Anisotropy in englacial radar power was measured using 60-MHz and 179-MHz copolarized pulse-modulated radar at 19 sites in central West Antarctica. The study region is a 100 × 300 km2area near the West Antarctic Ice Sheet Divide that separates ice flow toward the Ross and Amundsen Embayments. The frequency dependence of the returned power indicates that most of the radar data are affected by vertical variations in the crystal-orientation fabric (COF), though the 60-MHz data are more affected by acidity contrasts in the top 1000 m. Significant polarimetric variations occur at most sites, likely due to effects of the anisotropic COF patterns. More anisotropic variations occur at sites with significant horizontal strain, whereas more isotropic variations occur at sites where vertical compression dominates. Azimuthal shifts with depth of the principal axes of COF were found in shallow ice near the current flow divide and at greater depths over locations of rough bed. The former indicates that the divide has differentially migrated, resulting in a rotation of the principal COF axes. Nevertheless, the regionally consistent radar signatures suggest that the first-order ice properties in this area have remained constant and that no major changes in the strain configuration or ice topography have occurred for the past five to eight thousand years. We conclude that shallow polarimetric features can be related to the current strain configurations, and that englacial polarimetric features can help constrain current ice rheology and evolution of the ice topography.
 The mass balance of ice sheets provides crucial knowledge about freshwater discharge to the ocean. Millennial changes in the local ice thickness have been revealed by studying exposed bedrock [e.g., Ackert et al., 2007] and ice cores [e.g., Waddington et al., 2005], but little exposed bedrock exists in the central part of the Antarctic ice sheet and it is impractical to drill many deep ice cores. Another method is to study the spatial patterns of englacial radar reflectors. Such reflectors can be interpreted in terms of ice-thickness evolution using ice-flow models [e.g.,Nereson et al., 1998]. However, in many cases, these radar data are collected along the present-day flow line, and the flow-model-aided radar data analyses assume that the flow lines have not moved significantly through time. Additional field data are necessary to examine possible changes in the flow patterns.
 Here, we present englacial polarimetric radar signatures and surface strain configurations in the West Antarctic Ice Sheet (WAIS) Divide area that separates ice flow toward the Ross and Amundsen Embayments (Figure 1). Two locations of elevated bed have a major control of the ice sheet topography in the divide, one associated with the Executive Committee Range and the other between the Ross, Amundsen, and Weddell catchments, hereafter the RAW summit [Huybrechts, 2002]. Our study area is a saddle between these two elevated beds. The area is currently migrating toward the Ross Embayment at 10 m a−1 due to asymmetric thinning that is primarily caused by ice dynamics rather than accumulation patterns [Conway and Rasmussen, 2009]. Asymmetric behavior between the downstream Ross and Amundsen catchments occurs over a range of timescales [Conway et al., 1999; Joughin and Tulaczyk, 2002; Shepherd et al., 2002], which presumably cause a complicated history of ice flow in the uppermost parts of these catchments. Such flow could have caused residual complexity in the form and spatial pattern of crystal alignments in these areas.
 Englacial polarimetric radar signatures in East Antarctica have identified the statistical alignments of ice crystals (crystal-orientation fabrics, or COF) [Fujita et al., 2006; Matsuoka et al., 2003]. Because the refractive index of single ice crystals is ∼1.1% larger along the crystal (c) axis than the other axes [Matsuoka et al., 1997], a nonuniform COF indicates dielectric anisotropy. The ice-flow pattern can influence COF since the mechanical properties of single ice crystals are highly anisotropic [Azuma and Higashi, 1985]. Ice deformation produces preferred COFs, which then influence further deformation. Therefore, by revealing spatial variations in the COF patterns, we can examine the variability of current ice rheology, and infer past changes in the strain configurations associated with the ice-flow patterns.
 Radar surveys are the most practical way to examine COF patterns over wide areas. The present study is the first study that combines GPS and polarimetric radar surveys at many sites to examine the relationships between COF-origin polarimetry and current strain configurations. As larger gradients of surface mass balance yield larger strain rates if the ice sheet remains in a steady state, the development of COF near the WAIS Divide is likely more rapid and complicated than that in previous study areas in East Antarctica. The goals of this paper are to reveal spatial patterns of COF using radar, to examine the relationships between the radar-detected COF and current surface-strain configurations, and to use radar data to assess the feasibility of inferring possible changes in strain configurations in the past.
2.1. Radar Survey
 Radar measurements were done at 19 sites within 30 km from the current ice-flow divide (Figure 1). We installed 60-MHz and 179-MHz radar systems on a single platform (sled) and operated them asynchronously to avoid interference [Matsuoka et al., 2002]. Transmitting and receiving antennae were installed on each side of the sled (approximately 2 m apart) and aligned parallel to the moving direction of the platform to collect co-polarized data. This antenna configuration was fixed throughout the entire campaign. In this study, we used a 3-element Yagi for 60 MHz and an 8-element Yagi for 179 MHz to increase the detection range of the 179-MHz data. Due to their size, 60-MHz antennae with additional elements are impractical to use.
 At each site, we used the multipolarization plane technique [Matsuoka et al., 2003] (Figure 2a). First, the azimuth of the sled was set to the local fall line (i.e., steepest descent path on the surface), as determined with a large-scale, 5-km-grid, digital elevation model of the ice surface [Liu et al., 1999]. At this azimuth (i = 0), we first obtained radar data at orientation β = 0 (degree). After acquiring this data set, the platform was rotated clockwise in 15° increments so that radar data were collected at 12 polarization planes (β = 15i degrees, i= 0, …, 11). The accuracy of the platform orientation was better than ±2°. During measurements at each orientation, the platform moved several meters forward or backward slowly to prevent speckle noise, which can be canceled by averaging the radar data over several radio-wave wavelengths (3 m at 60 MHz and 1 m at 179 MHz) [Ulaby et al., 1986].
