Slip-band distributions and microstructural fading memory beneath the firn ice transition of polar ice sheets

Slip-band distributions and microstructural fading memory1 beneath the firn–ice transition of polar ice sheets∗ 2 S´ergio Henrique FARIA Basque Centre for Climate Change (BC3), 48940 Leioa, Spain IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Spain 3 September 27, 20184 Abstract5 The Antarctic Ice Sheet is a continental ice mass with circa 23 million gigatons of ice, which6 represent roughly 67 % of world’s freshwater supply. This colossal mass of ice is by no means7 static, as the old ice slowly creeps under its own weight towards the ocean, while new ice8 is continually formed through the sintering of snow deposited on the ice sheet surface. A9 crucial role in this metamorphism is played by firn, which is the porous material in an inter-10 mediate state between the granular snow and the solid polycrystalline ice. Understanding the11 snow–firn–ice metamorphism is essential not only for a precise determination of the mechanical12 (creep) properties of polar ice, but also for comprehending the formation and decay of climate13 proxies widely used in ice-core studies. This work investigates the transition from firn to ice14 through the spatial and directional distributions of slip bands in bubbly ice. The analysis of15 high-resolution micrographs of ice sections extracted from the EPICA-DML Deep Ice Core16 allows us to identify a clear influence of strain-induced anisotropy (viz. c-axis preferred orien-17 tations) on the evolution of slip-band inclinations in deep bubbly ice. In contrast, we discover18 an unanticipated behaviour of slip bands in shallow bubbly ice, which prompts the introduc-19 tion of the hypothesis of microstructural fading memory and the definition of a stabilization20 zone that may penetrate hundreds of metres into the bubbly ice. Within this stabilization21 zone, highly localized concentrations of strain energy and internal stresses once generated by22 force chains in the ancient firn are gradually redistributed by the newly formed bubbly-ice23 microstructure. We show that this hypothesis is compatible with the localized dynamic re-24 crystallization episodes observed in polar firn (even at temperatures close to −45 ◦C), and it25 may also explain the sluggish rotation of c-axes observed in the upper hundreds of metres of26 polar ice sheets.27 key-words: Antarctica; Dronning Maud Land; ice; firn; snow; slip band; microstructure;28 force chain; heterogeneous deformation; internal stress; stored strain energy; recrystallization;29 recovery; ice flow; polycrystal30 1 Introduction31 With an average thickness close to 2 km (and in many places surpassing the 3 km mark), the32 Antarctic Ice Sheet covers a continental area larger than 13×106km2. This amounts to astonishing33 23 million gigatons of ice (or 25 ×106km3, including ice shelves), which represent roughly 67 %34 ∗Dedicated to my mentor and friend, Kumiko Goto-Azuma, on occasion of her 60th birthday. 1 This document is the Accepted Manuscript version of a Published Work that appeared in final form in: Faria S.H. 2018. Slip-band distributions and microstructural fading memory beneath the firn ice transition of polar ice sheets. MECHANICS RESEARCH COMMUNICATIONS. 94. 95-101. DOI (10.1016/j.mechrescom.2018.09.009). © 2018 Elsevier Ltd.This manuscript version is made available under the CC-BY-NCND 3.0 license Faria S.H. 2018. Slip-band distributions and microstructural fading memory beneath the firn--ice transition of polar ice sheets. MECHANICS RESEARCH COMMUNICATIONS. 94. 95-101. DOI (10.1016/j.mechrescom.2018.09.009). of world’s freshwater supply and a potential contribution to global sea-level rise of 58 m (Lemke35 et al., 2007; Vaughan et al., 2013). Such a colossal mass of ice is by no means static. Old ice slowly36 creeps under its own weight towards the ocean, while new ice is formed through the sintering of37 snow that is continually deposited on the ice sheet surface.38 As it occurs with most crystalline solids, ice may undergo creep (viz. visco-plastic deformation)39 at rather low stresses, provided that its temperature is higher than roughly half of its pressure40 melting point (Durham et al., 2001; Petrenko and Whitworth, 1999). Seeing that this condition is41 fulfilled anywhere on Earth’s surface, it should be no surprise that glaciers and ice sheets creep un-42 der their own weight. Even though the creep of such large ice masses is an expected phenomenon,43 its microscopic mechanisms have been challenging glaciologists for decades. In particular, a funda-44 mental feature