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Book Chapter

Summit of the East Antarctic Ice Sheet underlain by thick ice-crystal fabric layers linked to glacial–interglacial environmental change

By
Bangbing Wang
Bangbing Wang
Zhejiang University, 38 Zheda Road, Hangzhou, 310027, China
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Bo Sun
Bo Sun
Polar Research Institute of China, 451 Jinqiao Road, Pudong, Shanghai, 310026, China
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Carlos Martin
Carlos Martin
British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 0ET, UK
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Fausto Ferraccioli
Fausto Ferraccioli
British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 0ET, UK
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Daniel Steinhage
Daniel Steinhage
Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research, PO Box 12 01 61, D-27515 Bremerhaven, Germany
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Xiangbin Cui
Xiangbin Cui
Polar Research Institute of China, 451 Jinqiao Road, Pudong, Shanghai, 310026, China
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Martin J. Siegert
Martin J. Siegert
Grantham Institute and Department of Earth Science and Engineering, Imperial College London, South Kensington, London SW7 2AZ, UK
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Published:
January 01, 2018

*
Correspondence: m.siegert@imperial@ac.uk

Gold Open Access: This article is published under the terms of the CC-BY 3.0 license.

Abstract

Ice cores in Antarctica and Greenland reveal ice-crystal fabrics that can be softer under simple shear compared with isotropic ice. Owing to the sparseness of ice cores in regions away from the ice divide, we currently lack information about the spatial distribution of ice fabrics and its association with ice flow. Radio-wave reflections are influenced by ice-crystal alignments, allowing them to be tracked provided reflections are recorded simultaneously in orthogonal orientations (polarimetric measurements). Here, we image spatial variations in the thickness and extent of ice fabric across Dome A in East Antarctica, by interpreting polarimetric radar data. We identify four prominent fabric units, each several hundred metres thick, extending over hundreds of square kilometres. By tracing internal ice-sheet layering to the Vostok ice core, we are able to determine the approximate depth–age profile at Dome A. The fabric units correlate with glacial–interglacial cycles, most noticeably revealing crystal alignment contrasts between the Eemian and the glacial episodes before and after. The anisotropy within these fabric layers has a spatial pattern determined by ice flow over subglacial topography.

Ice sheets contain several types of single ice crystals, such as a perfect single pole, an elongated single pole and a vertical girdle crystal (Fig. 1). Ice crystals experience an anisotropic response to stress, whereby their principal axes, termed C-axes, rotate during deformation towards the direction of compression and away from the tensional direction (Fig. 2; Alley 1988; Azuma et al. 1999; Durand et al. 2009; Montagnat et al. 2014). Collectively, ice-crystal alignment leads to macro-crystallographic orientations, or ice-sheet fabric, which is the product of both ice rheology and stress. As the strain rate in anisotropic ice under simple shear (Azuma 1994; Durand et al. 2007; Kennedy et al. 2013) can be up to an order of magnitude greater than in isotropic ice (Azuma 1994), a feedback is possible whereby ice fabrics lead to preferential deformation and, in turn, further anisotropy (Alley 1988; Azuma 1994). The spatial variation of ice rheology is fundamental to ice-sheet flow modelling, yet it is normally averaged through depth as an isotropic medium, as in Glen’s flow ‘law’ (Glen 1954). Differences in the velocity of cold-based ice between observations (Thorsteinsson et al. 1999) and modelling (Gillet-Chaulet et al. 2006; Martin & Gudmundsson 2012), in which respective ice-surface elevations can vary by hundreds of metres, and ice velocities by tens of metres per year, may be attributable to the rheological impacts of ice fabric development. Crystal alignment in ice cores is analysed routinely, revealing marked and step-wise changes in the fabric of ice deposited across glacial–interglacial periods (Durand et al. 2007; Montagnat et al. 2014). Additionally, sonic logging (Gusmeroli et al. 2012) shows how variations in ice-sheet fabric is correlated highly with oxygen isotope ratios, implying a link with atmospheric parameters (Paterson 1991; Kennedy et al. 2013). The spatial distribution of ice-sheet fabric is largely unknown, however, as ice cores are heavily restricted in number and distribution across Antarctica and Greenland. As a consequence, the crystallographic structure of ice in large ice sheets, including its development through time and space, and its potential rheological consequences, remains uncertain.

Fig. 1.

Schmidt diagrams demonstrating typical fabrics in ice sheets. The fabric can be identified by the difference in permittivity recorded between the primary axes. The axes x and y represent the horizontal plane, and z is vertical. (a) Random ice fabric. (b) A perfect single pole. (c) An elongated single pole. (d) A vertical girdle. The perfect single pole and vertical girdle can be considered as the two extremes (end members) of ice fabric under stress-induced deformation, and the elongated single pole is a transient state between changes in stress or shear.

Fig. 1.

Schmidt diagrams demonstrating typical fabrics in ice sheets. The fabric can be identified by the difference in permittivity recorded between the primary axes. The axes x and y represent the horizontal plane, and z is vertical. (a) Random ice fabric. (b) A perfect single pole. (c) An elongated single pole. (d) A vertical girdle. The perfect single pole and vertical girdle can be considered as the two extremes (end members) of ice fabric under stress-induced deformation, and the elongated single pole is a transient state between changes in stress or shear.

Fig. 2.