2.1.2. Returned Power
 The radar receivers stacked the waveforms incoherently using logarithmic amplifiers [Matsuoka et al., 2002]. We recorded only the returned power without phase information. The radar returned power P is a function of characteristics of radar instrumentation S and of ice Ialong a round-trip propagation path to a target at depthz. The geometric spreading G also affects P. In the decibel scale ([x]dB = 10log10(x)), their relationship is
The anomaly δ[Pi]dB of the returned power at the i-th polarization plane from the polarization-mean returned power [〈P〉]dB can be defined as
In this paper, we examine δ[Pi]dB as a function of radar frequency, radar polarization, depth, and location of the measurements. Below, the frequency and polarization dependences of S and G in equation (1) are discussed to define a framework for interpreting δ[Pi]dB in terms of ice properties I.
 Since the whole radar platform was rotated without change in the configuration, there is no polarization-plane variation inS. The instruments were calibrated before and after the field campaign, and the same pulse width (500 ns) was used for both frequencies. However, an accurate value of S remains unknown because we did not measure the in situ system gain (e.g., cable loss, antenna gain for our specific setting). As a consequence, the frequency dependence of S is not fully evaluated.
 The nominal antenna gain is 9.3 dB larger at 179 MHz than 60 MHz. Different half-power beam widths of the antennas at these frequencies result in different volumes of the ice being illuminated by the radar. Most of the backscattering originates from within the first several Fresnel zones (diameter is proportional to the square root of depth); the areas illuminated within the antenna-beam widths are larger than the first Fresnel zone by a factor of at least ∼2 (60 MHz) and ∼3 (179 MHz) at depths greater than 200 m. Therefore, the area primarily contributing to the backscattering is similar regardless of the antennae. Hereafter, to compensate the frequency difference inS, we account for only the nominal antenna gain and the wavelengths of the radio waves. This Scompensation is included in 179-MHz radar returned power [P179]dB, δ[Pi179]dB, and [〈P179〉]dB. Uncertainty in S does not affect the relative magnitudes of [〈P〉]dB at the two radar frequencies because Sis independent of the two-way travel time (seeMatsuoka et al. [2010, Appendix B] for requirements of the instrumental stability). Therefore, depth profiles of [〈P〉]dB for the two frequencies can be directly compared.
 The term G can be derived from the target depth zbelow the surface and the depth-averaged refractive indexm from the surface to depth z:
The refractive index m (∼1.78) is frequency independent, and its anisotropy causes only negligible (<0.05 dB) difference in G [Matsuoka et al., 2009]. Therefore, the term G associated with the radar power returned from the same depth is effectively independent of radar polarization plane and frequency.
 In summary, the polarization-plane dependence ofParises only from the polarization-plane dependence of ice propertiesI. The frequency dependence of depth profiles of P comes from the depth variation of I.
2.1.3. Ice Characteristics Controlling Returned Power
 The WAIS Divide area has stratified ice without major scatterers such as buried crevasses [Matsuoka et al., 2010]. Therefore, effects of I on the radar power returned from depth z come mainly from three terms:
Here, R is the reflectivity, L is the dielectric attenuation integrated along the propagation path, and Bis power reduction relative to the isotropic ice caused by COF-induced birefringence. Englacial reflections occur at permittivity and/or conductivity contrasts. The permittivity contrasts come from COF and density contrasts, whereas the conductivity contrasts come from acidity contrasts [Paren, 1981; Fujita and Mae, 1994; Fujita et al., 1999]. The attenuation L is nearly proportional to ice conductivity, which means that for frequencies below roughly 300 MHz, the attenuation depends on neither polarization nor radar frequency [Fujita et al., 2000; Matsuoka et al., 2009]. When COF patterns are not symmetric around the vertical radio-wave-propagation axis, the ice is birefringent, making [B]dB nonzero [Hargreaves, 1977]. Therefore, in this study, only B and R can depend on polarization.
 Since S and G are also polarization independent, δ[Pi]dB returned from depth z can be interpreted in terms of the combined polarization dependences of the radar reflectivity and the birefringence effects. From equations (1) and (5),
Here, δ[Ri(z)]dB and δ[Bi(z)]dB are defined similar to δ[Pi]dB (equation (2)). Polarimetric variations in reflectivity are related to abrupt variations of anisotropic permittivity in a narrow depth range close to depth z, whereas B is related to anisotropy of the refractive index in the horizontal plane integrated along the round trip from the surface to depth z. More details of the δ[Pi(z)]dB interpretations in terms of COF will be discussed in Section 4.2.
2.2. Strain-Grid Survey
 Horizontal strain and velocity measurements were made in the austral summers of both 2005–6 and 2006–7. We used geodetic, L1/L2 frequency GPS receivers at 18 sites, among which radar measurements were made at 15 sites (Figure 1). At each of the 18 sites, we installed a strain grid composed of five markers forming two triangles with a common vertex at the central marker (Figure 2b). The central markers are temporary base stations. The other four markers are separated from the central marker by a distance roughly equal to their (local) ice thickness (2–3.5 km). The markers were 3-m-long aluminum poles with about 1-m of the pole driven into the firn.Conway and Rasmussen  used the same marker arrangement in the vicinity of the WAIS Divide ice core site.
