Abstract

Subglacial stick-slip motion speeds erosion by hydrofracturing and in other ways, as determined from analysis of the growing body of field data. Microearthquake monitoring commonly detects subglacial earthquakes, likely mostly from stick-slip motion of debris-laden ice over bedrock. Source parameters show that many quakes cause enough motion to greatly lower water pressure in cavities on the lee sides of bedrock steps. We calculate that the resulting expansion of higher-pressure water in nearby cracks promotes hydrofracturing, with even relatively small cracks growing unstably under thick glaciers and all cracks growing faster than for aseismic behavior. This mechanism also helps generate the step-like topography favoring block plucking. This stick-slip glacier-erosion hypothesis suggests that the erosion rate will increase with ice thickness as well as basal shear stress, ice-flow velocity, and water supply.

INTRODUCTION

Glacial erosion impacts mountain-belt evolution and other geomorphic processes (e.g., Shuster et al., 2011; Champagnac et al., 2012). Under some conditions, glaciated basins yield sediment at a faster rate than comparable fluvial systems (Hallet et al., 1996). Glaciers erode their beds mainly by abrasion producing predominantly silt-sized particles (Hallet, 1981), and plucking of larger blocks from bedrock (Hallet, 1979). Subglacial streams rarely erode channels in bedrock but mainly transport sediment (e.g., Drewry, 1986; Alley et al., 1997), with bedload and suspended load subequal (Gurnell and Clark, 1987). Bedload is primarily from plucking, with cobbles common, and suspended load mainly from abrasion. Roughly half of the silt is abraded from plucked clasts, so plucking dominates subglacial bedrock erosion (Cohen et al., 2006; Gurnell and Clark, 1987; Hallet, 1981).

The dominance of plucking was difficult to explain, as ice is much softer than rock and plucking occurs in a subglacial setting not conducive to freeze-thaw processes. Key advances have come from Hallet (1996), Cohen et al. (2006), and Iverson (1991, 2012). Studies of deglaciated bedrock indicate subglacial bedrock steps with lee-side water-filled cavities, and nearly horizontal bedding planes or sheeting-type joints, as shown in Figure 1A. The rate-limiting process is taken to be the growth of near-vertical mode-I cracks from the free surface to connect with the bedding/sheeting, freeing blocks.

Extensive cavities focus basal shear stress on the small regions of remaining ice-rock contact (Hallet, 1996), aided by the drag caused by any abrading clasts (Cohen et al., 2005). Sufficiently rapid water-pressure fluctuations in cavities are at least partly decoupled from those in adjacent bedrock cracks; especially when cavity water pressure is dropping, higher pressure in cracks favors crack growth by hydrofracturing (Cohen et al., 2006). This suggests that the erosion rate increases with variability in the water system (Alley et al., 1999; Cohen et al., 2006). Preexisting rock weaknesses also favor plucking (Iverson, 2012).

Here, we present evidence that subglacial earthquakes from stick-slip motion of debris-laden ice are relatively common and cause large pressure fluctuations. This can speed erosion, at a rate that increases with stick-slip motion and ice thickness. Stick-slip motion also can increase the crack-opening drag from moving clasts compared to continuous motion, and may increase abrasion. This suggests that basal seismicity must be documented and understood to more accurately model glacier erosion.

SEISMIC OBSERVATIONS

Basal seismicity indicating stick-slip motion has been found in many places where passive seismometers with enough coverage and sensitivity have been deployed on fast-moving ice (Anandakrishnan and Bentley, 1993; Anandakrishnan and Alley, 1994; Zoet et al., 2012; Christianson, 2012); additional data show events that may record stick-slip motion (Smith, 2006; Weaver and Malone, 1979; Deichmann et al., 2000; Stuart et al., 2005) or crack growth as described below (Walter et al., 2008). With a few exceptions (e.g., the tunnel observations of Vivian and Bocquet [1973] and Goodman et al. [1979]), the data cannot unequivocally show whether stick-slip behavior occurred within ice, within substrate, or between ice and substrate; however, physical understanding plus the known motion at the glacier bed argue that quakes usually are from stick-slip motion of debris-laden ice over the substrate, most typically bedrock.

In a few cases, the seismic data allow estimation of source parameters. We summarize these next, to constrain the erosion-mechanism discussion that follows.