Schematic diagram of two possible evolutions of an elongated single-pole ice-fabric in ‘soft’ ice. (a) The fabric in the soft (glacial) ice evolves towards a vertical girdle but keeps the same axial orientation as the harder (interglacial) layers. (b) The fabric in soft layers rotates faster towards a new stable position as a consequence of flow reorganization. In theory, both can result in a change to the permittivity tensor and hence a change in the echo difference measured by polarimetric radars. The case in (a) is the most common type, as reported in the NEEM, Dome C and Dome Fuji ice cores. Case (b) is theoretical and has yet to be observed directly in the field.

Fig. 2.

Schematic diagram of two possible evolutions of an elongated single-pole ice-fabric in ‘soft’ ice. (a) The fabric in the soft (glacial) ice evolves towards a vertical girdle but keeps the same axial orientation as the harder (interglacial) layers. (b) The fabric in soft layers rotates faster towards a new stable position as a consequence of flow reorganization. In theory, both can result in a change to the permittivity tensor and hence a change in the echo difference measured by polarimetric radars. The case in (a) is the most common type, as reported in the NEEM, Dome C and Dome Fuji ice cores. Case (b) is theoretical and has yet to be observed directly in the field.

Dome A is the highest ice divide on the East Antarctic Ice Sheet (Jouzel & Masson-Delmotte 2010), with surface elevations reaching over 4100 m above sea-level. During the 2007–09 period of the International Polar Year the Dome A summit region was surveyed by an ice-penetrating polarimetric radar (Sun et al. 2009; Fig. 3). Initial inspection of the non-polarized radar data revealed the first detailed images of the Gamburtsev Subglacial Mountains, which were found to contain well-preserved upland glacial geomorphological features and a clearly defined water drainage pattern originating from fluvial activity in preglacial times (Sun et al. 2009). Numerical ice-flow modelling suggests these mountains were the nucleation site of the East Antarctic ice sheet, and are likely therefore to have been continuously glaciated for at least 14 Ma (DeConto & Pollard 2003).

Fig. 3.

Location of polarizing radar profiles at Dome A. Orientation of the radar transects superimposed on bed elevation, with ice-surface elevation contours also noted. Red inverted triangle denotes Kunlun station. Individual transects are identified by H1–H7 and V1–V7, referred to in subsequent figures. The location of Dome A is provided in the inset.

Fig. 3.

Location of polarizing radar profiles at Dome A. Orientation of the radar transects superimposed on bed elevation, with ice-surface elevation contours also noted. Red inverted triangle denotes Kunlun station. Individual transects are identified by H1–H7 and V1–V7, referred to in subsequent figures. The location of Dome A is provided in the inset.

Because radio-waves reflect off ice fabrics as a function of orientation, polarimetric radars, which measure radio-wave reflections simultaneously in orthogonal axes, are able to detect gross levels of ice-crystal orientations. Here, we analyse polarimetric data from the Dome A radar survey, revealing insights into the deep-ice crystal structure at and around the ice divide, and its relation with subglacial topography. By linking the data stratigraphically to the Vostok ice core, using airborne radar data, we also provide an assessment of the temporal evolution of ice fabric.

Typical fabrics in ice sheets

Deep ice cores, and some laboratory measurements confirm a direct association between ice-fabric changes and their permittivity (Matsuoka et al. 1997; Fujita et al. 2000, 2006; Drews et al. 2012). Figure 1 and Table 1 show the usual fabric types and their permittivity tensors. Electric permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. In tri-dimensional anisotropic media, the permittivity is a tensor relating the three components of the electric displacement with those of the electric field. The permittivity tensor can be expressed as a diagonal tensor, as follows:  

ε¯=[ε1000ε2000ε3]
(1)
We assume here that ε1 ≤ ε2 ≤ ε3.

Table 1.

The relationship between the typical ice fabric distributions found in ice sheets and their electrical behaviour

Permittivity in primary axis Electrical behaviour Magnitude of component in Figure 1 Type of fabric 
ε1 = ε2 = ε3 Isotropy εx ≅ εy ≅ εz Random ice (Fig. 1a
ε1 = ε2 ≠ ε3 Uniaxial crystal εz > εx, εx ≅ εy Perfect single pole (Fig. 1b
εx > εy, εy ≅ εz Vertical girdle (Fig. 1d
ε1 ≠ ε2 ≠ ε3 Biaxial crystal 0 < ׀εx−εy׀ < ׀εz−εx׀ Elongate single pole (Fig. 1c
Permittivity in primary axis Electrical behaviour Magnitude of component in Figure 1 Type of fabric 
ε1 = ε2 = ε3 Isotropy εx ≅ εy ≅ εz Random ice (Fig. 1a
ε1 = ε2 ≠ ε3 Uniaxial crystal εz > εx, εx ≅ εy Perfect single pole (Fig. 1b
εx > εy, εy ≅ εz Vertical girdle (Fig. 1d
ε1 ≠ ε2 ≠ ε3 Biaxial crystal 0 < ׀εx−εy׀ < ׀εz−εx׀ Elongate single pole (Fig. 1c

The main components of the permittivity tensor are shown in both the primary axis and in a Cartesian system of coordinates (x, y, z), where z represents the vertical.