 GPS measurements were made at the central makers longer than two hours. This data set was analyzed to determine the position of each central marker using the Canadian Geological Survey's precise point positioning service [Zumberge et al., 1997]. For the fastest ice speed in this study (6.02 m a−1), a 2-h survey involves a net ice motion of ∼1.4 mm. As this motion is much less than the ∼1 cm targeted positional uncertainty, this ice motion is negligible [King, 2004]. To position the four rover stations relative to the (central) temporary base station, each of the two triangular baselines, including the temporary base station, were occupied with three GPS receivers for more than 30 min. These baseline data were analyzed using Trimble Geomatics Office. By repeating the measurements about one year later, we determined the displacements of these markers and thus the flow vectors.
 According to the length of the baselines and uncertainty of the marker position relative to the ice, two independent measurements separated by one year give a strain rate uncertainty of ∼2 × 10−5 a−1. Additional uncertainties come from positioning errors using GPS. Therefore, we report compression and extension rates along the principal axes of strain in the horizontal plane only if they exceed 1 × 10−4 a−1. A full report of the estimated velocities and strain configurations is available at nsidc.org/data/nsidc-0503.html.
 There was already a network of 98 markers in the vicinity of a flow line through the WAIS Divide core site [Conway and Rasmussen, 2009]. In this region, we did not develop the strain grids described above and instead used GPS data measured during austral summers of 2002–2003 and 2003–2004. Separations between the markers are typically less than 5 km. Flow velocities at four radar-measurement sites in this network were estimated by a two-dimensional linear fit of the measured velocities. For these four radar sites, the coefficients of the linear fit are used as horizontal strain rates.
 Vertical strain rates cannot be reliably estimated using this method because firn compaction may move the markers vertically [Hamilton et al., 2005]. Thus, depth-averaged vertical strain rates are approximated with the surface mass balanceb divided by the ice thickness H. Although basal melting rates remain unknown, a model study estimates a melting rate at the drilling site of ∼10−4 m a−1 [Neumann et al., 2008], which is much less than the 0.17–0.34 m a−1 surface balance derived from the continental climate model [van de Berg et al., 2006]. If the basal melting is larger than the estimate above, the vertical strain rates would be smaller.
 Each column in Figures 3–6 show radar and GPS data collected at each site. Figures 3 and 4show the data collected at five sites each along a flow line through the WAIS Divide core site (core-site flow line) and along two flow lines in the vicinity of the ice dome north of the core site (north flow lines), respectively. The numbers in these site names give the approximate distance in kilometers along the flow lines from the current divide position.Figure 5shows the data collected at five sites south of the core-site flow line andFigure 6shows the data collected at the other four sites between the core-site and north flow lines. In this section, we examine frequency and polarization characteristics of the returned power as well as regional patterns of flow and strain configurations. Properties of the radar data and their interpretations are summarized inTable 1.
Table 1. Summary of the Properties of the Radar Data
Shallow Ice (<∼1000 m)
Deep Ice (>∼1000 m)
Depth trends of [〈P〉]dB
Linear, and independent of frequency
Orientation of radar axis at depth
Primary source of reflections
3.1. Frequency Dependence of the Returned Power
 The polarization-plane-averaged returned power [〈P60〉]dB and [〈P179〉]dB show common features at all sites (top row of Figures 3–6). Local variations of [〈P179〉]dB are small (<∼5 dB) through the entire depth range. Although local variations of [〈P60〉]dB have a similar range as [〈P179〉]dB at depths above 1000–1200 m, they increase to 20–30 dB at greater depths. Both [〈P60〉]dB and [〈P179〉]dB decrease with increasing depth at a similar rate down to about 1000–1200 m. Lower down, [〈P60〉]dB decreases more rapidly than it does at shallower depths, whereas [〈P179〉]dB keeps a similar rate of decrease until it reaches the noise floor. [〈P60〉]dB and [〈P179〉]dBreach the noise floor typically at around 1400 and 1800 m, respectively. These differences in detection range do not depend on the ice thickness at the radar-measurement sites.
3.2. Polarimetric Features in the 60-MHz Data
 Polarimetric variations δ[P60]dBof the 60-MHz returned power show many analogous features at most of the sites shown inFigures 3–6 (second row). We found that polarimetric features for deeper returns differ from those of shallower returns.
 The return from shallow ice shows relatively small polarimetric variations. Magnitudes of δ[P60]dB are mostly below ∼5 dB. At sites where this magnitude is close to 5 dB (sites CE1 and CW1 in Figure 6), δ[P60]dBshows a 180°-periodic feature. The largestδ[P60]dB value occurs at radar polarization planes close to the fall line and the orientation is nearly depth independent. Hereafter, we call the polarization plane where δ[P60]dBis largest the “60-MHz radar axis” (Table 1).
 The 60-MHz return from a deeper layer shows distinct periodic dependences on the polarization plane. The top of this layer is at 600–800 m, depending on location, the bottom at 1400–1600 m. Magnitudes ofδ[P60]dB reach 20 dB at many sites. We found three distinct features in this layer. First, δ[P60]dBshows only a 180°-periodic pattern. This periodicity is strongest at site SE3 (Figure 5); it is also visible at sites CE2 (Figure 6) and SE1 (Figure 5). The radar axis aligns with the fall line (β = 0°) at SE3 and CE2, while it is oblique to the fall line (β = ∼45°) at SE1. Second, δ[P60]dBshows a 90°-periodic pattern, as distinctly found at sites S-W17 (Figure 3) and SE2 (Figure 5). At these sites, the radar axes are parallel and perpendicular to the fall line. Third, δ[P60]dB has large values at two orientations, which are not evenly spaced, and the magnitudes of δ[P60]dBare not equal at these orientations. This feature occurs at sites S-E06 and S-W24 (Figure 3). At several sites in the deepest ice, the returned power was nearly isotropic because the returned power approaches the noise floor at some polarization planes. So, this apparent isotropic feature is not related to ice properties.
