This work assessed an ice core drilled at DF, one of the major dome summits in East Antarctica (see Fig. 1), located at 77∘19′ S, 39∘42′ E, with an elevation of 3800 m. The annual mean temperature at this location is -54.4 ∘C, the annual accumulation rate is 27.3 ± 1.5 kg m-2 yr-1 and the ice thickness is 3028 ± 15 m (Dome Fuji Ice Core Project Members, 2017). Figure 1b demonstrates that the ice coring site was very close (within 10 km) to the present dome summit. At present, under the Holocene climate, DF is associated with a steep north-south surface mass balance gradient (Fujita et al., 2011; Tsutaki et al., 2022). We suggest that this morphology demonstrates that the DF summit has migrated along this gradient in the north-south direction during glacial and interglacial periods over which the accumulation rate changed dramatically (e.g., Parrenin et al., 2016). Very deep ice cores were drilled twice at DF. The first 2503 m long core (DF1 ice core) was drilled between 1993 and 1997 (e.g., Watanabe et al., 1999) while the second 3035 m long ice core (DF2 ice core) was drilled between 2004 and 2007 (Motoyama et al., 2007; Dome Fuji Ice Core Project Members, 2017). Note that the DF1 and DF2 boreholes are only 48 m apart. We used the DF2 core in our study, but it should be noted that Azuma et al. (1999, 2000) used a thin-section method to conduct COF studies with the DF1 core. In contrast to this prior study, the present work employed the thick-section-based method to examine the DF2 core at 5 m intervals between the depths of 100 and 2400 m. At each sampling depth, we continually assessed a 1 m (comprising two sections of 0.5 m ) long ice core with a 0.02 m step size. Consequently, this work examined approximately 20 % of the entire ice core. Each ice core sample was approximately 0.5 m long and was formed into a slab shape with a thickness of 68–79 mm and width of 53–62 mm. A diagram of the core cutting geometry is shown in Fig. 2a. In the case of specimens acquired between 600 and 870 m, the slab thicknesses were approximately 33–38 mm. Each sample was effectively a cylinder penetrated by the microwave beam having a diameter of 38 mm and a thickness of 33–79 mm. In this study, we focus on COF development within the upper 80 % of the ice thickness, meaning depths of up to 2400 m within the 3028 (± 15) m thick ice sheet (Fujita et al., 1999). The age of the ice to a depth of 2400 m was approximately 300 kyrs BP. Note that interpretation of the COF data obtained from dielectric measurements is challenging below 2400 m due to the presence of inclined layers and extremely coarse crystal grains. At these depths, the layered structures begin to incline relative to the horizontal plane, with inclinations of less than 5∘ above 2400 m but much larger values of 20 and 50∘ at 2800 and 3000 m, respectively (Dome Fuji Ice Core Project Members, 2017). Additionally, visual inspection of the samples showed extremely large coarse grains (with grain sizes > 50 cm) in samples from the deepest part of the dome. The effects of these factors should be confirmed by future research but, for the present, we restricted our analyses to a depth of 2400 m for these reasons. The COF development within the bottom 20 % of the ice thickness (from 2400 m to the ice sheet bottom) will be reported elsewhere.

The Δε values for ice cores were determined using an open microwave resonator, employing frequencies between 14 and 20 GHz (Saruya et al., 2022). The operating principle and applications of the open resonator method with respect to obtaining relative permittivity values have been previously described in the literature (Jones, 1976a, b; Cullen, 1983; Komiyama et al., 1991). Using this system, we developed a means of performing continuous measurements of thick slab samples. The present research constructed a semi-confocal type of open resonator incorporating a flat mirror and a concave mirror having a 250 mm radius of curvature, set 225 mm apart. A diagram of the experimental set-up is provided in Fig. 2b. A microwave beam having a Gaussian profile was generated with a half-power diameter of 38 mm. The ε values obtained in this work were volume-weighted averages within the volume covered by the Gaussian distribution of the beam. When the angle between the core axis and the electric field was set to 45∘, radio birefringence was observed, i.e., when the frequency was swept to detect resonances that corresponded to transverse electromagnetic (TEM) 0,0,q modes (where q is an integer), two resonance peaks resulting from anisotropic permittivity components were detected. The two radio birefringence components corresponded to the ε values in the horizontal and vertical directions within the core. Because each ice crystal is uniaxially symmetric around its c axis with respect to ε, the degree of c axis clustering around the vertical direction could be evaluated by measuring the macroscopic ε values both parallel and perpendicular to the ice core axis (e.g., Hargreaves, 1978). In this work, we measured ε continuously by moving the ice core sample using an automatic motor. These analyses were conducted at temperatures in the range of -30 ± 1.5 ∘C.