In the case of a random ice-crystal fabric, the response of the electric field within the medium is independent of its orientation and ε1 = ε2 = ε3. If ε1 = ε2 = ε and ε3 = ε//, an idealized perfect single-pole behaviour occurs (Fig. 1b). For a single-pole ice-fabric distribution, as the ice crystals are aligned in planes, distinct electrical properties will exist along and across those planes. If we denote ε and ε// the permittivity perpendicular and parallel to the normal vector of the crystal planes, respectively, the permittivity tensor can be expressed as ε1 = ε2 = ε and ε3 = ε// (Fig. 1b).

In the case of a vertical girdle fabric, the crystal planes are randomly oriented in a vertical plane. In this situation, the two permittivities are (1) the average between ε and ε// in the vertical plane where fabric is random, and (2) equal to ε// in the normal direction, as follows: ε2 = ε3 = (ε// + ε)/2 and ε1 = ε// (Fig. 1d).

If the ice crystals have elongated single poles then ε1 < ε2 < ε3 (Fig. 1c). The ellipse ratio in this fabric corresponds to the anisotropy of permittivity in the horizontal direction. The larger this ratio is, the higher the level of anisotropic permittivity.

Polarimetric radio waves and Stokes parameters

Polarimetric radars have orthogonal transmitting and receiving antennas, receiving four series of polarized echo (noted as HH, HV, VH and VV). Relative echo powers from these configurations vary through anisotropic media. The classic Stokes vector parameters (referred to below as S0, S1, S2 and S3) can be used to evaluate and quantify the polarization of such radio-waves as follows.

The Stokes vector parameters, defined by George Gabriel Stokes in 1852, are widely used in electromagnetics and optics for describing the polarization state of electromagnetic radiation, such as its total intensity and degree of polarization and the shape parameters of the polarization ellipse (Stokes 1852; Chandrasekhar 1960; Doake 1981; Mott 2006). As H and V are orthogonal, we can regard them as axes to build the corresponding Stokes parameters, which can be represented as a vector as follows:  

ε¯=[S0S1S2S3]
(2)

Here 

S0 = |EH|2 + |EV|2
(3)
 
S0 = |EH|2 – |EV|2
(4)
 
S2=2|EH||EV|cosφ=2Re(EHEV)
(5)
 
S3=2|EH||EV|sinφ=2Im(EHEV)
(6)
where EH and EV are the components of electrical field from the orthogonal receiver antennae; φ is the phase difference between EH and EV; and Re and Im are the real and imaginary parts of an electrical field E. The normalized Stokes vector parameters can effectively eliminate the influence of transmitting power, antenna interval and so on, and is represented as follows:  
S=[1S1/S0S2/S0S3/S0]
(7)

While an electromagnetic wave propagates in an anisotropic media, it can induce both ordinary waves and extraordinary waves in orthogonal directions, each with different propagating velocities. Therefore the incident wave in the H or V direction can induce reflections both in the same direction and orthogonally. We can describe the relationship of reflection and incident waves as:  

Er=[EHrEVr]=R¯E1=[RHHRHVRVHRVV][EHiEVi]
(8)

Here, E represent the electrical field vector. Its superscript ‘i’ means that it is the incident wave and ‘r’ indicates the reflection wave. R¯ is a 2 × 2 reflection coefficient matrix describing the relationship between the incident and reflecting waves.

For induced reflections recorded in the H antenna, we can obtain:  

Er=[EHrEVr]=[RHHRHVRVHRVV][EHi0]=[RHHEHiRVHEHi]
(9)

Substituting equation (9) into equation (2), we get the following four relations:  

S0 = |EHr|2 + |EVr|2=|EHi|2(|RHH|2+|RVH|2)
(10)
 
S1=|EHr|2|EVr|2=|EHi|2.(|RHH|2|RVH|2)
(11)
 
S2=2.Re(EH.EV)=2.|EHi|2.|RHH|.|RVH|.cos(φH+φHHφVH)
(12)
 
S3=2.Im(EH.EV)=2.|EHi|2.|RHH|.|RVh|.sin(φH+φHHφVH)
(13)

For inducing reflections measured in the V antenna we obtain similar expressions.

S0 refers to the total echo-power from the orthogonal antennae, and resembles the reflected power using in the conventional sole-channel radar system. S1, S2 and S3 provide the difference in reflected power between the orthogonal electric fields in the standard Cartesian arrangement, a Cartesian system rotated by 45° and in a circular coordinate arrangement, respectively, thus providing measures of the anisotropy in ice permittivity.

Several authors have confirmed the relationship between the echo difference in orthogonal directions and the permittivity tensor of ice (Hargreaves 1977; Fujita et al. 2006; Matsuoka et al. 2012), which is linked to the second-order tensor of ice fabric (Matsuoka et al. 2009). Hence, in the absence of plausible alternative explanations, it can be assumed that the Stokes vector parameter description of the polarimetric radar reflections S1, S2 and S3 expresses ice-sheet anisotropy caused by ice crystal fabric.

Radar survey

The polarimetric radar used a frequency of 179 MHz and recorded radio waves in orthogonal orientations over a square grid of fourteen 30 km-long transects with along-track sample acquisition every c. 17 m (Fig. 3). The radar employed dual receivers in orthogonal orientations (H and V) with a time-sharing sole transmitter (H or V). It comprised four assembly antenna pairs: HH, HV, VH and VV. An in-phase/quadrature (I/Q) demodulator can measure the amplitude, phase and instantaneous frequency of radar signals, so it is widely used in polarimetric radar systems. Normally each antenna pair records both I and Q components for detecting phase. Therefore there are eight data records in the polarimetric radar files necessary to measure information of both the amplitude and phase of reflected waves. Further details of the radar are provided in Sun et al. (2009).