3.3. Polarimetric Features in the 179-MHz Data
 Polarimetric features at 179 MHz generally vary more than those at 60 MHz. Throughout the observed depth range, 180°-periodic pattern are most distinct, though the magnitudes ofδ[P179]dBvary. At site N-Div (Figure 4), smaller magnitudes of δ[P179]dBoccur at depths of 400–700 m and 1100–1400 m, and larger magnitudes occur at 200–400 m, 700–1100 m, and deeper than 1400 m. Most sites have a similar five-layered structure, although their magnitudes of the anisotropy and depth ranges vary.
 At greater depths, the polarimetric patterns are more complicated. We found 90°-periodic patterns together with the 180°-periodic pattern at site CW1 (Figure 6). At the greatest depths, the nearly isotropic returned power most likely results from instrument detection constraints rather than ice properties.
 The radar axis, at which the returned power is largest, depends on depth at most sites. However, in each depth range, the radar axis shows a uniform depth pattern; at site S-E30 (Figure 3), the radar axis is nearly depth independent in the shallower four depth ranges, but it varies with depth in the deepest one. In general, the radar axis is more variable at greater depths. Four distinct features are (1) fluctuations of the radar axis around a certain orientation (S-E06 inFigure 3and N-W30 inFigure 4), (2) large shifts of the radar axis (CE3 in Figure 6and N-W30 inFigure 4both of which), happen in relatively shallow ice, (3) abrupt variations in the radar-axis orientation at greater depths of roughly 1000–1400 m (S-W17 inFigure 3 and SE3 in Figure 5), and (4) a more gradual variation (S-Div inFigure 3).
3.4. Regional Patterns of the Ice Motion
 Strain configurations and ice-flow vectors are shown inFigure 1d and the bottom row of Figures 3–6. In general, the estimated directions of fall line and ice flow are roughly aligned and ice-flow speeds increase with increasing distance from the ice-flow divide. However, regional differences exist. Horizontal extension is significant at many sites, and horizontal compression is also significant, especially in association with variable subglacial topography. The approximate vertical strain rates range between 5.2 × 10−5 and 1.4 × 10−4 a−1. The surface mass balance monotonically increases from west to east [Morse et al., 2002; Neumann et al., 2008]. Ice is significantly thinner near north flow lines (∼2 km) than in southern parts of the study area (3–4 km). These regional patterns make the vertical strain rates larger in the northeast and smaller in the other areas, particularly the southwest. At some sites, one or two principal strain rates are larger than the other(s) by more than a factor of two: Figures 3, 5, and 6show that vertical compression dominates at SE1 and SE2; horizontal extension dominates at CE1, SW1, and SW2; vertical compression and horizontal extension are larger at N-Div and SE3; and horizontal compression and extension are larger at CE2.
4. Causes of Reflections and Polarimetric Variations
4.1. Theory to Interpret the Frequency Dependence
 Radar reflections occur at contrasts of COF, density, and acidity [Robin et al., 1969; Millar, 1981; Fujita et al., 1999], but not at air hydrates [Matsuoka et al., 2004]. Fresnel reflectivity Racid for the acidity contrasts is inversely proportional to the square of the radar frequency [Fujita and Mae, 1994]. Thus, [Racid]dB at 60 MHz is 9.5 dB (=10log10(60/179)2) larger than [Racid]dB at 179 MHz, though the absolute magnitudes will depend on the acidity contrasts and ice temperature. In contrast, Fresnel reflectivity [RCOF]dB for the COF contrasts and [Rdensity]dB for the density contrasts are frequency independent, though their magnitudes will depend on their respective contrasts.
4.2. Theory to Interpret Polarimetric Variations
 The birefringence δ[B]dB and anisotropic reflectivity δ[R]dB can affect the observed polarimetric features (equation (6)). Here, we first discuss polarimetric variations of δ[B]dB and δ[R]dB separately, and then discuss their combined effects on δ[P]dB.
4.2.1. Effects of Birefringence
 When the COF has non-uniform patterns, the ice sheet ice is considered to be birefringent. Radio-wave propagation in the birefrigent ice is affected when the COF patterns are nonuniform in the (horizontal) plane perpendicular to the (vertical) radio-wave propagation axis. The indicatrix of the refractive index of the ice has principal axes aligned with COF's principal axes c1, c2, and c3. The corresponding principal values are m1, m2, and m3 (m1 + m2 + m3 = 1; usually m1 < m2 ≪ m3). Because c3 is nearly vertical in most cases, we assume that the radio wave propagates along c3 (for more general cases, see Matsuoka et al. ). When the radio wave is transmitted with a polarization plane that does not include either horizontal principal axes c1 or c2, the transmitted radio wave can be viewed as a superposition of two wave components that travel in these two planes at different speeds of c/m1 and c/m2, where c is the speed of light in vacuum. When the two waves return to the radar receiver, their phases may differ. Thus, there is a rotation of polarization that affects the returned power measured at a given polarization plane. This power depends on the phase difference θ and on the angle γof the radar-polarization plane in respect toc1. The phase difference θ is proportional to radar frequency f, depth z, and anisotropy of the refractive index (δm = m2 − m1) averaged along the propagation path:
When the phase difference is close to 2nπ (n: nonnegative integers), the two wave components are in phase, so δ[B]dB equals zero regardless of the radar polarization plane (Figure 7a). When the phase difference is close to (2n − 1)π, the two wave components are out of phase. In this case, δ[B]dB becomes nonzero at the radar polarization plane that does not include the principal axis c1 or c2. As a result, δ[B]dB has a minimum at the radar polarization planes 45° off from c1 and c2, but a maximum at the radar polarization planes that includes c1 or c2. Also, when the phase difference θ ranges between ∼3/4π and ∼5/4π, δ[B]dB differs more than 5 dB. Polarimetric variations of δ[B]dBare 90°-periodic (bimodal), but not sinusoidal.
