Development of crystal orientation fabric in the Dome Fuji ice core in East Antarctica: implications for the deformation regime in ice sheets

. The crystal orientation fabric (COF) of a polar ice sheet has a significant effect on the rheology of the sheet. With the aim of better understanding the deformation regime of ice sheets, the work presented here investigates the present work 15 investigated the COF in the upper 80% of the depth within the 3035 m long Dome Fuji Station ice core drilled at one of the dome summits in East Antarctica. Dielectric anisotropy ( De ) data were acquired as a novel indicator of the vertical clustering of COF resulting from vertical compressional strain within the dome. at which the ice cover has an age of approximately 300 kyrs BP, The De values were found to exhibit a general increase with depth moving in the depth direction, but with fluctuations over distances on the order of 10-10 2 m. In addition, significant decreases in De were found to be associated with depths 20 corresponding to three major glacial to interglacial transitions. These changes in De are ascribed to variations in the deformational history caused by dislocation motion occurring from near-surface depths to deeper layers. Fluctuations in De over distances of less than 0.5 m exhibited a strong inverse correlation with De at depths greater than approximately 1200 m, indicating that they were enhanced during the glacial/interglacial transitions. The De data also exhibited a positive correlation with the concentration of chloride ions and together with an inverse correlation with the amount of dust particles in the ice 25 core at greater depths corresponding to decreases in the degree of c -axis clustering. Finally, we found that fluctuations in De persisted to approximately 80% of the total depth of the ice sheet. These data suggest that the factors determining the deformation of ice include the concentration of chloride ions and the amount of dust particles, and that the layered contrast associated with the COF is preserved all the way from the near-surface to a depth corresponding to approximately 80% of the thickness of the ice sheet. These findings provide important implications regarding further development of the COF under the 30 various stress-strain configurations that the ice will experience in the deepest region, approximately 20% of the total depth from the ice/bed interface. core samples taken from Dome Fuji in East Antarctica. This method is a useful means of determining the degree of COF vertical clustering resulting from vertical compressional strain at the dome. The present investigation covered the upper 80% 600 of the entire dome thickness, from depths of 100 to 2400 m, representing an ice cover to an age of approximately 300 kyrs BP. Examining thick, 1-m long ice core specimens acquired at 5 m intervals, this study was able to generate high-resolution COF data. Compared with to existing thin-section-based methods, the new method described herein provided information with greatly improved statistical significance. The major findings of the present study can be summarized as follows.


Introduction
The crystal orientation fabric (COF) is one of the most important factors determining the physical properties of polar ice sheets, 35 as both the deformation and flow of ice sheets are highly dependent on the COF. It is commonly accepted that dislocation creep is the dominant deformation process in polar ice sheets (e.g., Cuffey and Paterson, 2010;Petrenko and Whitworth, 1999).
In addition, in the dome summit regions of ice sheets, the vertical compressional stress imparted by the mass of the ice is the primary deformation stress. In such cases, the c-axes of the ice crystal grains rotate toward the compression direction and the sections has yet to be established. As an example, even when evaluating the same samples taken from the EDC Antarctic ice core, two independent groups determined different COF eigenvalues (Wang et al., 2003;Durand et al., 2007Durand et al., , 2009. It is also important to eliminate possible biases and errors resulting from the use of automatic fabric analysers. In short, thin-sectionbased methods have inherent limitations related to obtaining statistically significant data. Consequently, it has thus far been 70 challenging to examine small fluctuations in the COF or to compare COF data generated using different algorithms (e.g., Wang and Azuma, 1999;Wilen et al., 2003;Wilson et al., 2003).
To overcome these limitations, Saruya et al. (2022) proposed a technique that permits the continuous non-destructive and rapid assessment of the COF in thick ice sections, based on measuring the tensorial components of the relative permittivity, e, using microwave open resonators. In this process, the difference in e between the vertical and horizontal planes is defined as the 75 dielectric anisotropy, De. Saruya's group demonstrated that De is a direct substitute for the normalized COF eigenvalues when assessing thick sections. Compared to thin-section-based methods, this technique provides COF data with greatly improved statistical significance.
In the present study, we applied this thick-section-based method to an investigation of the COF within an approximately 2300 m long portion of the DF ice core drilled at one of the major dome summits in East Antarctica. The De values in this sample 80 were measured at 0.02 m intervals in 1 m long ice core specimens acquired every 5 m at depths from 100 to 2400 m. The resulting data were compared with the profiles of various physicochemical parameters, such as major ions, dust particles, salt inclusions and grain sizes, obtained from analyses of the DF ice core. The goal was to better understand the factors influencing COF development. Based on the results, we discuss the possible causes of COF variations, as well as flow mechanism contrast within ice sheets. This paper also discusses the implications for further deformation of the ice in these locations under specific 85 conditions, including the very deep part of the ice sheet near the ice/bed interface. Comparison of sampling intervals and dimensions (width × height × thickness) for each ice core. The sample width in the present study indicates the half-power diameter of the Gaussian beam. Although the precise thicknesses of thin sections are not provided in Wang et al. 90 (2003) or Durand et al. (2007Durand et al. ( , 2009 ( 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 from the depths of 100 and to 2400 m. from 100 m to a depth of 2400 m. At each sampling depth step, we continually assessed a 1 m (comprising two 0.5 m sections) long ice core with a 0.02 m step size. Consequently, 110 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 115 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 120 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.

