The Physical Basis of Ice Sheet Modelling (Proceedings of the Vancouver Symposium, August 1987). IAHS Publ. no. 170.

Continuous till deformation beneath ice sheets

R.B. Alley, D.D. Blankenship, S.T. Rooney & C.R. Bentley Geophysical and Polar Research Center University of Wisconsin 1215 W. Dayton St. Madison, Wl 53706, USA

ABSTRACT Either advance of a glacier over unconsolidated sediments or water-pressure fluctuations in unconsolidated subglacial sediments can trigger sediment deformation and changes in glacier flow and glacier-margin position without further climatic forcing. However, for a wet-based glacier beneath which bedrock erosion balances till transport by continuous subglacial deforma­tion, internal instabilities are less likely and glacier changes that record climatic forcings are more likely. We present evidence here that the West Antarctic ice sheet is a modern example of such continuous till deformation, and that other ice sheets, including the Laurentide ice sheet, may have been similar. An ice sheet with continuous till deformation will leave a more regular sedimentary record than one with discontinuous deformation, so careful glacial-geological studies should allow distinction of these cases for former ice sheets.

Déformation continuelle de la moraine déposée sous une calotte glaciaire

RESUME L'avance d'un glacier sur des sédiments non consolidés, ou des fluctuations de la pression de l'eau des sédiments sous-glaciaires non consolidés peut amorcer une déformation des sédiments, et des changements dans l'écoulement du glacier et la position de son front sans forçage par le climat. Toutefois, dans un glacier à base humide où l'érosion du lit équilibre le transport de débris par déformation continuelle sous-glaciaire, des instabilités internes sont moins probables, et il est plus probable que les variations du front reflètent les variations du climat On fournit des preuves que la calotte de l'Antarctide Occidentale est un exemple actuel d'une telle déformation con­tinuelle de la moraine de fond, et que d'autres calottes de glace, inclus la calotte Laurentide, ont dû être analogues. Une nappe de glace avec une moraine de fond se déformant continuellement laissera une séquence stratigra-phique plus régulière qu'une sujette à une déformation discontinue; aussi des études glacio-géologiques soigneuses devraient permettre de distinguer les deux cas parmi les calottes de glace passées.

INTRODUCTION

The importance of deforming till as a basal boundary condition for ice-sheet flow has been established by direct observation (Engelhardt et al, 1978; Boulton, 1979) and indirect

81

82 R.B. Alley et al.

observation (e.g., MacClintock & Dreimanis, 1964; Hodge, 1979; Alley et al, 1986). Here we define till deformation as shearing of water-saturated, unconsolidated subglacial sediments to large strains. Some authors have emphasized that the existence of deforming subglacial till can lead to internal instabilities (Boulton, 1979; Clarke et al, 1984) such that till-based ice sheets can fluctuate without external forcing; however, other authors have considered the possibility of internal stability in deforming till (Alley et al, 1986; in press, a, b), in which case ice-sheet fluctuations would indicate climatic or other external forcing.

For this discussion we will call till deformation "continuous" for a flow band if it occurs everywhere beneath that flow band and at all times. Till deformation then is "discontinuous" for a flow band if it is limited in space or time. (We define a flow band as a section of a gla­cier or ice sheet bounded by the grounding line or ice front, the ice divide, and two flow lines, such that no ice flows across the head or sides of the flow band. The flow-band width is chosen so that conditions vary little across it.) Internal instabilities in the ice-water-till system will cause till deformation to be discontinuous, whereas till deformation may be continuous if no internal instabilities occur.

Broadly speaking, fluctuations of a glacier on a deformable bed can be induced by changes in the balance of ice, water, or till, or some combination of these. Clarke et al. (1984) and Boulton (1979) have discussed how changes in water or till can occur without external forcing and cause temporally or spatially discontinuous till deformation.