 The term 〈δm〉0zz can be estimated using COF patterns measured with thin sections sampled from ice cores. Seven ice cores drilled in Greenland and Antarctica show that 〈δm〉0z, averaged over the entire core length, range from 2.8 × 10−4 (GISP2) to 1.8 × 10−3 (Mizuho) with a mean of 7.4 × 10−4 [Matsuoka et al., 2009]. Corresponding to these 〈δm〉0z values, depths at which θ becomes πare 1480, 230, and 570 m in this order for 179-MHz radio waves, but three times these depths for 60-MHz radio waves. These depths correspond to the shallowest depths where largeδ[Bi]dBvariations are expected. A previous study, using an ice core from Dome Fuji and one from Mizuho, found extinctions of the radar-returned power at the depths whereθ is predicted to reach π [Fujita et al., 2006]. Such extinction depths support the hypothesis that radar power extinction at these two sites is caused by its birefringence.
4.2.2. Effects of Anisotropic Reflections
 Previous radar studies found 180°-periodic reflectivity from three sources (Figure 7b). The first source is COF alternations between single-pole patterns (m1 ∼ m2 ∼ 0, m3∼ 1) with different strengths. The second source is between vertical-girdle patterns (m1 ∼ 0, m2 ≪ m3) with different strengths. And the third source is between a single-pole pattern and a vertical-girdle pattern [Fujita et al., 2003; Matsuoka et al., 2003]. The first makes nearly isotropic returns, whereas the second and third make more anisotropic returns. These studies found that δ[R]dB reaches 10–20 dB in the midstream area, whereas δ[R]dBis virtually zero near the ice-flow divide. More complicated contrasts in the COF patterns can further complicate the reflection anisotropy, but so far no data have yielded to such analysis.
 We assume that other sources cannot make anisotropic reflectivity because 1) the acidity-contrast reflectivity is isotropic and 2) density contrasts are significant only at depths smaller than 500 m in the WAIS Divide area [Matsuoka et al., 2010].
4.2.3. Combined Effects of Birefringence and Anisotropic Reflections
Figures 7c and 7d illustrate predicted polarimetric variations of the returned power as a combination of δ[R]dB and δ[B]dB. Here, principal axes of the reflectivity and COF are assumed to be aligned, as required by the assumption that only COF contrasts cause anisotropic reflections. When the phase difference between two wave components is 2(n − 1)π (δ[B]dB∼ 0), the returned power shows a clear 180°-periodic pattern. However, when the phase difference nears (2n − 1)π, the polarimetric pattern of the returned power becomes complicated. The 90°-periodic features are caused by birefringence, which is clearer when the anisotropy of the reflectivity is small (5 dB,Figure 7c). Although the periodicity is 90°, the polarimetric variations of the returned power are not a sinusoidal function of the polarization-plane orientation. The 90° periodicity in the returned power becomes less distinct as the anisotropy of the reflectivity becomes larger (e.g., 10 dB,Figure 7d). Indeed, the observed range of δ[R]dB is up to 10–20 dB [Fujita et al., 2003; Matsuoka et al., 2003], which exceeds the examples in Figures 7c and 7d. Thus, more complicated polarimetric variations than these examples are expected when the anisotropy of the reflectivity is significant.
4.2.4. Previous Application of the Theory to the Data Interpretation
 Along a 670-km-long flow line in East Antarctica,δ[P179]dBare dominated by 90°-periodic in the upstream region and 180°-periodic features in the midstream [Matsuoka et al., 2003]. That study used the same co-polarized multipolarization-plane technique. The regional distribution of these polarimetric features agrees with theoretical predictions of the COF development under strain configurations estimated from regional ice topography.Fujita et al. did both co- and cross-polarized measurements at two ice core sites and found that the simplified theoretical framework using only co-polarized data (Figure 7) is useful to remotely examine COF. These previous studies show that the theory discussed in Section 4.2 is applicable for interpretation of the observed radar data.
4.3. Data Interpretation
 Density-contrast reflectivity is significant only at depths smaller than 500 m in the WAIS Divide area [Matsuoka et al., 2010]. In this study, the 60-MHz radar data have depth-independent features from 200 m to depths beyond 500 m. The 179-MHz radar axis does not change its orientation at this boundary in the top 500 m. These two findings indicate that the source of the reflection stays the same between 200 and 500 m. Therefore, we argue that the sources of the reflected signal are the COF and acidity contrasts.
 If [S]dB is stable, the frequency dependence of [〈P〉]dB can be interpreted in terms of the frequency dependence of [〈R〉]dB (see Matsuoka et al. [2010, Appendix B] for requirements of stability in [S]dB). This is because [〈B〉]dB = 0 and both [G]dB and [L]dB are uniform at 60 MHz and 179 MHz (equations (1) and (5)). When the reflection surface is smooth and flat within the first several Fresnel zones, the in situ reflectivity can be approximated by the Fresnel reflectivity [Peters et al., 2005]. Even when the reflection surface is slightly rough and/or tilted, the in situ reflectivity remains proportional to the Fresnel reflectivity. Therefore, the frequency dependence of the Fresnel reflectivity (Section 4.1) can be used to guide our interpretation of the data. As the absolute values of [S]dB remain unknown, we can interpret only the depth variations of [〈P179〉]dB − [〈P60〉]dB.