of the micro-mechanics of ice is its exceptional propensity to form slip bands, which45 are characteristic, microscopic fringes visible within certain ice grains or crystals undergoing simple46 shear (Hobbs, 1974; Nakaya, 1958). Considering that such slip bands are microscopic expressions47 of basal slip (viz. simple shear along a particular family of crystallographic planes, called basal48 planes) within an ice grain, we conclude that the occurrence of these fringes depends not only on49 the macroscopic deformation regime, but also on the crystalline properties of the grain and its50 interactions with neighbours.51 The neighbourhood of a particular ice grain is mainly defined by the positions, crystalline orien-52 tations, shapes and sizes of the surrounding grains, which combined describe the local orientation53 stereology (Bunge and Schwarzer, 2001; Faria et al., 2014b, 2018). Under this perspective, the54 current neighbourhood of an ice grain is in fact a fading record of the local orientation-stereology55 history (Faria and Kipfstuhl, 2005), which begins with the deposition of snow crystals on the56 glacier or ice-sheet surface, and develops through the metamorphism of snow into firn and ice.57 Such a record is evanescent because it is gradually obliterated by thermomechanical processes of58 deformation, recovery, and recrystallization (following Faria et al. 2014b, 2018, the terms recov-59 ery and recrystallization are used here in a wide sense, including static and dynamic processes60 of structural change, like grain growth, grain boundary migration, and subgrain rotation). While61 ice microstructural changes directly related to deformation (e.g. crystalline lattice rotation, grain62 elongation, etc.) are relatively well understood and reproducible by models (Alley, 1988; Azuma,63 1994; Azuma and Higashi, 1985; Faria et al., 2002; G¨odert and Hutter, 1998; Placidi et al., 2010),64 rates of recovery and recrystallization of natural firn and ice are largely unknown (Faria et al.,65 2014b; Placidi et al., 2004). This lack of knowledge severely impairs the modelling of ice mi-66 crostructure evolution and consequently limits the current predictive power of ice flow models and67 the interpretations of ice-core climate proxies.68 This work aims to help clarifying the roles played by recovery and recrystallization in the fading69 memory of the local orientation stereology of polar firn and ice, therefore paving the way to a future70 quantification of these thermodynamic processes. This objective is achieved through the analysis71 of the orientation distributions of slip bands, which are identified in high-resolution, microscopic72 images of ice sections extracted from eight distinct depths of the EPICA-DML Deep Ice Core, from73 the EPICA (European Project for Ice Coring in Antarctica) drilling site in Dronning Maud Land74 (DML), Antarctica.75 Precise definitions of the technical terms used in this work can be found in the glossaries76 presented by Faria et al. (2014b, 2018). The following section introduces the most fundamental77 concepts and put them into the context of the current study.78 2 Fundamental Concepts79 Under the natural conditions typically found on Earth’s surface, ice occurs in the ordinary hexag-80 onal form named ice Ih. With an atomic packing factor of less than 34 %, ice Ih has a rather open,81 wurtzite-like crystalline lattice (Evans, 1976; Hobbs, 1974), which is characterized by oxygen ions82 arranged in layers (called basal planes) of “puckered” hexagonal rings piled in an alternate sequence83 of mirror images normal to the axis of optical and crystallographic (hexagonal) symmetry of the84 crystal, viz. the c axis. Hydrogen nuclei (protons) remain statistically distributed in the oxygen85 lattice, building covalent and hydrogen bonds along the lines joining pairs of oxygen ions (Bernal86 and Fowler, 1933; Pauling, 1935). This proton disorder plays a fundamental role in ice plasticity,87 as it affects the motion of the main agents of plastic deformation of ice: dislocations (Glen, 1968,88 1974; Petrenko and Whitworth, 1999).89 Experience shows that the plasticity of monocrystalline ice is strongly anisotropic, with ice single90 crystals deforming very readily when the applied shear stress acts on the basal plane (Duval et al.,91 1983; Hobbs, 1974), through a process called basal slip and epitomized more than a century ago by92 McConnel’s (1890) “deck of cards” metaphor. This phenomenon was later beautifully illustrated93 by Nakaya (1958), who used shadow photography to reveal slip bands in deformed monocrystalline94 ice bars. Not long after, Bryant