Dielectric anisotropy measurements
The De 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 regard 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 130 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 setup is provided in Fig. 2b. A microwave beam having a Gaussian profile was generated with a half-power diameter of 38 mm. The e values obtained in this work were volumeweighted 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. That is, when the frequency was swept to detect 135 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 e values in the horizontal and vertical directions within the core. Because each ice crystal is uniaxially symmetric around its c-axis with respect to e, the degree of c-axis clustering around the vertical direction could be evaluated by measuring the macroscopic e values both parallel and perpendicular to the ice core axis (e.g., Hargreaves, 1978). In this work, we measured 6 e 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.

Eigenvalues derived from De
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 De 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. 200 Saruya et al. (2022) reported that the relationship between De and these eigenvalues is: De = Des (a3 (2) -(a1 (2) + a2 (2) ) / 2). (1) Here, Des is the dielectric anisotropy of a single ice crystal. In the case of the present measurements at -30 °C, Des 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), equation (1) can be rewritten as: 205 Using these equations, we were able to derive the eigenvalues from the De data. Assuming that the approximation noted above is valid, the normalized eigenvalues obtained from earlier COF studies could then be directly compared with De data derived using our newly developed method that we present here. our present newly developed method. Figure 5 provides such a comparison between eigenvalues estimated from De and those generated using an optical method on the basis of the DF1 core 210 samples (modified from Azuma et al., 2000). Here, the black and red lines indicate dielectrically derived (that is, thick-sectionbased) and optically derived (that is, thin-section-based) values, respectively. In Fig. 5a panel (a), we compare the thicksection-based De and thin-section-based eigenvalue anisotropy values defined as ∆a (2) = a3 (2) -(a1 (2) + a2 (2) )/2. Figure 5b Panel (b) 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 215 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 De 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 220 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-and thin-section-based eigenvalues is the size of the fluctuations and the continuity of the data distribution. Specifically, the thin-section-based eigenvalues exhibit sudden fluctuations well above 225 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 De values for each 0.02 m interval and thin-section-based eigenvalue anisotropy data. Even using the raw De 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 230
(that is, 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 ex = e⊥ + Des a1 (2) , where ex is the relative permittivity along the principal x axis and e⊥ is the permittivity perpendicular to the c-axis. Thus, if ex and ey (the relative permittivity along the principal y axis) are approximately equal, these permittivity components will have vary over the variable range of as Des a1 (2) . The eigenvalue a1 (2) 235 changes from 0 to 1 while Des = 0.0334. A value for e⊥ 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 240 sheet. Specifically, e changes as small as 0.002 (the typical magnitude size of changes at depths deeper than ~ below approximately 1500 m) are sufficient to cause internal radio echo reflections (with strengths of approximately about -75 dB) that are detectable by ice radar instrumentation (e.g., Fig. 1 in Fujita et al., 1994 andFig. 10 in Fujita et al., 2000). Thus, the large depressions of De as well as the small-scale fluctuation in De should be detectable using ice sounding radars (Fujita et al., 1999). 245  The scatter of the thin-section-based data (red symbols and lines) is far larger than that of the thick-section-based data. Figure 7. Eigenvalues in the horizontal direction derived from dielectric measurements (that is, a1 (2) or a2 (2) in Fig. 5b). The right-side yaxis is the permittivity corresponding to the eigenvalue on the left-side y-axis. See Saruya et al. (2022) for the relationship between the normalized eigenvalues and permittivity. Corresponding ε 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 De values, and the magnitude of a3 (2) reflects the degree of c-axis clustering toward the core axis, just as De does. The DF1 and EDC data are from Azuma et al. (2000) and Durand et al. (2009), respectively, and 265 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 year -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 year -1 and -54.5 °C (EPICA Community Members, 2004). The conversion from depth to age was performed using Supplemental Materials 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 270 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 (that is, 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 275 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 Durand's data, 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 280 as those in our measurements.