Figure 3 presents typical examples of the continuous variation of Δε along 0.5 m core samples, based on ice core samples acquired at depths of 125.0–125.5 m, 1300.0–1300.5 m and 2398.5–2399.0 m. The span of the y axis equals the dielectric anisotropy of a single ice crystal (0.0334) at -30 ∘C (see Saruya et al., 2022). Small fluctuations of Δε over distances from 0.02 m to 0.5 m are apparent, indicating minor but significant variations in the COF within each 0.5 m long piece of ice core. The mean values and standard deviations for each 0.02 m long portion were derived based on different TEM 0,0,q resonance modes using the open resonator method. In the case of the example data presented in Fig. 3, the mean values (standard deviations) were 0.0076 (0.0005), 0.0194 (0.0006) and 0.0300 (0.0005) for the 125.0 m, 1300.0 m and 2398.5 m depth samples, respectively.

Figure 4 shows the variations in the mean Δε values (Fig. 4a), the standard deviations (SD) of Δε values (Fig. 4b), the detrended Δε values (defined as the difference between each data point and the third-order polynomial fitting curve to the Δε data; Fig. 4c), and the oxygen isotope ratio values (δ18O; Fig. 4d). The latter data were obtained from Dome Fuji Ice Core Project Members (2017). The mean values and SD were determined at intervals of approximately 0.5 m along the core sample, using approximately 23 data points for each interval. The detrended Δε data represent the relative degree of c axis clustering and the extent of deformation relative to those in the surrounding depth. These detrended values are more useful than the original values as a means of assessing fluctuations in the COF and for comparison with other physicochemical properties.

Figure 4a demonstrates that the overall trend of the Δε values increase with increasing depth, although small fluctuations are evident within a length scale of approximately 100 m. These variations in Δε also appear to be continuous rather than abrupt. Large decreases in Δε are also apparent at depths of 1800, 2150 and 2300 m as indicated by the three arrows in Fig. 4a. The depths of 1800 and 2300 m correspond to the transition periods from glacial to interglacial, while the depth of 2150 m corresponds to Marine Isotope Stage (MIS) 7a, b, c. At shallower depths above approximately 300 m the Δε values are instead relatively constant and the detrended Δε values are larger than the general mean of the data.

Figure 4b indicates that the SD values for each approximately 0.5 m long core sample exhibit both a long-term trend and short-term fluctuations. Over the whole dataset, the SD are approximately constant down to a depth of about 1300 m but then increase between that point and 1800 m. During the termination II event, the SD values exhibit a rapid decrease while below 2000 m large increases appear at approximately 2150 and 2300 m, and a decrease in SD is also seen during the termination III event. The variations in the detrended Δε values in Fig. 4c reflect the fluctuations noted above. In this panel, the gray shading indicates three periods, from the early stage of each interglacial period to the termination event. In this plot, positive/negative values indicate a high/low degree of c axis clustering relative to the regression line in terms of depth, as a consequence of specific mechanisms. The amplitude of these fluctuations becomes larger at greater depths. As an example, the amplitude at shallow depths (< 500 m) is approximately 0.001, while that at greater depths (> 1800 m) is 0.003.