The I and Q components of the four antenna pairs were imported from raw data files, from which the Stokes vectors of both H and V transmitters were calculated. The four parameters in the Stokes vector each have an explicit physical meaning. S0 represents the average power of the EM waves. S1 provides the echo difference between H and V components. Its value can be positive, zero or negative depending on whether linear polarization of H or V is dominating. S2 provides the echo difference of orthogonal components between 45 and −45°. S3 represents the echo difference of orthogonal components within a circular coordinate system. After normalization, S1, S2 and S3 all range between −1 and +1.

S0 has similar results to traditional (non-polarimetric) radar reflections. It can display clear isochrones and subglacial topography. In contrast S1, S2 and S3 display obvious bands within the normal isochrone arrangements (e.g. red (positive) and blue (negative) layers in Fig. 4). The units in S1 and S2 are more distinct than in S3 and show little difference between the H and V transmitters. By adding S0, S1 and the average power from H and V together, the positive layers link to reflections recorded in the V component, and the negative layers link to the H component. If the coordinates are fixed (i.e. as in a straight survey line), variation of the Stokes vectors in the H and V components within different layers of ice must be attributed to differences in the ice crystal fabric (i.e. different layers have different fabric and orientation tensors).

Fig. 4.

The radar images of lines H7 and V4. (a, c) The S0 cross-section (Z scopes) of H7 and V4 lines derived from the Stokes vector. (b, d) The corresponding S1measurements, revealing ice-sheet anisotropic variations. Units T1–T4 refer to ice fabric units (discussed in the text) and T0 is the bed reflector. The locations of H7 and V4 are provided in Figure 3. The red inverted triangle V4 denotes Kunlun station, as in Figure 3.

Fig. 4.

The radar images of lines H7 and V4. (a, c) The S0 cross-section (Z scopes) of H7 and V4 lines derived from the Stokes vector. (b, d) The corresponding S1measurements, revealing ice-sheet anisotropic variations. Units T1–T4 refer to ice fabric units (discussed in the text) and T0 is the bed reflector. The locations of H7 and V4 are provided in Figure 3. The red inverted triangle V4 denotes Kunlun station, as in Figure 3.

The Stokes vectors were calculated in each of the transects (Fig. 4), revealing four obvious englacial layered units in which discrete variations in S1 were noticed, named T1, T2, T3 and T4, respectively (T0 designates the bed). Beneath T4, further units of alternating S1 occur, but they are less obvious and not as easy to trace owing to the lack of returned power from deeper englacial reflectors. Broadly, positive S1 units (red–yellow zones in Fig. 4) correspond to high levels of anisotropy in the horizontal plane (as the radar is insensitive to the anisotropy in the direction of transmission), and negative S1 units (blue zones) are derived from either isotropic ice or low levels of anisotropy in the horizontal plane. As expected, the deeper S1 ice fabric units thin gradually with depth owing to vertical compression (Fig. 4). Unit T1 is the thickest of those measured, from the surface to ice depths of c. 800–1000 m. Based on crystallographic information from deep ice cores, this upper unit will have a nearly random (isotropic) fabric (Azuma 1994; Azuma et al. 1999; Fujita et al. 2006; Durand et al. 2009; Montagnat et al. 2014). Unit T2 (positive S1) is up to c. 400 m thick and contains an abundance of highly anisotropic ice related to a vertical girdle fabric distribution. T3 (negative S1) is a product of low levels of horizontal anisotropy, as the fabric clusters towards a broad single-pole distribution (Hargreaves 1977; Eisen et al. 2007; Matsuoka et al. 2009). T4 (highly positive S1) is similar in crystal arrangement to T2. While both the thickness and depth of the units fluctuate horizontally substantially, we estimate that c. 20% of the ice column beneath Dome A, and up to c. 50% of the ice column at depths >1 km around this ice dome, are characterized by high levels of anisotropy (primarily from T2, T4 and T6; Fig. 4).

Dating fabric units

Link to Vostok ice core

We are able to link radar isochrones from Kunlun Station to the Vostok ice core, allowing us to estimate a depth–age relationship at Dome A (Figs 5 & 6). The depth of the ice fabric units at Kunlun is then used to assign estimated ages to the fabric units (Table 2). We also used the stratigraphic connection to Vostok to translate the ice core dust and ΔT records to Dome A (Fig. 7).

Fig. 5.

Radar transect and internal layers between Vostok Station and Kunlun Station at the summit of Dome A. (a) Map of radar profiles. The transects yielded well-resolved RES data, from which internal layers between the stations were traced. Ice surface elevation contours at intervals of 100 m are provided. (b) Traced internal layers along the profiles given in (a), so revealing the depth–age relationship at Kunlun Station (Fig. 6).

Fig. 5.

Radar transect and internal layers between Vostok Station and Kunlun Station at the summit of Dome A. (a) Map of radar profiles. The transects yielded well-resolved RES data, from which internal layers between the stations were traced. Ice surface elevation contours at intervals of 100 m are provided. (b) Traced internal layers along the profiles given in (a), so revealing the depth–age relationship at Kunlun Station (Fig. 6).

Fig. 6.

Depth–age curve at the Dome A summit. The blue points denote the age–depth data from dated radar internal horizons tracked from the Vostok ice core site (Fig. 5). The line is the ‘best-fit’ (polynomial) curve to the data points, and serves as an approximate depth–age relationship at Dome A.