255
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 Section 3.3, the limited statistical reliability of the thinsection-based method prevents a reliable comparison. 285

Basic facts and questions
As a basis of for the present discussions, we first need to determine if the observed variations in De are significant or simply the result of measurement error. Saruya et al. (2022) reported that such errors were minimized by solving equations for multiple 295 resonance frequencies simultaneously to find a unique solution for e. They determined the total error in e to be -0.01 ± 0.01, and this systematic error was primarily attributed to the limited widths of the ice core samples. The data show dielectric anisotropy in the horizontal direction (that is, perpendicular to the core axis) in addition to the vertical direction, which is a potential source of error when determining the depth-dependent variation of De (Saruya et al., 2022). The COF in the DF ice core exhibits so-called single pole fabric characteristics. However, as a result of an imbalance in the strain in the horizontal 300 directions, this single pole fabric shows elliptically elongated distributions (Azuma et al., 1999(Azuma et al., , 2000Saruya et al., 2022). Saruya et al. (2022) reported that the error in De could be as large as 10-15% in extreme cases based on accidental core rotation occurring in conjunction with irregular core breaks at the drilling site. According to Saruya et al. (2022), accidental core rotation is a rare event that can occur a few or several times within every 1000 m length of the core. In addition, the probability of the maximum error (that is, 10-15% of De) is small. In the case of accidental (that is, abrupt) rotation of the ice core, the mean value of the error will be half the maximum. Thus, the data must be examined to identify any suspiciously abrupt steps/jumps in De. One such inspection within the brittle zone between 600 and 900 m identified suspicious abrupt changes in De values at depths of 750 and 800 m. Because the ice core samples in this zone are sometimes brittle, the continuity of the core in terms of core orientation could have been broken. These abrupt changes in De could have therefore resulted from accidental core rotation. In contrast, the De values at other depths were found to change continuously, without any anomalous 310 steps/jumps. On this basis, with the exception of the brittle zone, we believe that the evident variations in De are true reflections of continuous changes in COF development, and that the present data contain only minor systematic errors in De, the magnitude of which changes at several depths. We also note that the S.D. values for the De data were only minimally affected by possible rotations of the core. Saruya et al. (2022) have shown that changes in cluster strength occur simultaneously in all horizontal orientations. 315 Complex permittivity data obtained for ice based on analyses using MHz megahertz frequencies were reviewed by Fujita et al. (2000). The real part of the complex permittivity of the ice in ice sheets is a function of the COF as well as the density, the concentration of soluble impurities (primarily acidic impurities) and the temperature. In contrast, both the hydrostatic pressure and the shape of air bubbles have relatively minor effects. In addition, the effect of plastic deformation can be significant and needs to be investigated further. What we are interested in here is whether or not some factors other than COF can modify the 320 anisotropic values of permittivity.; Iin the case of ice containing bubbles, the density, soluble impurity concentration and temperature do not modify the dielectric anisotropy (Fujita et al., 2000). Thus, COF is the only factor responsible for anisotropic permittivity in the polycrystalline ice in the ice sheet. In addition, to date, grain boundaries, dust inclusions, clathrate hydrate inclusions or salt inclusions in ice have not been shown to produce detectable changes in permittivity.
It is also important to note that the De values were fully compatible with the normalized COF eigenvalues assuming a single 325 pole fabric with c-axis clustering along the vertical direction (Saruya et al., 2022). Therefore, the degree of clustering can be expressed using De instead of the normalized COF eigenvalues for the sake of simplicity. The overall trend of the De values was to increase down to a depth of 2400 m (Fig. 4a). This trend was consistent with previous findings that the degree of c-axis clustering is strengthened at greater depths within the dome summits of ice sheets, as described in the Introduction (Sect. 1) to this paper. This large-scale trend is explained primarily by the rotation of the c-axes toward the compressional axis associated 330 with dislocation creep. The data also indicate continuous variations within depth scales on the order of 10 to 10 2 m. In particular, the three depressions indicated by arrows in Fig. 4a at depths corresponding to interglacial/glacial transitions at approximately 1800 and 2300 m and to the MIS7abc event at 2150 m are significant. These results raise many questions and it would be helpful to identify the following: (i) the factors controlling variations associated with changes in time and depth, either initial microstructural conditions, effects of impurities that modify dislocation movements and/or microstructure, positive/negative 335 feedback effects from COF evolutions, or a complex mixtures/interplay of these, (ii) the reasons for the increased fluctuating amplitude of De over depth scales on the order of 10 to 10 2 m with increasing depth, (iii) the reasons for the increase in the S.D. of De values with increasing depth, (iv) the further growth of these variations under shear and at deeper englacial environments, and (v) as to how we can means of applying our new understanding of at DF to wider range of ice sheets.
Answering these questions may lead us to a better understanding of ice rheology. 340