Near the head of David Glacier, a large (10-km-wide, 1800-m-thick), steep outlet glacier through the Transantarctic Mountains of Antarctica, thousands of seismic events have been observed over many years, including a remarkable series of over 20,000 repeating events (Fig. 2), with a mean spacing of 25 min (Zoet et al., 2012). These repeating events have a narrow range of seismic moments centered on Mo ∼7.65 × 1011 N m, giving a moment magnitude, Mw, of 1.8. They are consistent with a fault radius of ∼380 m and a slip of ∼1.9 mm per event (Zoet et al., 2012).

The amount of time over which this slip occurs at a single point on the fault plane is important for estimating the effect on subglacial water pressure. For an order-of-magnitude estimate, we follow McGarr et al. (2010), who found that local slip velocity, v (m/s), increases with shear stress, τs (MPa), at failure as 
graphic
assuming the slip velocity averages half its peak value. A locked fault plane will support the shear stress from adjacent well-lubricated regions; assuming this affects an annulus of width slightly greater than the fault-plane diameter yields the order-of-magnitude estimate 
graphic
where τb is the typical basal shear stress averaged across regions larger than the local “sticky spot.” For David Glacier, the basal shear stress τb is ∼0.3 MPa, giving v = 0.09 m/s, and 0.02 s to slip 1.9 mm (Zoet et al., 2012).

Widespread events occur on the Kamb Ice Stream, a low-surface-slope, 900-m-thick West Antarctic ice stream feeding the Ross Ice Shelf (Anandakrishnan and Alley, 1997). The events are modulated by the tides, with a falling ocean tide providing less backstress on the ice and allowing faster motion, producing more microearthquakes, and with events triggering additional events on nearby sticky spots. The glacier bed is mainly basal till, but likely has local regions where weakly lithified sedimentary rocks protrude through the till (Smith, 2006; Blankenship et al., 1986). This mostly soft bed produces smaller events than on David Glacier, with Mo ∼2.3 × 107 N m (Mw = –1.8). The stick-slip regions are also smaller (on the order of 10 m radius; Anandakrishnan and Alley, 1994), based on the corner frequency of the event spectra; calculations indicate a typical event slip of 0.9 mm (Anandakrishnan and Bentley, 1993). For a typical basal shear stress τb of ∼0.015 MPa (Joughin et al., 2004), most of the slip would occur over 0.02 s.

Events have also been located and recorded at the base of the glacier Engabreen, a relatively steep temperate glacier in Norway with a “hard” bed of schist and gneiss (Christianson, 2012). These include periodic events with a spacing of 20–30 min and Mo on the order of 108 N m (Mw = –0.7). For a fault radius of ∼10 m, event motion is on the order of 0.1 mm. With a driving stress of 0.44 MPa, the slip time is 0.001 s.

Finally, we note that early seismic observations on Mount Rainier (Washington State, USA) identified large events, likely at the base of Nisqually Glacier, with an estimated Mo = 7.65 × 1011 N m (mean Mw = 1.9). The size of the fault plane is poorly constrained, but stick-slip behavior on the entire width of the glacier would give 0.2 mm of slip, and with the fault plane likely smaller, the slip is correspondingly larger (Weaver and Malone, 1979).

We thus find, from the limited available data set, that basal stick-slip behavior is common, with typical slips on the order of 1 mm over times on the order of 0.01 s or less (by as much as an order of magnitude). We use 1 mm slip over 0.01 s as a reference case, and apply it to a reference cavity (see below), to show how the influence of stick-slip motion on subglacial water pressure can speed erosion.

EROSION MECHANISMS

Except for limited regions beneath cold ice sheets, and some high-elevation or high-latitude sites, the bed of a glacier is generally at the pressure melting temperature, with a water system between ice and substrate that carries melt generated at the bed plus any supply from melting above (e.g., Cuffey and Paterson, 2010). The average pressure at the bed supports the weight of the ice above, but water preferentially occupies lower-pressure regions; hence, the water pressure is typically slightly less than the ice-overburden pressure. Viscous dissipation in vigorous channelized water flow may generate enough heat to melt ice rapidly enough to reduce water pressure substantially, by as much as on the order of 1 MPa, but the requisite water flux to cause notable pressure drop means such channels are greatly restricted in space and time. Most of the glacier bed then is drained by some sort of distributed water system, in which the pressure drop results especially from ice flow over an irregular bed, and is commonly on the order of 0.1 MPa or less.

