Slip-band dis ibu ions and mic os uc u al ading memo y1
benea h he i n–ice ansi ion o pola ice shee s∗
2
S´e gio Hen ique FARIA
Basque Cen e o Clima e Change (BC3), 48940 Leioa, Spain
IKERBASQUE, Basque Founda ion o Science, 48013 Bilbao, Spain
3
Sep embe 27, 20184
Abs ac 5
The An a c ic Ice Shee is a con inen al ice mass wi h ci ca 23 million giga ons o ice, which6
ep esen oughly 67 % o wo ld’s eshwa e supply. This colossal mass o ice is by no means7
s a ic, as he old ice slowly c eeps unde i s own weigh owa ds he ocean, while new ice8
is con inually o med h ough he sin e ing o snow deposi ed on he ice shee su ace. A9
c ucial ole in his me amo phism is played by i n, which is he po ous ma e ial in an in e -10
media e s a e be ween he g anula snow and he solid polyc ys alline ice. Unde s anding he11
snow– i n–ice me amo phism is essen ial no only o a p ecise de e mina ion o he mechanical12
(c eep) p ope ies o pola ice, bu also o comp ehending he o ma ion and decay o clima e13
p oxies widely used in ice-co e s udies. This wo k in es iga es he ansi ion om i n o ice14
h ough he spa ial and di ec ional dis ibu ions o slip bands in bubbly ice. The analysis o 15
high- esolu ion mic og aphs o ice sec ions ex ac ed om he EPICA-DML Deep Ice Co e16
allows us o iden i y a clea in luence o s ain-induced aniso opy ( iz. c-axis p e e ed o ien-17
a ions) on he e olu ion o slip-band inclina ions in deep bubbly ice. In con as , we disco e 18
an unan icipa ed beha iou o slip bands in shallow bubbly ice, which p omp s he in oduc-19
ion o he hypo hesis o mic os uc u al ading memo y and he de ini ion o a s abiliza ion20
zone ha may pene a e hund eds o me es in o he bubbly ice. Wi hin his s abiliza ion21
zone, highly localized concen a ions o s ain ene gy and in e nal s esses once gene a ed by22
o ce chains in he ancien i n a e g adually edis ibu ed by he newly o med bubbly-ice23
mic os uc u e. We show ha his hypo hesis is compa ible wi h he localized dynamic e-24
c ys alliza ion episodes obse ed in pola i n (e en a empe a u es close o −45 ◦C), and i 25
may also explain he sluggish o a ion o c-axes obse ed in he uppe hund eds o me es o 26
pola ice shee s.27
key-wo ds: An a c ica; D onning Maud Land; ice; i n; snow; slip band; mic os uc u e;28
o ce chain; he e ogeneous de o ma ion; in e nal s ess; s o ed s ain ene gy; ec ys alliza ion;29
eco e y; ice low; polyc ys al30
1 In oduc ion31
Wi h an a e age hickness close o 2 km (and in many places su passing he 3 km ma k), he32
An a c ic Ice Shee co e s a con inen al a ea la ge han 13×106km2. This amoun s o as onishing33
23 million giga ons o ice (o 25 ×106km3, including ice shel es), which ep esen oughly 67 %34
∗Dedica ed o my men o and iend, Kumiko Go o-Azuma, on occasion o he 60 h bi hday.
1
This documen is he Accep ed Manusc ip e sion o a Published Wo k ha appea ed in inal o m in:
Fa ia S.H. 2018. Slip-band dis ibu ions and mic os uc u al ading memo y benea h he i n ice ansi ion o pola ice shee s. MECHANICS RESEARCH
COMMUNICATIONS. 94. 95-101. DOI (10.1016/j.mech escom.2018.09.009). © 2018 Else ie L d.This manusc ip e sion is made a ailable unde he CC-BY-NC-
ND 3.0 license
Fa ia S.H. 2018. Slip-band dis ibu ions and mic os uc u al ading memo y
benea h he i n--ice ansi ion o pola ice shee s. MECHANICS RESEARCH
COMMUNICATIONS. 94. 95-101. DOI (10.1016/j.mech escom.2018.09.009).