Comparison of De with physicochemical properties in the DF ice core 355
To address the questions raised in Section 4.1, we attempted to establish correlations between the detrended De values and impurities and crystal grain size data acquired for the DF1 ice core. These factors could possibly affect the behaviour of deformation (e.g., Paterson, 1991;Cuffey et al., 2000;Cuffey and Paterson, 2010;Fujita et al., 2014Fujita et al., , 2016Saruya et al., 2019).
It is known that glacial ice includes many soluble impurities as well as dust particles. Furthermore, glacial ice exhibits finer grains and more rapid deformation (that is, a large value of the flow-enhancement factor) in comparison with interglacial ice 360 (e.g., Paterson, 1991). However, the direct influence of these factors on COF development is unclear.

Effect of chloride ions 395
Various soluble impurities, including Cl -, SO4 2and Ca 2+ ions, have been examined in terms of their deformation enhancement effect (e.g., Nakamura and Jones, 1970;Hörhold et al., 2012;Freitag et al., 2013;Hammonds and Baker, 2018). However, the depth-dependent variations of Cl -, SO4 2and Ca 2+ ions are similar, therefore so that it is difficult to identify the most important ion species from the time-dependent profiles. The correlation coefficients between the detrended De values and the Cl -, SO4 2and Ca 2+ concentrations were determined to be 0.21, 0.16 and 0.21, respectively (as estimated from data extracted at 5 m 400 intervals between 130 and 2400 m, n = 455). However, to the best of our knowledge, only Cl -, Fand NH4 + ions have been shown to modify the dislocation movement (including the dislocation density) within the ice crystal lattice when substituted for H2O molecules (Jones, 1967;Jones and Glen, 1969;Nakamura and Jones, 1970). Fujita et al. (2014Fujita et al. ( , 2016 hypothesized that layered deformation in firn results from a combination of the texture initially formed by seasonal variations in metamorphism and the effects of ions such as Cl -, Fand NH4 + . The same group also attributed high correlations between the 405 concentration of Ca 2+ ions and deformation (reported by Hörhold et al., 2012;Freitag et al., 2013) to seasonal synchronization with cycles of Cl -, Fand NH4 + ions and seasonal variations in metamorphism. Although data regarding Among these Cl -, SO4 2and Ca 2+ ions are included that we show in Fig. 10e, we suggest that only Clions have has the effect of softening the ice, while SO4 2and Ca 2+ do not play any direct role in terms of substitution for H2O molecules. Typically, the concentration of Clions is much higher than those of Fand NH4 + ions in Antarctic ice cores (e.g., Udisti et al., 2004), and so the present 410 study that we focuses on the concentration of Clions in this study. Dissolved and substituted Clions can increase the dislocation (point defect) density in ice and promote dislocation movement, which in turn will result in active plastic deformation and c-axes clustering. Therefore, the Ttype A relationship could be explained by variations in the level of Clions in the ice. It should also be noted that the distribution of Clions in firn and ice is readily homogenized by various diffusion mechanisms taking place in the solid, liquid or vapour phase (e.g., Barnes et al., 2003). In such cases, rather than the 415 development of layered, heterogeneous deformation, the Clions would be expected to promote the homogeneous deformation of the firn and ice . This effect explains the aspect of the Ttype A relationship in which limited the reduced c-axes clustering brought about by the dust particles was evidently more powerful than the deformation 450 enhancement resulting from the Clions.