Using the geometry of Figure 1A, which is based on extensive observations of deglaciated bedrock, cavity length, L, increases with step height, h, sliding velocity, and water pressure (Iverson, 2012; Iverson and Petersen, 2011). Consider a reference cavity with h = 0.1 m, L = 0.3 m, and volume (per unit width transverse to flow) between hL and hL/2; we use 2hL/3 for simplicity. Much larger and smaller cavities exist, but this is consistent with production of the commonly observed cobbles discharged by glaciers, and with many observed features on deglaciated bedrock (Walder and Hallet, 1979). A slip (s) event of s = 1 mm would increase the cavity volume by hs.

The compressibility of water is 5 × 10−10 Pa−1 at 0 °C (Fine and Millero, 1973). For the limit of zero water inflow to the cavity during a slip event, the expansion hs/(2hL/3) = 0.005 implies a pressure drop of 10 MPa, sufficient to lower water pressure to 0 beneath ice less than ∼1100 m thick, and thus to induce bubbles (often called “cavitation” in engineering literature).

For David Glacier, Kamb Ice Stream, and Engabreen (our best-documented cases), the maximum pressure drop is close to or exceeds the overburden pressure. The maximum possible pressure fluctuation from stick-slip motion increases with ice thickness because of the limitation of zero pressure in a cavity.

Physical processes will tend to moderate such large pressure fluctuations, but we estimate that very large pressure fluctuations are still likely in some cases. First, water inflow to a cavity during an event could decrease the pressure fluctuation. Water films are often assumed, using the equations for viscous flow between parallel plates (Cuffey and Paterson, 2010; Turcotte and Schubert, 2002). In our reference case, for a pressure drop of 10 MPa over 1 m (cf. Walder and Hallet, 1979), a film on the order of 0.3 mm thick would, in 0.01 s, supply enough water to fill the space created. However, that much water would completely drain that 0.3 mm × 1 m film, with transmissivity dropping greatly as the film nearest the cavity thinned first. Hence, a substantially thicker film would be required to supply that much water. Also, while some regions of the glacier bed have sufficiently well-connected water systems to supply that much water, others do not (e.g., Cohen et al., 2005). Thus, physical understanding indicates that at least some cavities will be sufficiently isolated from the water system to allow large water-pressure drops from stick-slip motion.

An additional buffering mechanism may arise from water degassing. Using the Henry’s Law coefficient, assuming water starts fully saturated with nitrogen and that equilibrium degassing is achieved during a slip event, the magnitude of pressure drops would be reduced by ∼80% (∼2 MPa instead of 10 MPa; see the GSA Data Repository1). However, the nitrogen diffusion coefficient in water is ∼10−9 m2/s, so over 0.01 s the diffusion distance is only 0.003 mm. Thus, equilibrium would require essentially instantaneous nucleation of more than 10 × 106 bubbles/mm3. Homogeneous nucleation of nitrogen bubbles requires a pressure drop of ∼180 atm, or 18 MPa, with values for oxygen and argon almost as large (Hemmingsen, 1977). Thus, large pressure drops can occur unless appropriate nucleation sites are suspended throughout the water-filled cavity. Given the well-known difficulty of nucleating nitrogen or air bubbles (e.g., Lee and Devereux, 2011), and the surface-tension and other issues raised by such nucleation, we consider it unlikely that degassing would be achieved fast enough to notably buffer the pressure drop during stick-slip motion.

Returning to Figure 1A, the water pressure in the crack will be close to the overburden pressure during a stick-slip–induced pressure drop in the adjacent cavity, generating a large crack-opening stress. For a circular crack of radius a and mode-I crack-opening stress σ, the stress-intensity factor depends on the rock thickness and other geometric considerations, but unstable fracture propagation generally occurs when the quantity σ(πa)0.5 equals or exceeds a critical value for the rock, often ∼1.8 MPa m0.5 (Meredith and Atkinson, 1985). A pressure drop of 10 MPa then would drive unstable propagation of a crack with a ≥10 mm. Even much smaller water-pressure drops may achieve unstable crack propagation by adding to the crack-opening stress from glacier friction (Cohen et al., 2005).

Hallet (1996) suggested that the rate of subcritical crack growth increases with approximately the 40th power of the crack-opening stress, so even short-lived and subcritical stresses can speed erosion. Because static friction typically exceeds kinetic friction, often by ∼15% (Rabinowicz 1951), the transition from smooth sliding to stick-slip behavior should speed subcritical crack growth from particle drag. The 40th power of a 15% stress increase gives 268-fold faster crack growth, so even a very short duration of high stress will speed crack growth during a stick-slip cycle. The transition to stick-slip behavior also may speed abrasion (Engelder and Scholz, 1976; Scholz and Engelder, 1976).

