemented here is one-dimensional.

[42] We therefore propose a physical model for melt triggered seismicity that produces the observed compressive first motions as follows. First, our model initial conditions impose that the Blood Falls crack system is under stress near the brine seep. This is required by the presence of the artesian well at the ice surface and indicates that the brine is under a pressure of at least ϱ_{B}gH ≥ 290 kPa to exceed ice overburden, where ϱ_{B} is brine density (which exceeds water density) and His the local ice thickness. During the December-January melt season, surface and subsurface melt produced flows down-gradient toward the Blood Falls seep as input into the crack system. Any channel down-cutting that occurs englacially as proposed in temperate glaciers [Fountain and Walder, 1998] and observed in the high arctic [Boon and Sharp, 2003] would then increase the stress intensity factor of the crack by lengthening it. Any sustained water catchment within the crack would further increase the stress intensity factor through the additional hydrostatic stress. This, combined with the pressurized brine source, provides conditions favorable for hydrofracture [van der Veen, 1998]. Melt input would thereby promote hydrologically triggered fracture events that are then observed as icequakes. Once the melt production abates, inflow rates decrease, and englacial water at depth freezes quickly where the ice is cold (−17°C). However, some liquid water may persist at depth on wetted ice or rock surfaces as a thin film. The thermomolecular forces responsible for flow within the films have a net body-force equivalent that is proportional to the film-equivalent ice mass [Dash et al., 2006]. This proposed process can generate ∼2 MPa stresses in porous bed material and induce fracture [Murton et al., 2006]. We therefore suggest that the presence of this crack allows a persistent surface pathway for the Blood Falls source by acting as both a catchment for meltwater and site for bed fracture via ice segregation. A more focused seismic study is required to assess post-melt bed fracture as a source of seismicity, however.

[43] Finally, we compare the volume change at the source region with melt input volumes. We first assume the icequakes from the crack region have similar, volumetric source mechanisms so that the moment is proportional to the volumetric increase and sum the cumulative scalar moment with equations (7) and (8):

λ+2μΔV=∑kM0(k)

From equation (9), we compute a source volume change of ≅2.3 m^{3}at the source region. When we average this volume over the Blood Falls crack face dimensions (80 m × 15 m), we measure a cumulative crack opening displacement of 2 mm. The melt rates modeled during this time exceed the cumulative water volume required to explain source-volume increase computed fromequation (9) (Figure 11). The relatively small displacements may explain why no obvious GPS speed-up is observed during the melt season in spite of icequake activity.

6. Synthesis

[44] Our goal in conducting this study was to determine the response characteristics of a dry, polar glacier during the transition into a melt season when meltwater influences ice deformation. Our methodology consists of comparing passive seismic data that we process using network-based analyses with meltwater produced form a calibrated surface energy balance model. From our estimate of surface melt and interpretation of the icequake observables, we make three primary conclusions: first, very little meltwater initiates a mode of seismicity distinct from the diurnally responsive, dry, cold mode. The melt-driven mode is composed of comparatively few but large energy icequakes, with diminished response to diurnal forcing. Second, the response time at Taylor Glacier is effectively immediate, with most large icequakes triggered nearby the Blood Falls seep. Third, the firstp-wave motions from sources indigenous to the fractured region are consistent with opening cracks. One implication of water triggered fracture in cold ice is that surface melt may reach the sub-freezing bed, and hence allow brief input of heat and mass to the cold basal interface. This does not seem to require the existence of persistent englacial water that exists in temperate ice, and has been observed in the Canadian arctic [Boon and Sharp, 2003]. The velocities as determined from GPS show no speedup above measurement noise; hence if meltwater does penetrate to the bed, no basal sliding likely takes place. A combination of melt input and a pressurized brine source below the seep may trigger sufficient crack tip propagation to allow persistent hydrological communication to the bed during the melt season. We propose that once the crack formed and enabled brine to escape, it acted as a catchment during melt seasons and induced further fracture through downcutting above pressurized brine, thereby allowing the crack to persist. In wetter conditions, other surface cracks may catch comparable water and create additional pathways to the surface. Thus, the singularity of the release point for the brine may be due to the low melt and deformation rate at Taylor Glacier. Thus, broader impacts of this study may include providing the subglacial-systems community an opportunity to assess the role of surface controls on the brine release episodes.

Appendix A:: Unsupervised Clustering of Record Sections

[45] Here we provide criteria for assigning cluster membership for multiplet identification to avoid manual template selection and maintain detection consistency when record section stacks (record section sums) are cluster templates (match filters).

[46] Define a Hilbert space H equipped with an inner product 〈•, •〉 whose elements are 3N channel record sections v(t). Suppose that vk(t), k = 1, …, n, …, M, are record sections as defined by equation (4) that give samples of ground velocity from M icequakes. Consider a set S⊂H according to the membership criteria:

S=v(t):v(t),w^n(t)≥ρ0v(t),

Set S in equation (A1) defines the set of all record sections that belong to a multiplet and represents a higher dimensional convex cone whose vertex is parallel to w^n(t) [Stark and Yang, 1998, pp. 113]. Seismic clustering methods often implicitly use sets of this form [Lees, 1998]. We address two drawbacks of clustering with this set constraint: first, populating S requires prescribing w^n(t) and second, template matching with stacks depends on detection order.