Clarke et al. (1984) and Clarke (in press) have considered the surging of Trapridge Gla­cier, which overlies a thick layer of till. Field and theoretical studies indicate that a change in water balance at the base of the glacier can raise water pressures and decrease AP, the difference between the overburden pressure and the pore-water pressure in till. The shear strength of till varies with AP (Boulton, 1979), and Clarke (in press) has shown that till defor­mation can begin and trigger a surge if AP becomes small enough. The surge may terminate when water pressures fall and till deformation slows or stops, possibly in response to changes in ice or till.

Boulton (1979) presented a mechanism by which till balance could cause fluctuations of a glacier margin. He considered a glacier resting on a till layer, and noted that AP and thus till shear strength should increase upglacier. Boulton showed that if the subglacial water-drainage system is efficient (e.g., if a subglacial till overlies a thick bed of highly permeable gravel), then till deformation may be limited to a narrow band near the glacier terminus. Boulton also argued that till transport by subglacial deformation is typically faster than till supply by engla-cial transport and basal melting, so till deformation limited to a marginal zone will erode a hol­low in pre-existing till near the upglacier end of the deforming zone. When the available unconsolidated sediments are eroded entirely, the basal boundary condition will change, caus­ing a change in the glacier unrelated to climatic forcing.

In contrast to fliese "discontinuous" models of till deformation, Alley et al. (1986; in press, a, b) have argued that in some cases (specifically ice stream B, West Antarctica), an ice sheet will generate high water pressures and that the subglacial transport of till past any point will be balanced by erosion upglacier. In this case of "continuous" till deformation, non-steady behavior of the ice sheet will be caused by the traditional glaciological forcings of cli­mate' and of sea or lake level at the grounding line.

In this paper we consider further the conditions under which continuous till deformation can occur, the mechanisms of till transport in continuous deformation, and the differences in behavior and sedimentary record between discontinuous and continuous deformation. We draw heavily on the record from ice stream B in West Antarctica, but our discussion is not limited to this single case.

Continuous till deformation 83

CONDITIONS FOR CONTINUOUS DEFORMATION

Water pressure

Continuous till deformation will occur beneath an ice sheet if till is generated and water pres­sures ate high. For till to be saturated, it is necessary that the basal melt rate equal the rate of production of porosity by erosion (i.e., basal-melt rate = 2/3 of rock-erosion rate). The water pressure will increase toward the overburden pressure if the water-generation rate exceeds this value and the subglacial hydraulic system is unable to evacuate the excess water efficiently.

The nature of the basal hydraulic system in the presence of deformable till is a difficult problem that has not been solved. Relatively high water pressures (low AP) may be transient or localized features of mountain glaciers and small ice caps (e.g., Kamb et al., 1985) but available evidence indicates that low AP may be common and widespread beneath large ice sheets. Both Boulton & Jones (1979) and Lingle & Brown (1987) have modelled the ability of meters-thick, unconsolidated aquifers beneath wet-based glaciers to transmit meltwater. Such models show that for small ice sheets and glaciers, short transport distances and small basal water volumes allow efficient water transport and low basal water pressures. However, these models also show that physically reasonable unconsolidated aquifers under larger ice sheets are unlikely to be able to drain the meltwater produced. Highly permeable bedrock aquifers also can cause low subglacial water pressures (e.g., Paterson, 1981, p. 142), but must be continuous over a distance equal to a large fraction of the ice-sheet extent to reduce water pressures significantly, and thus are more likely to affect small glaciers than large ice sheets. Aquifer models thus suggest that water pressures beneath large ice sheets wil be high and that defor­mation of subglacial till will be likely.

These models ignore the possible role of water drainage through systems of channels and cavities at the base of the ice. A well-developed channel system would allow relatively large values of AP even beneath a large ice sheet (Bindschadler, 1983). However, well-developed channel systems are unlikely to be stable in the absence of large supplies of surface meltwater to the bed (Weertman, 1972), especially where velocities of basal ice become large (Kamb et al., 1985). Thus, models suggest that small glaciers may have low, high or variable basal water pressures but that large, wet-based ice sheets will have high basal water pressures throughout.