Fig. 6.

Depth–age curve at the Dome A summit. The blue points denote the age–depth data from dated radar internal horizons tracked from the Vostok ice core site (Fig. 5). The line is the ‘best-fit’ (polynomial) curve to the data points, and serves as an approximate depth–age relationship at Dome A.

Fig. 7.

Comparison between ice fabric units and the Vostok dust and ΔT records. We construct a new age–depth relation at Dome A by dating radar internal horizons by tracking them from Kunlun Station to the Vostok ice core site (Fig. 6). T2–T4 refer to the same fabric units as presented in Figure 4d. T5 and T6 are deeper units, and because both are faint we can only infer approximate ages.

Fig. 7.

Comparison between ice fabric units and the Vostok dust and ΔT records. We construct a new age–depth relation at Dome A by dating radar internal horizons by tracking them from Kunlun Station to the Vostok ice core site (Fig. 6). T2–T4 refer to the same fabric units as presented in Figure 4d. T5 and T6 are deeper units, and because both are faint we can only infer approximate ages.

Table 2.

Ice fabric layer depths and their ages at Kunlun Station

Fabric layers Radar travel time (ns) Ice depth (m) Age (kyr) Period 
T1 956 807.3 0–57 Holocene and Late Wisconsin 
T2 1452 1226.2 57–106 Early Wisconsin 
T3 1657 1399.3 106–135 Eemian 
T4 1952 1648.4 135–190  
T52206 1862.9 190–240  
T62429 2051.3 240–296  
Fabric layers Radar travel time (ns) Ice depth (m) Age (kyr) Period 
T1 956 807.3 0–57 Holocene and Late Wisconsin 
T2 1452 1226.2 57–106 Early Wisconsin 
T3 1657 1399.3 106–135 Eemian 
T4 1952 1648.4 135–190  
T52206 1862.9 190–240  
T62429 2051.3 240–296  

Isochrone layers were picked along two airborne radar transects, collected by the Alfred Wegener Institute. The radar used operates at 150 MHz, alternating between 600 and 60 ns bursts, with internal stacking of shots prior to storage and a pulse repetition frequency of 20 Hz. The effective distance between 60 ns shots is c. 8 m, and for interpretation the shots are stacked two-fold (so that c. 8 m becomes c. 16 m). The two-way travel times of the layers were converted into ice depth using the Kovacs formula (Kovacs et al. 1995) and ice density information (Barkov 1970; Ekaykin et al. 2010), with an accuracy of c. 5%. The radar data were differentiated and amplitude balanced to aid the extraction of the layers. The age–depth relationship at Vostok Station was taken from Parrenin et al. (2004). The layers were traced using a commercial software package from Landmark, which displays picked horizons at cross-over points and thus allows an evaluation the quality of the data to ensure the correct isochrone is identified along the transect. Importantly, layers were traced along both transects from Dome A and compared at their intersection at Vostok Station. Agreement between the layers at Vostok Station provides confidence that the correct layers were followed to Dome A, and that the depth–age relationship there is reliable. The error for picking both the ice-surface reflection and an isochrone is about five sample points, which corresponds to 66.65 ns or c. 5.6 m in ice thickness.

Ages of fabric layers

From the stratigraphic correlation between Vostok and Dome A, we estimate that the base of T2 is c. 105 kyr, which roughly corresponds with the end of the Eemian interglacial period. T3 is aged between c. 105 and c. 136 kyr, and there is a good correspondence between the peak of S1 within T3 and the peak of the Eemian. T4 is between c. 136 and c. 190 kyr, similar to MIS 6. Two faint units below T4, named T5 and T6, are possibly consistent with previous glacial/interglacial periods.

Broadly, positive S1 units (T2, T4) correspond well to glacial periods and negative S1 units (T3, T5) are associated with interglacials (Fig. 7). This suggests that gross crystal fabric across Dome A is influenced by past environmental change at the glacial–interglacial transition.

Crystal fabrics at Dome A: distribution and significance

In a vertical column of ice near the ice divide, the orientation of ice crystals will gradually tend to a predominant (vertical) orientation under compression. In doing so, the ice fabric develops from ‘random’ to ‘single pole’. Horizontally, perfect single pole and ‘vertical girdle’ crystal alignments represent the two end-member extreme fabrics (Figs 1 & 2a) that could be expected in idealized ice-divide and ice-sheet margin regions, respectively. The resulting development of ice fabric in layers T1T5 is illustrated in Figure 8. An alternative, theoretical, explanation is that under shear the crystal axis experiences rotation in line with the stress field (Fig. 2b). Both explanations, summarized in Table 3, would yield similar polarimetric radar measurements.

Fig. 8.

Conceptual model for the development of ice-sheet fabric within layers of soft (glacial) and hard (interglacial) ice over and near an ice divide.

Fig. 8.

Conceptual model for the development of ice-sheet fabric within layers of soft (glacial) and hard (interglacial) ice over and near an ice divide.

Table 3.

Proposed dominant crystal fabrics at Dome A, following two possible crystal evolutions illustrated in Figure 2

Layer Option a in Figure 2 Option b in Figure 2 
T1 
T2 
T3 
T4 
T5 
Layer Option a in Figure 2 Option b in Figure 2 
T1 
T2 
T3 
T4 
T5 

Symbols are as follows: O = isotropic; / and \ = elongate single pole or vertical girdle in different horizontal directions; and o = single pole.