[47] Consider a multiplet sequence that produces five (normalized) record sections v^1(t),v^2(t),⋯,w^(t) that satisfy 〈v^k(t),w^(t)〉 = ρ_{0}, where k = (1, ⋯, 4). Each v^k(t) is representable as the sum of its projection onto w^(t) and an orthogonal complement (residual). It follows v^k(t),v^n(t) = ρ_{0}^{2} + (1 − ρ_{0}^{2}) cos(θ_{kn}) where θ_{kn} represents the angle between the residuals of v^k(t) and v^n(t). Suppose we detect three signals that include w^(t) from this sequence and stack them to form a cluster template v¯(t). Now suppose we then detect an additional signal v^m(t) from this same sequence and test it for cluster membership. We now show that it's membership is conditional upon the detection order using two distinct scenarios. The initial triplets detected in either scenario include a different pair of signals together with w^(t), and a different value for m. The correlation of v^m(t) with the stack in general is:

If the residuals in the initial stack are anti-correlated but the residual of v^m(t) projected onto w^(t) is within π/4 of v^k(t) and v^n(t), ρ_{m} = ρ_{0} so v^m(t) is included in the cluster set. However, if the residuals in the initial stack are orthogonal but the residual of v^m(t) projected onto w^(t) is within 3π/4 of v^k(t) and v^n(t), ρ_{m} < ρ_{0}. In particular, if ρ_{0} = 0.65, ρ_{m} = 0.27, and v^m(t) would be rejected from the cluster set.

[48] We avoid this inconsistency in cluster assignment and alternatively define a cluster as a smaller convex set using a more restrictive membership criteria:

SL=v(t):v(t),w^k(t)≥ρ0v(t),∀k∈1,2,⋯L

where L ≤ M. Elements of S_{L} correlate above ρ_{0} with every record section wk(t), k = 1, …, n, …, L, so that S_{L} ⊆ S. It also represents record sections produced by a multiplet, but the characteristic ground velocity is provided by L observations, rather than one. Hence, clustering record sections into sets defined by equation (A3) requires high mutual correlation between elements.

[49] We implement this requirement as follows. Suppose we detect M icequakes on a given day and record M corresponding record sections. From equation (5), we define an upper-triangular matrixρ whose elements ρ_{ij} provide the 12M2−M normalized correlation coefficients between record sections:

ρij=maxτvi(t),vj(t+τ)Fvi(t)Fvj(t)F,i<j

Suppose now that a subset of L ≤ M record sections with indices γ ⊆ {1, …, L} cross-correlate aboveρ_{0} with a particular record section wn(t), so that ρ_{nγ} ≥ ρ_{0} ∀ γ. This does not guarantee that vγ(t)∈SL∀γ . We therefore test all entries of ρwhose indices are derived from pair-wise combinations ofγ as power sets. For example, if ρ_{1γ} ≥ ρ_{0} ∀ γ = {2, 3, 7}, then vγ(t)∈SL∀γ only if ρ_{23}, ρ_{27}, and ρ_{37} each exceed ρ_{0} as well. If this condition holds, we define SL=v(t):v(t),v^k(t)≥ρ0v(t),∀k∈1,2,3,7, as the cluster for a multiplet event.

[50] In general, we identify the clusters from (equation A4) from a desired catalog, and aggregate them over a record section database by computing ρ. To populate the final clusters that are plotted in Figure 8 (top), we check mutual correlation between all elements that satisfy ρ_{ij} ≥ ρ_{0}as for catalog record sections. We obtain a representation of a each cluster by coherently aligning the elements to sub-sample precision and linear stacking. BecauseS_{L}is convex, any linear combination of record sections with non-negative weights is also contained inS_{L}. Other weighting schemes for stacking are useful but depend on the performance measure applied to the record section output. A representation model for multiplets from signal subspaces described is elsewhere [Harris, 1989].

Acknowledgments

[51] We extend thanks to Ian Joughin, Ken Creager, and Steve Malone who provided input concerning glaciological and seismic aspects of the work. We thank UNAVCO, IRIS-PASSCAL, and Raytheon for providing instrumentation and logistical support. We thank the University of Washington Statistical Consulting Service members Paul D. Sampson, Bailey Fosdick, and Roddy Theobald that provided input concerning the STA/LTA detection statistics. We thank the members of the Blood Falls field team Matt Szundy, Erin Whorton, Hassan Basagic, Michelle Koutnik and Thomas Nylen that assisted in the collection of the seismic data used in this work. We thank Steven Gibbons, Weston Thelen, and Fabian Walter for manuscript input. All processing code was generated using MATLAB. This work was supported by NSF grants 0230338 and 0233823.