This prediction is supported by evidence from the modern West Antarctic ice sheet. The subglacial water pressure can be determined at two sites in West Antarctica. One is the Upstream B camp (UpB) on ice stream B, an active ice stream, and the other is the Byrd Sta­tion borehole, in a sheet-flow region well inland.

At UpB, Blankenship et al. (1986, in press) have estimated basal water pressures from careful analysis of seismic velocities in subglacial till. They find that AP = 50 ± 40 kPa, which is only about 0.5% of the overburden pressure.

Byrd Station is in the drainage basin of ice stream D, an ice stream that appears quite similar to ice stream B. The drilling at Byrd Station provided the necessary data to estimate the basal water pressure, although we know of no previously published estimate. When the bed was reached in the Byrd Station hole, about 55 m of water rose into the borehole, which already contained 1593 m of drilling fluid (arctic diesel fuel plus trichloroethylene) and 420 m of an ethylene-glycol+water mixture (Ueda & Garfield, 1970). The density of the drilling fluid was within 1% of 920 kg m-3 (Ueda & Garfield, 1970; A.J. Gow, personal communication, 1986). The glycol-water mixture, occupied a region where temperatures varied from about -1.7°C to -16°C, and was compressed under the weight of the drilling fluid. Assuming that

84 R.B. Alley et al.

the glycol-water mixture was in equilibrium at -9°C and allowing for compressibility (Curme & Johnston, 1952; Weast, 1973) gives a density of about 1042 kg m-3; densities of equilibrium concentrations at -16°C and -1.7°C differ from this by no more than 3%. At the pressure-melting point of about -1.7°C under the weight of the drilling fluid plus the glycol-water mix­ture, the basal water had a density of about 1010 kg m-3 (Weast, 1973). The basal water pres­sure then can be calculated as 19.195 ± 0.020 MPa, if column lengths of drilling fluid, water, and glycol mixture are assumed known within ±1 m. Ice densities in the 2164 m long core were measured to better than 0.1% by A.J. Gow and give a load of about 19.335 ± 0.002 MPa (Gow, 1970; Gow & Williamson, 1976; A.J. Gow, personal communication, 1986). The value of AP is then within 140% of 140 kPa. The physical lower limit of AP is zero, so we can say that 0 < AP < 330 kPa, with 140 kPa our best estimate.

We thus estimate that the basal water pressure at Byrd Station exceeds 99% of the over­burden pressure, although it could fall as low as 98% or approach 100% of the overburden pressure. In any case, this is a very small value for AP (cf. Kamb et al., 1985), and is only slightly larger than AP at UpB. Because water pressures are relatively high at two very different sites on the only large, wet-based ice sheet ever sampled, in accord with theoretical predictions, we propose that high water pressures are likely elsewhere beneath the Antarctic ice sheet and beneath other large, wet-based ice sheets.

Till transport

In addition to high water pressures, continuous till deformation requires production and tran­sport of till. Again, both theory and observation suggest that this is likely beneath large ice sheets.

The West Antarctic ice sheet provides an excellent example. Blankenship et al. (1986; in press) and Rooney et al. (in press) have shown that UpB is underlain by a till layer about 6 m thick; based on these results Alley et al. (1986; in press, a) have argued that the till is deform­ing there and that the till flux is equivalent to a steady-state erosion of 0.4 mm a-1 of rock averaged over the entire drainage basin of the ice stream.

The core from Byrd Station suggests two mechanisms by which till may be transported to the ice streams. The bottom 4.83 m of the Byrd Station core contained about 14% by weight rock debris (Gow et al, 1979), which would produce approximately 1/2 m of till on melting. Also, the drilling at Byrd Station penetrated subglacial material to a depth of 1.3 m without recovering core, although the system was designed to recover consolidated materials including rock and ice (Gow, 1970). The subglacial material contained fresh water, caused rapid dulling of drill bits, and yielded clay films adhering to drill surfaces (Ueda & Garfield, 1970). The probable explanation is that the ice at Byrd Station is underlain by at least 1.3 m of unconsoli­dated, water-saturated till (Ueda & Garfield, 1970; Gow et al, 1979). Given the small value of AP and the moderate basal shear stress at Byrd Station (~ 40 kPa; Whillans, 1983), it is likely that this till is deforming (e.g., Alley et al., 1986).