We suggest two possible reasons for reduced c-axis clustering:. (i) These are restricted deformation due to the dislocation inhibition effect of dust particles and (ii) the various mechanisms that contribute to deformation (other than dislocation creep).
In the first case, if the deformation In the case of the first reason above, if the deformation of an ice sheet proceeds solely via dislocation creep, weak c-axis clustering indicates that the degree of deformation must be impeded by dust particles. The 455 hardening of artificial polycrystalline ice following the addition of high concentrations of sand particles was reported by Hooke et al. (1972), who suggested that sand particles surrounded by tangled networks of dislocations impeded dislocation movement.
This effect could restrict both deformation and c-axis clustering. In the second case, deformation In the case of the second point, deformation mechanisms other than dislocation creep could contribute to deformation, with smaller crystal grains in Ttype B relationships being a potential cause of reduced COF clustering. In one example, Azuma et al. (2000) proposed that 460 the weakening of c-axis clustering is caused by the contribution of diffusional creep that does not contribute to the c-axis rotation. According to Azuma's group them, the contribution of diffusional creep at depths having finer grains significantly increases in the DF ice core. The ice sheet conditions (that is, the pressure and temperature) in Antarctica are situated within a boundary zone between dislocation and diffusional creep on the deformation mechanism map (e.g., Shoji and Higashi, 1978;Goodman et al., 1981;Duval et al., 1983). Therefore, the contribution of diffusional creep might be significant at depths with 465 smaller grains. In this case, a weakening of c-axis clustering does not necessarily indicate a restriction of the extent of deformation. In this study, we are not able to resolve the possible effects of grain size and the presence/absence of diffusional creep. Although we can observe periods with higher concentrations of dust particles are evident around 25 and 65 kyrs BP, these regions are not associated with decreased De values. Because the extent of deformation is minimal at shallower depths, it is likely that the effect of dust particles was not yet significant at these locations. 470

Influence of salt particles
Salt particles could also possibly affect COF development and are known to exist in polar ice cores at volume fractions much larger than those of dust particles (Ohno et al., 2005). However, the amount of salt particles is not reflected in the dust profile in DF1 (Fig. 10h). The time-based profiles of the sulphate salt (Na2SO4 and CaSO4) concentration data obtained from Iizuka et al. (2012) are shown in Fig. 10g. Although the concentrations of salt particles in the DF1 ice core were not determined, 475 Iizuka et al. (2012) estimated sulphate salt concentrations using the relationship between ion balance and the chemical compounds found in salt inclusions (Iizuka et al., 2008). The resulting plots of salt concentrations over time are similar to the profiles of the Clion and dust particle concentrations. Basically, sSalt particles might be expected to act as solid particles, which may and so could impede c-axis clustering. However, On the other hand, the formation of salt particles is associated with the generation of HCl, which is likely that expected to activate dislocation movement (e.g., Iizuka et al., 2012; particles both impede and enhance deformation, their contribution to the degree of c-axis clustering could be determined by the balance between these effects. The influence of salt particles was not considered in previous studies; however, it might be important to both deformation and COF development.