 At depths shallower than ∼1000 m, [〈P179〉]dB − [〈P60〉]dB is nearly zero, but the value increases at deeper depths (top row in Figures 3–6). This trend suggests that the source of the reflection changes near ∼1000 m. At depths exceeding ∼1000 m, the most prominent feature in the observed δ[P]dB is the 180° periodicity (Table 1). This feature occurs at both frequencies. Because the 180° periodicity in δ[P]dBcan be made only by 180°-periodic reflectivity (Figure 7), not by birefringence, we argue that the primary reflection source is COF contrasts for both frequencies in the deeper ice.
 The COF-contrast Fresnel reflectivity is uniform for 60 MHz and 179 MHz, and [〈P179〉]dB − [〈P60〉]dB is roughly 10 dB in the deeper ice. This uniformity indicates that [S179]dB − [S60]dB is approximately 10 dB. Consequently, similar values of [〈P179〉]dB and [〈P60〉]dB in the shallow ice show that [R179]dB is roughly 10 dB smaller than [R60]dB. Therefore, we argue that the primary reflection source is acidity contrasts for 60 MHz and COF contrasts for 179 MHz in the shallower ice.
 Only in the deeper ice did we observe 90°-periodic features at both frequencies. There are two possible sources of these features. The first source is 90°-periodic reflectivity. Since the primary source of reflections is COF contrasts at great depths for both radar frequencies the 90°-periodic reflectivity should give a very similar polarimetric pattern in the returned power at both frequencies. However, the observed polarimetric patterns clearly depend on frequency. Therefore, we reject this possibility. The other source is that birefringence producesδ[B]dBminima. We observed 90°-periodic variations only in the deeper ice. However, the ratio of the radar frequencies shows that theδ[B179]dB minima appear at 0.34, 0.67, and 1.01 times the depths at which δ[B60]dB have minima. The absence of δ[B179]dBminima in the shallower ice is probably caused by a combination of effects from birefringence and COF-contrast anisotropic reflections (Figure 7d). Polarimetric variations for 179 MHz show moderate 180° periodicities due to the biaxial reflectivity in the shallower ice, which weaken the 90° periodicity made by birefringence.
 In summary, for ice deeper than 1000 m, the primary source of reflections is COF contrasts for both frequencies. COF contrasts are also the primary source of 179-MHz reflections in the shallower ice. In this ice, however, the primary source of 60-MHz reflections is acidity contrasts. The 180°-periodic variations are caused by 180°-periodic COF-contrast reflectivity, whereas the 90°-periodic variations are caused by birefringence (Table 1).
5. Effects of COF on Other Methods of Radar-Data Interpretation
5.1. Are COF Reflectors Isochrones?
 Englacial radar reflectors caused by density and acidity contrasts are widely accepted as isochrones. However, this wide acceptance does not extend to englacial reflectors caused by COF contrasts. Are COF-contrast reflectors really isochrones?
 The present study shows that COF is the primary source of reflections even at small depths (200–500 m) in the vicinity of the ice-flow divide. Previous studies reported COF-contrast reflections only at greater depths in the upstream areas, and at depths as shallow as 250 m only in the midstream area, not in the flow divide [Fujita et al., 1999, 2003; Matsuoka et al., 2003; Eisen et al., 2007; Drews et al., 2012]. Seismic surveys also found COF contrasts at greater depths in Jakobshavn Glacier in Greenland [Horgan et al., 2008], the WAIS Divide, mid- and down-stream on Thwaites Glacier, and in the onset region of Bindschadler ice stream in West Antarctica [Horgan et al., 2011]. COF contrasts therefore occur widely in polar ice sheets.
 As the radar frequency increases, COF contrasts become the main source of reflection (Section 4.1). This study found that the transition frequency for the relative importance of COF and acidity contrasts lies between 60 and 179 MHz in the shallower ice and less than 60 MHz in the deeper ice. The transition frequency was also somewhere between these two frequencies along a 1050-km-long profile from Dome Fuji to the coast in East Antarctica [Fujita et al., 1999]. The transition frequency is higher with higher temperature and/or larger acidity contrasts, but lower with larger COF contrasts. Nevertheless, airborne deep-sounding radar surveys have been done at 60 MHz [Young et al., 2011], 150 MHz [Nixdorf et al., 1999; Vaughan et al., 2006; Gogineni et al., 2007], and 435 MHz [Dall et al., 2010]. So a significant fraction of these radar data involve COF-contrast reflectors. But at a frequency of 1 MHz, a widely used frequency for ground-based and airborne impulse radar measurements [e.g.,Conway et al., 2009], the acid-contrast reflectivity is 36 dB larger than that at 60 MHz. This magnitude of the reflectivity difference would correspond to the COF-contrast reflectivity if 70% of the c axes suddenly changed their orientations to being perpendicular with the wave propagation direction [Matsuoka et al., 2009], which is unlikely to happen.
 According to Matsuoka et al. , no notable transitions occur in the ice at depths where the main source of the 60-MHz reflections changes (∼1000 m;Figure 4ain the reference). The 60-MHz and 179-MHz englacial reflectors appear nearly parallel to each other and they can be trackable over regions with different major reflection sources, though their exact depths differ [Fujita et al., 1999]. One of the ten reflectors tracked over ∼1200 km between Dome Fuji and EPCIA DML ice cores by Huybrechts et al.  corresponds to a COF contrast found in the EPICA ice core [Eisen et al., 2007]. These results indicate that the COF-contrast reflectors are indeed isochrones.