In previous studies, COF development was examined based on variations in the normalized eigenvalues a1(2), a2(2) and a3(2). To allow a direct comparison with other ice cores, we therefore derived normalized eigenvalues from the present Δε data. The magnitude of a3(2) indicates the extent of clustering of the c-axes toward the vertical that is the same as the core axis. In fact, the value of a3(2) has been shown to increase with increasing depth in ice cores drilled at dome summits due to c axis clustering. Saruya et al. (2022) reported that the relationship between Δε and these eigenvalues is: 1Δε=Δεsa3(2)-a1(2)+a2(2)/2.

Here, Δεs is the dielectric anisotropy of a single ice crystal. In the case of the present measurements at -30 ∘C, Δεs was determined to be 0.0334 (see the Appendix in Saruya et al., 2022). Using the relationship a1(2)+a2(2)+a3(2)=1 and assuming that a1(2) and a2(2) are approximately equal (that is, horizontal isotropy), Eq. (1) can be rewritten as: 2a3(2)=2Δε/Δεs+1/3.

Using these equations, we were able to derive the eigenvalues from the Δε data. Assuming that the approximation noted above is valid, the normalized eigenvalues obtained from earlier COF studies could then be directly compared with Δε data derived using our newly developed method that we present here. Figure 5 provides such a comparison between eigenvalues estimated from Δε and those generated using an optical method on the basis of the DF1 core samples (modified from Azuma et al., 2000). Here, the black and red lines indicate dielectrically derived (i.e., thick-section-based) and optically derived (i.e., thin-section-based) values, respectively. In Fig. 5a, we compare the thick-section-based Δε and thin-section-based eigenvalue anisotropy values defined as Δa(2)=a3(2)-(a1(2)+a2(2))/2. Figure 5b compares the normalized eigenvalue components obtained from the thick-section-based and thin-section-based approaches. In both panels, the fluctuations of the thick-section-based eigenvalues and the anisotropy are smaller than those of the corresponding thin-section-based values.

Since the thin-section-based eigenvalues were determined using sections with thicknesses of approximately 0.5 mm, the normalized eigenvalues reflect the statistically averaged c axis clustering of several hundred to thousands of ice grains. In contrast, a single thick-section-based Δε data point is representative of an ice specimen as thick as 33–79 mm. Therefore, the sampling volumes between the two methods differ by a factor of 85–190. In addition, the thick-section-based eigenvalues presented here are the averaged values for each 0.5 m long core, meaning that the sampling volumes actually differ by more than three orders of magnitude. Thin-section measurements can provide information regarding localized distributions of c axis orientations for each grain within thin-sections, while thick-section measurements indicate the COF characteristics on a bulk scale. An obvious difference between the thick-section-based and thin-section-based eigenvalues is the size of the fluctuations and the continuity of the data distributions. Specifically, the thin-section-based eigenvalues exhibit sudden fluctuations well above 0.1 within many depth ranges that are not observed in the thick-section-based eigenvalues. Figure 6 presents a modified version of the comparison in Fig. 5a based on a direct comparison between Δε values for each 0.02 m interval and thin-section-based eigenvalue anisotropy data. Even using the raw Δε data without averaging over each 0.5 m long ice core, the scatter of the thin-section-based eigenvalue anisotropy values is typically far greater.

Figure 7 plots the variations in the eigenvalues for the horizontal direction derived from the thick-section-based measurements (i.e., a1(2) or a2(2) as shown in Fig. 5b). The right axis indicates the permittivity values corresponding to the normalized eigenvalues on the left axis.

Saruya et al. (2022) reported the relationship εx=ε⊥+Δεs a1(2), where εx is the relative permittivity along the principal x axis and ε⊥ is the permittivity perpendicular to the c axis. Thus, if εx and εy (the relative permittivity along the principal y axis) are approximately equal, these permittivity components will vary over the range of Δεs a1(2). The eigenvalue a1(2) changes from 0 to 1 while Δεs=0.0334. A value for ε⊥ of 3.1367 is also provided in the appendix to Saruya et al. (2022). Using this relationship, we can compare eigenvalues and permittivities.