Growth of variation amplitude in De 485
The growth of the variation amplitude associated with the De fluctuations provides insights into the nature of the deformation process. In the case of the Ttype A relationships, the depressions in De 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 490 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 495 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 De values indicating enhanced c-axis clustering are attributed 500 to restrictions of dislocation movement with increased deformation due to the work hardening resulting from dislocation pileup. Therefore, excessive deformation and c-axis clustering is limited even in layers with high levels of Clions. In contrast to the Ttype A relationships, the depressions associated with Ttype 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.

Initial conditions in microstructures 505
At the point of bubble close-off, where the transition from firn to ice occurs (approximately 100 m in depth), De is already about 0.008, which is and so approximately 25% of the value for a single ice crystal (Saruya et al., 2022). In fact, De values of this magnitude have also been observed at the base of the firn (that is, at the top of the bubble-containing ice; Fujita et al., 2009Fujita et al., , 2014Fujita et al., , 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 510 demonstrated that the COF c-axes tend to cluster around the vertical direction or become inclined near this bubble close-off horizon the 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 , with variations in density, impurity concentration and dielectric properties as well as and/or in the correlations between these 515 parameters (see Table 7 in Fujita et al., 2016). It is therefore likely that De 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 metamorphism/deformation of the firn. This initial phenomenon is likely to be greatly affected by the presence of Clions and dust particles because vertical deformation of the ice is dominant in firn. Because Clions have the greatest effect on the densification of firn , we suggest that these ions are among the main major factors determining the 520 depth of the transition from firn to bubble-containing ice, known as the lock-in depth (LID). It is also likely that the De values along deep ice cores are valuable indicators that can be used to determine the timescale of the LID in detail. In addition, these De values 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 Clions and the temperature of the ice, it is apparent 525 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.