A second line of evidence also suggests that subglacial till at Byrd Station may be deforming. Weertman (1970) assumed that the subglacial water at Byrd Station occurs in a thin film and estimated the thickness of that film from the observed rate at which water rose in the borehole after the bed was penetrated. However, observations beneath other glaciers with slow basal velocities and basal till suggest that water flow occurs through the till and that the base of the ice and the top of the till maintain intimate contact (Engelhardt et al, 1978; Boul-ton, 1979; Boulton & Hindmarsh, in press). If so, then the rate of water influx to the Byrd Station hole is a measure of the hydraulic conductivity of the basal till there. (If both till and a Weertman film are present, then the rate of water influx gives only an upper limit on the hydraulic conductivity of the basal till.) We have modified Weertman's (1970) analysis to

Continuous till deformation 85

calculate the hydraulic conductivity of basal till assuming no Weertman film. A unique solu­tion is not possible, because the exact till thickness and the extent to which the hydraulic con­ductivity of the till was enhanced directly beneath the borehole are not known. However, several possible solutions (cf. Hvorslev, 1951; Weertman, 1970) for till thicknesses near 1-2 m, with or without enhanced hydraulic conductivity beneath the hole, yield hydraulic conductivi­ties within an order of magnitude of 10-6 m s-1. This is the hydraulic conductivity we expect for deforming till (Boulton et al., 1974) but exceeds the conductivity of most (though not all) collapsed basal tills (Freeze & Cherry, 1979, p. 29).

We cannot calculate the till flux at Byrd Station accurately because the till thickness and basal velocity are unknown, owing to blockage of the hole at about 1500 m depth before it was resurveyed (Garfield & Ueda, 1975). Whillans (1983) estimated that the basal velocity is between 0 and 8 m a-1, but noted that the stationary base requires a "more extreme" extrapo­lation of the available inclinometry data. When combined with the evidence favoring till defor­mation, presented above, this suggests that till transport occurs by subglacial till deformation and by englacial transport.

Of these two transport mechanisms, subglacial deformation is calculated to be the more efficient in most cases (Boulton, 1979). For example, the annual subglacial till flux at Upstream B estimated by Alley et al (in press, a) is about equal to the flux that would occur englacially if the basal 25 m of ice there contained debris at the concentration measured at the base of the Byrd Station core. Because basal melting and longitudinal extension are likely to occur for more than 100 km upglacier of Upstream B (Jenssen et al, 1985), a 25 m thick layer of debris-rich ice at Upstream B would require freezing-on or shearing-in of a substantially thicker layer of debris-rich ice farther upglacier. Although not impossible, such a thickness of debris-rich basal ice seems highly improbable.

If most debris is transported subglacially rather than englacially, then significant down­stream increase in till flux on an ice sheet with continuous till deformation requires erosion beneath deforming subglacial till. Evidence that this does occur comes from the work of Mac-Clintock & Dreimanis (1964) in the St Lawrence Valley. There, glacial-geological studies suggest that water-saturated nil from an earlier glaciation was deformed to a depth of 10 m by a glacial readvance in a different direction. Where the deforming layer intersected bedrock, the rock was striated in the direction of readvance. In some cases these striations cut across older striations, but in other cases only the new striations were evident. These striations demonstrate that erosion can occur beneath a meters-thick till layer during deformation. Other evidence also supports abrasion beneath deforming till. Based on a detailed study of the morphology and striations of plastically scoured forms (p-forms: grooves, roche moutonées, etc.), Gjessing (1965) argued that such forms are produced by abrasion beneath deforming till. Debris flows, which are analogous to deforming till, are observed to erode their channels free of debris and to remobilize older, subjacent debris flows (Johnson, 1984).