o wo ld’s eshwa e supply and a po en ial con ibu ion o global sea-le el ise o 58 m (Lemke35
e al., 2007; Vaughan e al., 2013). Such a colossal mass o ice is by no means s a ic. Old ice slowly36
c eeps unde i s own weigh owa ds he ocean, while new ice is o med h ough he sin e ing o 37
snow ha is con inually deposi ed on he ice shee su ace.38
As i occu s wi h mos c ys alline solids, ice may unde go c eep ( iz. isco-plas ic de o ma ion)39
a a he low s esses, p o ided ha i s empe a u e is highe han oughly hal o i s p essu e40
mel ing poin (Du ham e al., 2001; Pe enko and Whi wo h, 1999). Seeing ha his condi ion is41
ul illed anywhe e on Ea h’s su ace, i should be no su p ise ha glacie s and ice shee s c eep un-42
de hei own weigh . E en hough he c eep o such la ge ice masses is an expec ed phenomenon,43
i s mic oscopic mechanisms ha e been challenging glaciologis s o decades. In pa icula , a unda-44
men al ea u e o he mic o-mechanics o ice is i s excep ional p opensi y o o m slip bands, which45
a e cha ac e is ic, mic oscopic inges isible wi hin ce ain ice g ains o c ys als unde going simple46
shea (Hobbs, 1974; Nakaya, 1958). Conside ing ha such slip bands a e mic oscopic exp essions47
o basal slip ( iz. simple shea along a pa icula amily o c ys allog aphic planes, called basal48
planes) wi hin an ice g ain, we conclude ha he occu ence o hese inges depends no only on49
he mac oscopic de o ma ion egime, bu also on he c ys alline p ope ies o he g ain and i s50
in e ac ions wi h neighbou s.51
The neighbou hood o a pa icula ice g ain is mainly de ined by he posi ions, c ys alline o ien-52
a ions, shapes and sizes o he su ounding g ains, which combined desc ibe he local o ien a ion53
s e eology (Bunge and Schwa ze , 2001; Fa ia e al., 2014b, 2018). Unde his pe spec i e, he54
cu en neighbou hood o an ice g ain is in ac a ading eco d o he local o ien a ion-s e eology55
his o y (Fa ia and Kip s uhl, 2005), which begins wi h he deposi ion o snow c ys als on he56
glacie o ice-shee su ace, and de elops h ough he me amo phism o snow in o i n and ice.57
Such a eco d is e anescen because i is g adually obli e a ed by he momechanical p ocesses o 58
de o ma ion, eco e y, and ec ys alliza ion ( ollowing Fa ia e al. 2014b, 2018, he e ms eco -59
e y and ec ys alliza ion a e used he e in a wide sense, including s a ic and dynamic p ocesses60
o s uc u al change, like g ain g ow h, g ain bounda y mig a ion, and subg ain o a ion). While61
ice mic os uc u al changes di ec ly ela ed o de o ma ion (e.g. c ys alline la ice o a ion, g ain62
elonga ion, e c.) a e ela i ely well unde s ood and ep oducible by models (Alley, 1988; Azuma,63
1994; Azuma and Higashi, 1985; Fa ia e al., 2002; G¨ode and Hu e , 1998; Placidi e al., 2010),64
a es o eco e y and ec ys alliza ion o na u al i n and ice a e la gely unknown (Fa ia e al.,65
2014b; Placidi e al., 2004). This lack o knowledge se e ely impai s he modelling o ice mi-66
c os uc u e e olu ion and consequen ly limi s he cu en p edic i e powe o ice low models and67
he in e p e a ions o ice-co e clima e p oxies.68
This wo k aims o help cla i ying he oles played by eco e y and ec ys alliza ion in he ading69
memo y o he local o ien a ion s e eology o pola i n and ice, he e o e pa ing he way o a u u e70
quan i ica ion o hese he modynamic p ocesses. This objec i e is achie ed h ough he analysis71
o he o ien a ion dis ibu ions o slip bands, which a e iden i ied in high- esolu ion, mic oscopic72
images o ice sec ions ex ac ed om eigh dis inc dep hs o he EPICA-DML Deep Ice Co e, om73
he EPICA (Eu opean P ojec o Ice Co ing in An a c ica) d illing si e in D onning Maud Land74
(DML), An a c ica.75
P ecise de ini ions o he echnical e ms used in his wo k can be ound in he glossa ies76
p esen ed by Fa ia e al. (2014b, 2018). The ollowing sec ion in oduces he mos undamen al77
concep s and pu hem in o he con ex o he cu en s udy.78
2 Fundamen al Concep s79
Unde he na u al condi ions ypically ound on Ea h’s su ace, ice occu s in he o dina y hexag-80
onal o m named ice Ih. Wi h an a omic packing ac o o less han 34 %, ice Ih has a a he open,81
wu zi e-like c ys alline la ice (E ans, 1976; Hobbs, 1974), which is cha ac e ized by oxygen ions82
a anged in laye s (called basal planes) o “pucke ed” hexagonal ings piled in an al e na e sequence83
o mi o images no mal o he axis o op ical and c ys allog aphic (hexagonal) symme y o he84
c ys al, iz. he c axis. Hyd ogen nuclei (p o ons) emain s a is ically dis ibu ed in he oxygen85