The size and fluctuation of the horizontal eigenvalue is directly related to the magnitude of the permittivity, and thus to the refractive index or speed of radio waves within the ice sheet. In addition, the fluctuation size and the change in fluctuation with depth provide reliable information concerning the magnitude of ice-fabric-based radio wave reflections within the ice sheet. Specifically, ε changes as small as 0.002 (the typical magnitude of changes below approximately 1500 m) are sufficient to cause internal radio echo reflections (with strengths of approximately -75 dB) that are detectable by ice radar instrumentation (e.g., Fig. 1 in Fujita Fujita and Mae, 1994 and Fig. 10 in Fujita et al., 2000). Thus, the large depressions of Δε as well as the small-scale fluctuations in Δε should be detectable using ice sounding radar (Fujita et al., 1999).

Figure 8 summarizes the development of the normalized eigenvalues a3(2) along the DF2, DF1 and EDC ice cores. Here, we use the normalized eigenvalues instead of Δε values, and the magnitude of a3(2) reflects the degree of c axis clustering toward the core axis, just as Δε does. The DF1 and EDC data are from Azuma et al. (2000) and Durand et al. (2009), respectively, and are derived from thin-section measurements. Note that the glaciological conditions in DF and EDC are similar. The ice thickness, annual accumulation rate and mean surface temperature values for DF are 3028 ± 15 m, 27.3 ± 1.5 kg m-2 yr-1 and -54.4 ∘C (Dome Fuji Ice Core Project Members, 2017) while those for EDC are 3309 ± 22 m, 25 ± 1.5 kg m-2 yr-1 and -54.5 ∘C (EPICA Community Members, 2004). The conversion from depth to age was performed using the Supplement in Bazin et al. (2013) and Dome Fuji Ice Core Members (2017). The general data trend is the same for both cores, in that the a3(2) values increase with increasing depth. However, the small fluctuations over spans of less than 10 kyrs are different. Durand et al. (2007) reported a rapid increase in c axis clustering along with a decrease in grain size during the termination II event (i.e., the transition from interglacial to glacial) in the EDC ice core. In contrast, such variations were not observed in the case of the termination I event. This difference was attributed to a transition to enhanced horizontal shear in the glacial ice in conjunction with the termination II event, although our own view is different. Durand et al. (2007) did not report a change in association with the termination III event, but a possible strengthening of c axis clustering does appear at this point. Durand et al. (2007) also suggested that a 60 m thick layer indicating reduced clustering of the c-axes exists below 1680 m (approximately 125 kyrs BP) and corresponds to the MIS5e event. In the data of Durand et al. the local minimum in the degree of c axis clustering was accompanied by a local maximum in the deuterium concentration. It should also be noted that the variation trends observed at the termination II/MIS5e and termination III/MIS7e events in the EDC core were approximately the same as those in our measurements.

Although glaciological conditions (such as surface temperature, accumulation rate and ice thickness) are similar at the EDC and DF, the development of COF within the DF1 ice core (as determined using thin sections) is inconsistent with those in the EDC core and with our own analysis of DF2 core samples. As stated in Sect. 3.3, the limited statistical reliability of the thin-section-based method prevents a reliable comparison.