and Mason (1960) found grouped etch pits and channels along slip95 bands in resin replicas of deformed ice monocrystals, corroborating the prevalent hypothesis that96 slip bands consisted of microscopic layers with high density of dislocations undergoing basal slip.97 In contrast to laboratory tests, the optical observation of slip bands in polar ice turns out to be98 much more challenging, because of the very low strain rates typical of ice-sheet flow. Nevertheless,99 modern microscopy techniques, like the microstructure mapping (µSM) method adopted in this100 study, have revealed that slip bands are indeed a common feature also of polar ice (Faria and101 Kipfstuhl, 2004; Kipfstuhl et al., 2006; Wang et al., 2003).102 3 Methods103 All ice samples investigated here stem from the EPICA-DML Deep Ice Core (Faria et al., 2018):104 a 2774.15 m long ice core extracted from the EPICA (European Project for Ice Coring in Antarctica)105 drilling site at Dronning Maud Land (DML), Antarctica (75◦00’09”S, 00◦04’06”E, 2892 m a.s.l.).106 Eight ice samples were selected, consisting of vertical thick sections (≈50 ×100 ×5 mm) cut107 lengthwise the EPICA-DML Deep Ice Core at roughly 100 m intervals. Details of the samples are108 described in Table 1. Following the usual convention of the ice-core physical-properties community,109 all depths are rounded down. The sampling approximately covered the upper 850 m of ice, i.e. the110 last 16 ka BP (Ruth et al., 2007). The reason to chose this depth range is threefold, being mainly111 related to changes in the physical properties of the ice core, as well as changes in the ice flow and112 climatic conditions in Antarctica, namely:113 1. Below 800 m depth commences the EPICA-DML bubble–hydrate transition zone, where air114 bubbles are no longer thermodynamically stable and start transforming themselves into air115 hydrates (Bendel et al., 2013; Faria et al., 2010, 2014a; Ueltzh¨offer et al., 2010).116 2. Even though no well-defined “brittle zone” has been discerned in the EPICA-DML site, the117 ice-core quality between 800 m and 1000 m depth was conspicuously lower (Faria et al., 2010,118 2018; Wilhelms et al., 2014).119 3. The onset of the Antarctic Ice Sheet retreat from its Last Glacial maximum extent is esti-120 mated to have occurred not longer after 16 ka BP (Clark et al., 2009).121 Ice samples were prepared and analysed through the method of Microstructure Mapping (µSM),122 which is essentially a digital form of optical microscopy (Faria and Kipfstuhl, 2004; Kipfstuhl et al.,123 2006; Wang et al., 2003; Weikusat et al., 2009). The µSM method consists of a digital video124 camera with automatic gain control mounted on an optical microscope equipped with a computer-125 controlled xy-stage. The microscope automatically scans the whole sample, mapping a variety of126 microstructural features inside the ice (ranging from microinclusions and dislocation walls to air127 bubbles, clathrates, and slip bands) with a microscopic resolution of ca. 3 µm per pixel. Up to128 1800 photomicrographs may be needed to reconstruct a high-resolution digital mosaic image of a129 50 ×100 mm section. Micrographs are usually taken in transmitted light, with a standard size of130 2.5×1.8 mm and a typical overlapping of ca. 0.5 mm, which facilitates the later reconstruction of131 the full mosaic image through the matching of neighbouring micrographs.132 All µSM micrographs analysed in this work are freely available at the Pangaea digital data133 library (Kipfstuhl, 2007).134 The preparation of µSM samples follows the usual procedures for ice microscopy (Kipfstuhl135 et al., 2006; Weikusat et al., 2009). Band saws and microtomes are respectively used for cutting136 and polishing the sections. Clear surfaces are achieved by exposing the polished section to the free137 atmosphere: sublimation smooths the ice surface through the removal of superficial imperfections138 (e.g. microtome scratches), while it simultaneously highlights the sites where grain boundaries and139 other high-energy structures meet the surface, through the formation of characteristic thermal-140 etching grooves and pits (Hobbs, 1974; Kuroiwa and Hamilton, 1963; Mullins, 1957; Nishida and141 Narita, 1996). A sublimation time varying between half an hour and half a day is usually necessary142 to obtain a clear surface, with well-developed grain-boundary grooves. This sublimation time143 strongly depends on the conditions of temperature, humidity, and air circulation above the sample.144 After the first (lower) surface of the section is sufficiently clear, it is sealed off with a thin film145 of