la ice, building co alen and hyd ogen bonds along he lines joining pai s o oxygen ions (Be nal86
and Fowle , 1933; Pauling, 1935). This p o on diso de plays a undamen al ole in ice plas ici y,87
as i a ec s he mo ion o he main agen s o plas ic de o ma ion o ice: disloca ions (Glen, 1968,88
1974; Pe enko and Whi wo h, 1999).89
Expe ience shows ha he plas ici y o monoc ys alline ice is s ongly aniso opic, wi h ice single90
c ys als de o ming e y eadily when he applied shea s ess ac s on he basal plane (Du al e al.,91
1983; Hobbs, 1974), h ough a p ocess called basal slip and epi omized mo e han a cen u y ago by92
McConnel’s (1890) “deck o ca ds” me apho . This phenomenon was la e beau i ully illus a ed93
by Nakaya (1958), who used shadow pho og aphy o e eal slip bands in de o med monoc ys alline94
ice ba s. No long a e , B yan and Mason (1960) ound g ouped e ch pi s and channels along slip95
bands in esin eplicas o de o med ice monoc ys als, co obo a ing he p e alen hypo hesis ha 96
slip bands consis ed o mic oscopic laye s wi h high densi y o disloca ions unde going basal slip.97
In con as o labo a o y es s, he op ical obse a ion o slip bands in pola ice u ns ou o be98
much mo e challenging, because o he e y low s ain a es ypical o ice-shee low. Ne e heless,99
mode n mic oscopy echniques, like he mic os uc u e mapping (µSM) me hod adop ed in his100
s udy, ha e e ealed ha slip bands a e indeed a common ea u e also o pola ice (Fa ia and101
Kip s uhl, 2004; Kip s uhl e al., 2006; Wang e al., 2003).102
3 Me hods103
All ice samples in es iga ed he e s em om he EPICA-DML Deep Ice Co e (Fa ia e al., 2018):104
a 2774.15 m long ice co e ex ac ed om he EPICA (Eu opean P ojec o Ice Co ing in An a c ica)105
d illing si e a D onning Maud Land (DML), An a c ica (75◦00’09”S, 00◦04’06”E, 2892 m a.s.l.).106
Eigh ice samples we e selec ed, consis ing o e ical hick sec ions (≈50 ×100 ×5 mm) cu 107
leng hwise he EPICA-DML Deep Ice Co e a oughly 100 m in e als. De ails o he samples a e108
desc ibed in Table 1. Following he usual con en ion o he ice-co e physical-p ope ies communi y,109
all dep hs a e ounded down. The sampling app oxima ely co e ed he uppe 850 m o ice, i.e. he110
las 16 ka BP (Ru h e al., 2007). The eason o chose his dep h ange is h ee old, being mainly111
ela ed o changes in he physical p ope ies o he ice co e, as well as changes in he ice low and112
clima ic condi ions in An a c ica, namely:113
1. Below 800 m dep h commences he EPICA-DML bubble–hyd a e ansi ion zone, whe e ai 114
bubbles a e no longe he modynamically s able and s a ans o ming hemsel es in o ai 115
hyd a es (Bendel e al., 2013; Fa ia e al., 2010, 2014a; Uel zh¨o e e al., 2010).116
2. E en hough no well-de ined “b i le zone” has been disce ned in he EPICA-DML si e, he117
ice-co e quali y be ween 800 m and 1000 m dep h was conspicuously lowe (Fa ia e al., 2010,118
2018; Wilhelms e al., 2014).119
3. The onse o he An a c ic Ice Shee e ea om i s Las Glacial maximum ex en is es i-120
ma ed o ha e occu ed no longe a e 16 ka BP (Cla k e al., 2009).121
Ice samples we e p epa ed and analysed h ough he me hod o Mic os uc u e Mapping (µSM),122
which is essen ially a digi al o m o op ical mic oscopy (Fa ia and Kip s uhl, 2004; Kip s uhl e al.,123
2006; Wang e al., 2003; Weikusa e al., 2009). The µSM me hod consis s o a digi al ideo124
came a wi h au oma ic gain con ol moun ed on an op ical mic oscope equipped wi h a compu e -125
con olled xy-s age. The mic oscope au oma ically scans he whole sample, mapping a a ie y o 126
mic os uc u al ea u es inside he ice ( anging om mic oinclusions and disloca ion walls o ai 127
bubbles, cla h a es, and slip bands) wi h a mic oscopic esolu ion o ca. 3 µm pe pixel. Up o128
1800 pho omic og aphs may be needed o econs uc a high- esolu ion digi al mosaic image o a129
50 ×100 mm sec ion. Mic og aphs a e usually aken in ansmi ed ligh , wi h a s anda d size o 130
2.5×1.8 mm and a ypical o e lapping o ca. 0.5 mm, which acili a es he la e econs uc ion o 131
he ull mosaic image h ough he ma ching o neighbou ing mic og aphs.132
All µSM mic og aphs analysed in his wo k a e eely a ailable a he Pangaea digi al da a133
lib a y (Kip s uhl, 2007).134
The p epa a ion o µSM samples ollows he usual p ocedu es o ice mic oscopy (Kip s uhl135
e al., 2006; Weikusa e al., 2009). Band saws and mic o omes a e espec i ely used o cu ing136