It is known that soft layers (glacial ice) are more easily deformed under stress than hard layers (interglacial ice) and isotropic ice (e.g. Paterson 1991; Thorsteinsson et al. 1999; Durand et al. 2007; Matsuoka et al. 2012; Kennedy et al. 2013). The deformation leads to the glacial ice layers more easily experiencing crystal realignment (Fig. 2a), which is what is recorded by the Stokes vectors measurements (Fujita et al. 2006; Wang et al. 2008; Matsuoka et al. 2012). Hence, the polarimetric radar measures the thickness and distribution of layers with discrete ice fabrics.

The S1 units align well among the individual transverses and cross profiles. We picked the top and bottom surfaces of all the S1 units in each line (where S1 became 0) to make three-dimensional wall and surface diagrams (Fig. 9), which display the extent and thickness of each fabric horizon revealing two obvious features. The first is significant S1 variations in both ice depth and unit thickness. The second is changes to ice fabric caused by flow over macro-scale bed topography (Robin & Millar 1982). The fabric units are dominant across the left side of a major subglacial valley. On the right side of the subglacial valley, a cluster of relatively small peaks exists. Unit T2 pinches out immediately above these peaks (Fig. 9). In this area, an arcuate belt with no S1 signal covers the cluster of peaks. We infer that, above these smaller peaks, a pure compressive stress state (uniaxial or pure shear) dominates, causing the fabric to be characterized by a single-pole arrangement (Azuma 1994; Matsuoka et al. 2012). This induces isotropy in the horizontal direction, causing the S1 to be near zero (c. 25 km mark in Fig. 4d), leading to local disappearance of the fabric units. Away from the peaks, simple shear will increase gradually, leading to the redevelopment of fabric units that can be seen on both sides (Fig. 9d).

Fig. 9.

Three-dimensional visualization of T2, T3 and T4 fabric units and their relationship to the ice-sheet bed. (a, d) T2; (b, e) T3; and (c, f) T4 (see Table 3).

Fig. 9.

Three-dimensional visualization of T2, T3 and T4 fabric units and their relationship to the ice-sheet bed. (a, d) T2; (b, e) T3; and (c, f) T4 (see Table 3).

Our polarimetric radar data reveal widespread ice-sheet anisotropy at Dome A. However, polarimetric radar only captures relative contrasts in electric permittivity between two orthogonal directions in the horizontal plane rather than the actual values. Interpretation of our radar data has been guided by typical ice-fabric distributions sampled in ice cores sites (e.g. Durand et al. 2007 at Dome C; Drews et al. 2012 at EPICA DML; and Montagnat et al. 2014 at NEEM). Ice-core data only show subtle changes in fabric during climatic transitions, however, in contrast with the marked transitions we image in radar data. This suggests that widespread but locally subtle transitions in ice fabric are likely to have a large effect on the permittivity of the ice sheet. Hence subtle transitions in ice fabric could potentially have a larger effect on ice flow dynamics than currently considered.

Our observations at Dome A are likely to hold for other ice divides, including central Greenland, as noted above. At Dome F in East Antarctica, using a dual frequency radar, simple-shear-dominated ice flow over large subglacial obstacles has been shown to lead to preferential recrystallization along bands of relatively soft ice (Fujita et al. 1999), meaning that the rheological consequences of initial anisotropy will evolve downstream. At Dome C, Siegert & Fujita (2001) analysed 60 MHz radar, and discovered that the form of the depth-to-power relationship of the returned radar signal could be used as a proxy for the along-track development of ice-crystal fabric. A similar investigation revealed how ice fabric may evolve between Ridge B and Lake Vostok (Siegert & Kwok 2000).

One situation where the downstream modification to ice crystal fabric and rheology may be highly relevant is in the preservation of major blocks of basal ice, interpreted to be caused by widespread and thick basal accretion (Bell et al. 2011). Stress-induced anisotropy-may lead to preferential englacial flow along bands, leading to smooth englacial flow over rough topography and, potentially, a partial flow ‘decoupling’ of the bulk of the ice sheet from basal ice units frozen to the bed. This new and alternative explanation for the so-called ‘accretion ice’ identified atop the Gamburtsev Subglacial Mountains (and other ‘fuzzy’ lower-englacial features seen in both Greenland and Antarctica) is consistent with the lack of significant surface uplift and velocity anomalies that a high rate of basal freezing (of the order of the surface rate of ice accumulation) should lead to, and is consistent with meteoric radar layering above the basal ice that drapes smoothly over it (see Wrona et al. 2017). Such flow may preserve the basal ice units as ancient ice blocks, which means that the rate of ice accumulation by freezing will be lower, and the age of ice considerably older (possibly by millions of years), than first thought.

Conclusions and further work

Polarimetric radar measurements, linked stratigraphically to the Vostok ice core, demonstrate that ice-sheet crystal alignment at the centre of large ice sheets is a function of both climate-induced impurities acting to ‘soften’ the ice during periods of glaciation and internal stresses within the ice sheet, acting to preferentially deform the soft ice, yielding ice-sheet anisotropy. These observations at and around Dome A are likely to hold for other ice divides, including central Greenland, where soft anisotropic ice has been measured in the lower portion of the NEEM ice core (NEEM Community Members 2013).