silicone oil and frozen onto a glass plate. The second (upper) surface is treated in the same146 manner, but it is sealed off with silicone oil and glass only after the first surface scan is completed,147 in order to optimize the quality of the µSM images. Once both surfaces are sealed, further scans are148 often performed with the microscope focused inside the section, in order to map microstructural149 features not related to the etched surface, like air bubbles and hydrates, microinclusions, and slip150 bands. Examples of µSM micrographs showing real and “fake” slip bands are presented in Fig. 1.151 The portability of the µSM method permits the mapping of fresh ice sections in the field, while152 drilling is ongoing. This is crucial for minimizing the effects of recrystallization, recovery and post-153 drilling relaxation of the ice microstructure. Under optimal conditions, the mapping of a complete154 section (50 ×100 ×5 mm) takes about one hour and can be accomplished as early as a few hours155 after core extraction.156 Analysis of the µSM micrographs was performed with the open-source software Fiji–ImageJ157 (Schindelin et al., 2012). Circa 12,000 micrographs were manually analysed, through the identifi-158 cation of grain and subgrain boundaries, dislocation walls, and slip bands. Special care was taken159 at the overlapping regions between micrographs. Every time a grain with a set of parallel slip bands160 was manually identified, the software determined the position and inclination of the set, labelled161 it, and recorded the information in a spreadsheet. Thus, as a rule, each slip-band-inclination data162 point corresponds to the set of slip bands in an individual grain. An exception was made for some163 very large grains with well-defined slip bands: in such cases, the grain was decomposed into sectors164 of size comparable with the average grain size, and each sector was measured separately. The165 angular precision of the measurements was of approximately 2 degrees.166 Automatic analysis of slip bands was not possible, because the correct identification of slip167 bands is exceptionally difficult (cf. Fig. 1): software and untrained eyes often confuse them with168 defocused surface irregularities (e.g. sublimation grooves), or with occasional optical aberrations169 (caused e.g. by some internal grain-boundary edges). Therefore, to date, the manual identification170 of slip bands by a judicious and experienced specialist in ice microscopy and µSM is still the most171 reliable procedure. Hopefully, new techniques of machine learning applied to image analysis may172 enable the automation of these procedures in the near future.173 It should be noted that firn samples have not been analysed in this study. Whereas the µSM174 method has already been successfully employed to investigate the microstructure of firn (Faria et al.,175 2010, 2014b; Kipfstuhl et al., 2009), such investigations were restricted to reflected-light microscopy176 of sublimation grooves (of grain and subgrain boundaries) on the ice surface. The reason for this177 restriction is that firn is not transparent as ice: the porous structure of firn permeates through the178 whole section, scattering the transmitted light that would be necessary to reveal internal structures179 inside the ice section, like slip bands.180 4 Results181 Slip bands were identified and classified according to their inclinations with respect to the horizontal182 plane. Two remarks are relevant in this regard:183 Remark 1: Ice cores drilled to date (including the EPICA-DML Deep Ice Core) have arbitrary184 azimuths (Faria et al., 2018; Weikusat et al., 2017), and consequently, so have also their185 vertical sections.186 Remark 2: Owing to their faint nature and stacked arrangement, slip bands in polar ice are187 best discerned if they are nearly perpendicular to the view plane, i.e. the section’s surface188 (misorientation <10◦; Kipfstuhl et al. 2006).189 From Remark 1, it follows that only the slip band’s apparent dip angle (viz. perceived angle190 of inclination) can be determined. In general, the apparent dip angle represents a lower bound191 of the true dip angle (viz. maximum angle of inclination). Nevertheless, Remark 2 implies that192 discernible slip bands usually have apparent dip angles similar to their respective true dip angles.193 Be that as it may, here we stick to the expression “apparent dip angle”, in order to stress two194 important facts: (i) the apparent and true dip angles may not be identical; (ii) the azimuth of a195 vertical section, and consequently the slip band’s dip direction, is unknown.196 