and polishing he sec ions. Clea su aces a e achie ed by exposing he polished sec ion o he ee137
a mosphe e: sublima ion smoo hs he ice su ace h ough he emo al o supe icial impe ec ions138
(e.g. mic o ome sc a ches), while i simul aneously highligh s he si es whe e g ain bounda ies and139
o he high-ene gy s uc u es mee he su ace, h ough he o ma ion o cha ac e is ic he mal-140
e ching g oo es and pi s (Hobbs, 1974; Ku oiwa and Hamil on, 1963; Mullins, 1957; Nishida and141
Na i a, 1996). A sublima ion ime a ying be ween hal an hou and hal a day is usually necessa y142
o ob ain a clea su ace, wi h well-de eloped g ain-bounda y g oo es. This sublima ion ime143
s ongly depends on he condi ions o empe a u e, humidi y, and ai ci cula ion abo e he sample.144
A e he i s (lowe ) su ace o he sec ion is su icien ly clea , i is sealed o wi h a hin ilm145
o silicone oil and ozen on o a glass pla e. The second (uppe ) su ace is ea ed in he same146
manne , bu i is sealed o wi h silicone oil and glass only a e he i s su ace scan is comple ed,147
in o de o op imize he quali y o he µSM images. Once bo h su aces a e sealed, u he scans a e148
o en pe o med wi h he mic oscope ocused inside he sec ion, in o de o map mic os uc u al149
ea u es no ela ed o he e ched su ace, like ai bubbles and hyd a es, mic oinclusions, and slip150
bands. Examples o µSM mic og aphs showing eal and “ ake” slip bands a e p esen ed in Fig. 1.151
The po abili y o he µSM me hod pe mi s he mapping o esh ice sec ions in he ield, while152
d illing is ongoing. This is c ucial o minimizing he e ec s o ec ys alliza ion, eco e y and pos -153
d illing elaxa ion o he ice mic os uc u e. Unde op imal condi ions, he mapping o a comple e154
sec ion (50 ×100 ×5 mm) akes abou one hou and can be accomplished as ea ly as a ew hou s155
a e co e ex ac ion.156
Analysis o he µSM mic og aphs was pe o med wi h he open-sou ce so wa e Fiji–ImageJ157
(Schindelin e al., 2012). Ci ca 12,000 mic og aphs we e manually analysed, h ough he iden i i-158
ca ion o g ain and subg ain bounda ies, disloca ion walls, and slip bands. Special ca e was aken159
a he o e lapping egions be ween mic og aphs. E e y ime a g ain wi h a se o pa allel slip bands160
was manually iden i ied, he so wa e de e mined he posi ion and inclina ion o he se , labelled161
i , and eco ded he in o ma ion in a sp eadshee . Thus, as a ule, each slip-band-inclina ion da a162
poin co esponds o he se o slip bands in an indi idual g ain. An excep ion was made o some163
e y la ge g ains wi h well-de ined slip bands: in such cases, he g ain was decomposed in o sec o s164
o size compa able wi h he a e age g ain size, and each sec o was measu ed sepa a ely. The165
angula p ecision o he measu emen s was o app oxima ely 2 deg ees.166
Au oma ic analysis o slip bands was no possible, because he co ec iden i ica ion o slip167
bands is excep ionally di icul (c . Fig. 1): so wa e and un ained eyes o en con use hem wi h168
de ocused su ace i egula i ies (e.g. sublima ion g oo es), o wi h occasional op ical abe a ions169
(caused e.g. by some in e nal g ain-bounda y edges). The e o e, o da e, he manual iden i ica ion170
o slip bands by a judicious and expe ienced specialis in ice mic oscopy and µSM is s ill he mos 171
eliable p ocedu e. Hope ully, new echniques o machine lea ning applied o image analysis may172
enable he au oma ion o hese p ocedu es in he nea u u e.173
I should be no ed ha i n samples ha e no been analysed in his s udy. Whe eas he µSM174
me hod has al eady been success ully employed o in es iga e he mic os uc u e o i n (Fa ia e al.,175
2010, 2014b; Kip s uhl e al., 2009), such in es iga ions we e es ic ed o e lec ed-ligh mic oscopy176
o sublima ion g oo es (o g ain and subg ain bounda ies) on he ice su ace. The eason o his177
es ic ion is ha i n is no anspa en as ice: he po ous s uc u e o i n pe mea es h ough he178
whole sec ion, sca e ing he ansmi ed ligh ha would be necessa y o e eal in e nal s uc u es179
inside he ice sec ion, like slip bands.180
4 Resul s181
Slip bands we e iden i ied and classi ied acco ding o hei inclina ions wi h espec o he ho izon al182
plane. Two ema ks a e ele an in his ega d:183
Rema k 1: Ice co es d illed o da e (including he EPICA-DML Deep Ice Co e) ha e a bi a y184
azimu hs (Fa ia e al., 2018; Weikusa e al., 2017), and consequen ly, so ha e also hei 185
e ical sec ions.186
Rema k 2: Owing o hei ain na u e and s acked a angemen , slip bands in pola ice a e187
bes disce ned i hey a e nea ly pe pendicula o he iew plane, i.e. he sec ion’s su ace188