The next steps to this area of research are two-fold: first, to study ice crystal fabric developments using polarimetric radar around other ice divides, to understand the similarities to, and differences from, the situation at Dome A; and second, to investigate the degree to which the ice fabric uncovered at Dome A relates to modification in ice rheology. Ice-sheet modelling is capable of such analysis, through assimilation of three-dimensional internal layer structures into the ice flow parameter. This coupling between data and modelling is possible, but requires high-resolution radar data acquisition across study regions.

This paper is based on the work supported by the National Natural Science Foundation of China (40874060, 41176167, 41276200 and 41676181), the 973 projects of China (2012CB957702), the 863 projects of China (2011AA040202) and the UK Natural Environment Research Council (NE/D003733/1). This work was carried out while Bangbing Wang was a visiting research fellow at the British Antarctic Survey. We thank Richard Hindmarsh, Hugh Corr and Ed King for help and advice in developing the work for this paper. We also thank Neil Ross and Adam Booth for offering constructive and helpful reviews.

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Figures & Tables

Fig. 1.

Schmidt diagrams demonstrating typical fabrics in ice sheets. The fabric can be identified by the difference in permittivity recorded between the primary axes. The axes x and y represent the horizontal plane, and z is vertical. (a) Random ice fabric. (b) A perfect single pole. (c) An elongated single pole. (d) A vertical girdle. The perfect single pole and vertical girdle can be considered as the two extremes (end members) of ice fabric under stress-induced deformation, and the elongated single pole is a transient state between changes in stress or shear.

Fig. 1.

Schmidt diagrams demonstrating typical fabrics in ice sheets. The fabric can be identified by the difference in permittivity recorded between the primary axes. The axes x and y represent the horizontal plane, and z is vertical. (a) Random ice fabric. (b) A perfect single pole. (c) An elongated single pole. (d) A vertical girdle. The perfect single pole and vertical girdle can be considered as the two extremes (end members) of ice fabric under stress-induced deformation, and the elongated single pole is a transient state between changes in stress or shear.

Fig. 2.

Schematic diagram of two possible evolutions of an elongated single-pole ice-fabric in ‘soft’ ice. (a) The fabric in the soft (glacial) ice evolves towards a vertical girdle but keeps the same axial orientation as the harder (interglacial) layers. (b) The fabric in soft layers rotates faster towards a new stable position as a consequence of flow reorganization. In theory, both can result in a change to the permittivity tensor and hence a change in the echo difference measured by polarimetric radars. The case in (a) is the most common type, as reported in the NEEM, Dome C and Dome Fuji ice cores. Case (b) is theoretical and has yet to be observed directly in the field.

Fig. 2.

Schematic diagram of two possible evolutions of an elongated single-pole ice-fabric in ‘soft’ ice. (a) The fabric in the soft (glacial) ice evolves towards a vertical girdle but keeps the same axial orientation as the harder (interglacial) layers. (b) The fabric in soft layers rotates faster towards a new stable position as a consequence of flow reorganization. In theory, both can result in a change to the permittivity tensor and hence a change in the echo difference measured by polarimetric radars. The case in (a) is the most common type, as reported in the NEEM, Dome C and Dome Fuji ice cores. Case (b) is theoretical and has yet to be observed directly in the field.

Fig. 3.

Location of polarizing radar profiles at Dome A. Orientation of the radar transects superimposed on bed elevation, with ice-surface elevation contours also noted. Red inverted triangle denotes Kunlun station. Individual transects are identified by H1–H7 and V1–V7, referred to in subsequent figures. The location of Dome A is provided in the inset.

Fig. 3.

Location of polarizing radar profiles at Dome A. Orientation of the radar transects superimposed on bed elevation, with ice-surface elevation contours also noted. Red inverted triangle denotes Kunlun station. Individual transects are identified by H1–H7 and V1–V7, referred to in subsequent figures. The location of Dome A is provided in the inset.

Fig. 4.

The radar images of lines H7 and V4. (a, c) The S0 cross-section (Z scopes) of H7 and V4 lines derived from the Stokes vector. (b, d) The corresponding S1measurements, revealing ice-sheet anisotropic variations. Units T1–T4 refer to ice fabric units (discussed in the text) and T0 is the bed reflector. The locations of H7 and V4 are provided in Figure 3. The red inverted triangle V4 denotes Kunlun station, as in Figure 3.

Fig. 4.

The radar images of lines H7 and V4. (a, c) The S0 cross-section (Z scopes) of H7 and V4 lines derived from the Stokes vector. (b, d) The corresponding S1measurements, revealing ice-sheet anisotropic variations. Units T1–T4 refer to ice fabric units (discussed in the text) and T0 is the bed reflector. The locations of H7 and V4 are provided in Figure 3. The red inverted triangle V4 denotes Kunlun station, as in Figure 3.

Fig. 5.

Radar transect and internal layers between Vostok Station and Kunlun Station at the summit of Dome A. (a) Map of radar profiles. The transects yielded well-resolved RES data, from which internal layers between the stations were traced. Ice surface elevation contours at intervals of 100 m are provided. (b) Traced internal layers along the profiles given in (a), so revealing the depth–age relationship at Kunlun Station (Fig. 6).

Fig. 5.

Radar transect and internal layers between Vostok Station and Kunlun Station at the summit of Dome A. (a) Map of radar profiles. The transects yielded well-resolved RES data, from which internal layers between the stations were traced. Ice surface elevation contours at intervals of 100 m are provided. (b) Traced internal layers along the profiles given in (a), so revealing the depth–age relationship at Kunlun Station (Fig. 6).