Figure 2 displays four examples of apparent-dip-angle distributions of slip bands, with an ac-197 curacy of five degrees. The evolution of these distributions with depth, and consequently with198 age, is clearly visible. The most obvious feature of the whole depth interval is a net increase in199 the fraction of low-angle (<30◦) slip bands at the expense of mid-angle (between 30◦and 60◦)200 and high-angle (≥60◦) slip bands. Closer inspection reveals, however, a somewhat more complex201 development: down to a reversal zone at (415 ±60) m depth, there is actually a decrease in the202 frequency of low-angle slip bands, which is simultaneously compensated by an increase in the fre-203 quency of mid-angle slip bands. In contrast, at some point within that reversal zone this process204 is reversed and the mid-angle slip bands start to disappear, while low-angle slip bands gradually205 increase in number. These observations are illustrated in Fig. 3, which shows the depth evolution206 of low-, mid-, and high-angle slip bands in all eight sections analysed in this study. Notice also207 that the frequency of high-angle slip bands decreases through the whole depth range (94–854 m)208 in a rather linear fashion.209 5 Discussion210 The observation that the frequency of high-angle slip bands decreases monotonically with depth211 throughout the studied interval (94–854 m) should be no surprise for those aware of the ice-flow212 features at the EPICA-DML site: the decrease can be explained as a direct consequence of the213 developing strain-induced anisotropy of polycrystalline ice in that region (viz. lattice preferred214 orientations, so-called “fabric”). The EPICA-DML drilling site lies on an ice ridge. Therefore, by215 considering the general rule that the ice flow in the upper part of a stationary ice sheet can be216 roughly described by its surface down-slope combined with the ubiquitous vertical compression due217 to the overburden of continual snow accumulation, we conclude that the large-scale flow in the upper218 thousand metres at EPICA-DML has a triaxial character, dominated by horizontal extension across219 the ridge (∼10−4a−1), vertical compression (∼10−4a−1), and a slight horizontal compression rate220 along the ridge (one or more orders of magnitude smaller than the other two rates). These strain-221 rate estimates are compatible with airborne surface-velocity observations, numerical simulations,222 and microstructure analysis (Faria et al., 2014b, 2018; Steinhage, 2001; Weikusat et al., 2017).223 The anisotropic c-axis orientation distribution induced by this kind of deformation may be224 called a “vertical great-circle girdle with a vertical maximum,” which means that the caxes tend225 to reorient themselves with increasing depth away from the (horizontal) principal axis of extension226 and towards the principal axes of compression—especially the stronger vertical one. Accordingly,227 this means that the basal planes have an increasing tendency to become tangent to the principal228 axis of extension, as if they were arranging themselves on the elliptical cylindrical surface of a229 fictitious “horizontally flattened tube.” Therefore, irrespective of the orientation of the vertical230 section, most basal planes in deeper samples should be at low angles with respect to the horizontal,231 and so should also be the most frequently observed slip bands.232 Whereas the above description explains the monotonic decrease with depth in the frequency of233 high-angle slip bands, the observation that this decrease is approximately linear is unanticipated,234 especially if we consider the strongly non-linear evolution of the other two dip classes. This is a235 matter that deserves further investigation in the near future.236 In contrast to the relatively straightforward explanation for the evolution of high-angle slip237 bands, the evolution of lowand mid-angle slip bands is much less trivial. Two contrasting be-238 haviours are observed above and below a reversal zone identified at (415±60) m depth. Below this239 reversal zone, the evolution of lowand mid-angle slip bands follows the expected behaviour, with240 mid-angle slip bands gradually giving way to an increasing number of low-angle slip bands. Such241 a behaviour is “expected” in the sense that it can be explained with the same arguments already242 used to explain the progressive reduction in the frequency of high-angle slip bands. On the other243 hand, in the shallower depths above the reversal zone, the frequencies of lowand mid-angle slip244 bands behave in the opposite way: the fraction of low-angle slip bands observed