(miso ien a ion <10◦; Kip s uhl e al. 2006).189
F om Rema k 1, i ollows ha only he slip band’s appa en dip angle ( iz. pe cei ed angle190
o inclina ion) can be de e mined. In gene al, he appa en dip angle ep esen s a lowe bound191
o he ue dip angle ( iz. maximum angle o inclina ion). Ne e heless, Rema k 2 implies ha 192
disce nible slip bands usually ha e appa en dip angles simila o hei espec i e ue dip angles.193
Be ha as i may, he e we s ick o he exp ession “appa en dip angle”, in o de o s ess wo194
impo an ac s: (i) he appa en and ue dip angles may no be iden ical; (ii) he azimu h o a195
e ical sec ion, and consequen ly he slip band’s dip di ec ion, is unknown.196
Figu e 2 displays ou examples o appa en -dip-angle dis ibu ions o slip bands, wi h an ac-197
cu acy o i e deg ees. The e olu ion o hese dis ibu ions wi h dep h, and consequen ly wi h198
age, is clea ly isible. The mos ob ious ea u e o he whole dep h in e al is a ne inc ease in199
he ac ion o low-angle (<30◦) slip bands a he expense o mid-angle (be ween 30◦and 60◦)200
and high-angle (≥60◦) slip bands. Close inspec ion e eals, howe e , a somewha mo e complex201
de elopmen : down o a e e sal zone a (415 ±60) m dep h, he e is ac ually a dec ease in he202
equency o low-angle slip bands, which is simul aneously compensa ed by an inc ease in he e-203
quency o mid-angle slip bands. In con as , a some poin wi hin ha e e sal zone his p ocess204
is e e sed and he mid-angle slip bands s a o disappea , while low-angle slip bands g adually205
inc ease in numbe . These obse a ions a e illus a ed in Fig. 3, which shows he dep h e olu ion206
o low-, mid-, and high-angle slip bands in all eigh sec ions analysed in his s udy. No ice also207
ha he equency o high-angle slip bands dec eases h ough he whole dep h ange (94–854 m)208
in a a he linea ashion.209
5 Discussion210
The obse a ion ha he equency o high-angle slip bands dec eases mono onically wi h dep h211
h oughou he s udied in e al (94–854 m) should be no su p ise o hose awa e o he ice- low212
ea u es a he EPICA-DML si e: he dec ease can be explained as a di ec consequence o he213
de eloping s ain-induced aniso opy o polyc ys alline ice in ha egion ( iz. la ice p e e ed214
o ien a ions, so-called “ ab ic”). The EPICA-DML d illing si e lies on an ice idge. The e o e, by215
conside ing he gene al ule ha he ice low in he uppe pa o a s a iona y ice shee can be216
oughly desc ibed by i s su ace down-slope combined wi h he ubiqui ous e ical comp ession due217
o he o e bu den o con inual snow accumula ion, we conclude ha he la ge-scale low in he uppe 218
housand me es a EPICA-DML has a iaxial cha ac e , domina ed by ho izon al ex ension ac oss219
he idge (∼10−4a−1), e ical comp ession (∼10−4a−1), and a sligh ho izon al comp ession a e220
along he idge (one o mo e o de s o magni ude smalle han he o he wo a es). These s ain-221
a e es ima es a e compa ible wi h ai bo ne su ace- eloci y obse a ions, nume ical simula ions,222
and mic os uc u e analysis (Fa ia e al., 2014b, 2018; S einhage, 2001; Weikusa e al., 2017).223
The aniso opic c-axis o ien a ion dis ibu ion induced by his kind o de o ma ion may be224
called a “ e ical g ea -ci cle gi dle wi h a e ical maximum,” which means ha he caxes end225
o eo ien hemsel es wi h inc easing dep h away om he (ho izon al) p incipal axis o ex ension226
and owa ds he p incipal axes o comp ession—especially he s onge e ical one. Acco dingly,227
his means ha he basal planes ha e an inc easing endency o become angen o he p incipal228
axis o ex ension, as i hey we e a anging hemsel es on he ellip ical cylind ical su ace o a229
ic i ious “ho izon ally la ened ube.” The e o e, i espec i e o he o ien a ion o he e ical230
sec ion, mos basal planes in deepe samples should be a low angles wi h espec o he ho izon al,231
and so should also be he mos equen ly obse ed slip bands.232
Whe eas he abo e desc ip ion explains he mono onic dec ease wi h dep h in he equency o 233
high-angle slip bands, he obse a ion ha his dec ease is app oxima ely linea is unan icipa ed,234
especially i we conside he s ongly non-linea e olu ion o he o he wo dip classes. This is a235
ma e ha dese es u he in es iga ion in he nea u u e.236
In con as o he ela i ely s aigh o wa d explana ion o he e olu ion o high-angle slip237
bands, he e olu ion o low- and mid-angle slip bands is much less i ial. Two con as ing be-238
