A generalized hypothesis for ice sheet flow

At the shallowest depths within an ice sheet (at tens-of-metres depths), where effective stresses are <0.0001 MPa, deformation likely proceeds via diffusion creep (Goldsby & Kohlstedt, 2001). Diffusion creep in this shallow ice is consistent with the lack of c-axis fabrics near the surfaces of the ice sheets, although finite strains may be too small in this region to yield significant fabrics even if creep proceeded via a c-axis-fabric-producing mechanism.

With increasing depth (stress), a transition probably occurs from diffusion creep to GBS-limited flow. At Byrd Station (discussed below), this transition occurs at a depth of <135 m. Dislocation slip on the basal-slip system likely dominates the overall strain rate in the GBS-limited creep regime. Basal slip causes a rotation of c-axes toward the compressional axis, eventually forming a single-maximum fabric (Alley, 1992). The tightening of the c-axis pattern with depth results from the progressive rotation of grains (caused by basal slip) with increasing strain. Grain rotation, and hence basal slip, is accommodated and rate-limited by GBS.

Grain size increases via normal grain growth at shallower depths in the ice sheets (Alley, 1992) (e.g. up to ca. 400m depth at Byrd Station, see below), then remains constant at intermediate depths (e.g. over the range 400-1000 m at Byrd, as shown below) within the GBS-limited creep regime. It has been suggested that relatively constant grain sizes at intermediate depths result from a dynamic balance between normal grain growth and polygonization (subgrain rotation recrystallization) (e.g. Alley, 1992; Thorsteinsson et al., 1997; De La Chapelle et al., 1998). It seems difficult to reconcile a constant grain size in this region, however, with subgrain rotation recrystallization, given the well-

known inverse relationship between stress (which, for example, increases by more than a factor of two in the constant grain size regime at Byrd Station) and subgrain size (e.g. Twiss, 1986; Jacka & Li, 1994), suggesting that impurities segregated to grain boundaries may have the greater control on grain size by pinning grain boundaries (e.g. Evans etal., 2001; Barnes etal., 2002; Weiss etal., 2002). The decrease in grain size in the ice-age ices below the constant grain size regime may result from colder accumulation temperatures and the presence of impurities (Weiss et al., 2002). In general, equiaxed polygonal grains and single-maximum c-axis fabrics that become progressively tighter with increasing depth are likely characteristic features of GBS-limited creep.

Temperature increases with increasing depth in the ice sheets due to geothermal heat flux into their bases. With the onset of pre-melting at grain boundaries and at three- and four-grain junctions in ice at ca. 255 K (as indicated by the enhancement in creep rate at that temperature for both GBS-limited and dislocation creep, Goldsby & Kohlstedt, 2001), an abrupt increase in the rate of increase of grain size with depth is observed. This increase in grain size results from the orders-of-magnitude increase in grain-boundary mobility caused by the presence of water on grain boundaries (Duval et al., 1983; Dash et al., 1995), allowing grain boundaries to overcome the pinning forces due to the presence of impurities segregated to the grain boundaries. The depth at the onset of pre-melting (at a temperature of ca. 255 K) corresponds with the first occurrence with increasing depth of multiple maximum c-axis fabrics at both Byrd Station (Gow & Williamson, 1976) and the GRIP site (Thorsteinsson et al., 1997), demonstrating that multiple maximum c-axis fabrics are associated with grain-boundary migration (GBM) recrystallization.

Increases in grain size, temperature and stress with increasing depth conspire to bring the ice closer and closer to the dislocation creep regime (see Fig. 60.5 below). The activation of non-basal slip systems at the very highest stresses within the ice sheets may also contribute to the occurrence of multiple-maximum c-axis fabrics (e.g. Gow & Williamson, 1976; Alley, 1992). A transition from GBS-limited flow to dislocation creep in the basal ice of the ice sheets is consistent with values of n = 3 derived from analyses of ice-sheet shape (e.g. Hamley et al., 1985; Cuffey, this volume, Chapter 57), since the shape and velocity of the ice sheet are controlled in large part by deformation of the basal layer (Alley, 1992).

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