Implications for the deformation regime in ice sheets
The evolution of the COF clustering strength was investigated herein based on variations in De. On this basis, we suggest that the five questions posed in Section 4.1 can be answered as follows. 530 (i) The fFactors determining the time-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 positive/negative feedback effects of deformation enhancement associated with COF evolution will not play a major role other than to provide 535 weak positive feedback during the very initial stage of deformation and weak negative feedback in the later stage of deformation (Azuma, 1994).
(ii) The large decreases in De seen within specific depth ranges are attributed to Clions and dust particles, both of which primarily increase the amplitude of the De fluctuations within distances on the order of 10 to 10 2 m with increasing depth.
Considering the effects of Clions in terms of promoting dislocation movement, the amount of HCl is more important to COF 540 development than that of NaCl. Many, if not all, of the De fluctuations below 1200 m can be explained by these effects.
However, we also observed fluctuations that cannot be explained by the concentrations of Clions or dust particles alone. In particular, the causes of COF fluctuation at shallower depths (corresponding to the glacial period between AI and AII, see Fig.   10) are still unclear, and so. So further investigation of other factors determining COF development is required. Fand NH4 + ions are potential additional candidates. Although, we have no data concerning the Fand NH4 + concentrations within the DF 545 ice core, these ions have been shown to modify dislocation movement in ice in laboratory experiments and in polar ice sheets.
The effects of salt particles on COF development should also be clarified. Salt particles could potentially act as solid particles to impede c-axis clustering, while the formation of salt particles is closely associated with the generation of HCl that can promote dislocation movement. Because the volume fraction of salt particles is much larger than that of dust particles, the former would be expected to have a greater effect on microstructural evolution and deformation. 550 (iii) It is also highly likely that the same factors listed above were responsible for the increased S.D. values at greater depths.
It should also be noted that, in the case of low Clion concentrations, there were more significant increases in S.D.
(iv) The pPresent work examined the COF within the upper 80% of the DF ice core. which will be continuous to the deeper 20%. It is highly probable In addition, it is highly likely that the dome position migrated in the past (see Sect.ion 2.1). Thus, the current profiles of layered COF fluctuations contrasts will have direct implications regarding for further deformation. For 555 example, we would expect to encounter various stresses/strain configurations resulting from conditions near the base, such as ice flow, undulating bedrock topography and/or ice-thickness-dependent partial melting (Dome Fuji Ice Core Project Members, 2017). Under such variable conditions, in addition to the two major factors of Clions and dust particles, the layered COF fluctuations contrasts will have large effects in terms of enhancing or impeding deformation. The less clustered COF will be either softer or harder because it contains a greater variety of crystal orientation (and thus slip planes of hexagonal ice). Azuma 560 and Goto- Azuma (1996) discussed the deformation of ice sheets with perturbed and layered clustering of single pole COF and suggested the occurrence of heterogeneous layered thinning leading to layer folding or boudinage. In fact, layering disturbances and folding at the lower regions of ice cores have been previously observed on several occasions (e.g., Svensson et al., 2005;Faria et al., 2010;Jansen et al., 2016). As an example, Jansen et al. (2016) investigated small-scale disturbances at the bottom part of the NEEM ice core based on numerical modelling and concluded that the folding structures were initiated by the 565 formation of bands in which the lattice was tilted relative to the bulk COF. This conclusion is in agreement with a prior report by Azuma and Goto-Azuma (1996). Although visual inspections have not identified layering disturbances in the EDC ice core, Durand et al. (2009) found significant fluctuations in eigenvalues. This same group established that there were no clear correlations between the fabric fluctuations and climate or chemical composition. Below a depth of 2846 m, very small grains (less than 1 mm in size) appeared between larger grains, indicating the onset of crystal nucleation. Although signs of migration 570 recrystallization, such as interlocking grain boundaries, were not observed, their findings suggest the possibility of migration recrystallization at sufficiently high temperatures. Thus, further and more detailed investigations are required for a better understanding of the COF development and deformation regime in the deeper parts of the core. Currently, the retrieval of continuous ice core records corresponding to ages of more than 1 Myrs is an important challenge in palaeoclimatology (see topic of this special issue). Identifying suitable sites for the drilling of very old ice will require knowledge of the subglacial 575 topography and englacial layering. Radar sounding is a powerful means of observing englacial layering and can evidently apparently detect enhanced COF layering that is enhanced at deeper layers (see Fig. 7 in this paper and Fujita et al., 1999Fujita et al., , 2000. When identifying candidate sites using ice sounding radars, it will be important to distinguish between stable layering and heterogeneous thickness layers. Specifically, the presence of layers with heterogeneous thickness could the presence of heterogeneous thickness layers could indicate initiation of anomalous strain and thus layer disturbances. 580 (v) Finally, we suggest propose an important implication obtained from this study. Layered sequences of ice core signals in terms of resulting from Cland dust particles are basically commonly obtained from inland ice core sites over the entire widths of the Antarctic ice sheet, in wide Antarctic ice sheet, with minor local variations. Because both Cland dust particles are primary factors controlling the development of COF (as demonstrated by this study), the COF layering profiles established by these factors should be similar in many ice core sites located in the inland regions of the Antarctic ice sheet. Profiles of COF 585 layering should be similar not only at ice core sites but also over much wider areas of the ice sheet having common sequences of both Cland dust particles. Indeed, in It means, profiles of COF layering established toward very deep depths should be basically common in very wide areas within each ice sheet, as far as layered sequence of ice core signals is common within it.
In Figure 8, the variations in we discovered a similarity in time-series of a3 (2) eigenvalues over time in between the DF2 ice core (this study) and the EDC ice core are seen to be similar even though theseThe two sites are approximately 2,000 km apart 590 in East Antarctica. Two sites are apart by about 2,000 km in East Antarctica. This is the first and an important example of for the common features of COF variations within two very remote ice cores and is thus an important finding. Since we can use radars Considering that we can use radars Because radar data can be used to detect COF layering, it we now should be possible able to compare deep COF layers across very wide areas of ice sheets, COF layers in very wide area in ice sheets, and such analyses which should be performed at other locations. examined elsewhere. 595