ha iou s a e obse ed abo e and below a e e sal zone iden i ied a (415±60) m dep h. Below his239
e e sal zone, he e olu ion o low- and mid-angle slip bands ollows he expec ed beha iou , wi h240
mid-angle slip bands g adually gi ing way o an inc easing numbe o low-angle slip bands. Such241
a beha iou is “expec ed” in he sense ha i can be explained wi h he same a gumen s al eady242
used o explain he p og essi e educ ion in he equency o high-angle slip bands. On he o he 243
hand, in he shallowe dep hs abo e he e e sal zone, he equencies o low- and mid-angle slip244
bands beha e in he opposi e way: he ac ion o low-angle slip bands obse ed a shallow dep hs245
g adually dec eases wi h dep h down o he e e sal zone. Likewise, he ac ion o mid-angle slip246
bands obse ed a shallow dep hs p og essi ely inc ease in impo ance owa ds he e e sal zone.247
These wo con as ing beha iou s clea ly canno be explained wi h he a gumen s abou induced248
aniso opy in oked o high-angle slip bands and o he egion below he e e sal zone. Ano he 249
explana ion is needed.250
The eason o disca ding he induced-aniso opy explana ion in he case o shallow bubbly ice251
is ob ious: polyc ys alline ice in he uppe 450 m dep h o he EPICA-DML si e is nea ly iso opic252
(Weikusa e al., 2017). This is, howe e , also he eason why he beha iou o low- and mid-angle253
slip bands in he shallow ice abo e he e e sal zone seems coun e -in ui i e: he mac oscopic254
s ain a e anywhe e in he uppe 1000 m o EPICA-DML is essen ially he same— iz. he iaxial255
egime al eady desc ibed—and his ac combined wi h he nea -iso opy o shallow ice implies ha 256
he mos p obable slip bands in he uppe hund eds o me es should be a mid-angles, because257
basal planes a such inclina ions can bea he la ges esol ed shea s esses om he mac oscopic258
iaxial load (Asa o, 1983; Fa ia and Kip s uhl, 2004; Placidi e al., 2006).259
Thus, i u ns ou ha he c ucial ques ion abou he e olu ion o slip bands in shallow pola 260
ice a he EPICA-DML si e is: why do he equency o mid-angle slip bands in he uppe mos ew261
hund ed me es inc ease wi h dep h down o he e e sal zone? In a ecip ocal o mula ion: why262
do he equency o low-angle slip bands in he uppe mos ew hund ed me es dec ease wi h dep h263
down o he e e sal zone?264
He e we p opose an answe o he abo e ques ion in he o m o a no el hypo hesis o mic o-265
s uc u al ading memo y. In a ew wo ds, i s undamen al idea is ha he shallow bubbly ice266
inhe i s some mic os uc u al imp in s and localized s ain ene gy om he o me g anula and267
po ous s uc u es o snow and i n, which a ec he dis ibu ion o slip bands a shallow dep hs.268
Such inhe i ed o ce-chain elics g adually e anesce wi h ime and dep h, unde he ac ion o 269
dynamic eco e y and ec ys alliza ion, and he edis ibu ion o in e nal s esses.270
Mo e p ecisely, i is well known ha he sin e ing o g anula snow and po ous i n in o solid,271
polyc ys alline bubbly ice gene a es an in ica e ne wo k o o ce chains, iz. mo e o less s a-272
ble, load-bea ing ains o g ains wi hin he i n skele on (B own, 1980; Guble , 1978; K y, 1975;273
Scapozza and Ba el , 2003; on Moos e al., 2003; Wakahama, 1960). Such o ce chains ha e he274
abili y o ans e , modi y, and b eak down he applied mac oscopic s ess in o a se ies o complex275
and seemingly unco ela ed mic oscopic in e nal s esses, which gi e ise o s ong s ain he e o-276
genei ies in clus e s o g ains ha unde go la ge amoun s o s ain accommoda ion, acili a ed by277
he po e space. These in e nal s esses can some imes be so in ense ha hey may cause localized278
dynamic ec ys alliza ion in cold i n (down o −45 ◦C), a phenomenon i s obse ed by Kip s uhl279
e al. (2009) and heo e ically explained by Fa ia e al. (2014b).280
Wi hin he con ex o his s udy, a undamen al ea u e o he mic oscopic in e nal s esses281
gene a ed by o ce chains in i n is ha he di ec ions and in ensi ies o hei p incipal s esses may282
a y wildly among neighbou ing clus e s o g ains on he mic o- and meso-scales, and may also283
conside ably di e om he mac oscopic p incipal s esses ela ed o he la ge-scale ice low. Seeing284
ha slip bands o m and e ol e in ice in esponse o local, mic oscopic p incipal s esses ( h ough285
hei p ojec ions on o he basal planes o he c ys alline ice la ice as esol ed shea s esses), we286
conclude ha he o ien a ion dis ibu ion o slip bands in pola i n on he mesoscale (∼10−1m)287
should exp ess his di e si y o mic oscopic p incipal s esses h ough a mo e andom dis ibu ion288