at shallow depths245 gradually decreases with depth down to the reversal zone. Likewise, the fraction of mid-angle slip246 bands observed at shallow depths progressively increase in importance towards the reversal zone.247 These two contrasting behaviours clearly cannot be explained with the arguments about induced248 anisotropy invoked for high-angle slip bands and for the region below the reversal zone. Another249 explanation is needed.250 The reason for discarding the induced-anisotropy explanation in the case of shallow bubbly ice251 is obvious: polycrystalline ice in the upper 450 m depth of the EPICA-DML site is nearly isotropic252 (Weikusat et al., 2017). This is, however, also the reason why the behaviour of lowand mid-angle253 slip bands in the shallow ice above the reversal zone seems counter-intuitive: the macroscopic254 strain rate anywhere in the upper 1000 m of EPICA-DML is essentially the same—viz. the triaxial255 regime already described—and this fact combined with the near-isotropy of shallow ice implies that256 the most probable slip bands in the upper hundreds of metres should be at mid-angles, because257 basal planes at such inclinations can bear the largest resolved shear stresses from the macroscopic258 triaxial load (Asaro, 1983; Faria and Kipfstuhl, 2004; Placidi et al., 2006).259 Thus, it turns out that the crucial question about the evolution of slip bands in shallow polar260 ice at the EPICA-DML site is: why do the frequency of mid-angle slip bands in the uppermost few261 hundred metres increase with depth down to the reversal zone? In a reciprocal formulation: why262 do the frequency of low-angle slip bands in the uppermost few hundred metres decrease with depth263 down to the reversal zone?264 Here we propose an answer to the above question in the form of a novel hypothesis of micro-265 structural fading memory. In a few words, its fundamental idea is that the shallow bubbly ice266 inherits some microstructural imprints and localized strain energy from the former granular and267 porous structures of snow and firn, which affect the distribution of slip bands at shallow depths.268 Such inherited force-chain relics gradually evanesce with time and depth, under the action of269 dynamic recovery and recrystallization, and the redistribution of internal stresses.270 More precisely, it is well known that the sintering of granular snow and porous firn into solid,271 polycrystalline bubbly ice generates an intricate network of force chains, viz. more or less sta-272 ble, load-bearing trains of grains within the firn skeleton (Brown, 1980; Gubler, 1978; Kry, 1975;273 Scapozza and Bartelt, 2003; von Moos et al., 2003; Wakahama, 1960). Such force chains have the274 ability to transfer, modify, and break down the applied macroscopic stress into a series of complex275 and seemingly uncorrelated microscopic internal stresses, which give rise to strong strain hetero-276 geneities in clusters of grains that undergo large amounts of strain accommodation, facilitated by277 the pore space. These internal stresses can sometimes be so intense that they may cause localized278 dynamic recrystallization in cold firn (down to −45 ◦C), a phenomenon first observed by Kipfstuhl279 et al. (2009) and theoretically explained by Faria et al. (2014b).280 Within the context of this study, a fundamental feature of the microscopic internal stresses281 generated by force chains in firn is that the directions and intensities of their principal stresses may282 vary wildly among neighbouring clusters of grains on the microand meso-scales, and may also283 considerably differ from the macroscopic principal stresses related to the large-scale ice flow. Seeing284 that slip bands form and evolve in ice in response to local, microscopic principal stresses (through285 their projections onto the basal planes of the crystalline ice lattice as resolved shear stresses), we286 conclude that the orientation distribution of slip bands in polar firn on the mesoscale (∼10−1m)287 should express this diversity of microscopic principal stresses through a more random distribution288 of slip-band orientations than it would be expected for a solid piece of isotropic polycrystalline ice289 subjected to a well-defined triaxial load.290 The hypothesis of microstructural fading memory asserts that the most intense and stable force291 chains in firn should produce highly localized concentrations of strain energy around trains of292 load-bearing grains that remain partially active and preserved, together with some of the strongest293 slip bands, in the microstructure of shallow bubbly ice beneath the