To understand abrasion beneath deforming till, suppose that till on average exhibits Newtonian viscosity so that the average velocity decreases smoothly to zero at the bedrock. A clast of finite size in contact with bedrock will stick up into, and be dragged along by, faster-moving till above. Dragging of a clast over bedrock will cause abrasion (Alley et al, in press, b). In addition to such abrasion, it is quite possible that some plucking occurs. Seismic results from Upstream B are consistent with the removal of large clasts from bedrock beneath till (Rooney et al, in press). Joints are likely in bedrock, especially in light of the small AP, and would prepare blocks for incorporation (Addison, 1981). The shear stress from the deforming till, augmented by large stress concentrations that occur during the passage of individual clasts (Boulton et al, 1974, 1979) then may incorporate clasts, aided by injection of till into joints as they open in a process analogous to the "bedrock wedging" described by Broster et al (1979).

86 RJ3. Alley et al.

West Antarctic model

We thus see that a large, wet-based ice sheet is likely to maintain high water pressures and to generate and deform till subglacially, so that the basal boundary condition is likely to be con­trolled by continuously deforming till for entire ice sheets. A further test of this proposal is whether a model using deforming till as the basal boundary condition can successfully describe an ice sheet A simple numerical model that we have developed for the West Antarctic flow band from the ice divide through ice stream B to the grounding line is physically reasonable and does fit observations of the ice sheet well without extensive adjustment of parameters. The model allows internal deformation of ice, as well as basal ice motion coupled to linear-viscous till. Conservation of ice and till are assumed, but water balance is not treated explicitly. All driving stress is assumed to be balanced by resistance at the bed. The shear-stress-only model of Alley (1984) is used to calculate ice deformation. The basal model is that of Alley et al. (in press, b). Till generation is assumed proportional to the strain rate in till. Ice-accumulation data and surface and bedrock elevations are based on Bull (1971), Drewry (1983), Shabtaie & Bentley (1987), and Shabtaie et al. (in press).

We assume that the existing ice sheet is in steady state and calculate balance velocities from the observed accumulation rate and ice-sheet configuration. These balance velocities must arise from a combination of internal deformation plus till-lubricated basal motion. (Water-lubricated basal sliding between ice and till is unlikely to be significant along most of the flow band (Alley et ai, 1986; in press, a).) For internal deformation, values of the depth-averaged flow-law parameter must be chosen to match the balance velocity near the ice divide where basal velocities are low; away from the ice divide, the value of the flow-law parameter is taken to be a constant corresponding to a temperature of -10°C. However, basal motion comes to dominate downstream for any reasonable flow-law parameter, so that the exact values used are relatively unimportant. Ice velocity not caused by internal deformation must arise at the bed, allowing us to calculate basal velocities. These basal velocities, together with the requirement of till mass balance and the assumed abrasion-rate coefficient, then fix the till thickness. We adjust the model using the abrasion-rate coefficient to obtain about 6 m of till at UpB (Rooney et al., in press). From the till thickness, basal velocity, and basal shear stress, it is then possible to calculate the till viscosity required to reproduce the existing ice sheet.

Results of one simulation are shown in Fig. 1. Till thickens downstream. Maximum abrasion rates occur beneath the ice stream, the most active part of the ice sheet, but abrasion rates are not unreasonably large (^ 3 mm a-1 of rock). Internal deformation dominates inland and basal sliding dominates toward the coast. (Although to some extent this results from our choice of flow-law parameter, it is difficult to construct a physically reasonable model in which this is not true). Till viscosity increases inland, as expected for an inland increase in AP (Alley et al., in press, b).