Conclusion
With the aim of obtaining a better understanding of the deformation regime in ice sheets, we assessed the potential of using the dielectric anisotropy, we assessed the dielectric anisotropy, De, as a new indicator of crystal orientation fabric (COF) using ice core samples taken from Dome Fuji in East Antarctica. This method is a useful means of determining the degree of COF vertical clustering resulting from vertical compressional strain at the dome. The present investigation covered the upper 80% 600 of the entire dome thickness, from depths of 100 to 2400 m, representing an ice cover to an age of approximately 300 kyrs BP.
Examining thick, 1-m long ice core specimens acquired at 5 m intervals, this study was able to generate high-resolution COF data. Compared with to existing thin-section-based methods, the new method described herein provided information with greatly improved statistical significance. The major findings of the present study can be summarized as follows.

605
• The data establish that the overall trend of the De values was to increase with increasing depth and also show that De fluctuated over distance scales in the range of 10-10 2 m. This general pattern The overall trend, in which the values increased is consistent with previous findings that the c-axes of ice crystals concentrate toward the core axis due to grain rotation caused by uniaxial compression. In addition, we discovered large depressions in De during three major transition periods from glacial to interglacial (termination-I/MIS1, termination-II/MIS5e, termination-III/MIS7e) as well as the MIS7abc event. These results indicate that deformation variations occurred in a continuous manner from the near-surface to deeper layers. Moreover, fluctuations in De over distances of less than 0.5 m, as reflected by S.D. values, were inversely correlated with De at depths greater than 1200 m, meaning that such fluctuations were enhanced during the glacial/interglacial transition periods.
• A positive correlation between De and the concentration of Clions, along with a negative correlation with the 615 concentration amount of dust particles in the ice core were also established in those regions associated with significant decreases in De. Based on these results, we propose that there are several factors that may potentially affect COF clustering with changes in time and depth. These include the initial COF that is formed by metamorphism at near-surface depths, as well as ionic impurities, such as Clions, and dust particles. Clions released from HCl are known to increase the dislocation density and to promote dislocation movement throughout the deformation process, while dense 620 concentrations of dust particles may impede COF clustering. An additional factor is the difference between the amounts of Clions and dust particles. These parameters mainly determine the amplitude of the variations in De over distances on the order of 10 to 10 2 m and are also responsible for the increase in the S.D. of the De values with increasing depth.

•
The present data also have important implications concerning the deformation/flow of ice sheets, as we discussed in Sect.ion 4.5(iv) above. We suggest that the COF structure (and thus the deformation structure) of polar ice sheets should 625 be evaluated by focusing on the presence of impurities, the density of dust particles and COF layering, as well as changes in these factors. Importantly, the present study demonstrated presence of small perturbations of COF clustering in layered manner were apparently present in the upper 80 % of the ice sheet, showing growth of the COF contrast amplitude at deeper layers. In addition, we would like to emphasize an important consequence of this study. It should be emphasized that layered sequences of ice core signals related to Cland dust particles were common at inland ice core sites within 630 the wide Antarctic ice sheet. Because both Cland dust particles are among the major factors determining the development of COF, profiles of COF layering established by these factors toward very deep depths should be similar within many ice core sites located in the inland regions of the Antarctic ice sheet and even in wider areas of the ice sheet having similar sequences of both Cland dust particles. Layered sequence of ice core signals in terms of Cland dust particles are basically common in wide Antarctic ice sheet with minor local variations, which means, profiles of COF 635 layering toward very deep depths should be basically common in very wide areas within each ice sheet, as far as layered sequence of ice core signals is common.

•
It should also be noted that VHF/UHF radar sounding is a useful technique that provides information concerning permittivity contrast (and thus COF contrast) within the deep interior of polar ice sheets, and such analyses should be examined further in the future. Importantly, when searching for sites suitable for obtaining core samples of very old ice, 640 we must be careful to avoid layers with heterogeneous thicknesses heterogeneous thickness layers within the lowest approximately 20% of the ice sheet, as determined by ice sounding radars, because the presence of heterogeneous thicknesses indicates the initiation of disturbances in layered structures due to effective horizontal strains.