During an ice-age cycle, glaciers normally erode a layer of subglacial rock that is much thicker than the height of a typical bedrock step or roche moutonnée. Yet, such features are commonly observed on deglaciated bedrock, so it is likely that one or more mechanisms act to generate such features during glaciation.

We suggest that water-pressure fluctuations in cavities generate step features to replace those eroded away. If steps such as shown in Figure 1A are absent, as in Figure 1B, the drainage system includes wave cavities on lee sides of even gradual slopes (Kamb, 1970; Lliboutry, 1979; Gagliardini et al., 2007). In a basal stick-slip event, the pressure drop in a wave cavity will be larger than in an equivalent step cavity; unlike a step-cavity, the upglacier limit of a wave cavity shifts farther upglacier, so the wave cavity expands more. Also, almost any rock fracture created or enlarged in response to a wave-cavity pressure drop will tend to increase local relief beneath the cavity on the lee side, contributing to downglacier-facing steps.

DISCUSSION

Erosion during stick-slip motion does not change our understanding of other erosion mechanisms. Instead, we suggest that stick-slip motion speeds erosion compared to smooth sliding. Stick-slip behavior may contribute to faster abrasion. The greater drag of clasts overcoming static friction versus kinetic friction favors faster plucking by increasing crack-opening stresses near lee-side water cavities. Most importantly, stick-slip behavior will speed plucking through the very large water-pressure fluctuations that can be generated during rapid motion.

This suggests that understanding basal seismicity better is required in order to parameterize and model subglacial erosion. Available data suggest that most glaciers shift between smooth sliding and stick-slip, rather than between stick-slip and no basal motion (Zoet et al., 2012). If so, then processes increasing interactions between bedrock and clasts in ice should favor stick-slip motion and thus erosion. Basal till, which is essentially the fault gouge of glaciers, will be removed more efficiently by greater water flux in channels, increasing clast-bed interaction. Processes favoring more clasts in the basal ice, including erosion upglacier, contribute to faster abrasion and plucking. Higher ice velocities will increase convergence of clasts with upglacier-facing bed slopes, promoting stick-slip motion. Higher ice-flow velocity, higher basal shear stress, and higher geothermal flux all favor faster basal melting, increasing clast-bed interaction, which also increases with extensional ice flow that forces clasts toward the bed. More-extensive cavities, favored by faster flow, higher bedrock steps, and higher water pressure, focus shear stress on the bed but reduce the water-pressure drop in a slip event; the net effect will depend on a combination of these parameters. The maximum water-pressure drop contributing to erosion will increase with ice thickness, so erosion can be faster under thicker ice. In general, then, large, vigorously flowing, steep glaciers with rapid surface melt feeding subglacial streams are likely to erode most rapidly, and erosion may also be favored where ice stretches as it flows into an ice stream or other acceleration point.

We could suggest an erosion “law” based on these considerations, but given the large associated uncertainties and the small seismic database, we suspect that any such relation would be premature. Extensive additional microseismic observations, laboratory (Iverson et al., 1998; Thomason and Iverson, 2008; Byers et al., 2012; Iverson and Petersen, 2011) and subglacial (Iverson et al., 2003; Cohen et al., 2005) observations, and modeling likely are required to assess the full importance of this mechanism.

CONCLUSIONS

The available data show that small earthquakes are common beneath glaciers, with many of them likely related to stick-slip motion of debris-laden ice over bedrock. Source parameters indicate that these events cause sufficiently large and rapid motion to temporarily lower pressure in water-filled cavities, driving unstable crack growth in some cases, and contributing significantly to crack growth in many others. Onset of stick-slip behavior also increases the crack-opening stress from clast friction, and may increase abrasion. We thus suggest that stick-slip motion speeds glacial erosion, so accurate models require further understanding of the occurrence of basal seismicity.

Partial support for this work was provided by the U.S. National Science Foundation’s Office of Polar Programs, through grants 0424589, 0538195, 0852697, and 0907178. We are grateful for discussions with and comments from the Pennsylvania State University Ice and Climate Research group.

1GSA Data Repository item 2013039, Henry’s Law calculation for outgassing of pressurized water during subglacial earthquake, is available online at www.geosociety.org/pubs/ft2013.htm, or on request from editing@geosociety.org or Documents Secretary, GSA, P.O. Box 9140, Boulder, CO 80301, USA.