We wish to emphasize that although the model describes the modern ice sheet well, we have not attempted an exact fit. We could, for example, improve agreement by allowing non-steady effects (Whillans, 1983; Shabtaie & Bentley, 1987) and basal freeze-on of till upglacier with melt-out downglacier, and by adjusting input data within stated error limits. Our purpose is to show that the West Antarctic ice sheet can be described by a physically reasonable model based on continuous till deformation. When combined with the data from UpB and Byrd Sta­tion and with the theoretical discussions above, we believe that this result suggests that the West Antarctic ice sheet is controlled by continuous till deformation and that other wet-based ice sheets (e.g., the southern side of the Laurentide ice sheet) may have been as well. Direct observations of till deformation beneath West Antarctica are needed to test our suggestion, and we encourage the collection of such data.

Continuous till deformation 87

x (km) x(km)

FIG. 1 Results of simulation of West Antarctic flow band through ice stream B, plotted against horizontal position (x). The ice divide is at x = 0, UpB is at approximately x = 500 km, and the morainal bank or "till delta" (Alley et al., in press, a) begins downglacier of x = 650 km. (a) Depth-averaged ice velo­city (ïï). (b) Basal velocity of ice (ub) as percentage of total ice velocity, (c) Till viscosity (x>). (d) Till thickness (hb). (e) Rock-abrasion rate (r).

SEDIMENTARY RECORD

Current research in glacial geology may be leading toward the ability to distinguish tills that deformed to large strains while water-saturated from other basal tills (lodgement or basal melt-out) for which all deformation occurred englacially prior to deposition (e.g., Boulton & Dent, 1974; Boulton & Hindmarsh, in press; Brown et ai, in press). In some cases the glacial geo­logical record left by an ice sheet with continuous till deformation may be distinguished from that of an ice sheet on discontinuously deforming till. This is because the continuous-deformation ice sheet initially supplies its own lubricating till, whereas pre-existing till is deformed in the discontinuous case.

To see this, consider the ability of an ice sheet on continuously deforming till to transport that till. Boulton (1979) has shown that shear strain of till causes it to dilate and lose strength, but that the till collapses and gains strength when the strain rate is reduced. Based on this, Alley et al. (1986; in press, a) proposed that till possesses a minimum strain rate for dilation, e{. If the strain rate in till, è„ falls below è/, then some of the till will cease to deform and will be deposited. (Such deposition is analogous to classical lodgement, but occurs from the base of deforming till rather than from debris-rich ice.) When è, exceeds è;, the basal shear stress and water pressure are sufficiently high that a thicker layer of till than the one present would deform; the ability of the ice to transport till then exceeds the till available for transport, hence erosion will occur. The simplest relation for the rate of till generation, t, that incorporates these ideas is t = K(k, - è/), where K is the abrasion-rate coefficient. .(Mtey et al. (in press, b) used this relation with è; set to zero, but discussed the effect of è; on t)

88 R.B. Alley et al.

In the accumulation zone of an ice sheet, ice velocities and the ability to transport till increase downstream, causing basal erosion. However, ice velocities typically decrease down-glacier of the ice-equilibrium line on ice sheets with ablation zones (e.g., Paterson, 1981, p. 59-63). Therefore, at some point downglacier of the ice-equilibrium line the ability to transport till falls below the amount of till being supplied from upglacier. Deposition of till should then occur downglacier of this "till-equilibrium line." If the ice-equilibrium line of such an ice sheet advances, erosion of pre-existing till will be limited to the upglacier side of the till-equilibrium line, with the strongest erosion at the ice-equilibrium line. Till from the new advance will be deposited on older sediments downstream of the till-equilibrium line (Fig. 2). The pre-existing sediments will not be deformed unless their shear yield strength in the col­lapsed, lodged state is less than the shear yield strength of the dilated, deforming till. (Water-saturated deformation of unconsolidated sediments reduces their strength markedly (Boulton, 1979).) Deformation of pre-existing sediments will be suppressed further by the increase with depth in AP, and thus in shear strength, that will occur if water pressures are hydrostatic in these sediments. Some workers (e.g., Kemmis, 1986; Sharpe, 1986) have argued that the occurrence of tills over undeformed sediments in deglaciated terrains shows that the tills were not deforming; however, we argue that deformation of sediments beneath a deforming till, although possible, is unlikely.