firn–ice transition (pore close-294 off depth). Such remaining slip bands and trains of grains represent relics of the former firn295 structure, which gradually lose influence on the microstructure of shallow ice and decay through296 the redistribution of internal stresses and the action of dynamic recovery and recrystallization297 (including grain growth). Indeed, the slip-band distributions observed in the EPICA-DML sections298 from 94, 205 and 355 m depth express precisely this phenomenon: they describe the gradual299 transition from a nearly-random orientation distribution of slip bands at 94 m depth to a mid-300 angle-dominated distribution characteristic of solid, polycrystalline ice subjected to a well-defined301 triaxial load.302 The depth range in which all these decay processes take place and the memory of the ancient303 firn microstructure fades away defines the stabilization zone, which coincides with the shallow304 bubbly ice zone ranging from the pore close-off depth down to the end of the slip-band reversal305 zone identified in this work. It is in the stabilization zone that the last manifestations of the highly306 heterogeneous deformation nature of porous firn give way to the more homogeneous deformation307 regime of solid polycrystalline ice. This is valid not only for the distribution of slip bands, but308 also for other microstructural features, including the orientation of c-axes, as follows. The intricate309 force-chain network of firn induces a multitude of localized lattice preferred orientations within310 small clusters of grains, which together function as a “nearly isotropic noise” that easily outweighs311 the strain-induced anisotropy driven by the macroscopic stress acting on the firn skeleton. As312 firn turns into bubbly ice, such a strong “noise” fades away within the stabilization zone, being313 gradually eclipsed by the prevailing strain-induced anisotropy imposed by the macroscopic stress314 that drives the ice flow. This stabilization phenomenon may contribute to the sluggish rotation315 of c-axes generally observed in the upper hundreds of metres of polar ice sheets (Castelnau et al.,316 1996; Durand et al., 2007; Faria et al., 2002; Weikusat et al., 2017).317 6 Conclusion318 We cannot accept anything as granted beyond the first mathematical formulae. Question319 everything else.320 Maria Mitchell. Quoted by Holmes (2018).321 This work presented an analysis of the orientation distribution of slip bands in the upper 850 m of322 polar ice from the EPICA (European Project for Ice Coring in Antarctica) drilling site in Dronning323 Maud Land (DML), Antarctica. Circa 12,000 high-resolution micrographs from eight different324 vertical sections of the EPICA-DML Deep Ice Core, spaced at roughly 100 m depth intervals, have325 been manually analysed. The micrographs were taken from fresh ice, shortly after drilling, to avoid326 undesirable relaxation effects.327 The analysis revealed two distinct evolution regimes in the orientation distribution of slip bands.328 In the shallow bubbly ice beneath the firn–ice transition (viz. pore close-off depth ≈88 m) down329 to a reversal zone at (415 ±60) m depth, the slip-band orientation distribution evolves from nearly330 random to one with a strong mid-angle (30–60◦) mode. In contrast, below the reversal zone and331 down to the end of the depth range considered here (853 m), the slip-band orientation distribution332 becomes strongly unimodal, with a well-defined low-angle (0–30◦) mode, which follows the evolution333 of the strain-induced anisotropy (c-axis preferred orientations) of deep bubbly ice.334 While the features of the orientation distribution of slip bands below the reversal zone are, as335 expected, compatible with the c-axis anisotropy and the macroscopic stress that drives the large-336 scale ice flow, the evolution of the distribution of slip bands above the reversal zone turns out to337 be a puzzling result. In order to explain it, we introduced here the hypothesis of microstructural338 fading memory: force chains, which are characteristic features of the sintering and deformation of339 granular snow and porous firn, leave mechanical and structural imprints on the microstructure of340 polycrystalline bubbly ice. These imprints end up affecting the distribution of slip bands at shallow341 depths, while gradually evanescing under the the action of dynamic recovery and recrystallization,342 and the redistribution of internal stresses. The very heterogeneous strains associated to force chains343 are also responsible for the generation of a nearly-random orientation distribution of slip bands344 