5.2. Proxy for Englacial Attenuation Rates
 Depth profiles (vertical gradients) of the 60-MHz radar returned power were used as a proxy for englacial radar attenuation rates in the WAIS Divide area [Matsuoka et al., 2010]. The goodness of the proxy depends on depth variations of R and B (equation 5). In this study, dual-frequency measurements show that the main source of reflections for 60 MHz changes at a certain depth. However, this depth (approximately 1000 m) is uniform in the WAIS Divide area so the effect of the depth-variable reflectivity is uniform in this area. This uniformity allows us to use lateral patterns of the vertical gradients as a proxy for lateral patterns in the englacial attenuation. However, the absolute values of the attenuation rates depend on the depth variations of the reflectivity. Attenuation estimates using the vertical gradients should be made using multifrequency, multipolarization radar data.
6. Radar-Revealed Patterns of COF and Their Interpretations
6.1. Rapid Development of COF Contrasts
 COF-contrast reflections occurred at most depths. Radar features observed continuously from ∼200 m to greater depths indicate that vertical contrasts in permittivity due to COF are already developed sufficiently at ∼200 m to reflect radio waves. The [〈P60〉]dB and [〈P179〉]dBsignals decrease at a similar rate in the shallower ice, even though they come from a different source. This means that the acidity-contrast reflectivity, the COF-contrast reflectivity, and the attenuation rates are all separately uniform in this depth range, rather than that being uniform in their sum effect. Indeed, the attenuation rate over this depth range is presumably uniform [Matsuoka et al., 2010]. Therefore, we argue that magnitudes of COF contrasts are nearly uniform regardless of depth in the top 1000 m or so.
 We can gain insight about the COF contrasts by comparing to similar polarimetric data taken near Dome Fuji [Fujita et al., 1999, 2006; Matsuoka et al., 2003]. The WAIS Divide area has similar ice thickness to Dome Fuji but a surface mass balance that is 2–3 times larger, inducing correspondingly enhanced vertical strain rates. Lateral gradients in surface mass balance are much larger over the WAIS Divide area than at Dome Fuji. In a steady state, we also expect larger gradient of mass flux and horizontal extension. These differences probably explain why previous studies found nearly isotropic COF patterns only at mid and large depths in the flow-divide vicinity, whereas the present study finds anisotropic COF patterns over a wide depth range in the flow-divide area.Morse et al.  estimated the ice temperature to be nearly uniform roughly at −30°C in the depth range examined in our study in the WAIS Divide area. In contrast Hondoh et al. showed that ice temperature remains below −35°C at depths shallower than 1600 m in the Dome Fuji borehole. The acidity-contrast reflectivity is larger when ice is warmer, while the COF-contrast reflectivity is temperature independent [Fujita and Mae, 1994]. Therefore, more dominant COF-contrast reflections at the WAIS Divide than at Dome Fuji are caused not with the difference in the temperature dependences of reflectivities but with more anisotropic and more significant COF contrasts over a wider depth range at the WAIS Divide.
6.2. COF Patterns Revealed by Radar
 We interpret the observed polarimetric variations in terms of COF patterns at sites where the measured surface strain configurations are vertical compression dominant, horizontal extension dominant, or having significant horizontal extension (Figure 8). Polarimetric features of the reflection are caused by the contrast of the COF patterns at the interface, and do not explicitly show the COF patterns in the upper or lower layers. Polarimetric variations at the other sites are more complicated so it is not readily possible to infer their COF patterns.
 Shallow ice at sites SE1 and SE2 has relatively small δ[P]dBand an poor-defined radar axis where vertical compression is dominant near the surface (Figure 5). Under vertical compression, crystal c-axes rotate toward the vertical axis, greatly reducing the anisotropy of the COF patterns in the horizontal plane perpendicular to the vertical radio-wave propagation axis (Figure 8a). Therefore, the observed radar features can be explained with the preferred COF patterns under the current near-surface strain configurations.
 Horizontal extension dominates at sites CE1, SW1, and SW2 (Figures 5 and 6). At these sites, δ[P]dBis larger than those at sites where vertical compression dominates and the radar axes are more distinct. The radar axis near the surface (<∼1000 m) is well aligned with the measured extension axis. Under uniaxial extension, c-axes rotate away from the extension axis and cluster in the plane perpendicular to it. Larger reflections along the extension axis can be caused by vertical-girdle COF patterns with different cluster strengths (Figure 8b).
 At sites N-Div, SE3, and CE2 (Figures 4–6), two principal strain rates are more than twice the size of the other. Here, significant horizontal extension occurs together with significant vertical or horizontal compression. The observed polarimetric features at these sites are similar to those found at sites where horizontal extension dominates. However, unlike those sites, the radar axis and the extension axis here are separated by roughly 30°. We interpret the separation to mean that anisotropic returned power is caused by c-axes that cluster non-randomly in the vertical plane perpendicular to the extension axis (Figure 8c). Such a c-axes distribution should occur because it is preferred under pure shear and the observed strain configuration can be pure shear in some cases.
 An alternative interpretation is that the strain configurations changed recently, so that the COF near the surface has not fully adjusted to the current strain configuration. We do not prefer this interpretation because no other sites in the vicinity show radar signatures that represent temporal changes in the strain configuration. We found similar axial mismatches between the radar axis and the extension axis at sites CE3 and S-E30 (Figures 3 and 6), where the horizontal extension is significant but similar in magnitude to the other two strain rates.