o slip-band o ien a ions han i would be expec ed o a solid piece o iso opic polyc ys alline ice289
subjec ed o a well-de ined iaxial load.290
The hypo hesis o mic os uc u al ading memo y asse s ha he mos in ense and s able o ce291
chains in i n should p oduce highly localized concen a ions o s ain ene gy a ound ains o 292
load-bea ing g ains ha emain pa ially ac i e and p ese ed, oge he wi h some o he s onges 293
slip bands, in he mic os uc u e o shallow bubbly ice benea h he i n–ice ansi ion (po e close-294
o dep h). Such emaining slip bands and ains o g ains ep esen elics o he o me i n295
s uc u e, which g adually lose in luence on he mic os uc u e o shallow ice and decay h ough296
he edis ibu ion o in e nal s esses and he ac ion o dynamic eco e y and ec ys alliza ion297
(including g ain g ow h). Indeed, he slip-band dis ibu ions obse ed in he EPICA-DML sec ions298
om 94, 205 and 355 m dep h exp ess p ecisely his phenomenon: hey desc ibe he g adual299
ansi ion om a nea ly- andom o ien a ion dis ibu ion o slip bands a 94 m dep h o a mid-300
angle-domina ed dis ibu ion cha ac e is ic o solid, polyc ys alline ice subjec ed o a well-de ined301
iaxial load.302
The dep h ange in which all hese decay p ocesses ake place and he memo y o he ancien 303
i n mic os uc u e ades away de ines he s abiliza ion zone, which coincides wi h he shallow304
bubbly ice zone anging om he po e close-o dep h down o he end o he slip-band e e sal305
zone iden i ied in his wo k. I is in he s abiliza ion zone ha he las mani es a ions o he highly306
he e ogeneous de o ma ion na u e o po ous i n gi e way o he mo e homogeneous de o ma ion307
egime o solid polyc ys alline ice. This is alid no only o he dis ibu ion o slip bands, bu 308
also o o he mic os uc u al ea u es, including he o ien a ion o c-axes, as ollows. The in ica e309
o ce-chain ne wo k o i n induces a mul i ude o localized la ice p e e ed o ien a ions wi hin310
small clus e s o g ains, which oge he unc ion as a “nea ly iso opic noise” ha easily ou weighs311
he s ain-induced aniso opy d i en by he mac oscopic s ess ac ing on he i n skele on. As312
i n u ns in o bubbly ice, such a s ong “noise” ades away wi hin he s abiliza ion zone, being313
g adually eclipsed by he p e ailing s ain-induced aniso opy imposed by he mac oscopic s ess314
ha d i es he ice low. This s abiliza ion phenomenon may con ibu e o he sluggish o a ion315
o c-axes gene ally obse ed in he uppe hund eds o me es o pola ice shee s (Cas elnau e al.,316
1996; Du and e al., 2007; Fa ia e al., 2002; Weikusa e al., 2017).317
6 Conclusion318
We canno accep any hing as g an ed beyond he i s ma hema ical o mulae. Ques ion319
e e y hing else.320
Ma ia Mi chell. Quo ed by Holmes (2018).321
This wo k p esen ed an analysis o he o ien a ion dis ibu ion o slip bands in he uppe 850 m o 322
pola ice om he EPICA (Eu opean P ojec o Ice Co ing in An a c ica) d illing si e in D onning323
Maud Land (DML), An a c ica. Ci ca 12,000 high- esolu ion mic og aphs om eigh di e en 324
e ical sec ions o he EPICA-DML Deep Ice Co e, spaced a oughly 100 m dep h in e als, ha e325
been manually analysed. The mic og aphs we e aken om esh ice, sho ly a e d illing, o a oid326
undesi able elaxa ion e ec s.327
The analysis e ealed wo dis inc e olu ion egimes in he o ien a ion dis ibu ion o slip bands.328
In he shallow bubbly ice benea h he i n–ice ansi ion ( iz. po e close-o dep h ≈88 m) down329
o a e e sal zone a (415 ±60) m dep h, he slip-band o ien a ion dis ibu ion e ol es om nea ly330
andom o one wi h a s ong mid-angle (30–60◦) mode. In con as , below he e e sal zone and331
down o he end o he dep h ange conside ed he e (853 m), he slip-band o ien a ion dis ibu ion332
becomes s ongly unimodal, wi h a well-de ined low-angle (0–30◦) mode, which ollows he e olu ion333
o he s ain-induced aniso opy (c-axis p e e ed o ien a ions) o deep bubbly ice.334
While he ea u es o he o ien a ion dis ibu ion o slip bands below he e e sal zone a e, as335
expec ed, compa ible wi h he c-axis aniso opy and he mac oscopic s ess ha d i es he la ge-336
scale ice low, he e olu ion o he dis ibu ion o slip bands abo e he e e sal zone u ns ou o337
be a puzzling esul . In o de o explain i , we in oduced he e he hypo hesis o mic os uc u al338
ading memo y: o ce chains, which a e cha ac e is ic ea u es o he sin e ing and de o ma ion o 339
g anula snow and po ous i n, lea e mechanical and s uc u al imp in s on he mic os uc u e o 340