EQUILIB. LINES

CE TILL

I ACCUM. | ABLAT.

ERODE | DEPOSIT

RELATIVE ICE VELOCITY

BASE OF TILL I (MnnruMi _ - ^ ^ - , A A DEFORMATION

7 ^ BEWCK \ A A X

FIG. 2 Cartoon of ice sheet lubricated by continuously deforming till (labeled Till I (Modern)) advancing over pre-existing, unconsolidated sediments (labeled Till II (Old)). Notice the base of deformation (indicated by the dot-dash line); downglacier of the till-equilibrium line, the base of the modern till is not deforming.

In contrast, the discontinuous case discussed by Boulton (1979) predicts that either older drift or other unconsolidated sediments will be stripped away rapidly, leaving bedrock-floored hollows wherever till deformation is initiated. Initiation of deformation in turn will be con­trolled by the ability of the pre-existing sediments to drain subglacial water, with till deforma­tion and thus erosion localized in areas of low hydraulic conductivity (Boulton & Jones, 1979). The distribution of such regions in pre-existing drift typically will be highly irregular (e.g., Boulton & Paul, 1976), causing the distribution of erosional hollows to be irregular. Thus, the widespread existence of older unconsolidated sediments beneath deformed glacial till in the ablation zone of a former ice sheet is a signature of continuous till deformation, whereas patchy preservation of older sediments or restriction of older sediments to a narrow marginal

Continuous till deformation 89

zone may be diagnostic of discontinuous deformation.

DISCUSSION

Till deformation beneath a glacier may be either continuous or discontinuous in space or time. In the case of discontinuous deformation, glacier variations may result from climatic forcing, but also may reflect internal instabilities (surging glaciers) or exhaustion of a pre-existing sup­ply of unconsolidated sediment. In contrast, in the case of continuous deformation, water pres­sures remain high and till transport is balanced by bedrock erosion, so that glacier variations result only from climatic forcings except on geological time scales. (On a geological time scale, erosional stripping of sedimentary rock to expose harder crystalline rock can reduce both the erosion rate and the till flux and cause a change in an ice sheet analogous to that caused by stripping of pre-existing unconsolidated sediments; however, the response time for stripping of sedimentary rocks is likely to be K^-IO6 a, whereas the response time for most climatic forc­ing and for stripping of unconsolidated sediments is likely to be 10-105 a.)

Our analyses of the West Antarctic ice sheet suggest that it is characterized by continuous till deformation. If so, then recently observed nonsteady effects near Byrd Station and in the Ross Embayment (Whillans, 1983; Shabtaie & Bentley, 1987) are likely to be responses to changes in climate or sea level rather than internal (surging) instabilities, unless the ice-sheet/till system contains internal instabilities that we have not included in our model. (Our model allows internal feedbacks to magnify the nonsteady behavior, but requires that the non-steady behavior was initiated by external forcing.)

We also suggest that continuous deformation is likely to apply to many large ice sheets and some smaller ones, although either discontinuous deformation or no deformation cannot be ruled out. Continuous deformation should leave a more complete record of older unconsoli­dated sediments in marginal regions than discontinuous deformation, so careful glacial-geological study may reveal which case applied to a given ice margin. Such determination is important in distinguishing whether a given glacial event reflects climatic forcing or internal processes of an ice sheet.

ACKNOWLEDGEMENTS This work was supported in part by the U.S. National Science Foundation under grant DPP-8412404. We thank A.J. Gow for access to unpublished informa­tion, D.M. Mickelson and an anonymous reviewer for helpful comments, and S.H. Smith for figure preparation. This is contribution number 468 of the Geophysical and Polar Research Center, University of Wisconsin-Madison.

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