The growth of the variation amplitude associated with the Δε fluctuations provides insights into the nature of the deformation process. In the case of the type A relationships, the depressions in Δε are small within the AI region but deeper at AII, A7 and AIII. These results demonstrate that contrasting rheology was preserved all the way to deeper layers, so that the extent of clustering was weak compared with the surrounding layers. An initial shear strain would be expected to promote further deformation of the COF, because the ice would be softer due to a positive feedback mechanism (Azuma, 1994). At very shallow depths, at which the COF is almost random, the c-axes start to rotate toward the compressional axis as deformation progresses. In this early stage, the rotation of these c-axes in this manner increases the density of slip planes close to the plane of maximum shear stress (45∘ from the compressional axis). This deformation enhancement is temporarily higher than that of the initial random fabric, such that the initial deformation softens the ice in a positive feedback loop. In contrast, as the fabric continues to develop, the ice becomes harder as these c-axes rotate closer to the compressional axis. In the case of the majority of the crystal grains, the slip planes will tend to rotate away from the plane of maximum shear stress and so the ice will become progressively harder in a negative feedback loop. However, we note that the present rheology contrasts were not caused by positive feedback of the rheology due to the COF. In the case of vertical compression such as occurs at DF, the COF-based enhancement factor increases slightly during the very initial stage of deformation, after which the enhancement factor monotonically decreases (Azuma, 1994). The positive detrended Δε values indicating enhanced c axis clustering are attributed to restrictions of dislocation movement with increased deformation due to the work hardening resulting from dislocation pile-up. Therefore, excessive deformation and c axis clustering is limited even in layers with high levels of Cl- ions. In contrast to the type A relationships, the depressions associated with type B relationships are minimal regardless of the depth or age, suggesting the absence of feedback mechanisms in the case in which the DF is subjected primarily to vertical compression.

At the point of bubble close-off, where the transition from firn to ice occurs (approximately 100 m in depth), Δε is already about 0.008, which is approximately 25 % of the value for a single ice crystal (Saruya et al., 2022). In fact, Δεvalues of this magnitude have also been observed at the base of the firn (i.e., at the top of the bubble-containing ice; Fujita et al., 2009, 2014, 2016). At this depth in DF, there is almost no contribution of the dielectric polarization effect due to the vertical elongation of pore spaces and the ice matrix (Fujita et al., 2009). X-ray diffraction analyses of the DF firn have also demonstrated that the COF c-axes tend to cluster around the vertical direction or become inclined near this bubble close-off horizon depending on the sample (Fujita et al., 2009). More recently, similar results showing a stacked layer COF pattern were reported in snow within a 2 m deep pit at a plateau site in East Antarctica (Calonne et al., 2017). Going from the top to the bottom of the firn, a sequence exhibiting typical deformation phenomena was observed (Fujita et al., 2016), with variations in density, impurity concentration and dielectric properties as well as in the correlations between these parameters (see Table 7 in Fujita et al., 2016). It is therefore likely that Δε at a depth of approximately 100 m represents a superposition of the initial COF caused through metamorphism at the near-surface depth and subsequent metamorphism and deformation of the firn. This initial phenomenon is likely to be greatly affected by the presence of Cl- ions and dust particles because vertical deformation of the ice is dominant in firn. Because Cl- ions have the greatest effect on the densification of firn (Fujita et al., 2016), we suggest that these ions are among the main factors determining the depth of the transition from firn to bubble-containing ice, known as the lock-in depth (LID). It is also likely that the Δε values along deep ice cores are valuable indicators that can be used to determine the timescale of the LID in detail. In addition, these Δεvalues will be directly correlated with the vertical thinning of each layer and so can be extremely useful as a means of refining ice core dating models and providing constraints on strain values. Because both the LID and vertical thinning are related to the strain rate enhancement caused by the COF, the presence of Cl- ions and the temperature of the ice, it is apparent that the variations in the LID over time and the cumulative vertical thinning in each layer should be closely related. This possibility should be examined in future studies.

The evolution of the COF clustering strength was investigated herein based on variations in Δε. On this basis, we suggest that the five questions posed in Sect. 4.1 can be answered as follows. i.

The factors determining the time-dependent and depth-dependent variations of COF clustering are the initial microstructural conditions that occur at near-surface depths, the degree of deformation within the firn, the levels of ionic impurities that promote dislocation movement throughout the deformation processes and the amount of dust particles that tend to impede clustering. Because vertical compression is a major component of deformation, the positive and negative feedback effects of deformation enhancement associated with COF evolution will not play a major role other than to provide weak positive feedback during the very initial stage of deformation and weak negative feedback in the later stage of deformation (Azuma, 1994).