Fig. 6.

Depth–age curve at the Dome A summit. The blue points denote the age–depth data from dated radar internal horizons tracked from the Vostok ice core site (Fig. 5). The line is the ‘best-fit’ (polynomial) curve to the data points, and serves as an approximate depth–age relationship at Dome A.

Fig. 6.

Depth–age curve at the Dome A summit. The blue points denote the age–depth data from dated radar internal horizons tracked from the Vostok ice core site (Fig. 5). The line is the ‘best-fit’ (polynomial) curve to the data points, and serves as an approximate depth–age relationship at Dome A.

Fig. 7.

Comparison between ice fabric units and the Vostok dust and ΔT records. We construct a new age–depth relation at Dome A by dating radar internal horizons by tracking them from Kunlun Station to the Vostok ice core site (Fig. 6). T2–T4 refer to the same fabric units as presented in Figure 4d. T5 and T6 are deeper units, and because both are faint we can only infer approximate ages.

Fig. 7.

Comparison between ice fabric units and the Vostok dust and ΔT records. We construct a new age–depth relation at Dome A by dating radar internal horizons by tracking them from Kunlun Station to the Vostok ice core site (Fig. 6). T2–T4 refer to the same fabric units as presented in Figure 4d. T5 and T6 are deeper units, and because both are faint we can only infer approximate ages.

Fig. 8.

Conceptual model for the development of ice-sheet fabric within layers of soft (glacial) and hard (interglacial) ice over and near an ice divide.

Fig. 8.

Conceptual model for the development of ice-sheet fabric within layers of soft (glacial) and hard (interglacial) ice over and near an ice divide.

Fig. 9.

Three-dimensional visualization of T2, T3 and T4 fabric units and their relationship to the ice-sheet bed. (a, d) T2; (b, e) T3; and (c, f) T4 (see Table 3).

Fig. 9.

Three-dimensional visualization of T2, T3 and T4 fabric units and their relationship to the ice-sheet bed. (a, d) T2; (b, e) T3; and (c, f) T4 (see Table 3).

Table 1.

The relationship between the typical ice fabric distributions found in ice sheets and their electrical behaviour

Permittivity in primary axis Electrical behaviour Magnitude of component in Figure 1 Type of fabric 
ε1 = ε2 = ε3 Isotropy εx ≅ εy ≅ εz Random ice (Fig. 1a
ε1 = ε2 ≠ ε3 Uniaxial crystal εz > εx, εx ≅ εy Perfect single pole (Fig. 1b
εx > εy, εy ≅ εz Vertical girdle (Fig. 1d
ε1 ≠ ε2 ≠ ε3 Biaxial crystal 0 < ׀εx−εy׀ < ׀εz−εx׀ Elongate single pole (Fig. 1c
Permittivity in primary axis Electrical behaviour Magnitude of component in Figure 1 Type of fabric 
ε1 = ε2 = ε3 Isotropy εx ≅ εy ≅ εz Random ice (Fig. 1a
ε1 = ε2 ≠ ε3 Uniaxial crystal εz > εx, εx ≅ εy Perfect single pole (Fig. 1b
εx > εy, εy ≅ εz Vertical girdle (Fig. 1d
ε1 ≠ ε2 ≠ ε3 Biaxial crystal 0 < ׀εx−εy׀ < ׀εz−εx׀ Elongate single pole (Fig. 1c

The main components of the permittivity tensor are shown in both the primary axis and in a Cartesian system of coordinates (x, y, z), where z represents the vertical.

Table 2.

Ice fabric layer depths and their ages at Kunlun Station

Fabric layers Radar travel time (ns) Ice depth (m) Age (kyr) Period 
T1 956 807.3 0–57 Holocene and Late Wisconsin 
T2 1452 1226.2 57–106 Early Wisconsin 
T3 1657 1399.3 106–135 Eemian 
T4 1952 1648.4 135–190  
T52206 1862.9 190–240  
T62429 2051.3 240–296  
Fabric layers Radar travel time (ns) Ice depth (m) Age (kyr) Period 
T1 956 807.3 0–57 Holocene and Late Wisconsin 
T2 1452 1226.2 57–106 Early Wisconsin 
T3 1657 1399.3 106–135 Eemian 
T4 1952 1648.4 135–190  
T52206 1862.9 190–240  
T62429 2051.3 240–296  
Table 3.

Proposed dominant crystal fabrics at Dome A, following two possible crystal evolutions illustrated in Figure 2

Layer Option a in Figure 2 Option b in Figure 2 
T1 
T2 
T3 
T4 
T5 
Layer Option a in Figure 2 Option b in Figure 2 
T1 
T2 
T3 
T4 
T5 

Symbols are as follows: O = isotropic; / and \ = elongate single pole or vertical girdle in different horizontal directions; and o = single pole.

Contents

Geological Society, London, Special Publications

Exploration of Subsurface Antarctica: Uncovering Past Changes and Modern Processes

M. J. Siegert
M. J. Siegert
Imperial College London, UK
Search for other works by this author on:
S. S. R. Jamieson
S. S. R. Jamieson
Durham University, UK
Search for other works by this author on:
D. A. White
D. A. White
University of Canberra, Australia
Search for other works by this author on:
The Geological Society of London
Volume
461
ISBN electronic:
9781786203427
Publication date:
January 01, 2018

GeoRef

References

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