6.3. Causes of Azimuthal Shifts of COF Patterns
 Orientations of radar axes change with depth in shallow ice near the crest (ice-flow divide), at sites S-E06, S-Div, and N-Div (Figures 3 and 4). These changes are interpreted as the COF patterns shown in Figure 9. Strain configurations at great depths are not necessarily consistent with those at shallow depths, especially when the bed topography is rough. Also, COF patterns are a result of the past strain configurations along the ice-particle path, so they are affected by the strain configurations upstream of the current location. Current ice-flow speeds measured at these sites show that it takes more than 2.5 k years to travel horizontally over one local ice thickness. Furthermore, the bed is reasonably smooth at these sites. Therefore, COF in the shallow ice at these sites near the crest is likely related to the local near-surface strain configuration. We argue that the observed axial rotation suggests that the local strain configuration changed in the past or has been changing. Timescales for this temporal feature are uncertain, but the ice there is likely 5–8 k years old according to a depth-age relationship obtained using a one-dimensional ice-flow model constrained by radar-detected isochronous reflectors dated with the Byrd ice core [Neumann et al., 2008].
 If the crest migrated parallel to its current direction, the flow line would not change. This would mean that the principal axes of COF and thus the radar axis would have depth-independent orientations. Therefore, azimuthal shifts of the radar axes at small depths near the crest would be more related to the flow oblique to the current flow line. Due to ice flow from the RAW summit (Figure 1), ice flows northward relative to the regional fall line at sites S-E06 and S-Div (Figure 3). This situation suggests that flow directions near the crest upstream of the WAIS Divide core site are highly sensitive to the evolution of the RAW summit. Consequently, the COF development upstream of the core site has been affected not only by the migration of the divide perpendicular to the current crest that is currently ongoing [Conway and Rasmussen, 2009] but also by the evolution of the RAW summit.
 The radar axis in the shallow ice rotates at the current dome summit N-Div, but does not rotate at sites NE and NW (Figure 4), about 15–20 km away from N-Div. We argue that rotation of the radar axis at N-Div was caused by migration of the ice dome position, but the dome summit did not migrate beyond sites NE and NW. The north flow lines cross a local ice dome that has very weak topographic control (Figure 1c). However, the radar axes in the vicinity of the dome summit are less depth-variable than those in the crest vicinity along the core-site flow line. This indicates that topography of this ice dome did not change significantly in the past. However, the ice thickness of this dome might change at a regionally uniform rate, which changes the elevation but not the flow direction.
 We found azimuthal shifts of the radar axis in deep ice at the sites S-E30 (Figure 3) and N-W30 (Figure 4) where the bed is very rough. This is not necessarily related to temporal changes in the ice-flow fields, but rather to advection through a locally complex flow field.
 Ice in the WAIS Divide area had COF contrasts strong enough to produce 179-MHz reflections at 200–500 m and 60-MHz reflections at 1000 m. At sites where the current strain configurations are relatively simple, the polarimetric features could be interpreted in COF patterns expected under the current strain configurations. Rotation of the principal axes of COF with depth was found at small depths near the current ice-flow divide (crest) and at greater depths over locations with a rough bed. These features show that COF is highly variable in central West Antarctica.
 These findings show three important consequences for the WAIS Divide evolution. First, the regionally coherent radar signatures suggest that the first-order ice properties in this area are similar, suggesting no major change in ice topography for at least the past 5–8 k years. However, the data allow the possibility of very recent changes of the ice topography within the past millennium because accumulated strain over this period is too small for COFs to have fully adjusted to a new strain configuration. Second, the ice-flow divide has migrated non-uniformly, causing the azimuths of the COF patterns to shift at sites near the current ice-flow divide. The flow line through the core site has been affected by the evolution of the RAW summit that separates ice flow toward Ross, Amundsen, and Weddell Seas. This means that the core site may have a non-steady flow line. This result is consistent with the absence of upward-arch reflectors along the core-site flow line [Matsuoka et al., 2010; Neumann et al., 2008]. This absence suggests that either the divide has migrated more than several ice thicknesses (∼3 km) and/or the bed is highly lubricated. Third, because of a relatively smooth bed underneath it, the ice dome north of the core-site flow line has migrated within about 15 km from the current summit position. It is crucial to learn the migration history of local ice domes near the crest because migration can change the flow line significantly.
 Remote radar-based reconstructions of ice fabric can provide useful information relating to the 3D strain and strain history of ice sheets. However, the current method of englacial radar polarimetry is unable to address details of COF structures. Phase-sensitive radar is a viable tool to separately measure effects of birefringence (phase) and anisotropy in the reflectivity (power). A formal inverse approach could more quantitatively extract effects of COF and other ice properties (density, acidity, and temperature) from the radar data. Radar and seismic surveys, thin sections sampled from ice cores, and acoustic logging along ice core holes are established tools of COF measurements. Reconciling these methods is crucial to further develop methods to remotely measure all aspects of COF in a wide area, which helps assessing ice sheet evolution and heterogeneity of the present-day rheology of ice.
 U.S. National Science Foundation funded this work (ANT-0440847 and ANT-0944199). Most radar instruments used in this study were provided by National Institute of Polar Research, Tokyo. The radar-data recording system was developed primarily by Pavan Vaswani, as a part of his undergraduate summer research program at the University of Washington, which was partly supported by a Washington NASA Space Grant. We also thank P. Braddock, M. Conway, R. Eastman, L. Hormen, J.A. MacGregor, H.C. Steen-Larsen, and V. Palmer for assistance in the field, UNAVCO for GPS support, and Raytheon Polar Services, Air National Guard, and Ken Borek Air for logistical support. Discussion with H. Conway and A. Rasmussen improved the paper, and comments from Bryn Hubbard (Editor), Jeremy Bassis (Associate Editor), Edward King (reviewer), and two anonymous reviewers improved the paper.