and c-axes in firn, compatible with the one observed here in the shallowest ice sample just beneath345 the firn–ice transition depth.346 The impact and consequences of these results are remarkable. First, the hypothesis of mi-347 crostructural fading memory is compatible not only with the slip-band observations described348 here, but also with the notion and role of force chains in snow and firn (Brown, 1980; Gubler, 1978;349 Kry, 1975; Scapozza and Bartelt, 2003; von Moos et al., 2003; Wakahama, 1960), the observation350 of dynamic recrystallization in deep firn (Kipfstuhl et al., 2009) and its theoretical explanation in351 terms of internal stresses (Faria et al., 2014b). Furthermore, it allows the identification of a stabi-352 lization zone (which coincides with the shallow bubbly ice zone already described), where relics of353 the once strongly localized mechanical and structural heterogeneities of ancient firn are gradually354 dissipated. Whereas this stabilization manifests itself most clearly in the evolution of slip bands355 reported here, it may also be noticeable in other microstructural features of shallow bubbly ice,356 including the sluggish evolution of c-axis orientations often observed in this zone (Castelnau et al.,357 1996; Durand et al., 2007; Faria et al., 2002; Weikusat et al., 2017). At last, the observations of358 slip bands in the anisotropic, deep bubbly ice presented here are compatible with all EPICA-DML359 studies of ice microstructure and flow performed so far, including grain sizes and elongations, slip360 bands and subgrain boundaries, visual stratigraphy, c-axis preferred orientations and ice-flow sim-361 ulations (Faria and Kipfstuhl, 2004; Faria et al., 2010, 2014b, 2018; Kipfstuhl et al., 2006; Weikusat362 et al., 2009, 2017).363 Admittedly, the hypothesis of microstructural fading memory and its corollaries are still con-364 jectures open to further scrutiny and corroboration. Following Maria Mitchell’s advice quoted at365 the beginning of this section, we should not accept such conjectures as granted. They are, nev-366 ertheless, physically sound and consistent with a number of independent observations of physical367 phenomena and properties of polar ice, as reported in this work. Therefore, they deserve to be368 taken seriously, as their value lies also in the new ideas and questions they disclose, which shall369 promote future investigations of the fascinating phenomenon of firn–ice metamorphism. In this370 vein, the hypothesis of microstructural fading memory lays the foundations for a new experimental371 and theoretical framework to study of one of the most important and elusive processes in polar372 ice: dynamic recovery. After accounting for the effects of deformation and recrystallization on the373 grain stereology, one may use the evolution of slip bands in shallow bubbly ice to estimate the rate374 at which dislocations disappear from inactive slip bands. This line of research will be pursued in375 the near future.376 Acknowledgements377 My gratitude to Sepp Kipfstuhl, Nobuhiko Azuma, and Ilka Weikusat for many discussions and378 collaboration over the years on the physical properties of polar ice. Special thanks also to Luca379 Placidi for his excellent guest-editorial work, and to two anonymous reviewers for their invalu-380 able criticism. Financial support from the Ram´on y Cajal Grant RYC-2012-12167 of the Spanish381 Ministry of Economy, Industry and Competitiveness is kindly acknowledged. This work is a con-382 tribution to the European Project for Ice Coring in Antarctica (EPICA), a joint European Science383 Foundation/European Commission scientific programme, funded by the EU and by national con-384 tributions from Belgium, Denmark, France, Germany, Italy, the Netherlands, Norway, Sweden,385 Switzerland and the United Kingdom. The main logistic support was provided by IPEV and386 PNRA (at Dome C) and AWI (at Dronning Maud Land). This is EPICA publication no. 310.387 Figure 2: Examples of orientation distribution of slip bands of the even-numbered samples (the odd-numbered samples tell essentially the same story). The dashed grey lines describe a reference distribution of the ideal case of randomly oriented slip bands, taking into account the effects derived from Remarks 1 and 2. Figure 3: Evolution with depth (and age) of low- (0–30◦), mid- (30–60◦), and high-angle (60–90◦) dip classes of slip bands. The dashed grey lines serve as reference to the frequencies of low-, mid-, and high-angle dip classes in the ideal case of randomly oriented slip bands, taking into account the effects derived from Remarks 1 and 2.