polyc ys alline bubbly ice. These imp in s end up a ec ing he dis ibu ion o slip bands a shallow341
dep hs, while g adually e anescing unde he he ac ion o dynamic eco e y and ec ys alliza ion,342
and he edis ibu ion o in e nal s esses. The e y he e ogeneous s ains associa ed o o ce chains343
a e also esponsible o he gene a ion o a nea ly- andom o ien a ion dis ibu ion o slip bands344
and c-axes in i n, compa ible wi h he one obse ed he e in he shallowes ice sample jus benea h345
he i n–ice ansi ion dep h.346
The impac and consequences o hese esul s a e ema kable. Fi s , he hypo hesis o mi-347
c os uc u al ading memo y is compa ible no only wi h he slip-band obse a ions desc ibed348
he e, bu also wi h he no ion and ole o o ce chains in snow and i n (B own, 1980; Guble , 1978;349
K y, 1975; Scapozza and Ba el , 2003; on Moos e al., 2003; Wakahama, 1960), he obse a ion350
o dynamic ec ys alliza ion in deep i n (Kip s uhl e al., 2009) and i s heo e ical explana ion in351
e ms o in e nal s esses (Fa ia e al., 2014b). Fu he mo e, i allows he iden i ica ion o a s abi-352
liza ion zone (which coincides wi h he shallow bubbly ice zone al eady desc ibed), whe e elics o 353
he once s ongly localized mechanical and s uc u al he e ogenei ies o ancien i n a e g adually354
dissipa ed. Whe eas his s abiliza ion mani es s i sel mos clea ly in he e olu ion o slip bands355
epo ed he e, i may also be no iceable in o he mic os uc u al ea u es o shallow bubbly ice,356
including he sluggish e olu ion o c-axis o ien a ions o en obse ed in his zone (Cas elnau e al.,357
1996; Du and e al., 2007; Fa ia e al., 2002; Weikusa e al., 2017). A las , he obse a ions o 358
slip bands in he aniso opic, deep bubbly ice p esen ed he e a e compa ible wi h all EPICA-DML359
s udies o ice mic os uc u e and low pe o med so a , including g ain sizes and elonga ions, slip360
bands and subg ain bounda ies, isual s a ig aphy, c-axis p e e ed o ien a ions and ice- low sim-361
ula ions (Fa ia and Kip s uhl, 2004; Fa ia e al., 2010, 2014b, 2018; Kip s uhl e al., 2006; Weikusa 362
e al., 2009, 2017).363
Admi edly, he hypo hesis o mic os uc u al ading memo y and i s co olla ies a e s ill con-364
jec u es open o u he sc u iny and co obo a ion. Following Ma ia Mi chell’s ad ice quo ed a 365
he beginning o his sec ion, we should no accep such conjec u es as g an ed. They a e, ne -366
e heless, physically sound and consis en wi h a numbe o independen obse a ions o physical367
phenomena and p ope ies o pola ice, as epo ed in his wo k. The e o e, hey dese e o be368
aken se iously, as hei alue lies also in he new ideas and ques ions hey disclose, which shall369
p omo e u u e in es iga ions o he ascina ing phenomenon o i n–ice me amo phism. In his370
ein, he hypo hesis o mic os uc u al ading memo y lays he ounda ions o a new expe imen al371
and heo e ical amewo k o s udy o one o he mos impo an and elusi e p ocesses in pola 372
ice: dynamic eco e y. A e accoun ing o he e ec s o de o ma ion and ec ys alliza ion on he373
g ain s e eology, one may use he e olu ion o slip bands in shallow bubbly ice o es ima e he a e374
a which disloca ions disappea om inac i e slip bands. This line o esea ch will be pu sued in375
he nea u u e.376
Acknowledgemen s377
My g a i ude o Sepp Kip s uhl, Nobuhiko Azuma, and Ilka Weikusa o many discussions and378
collabo a ion o e he yea s on he physical p ope ies o pola ice. Special hanks also o Luca379
Placidi o his excellen gues -edi o ial wo k, and o wo anonymous e iewe s o hei in alu-380
able c i icism. Financial suppo om he Ram´on y Cajal G an RYC-2012-12167 o he Spanish381
Minis y o Economy, Indus y and Compe i i eness is kindly acknowledged. This wo k is a con-382
ibu ion o he Eu opean P ojec o Ice Co ing in An a c ica (EPICA), a join Eu opean Science383
Founda ion/Eu opean Commission scien i ic p og amme, unded by he EU and by na ional con-384
ibu ions om Belgium, Denma k, F ance, Ge many, I aly, he Ne he lands, No way, Sweden,385
Swi ze land and he Uni ed Kingdom. The main logis ic suppo was p o ided by IPEV and386
PNRA (a Dome C) and AWI (a D onning Maud Land). This is EPICA publica ion no. 310.387
Figu e 2: Examples o o ien a ion dis ibu ion o slip bands o he e en-numbe ed samples ( he
odd-numbe ed samples ell essen ially he same s o y). The dashed g ey lines desc ibe a e e ence
dis ibu ion o he ideal case o andomly o ien ed slip bands, aking in o accoun he e ec s de i ed
om Rema ks 1 and 2.
Figu e 3: E olu ion wi h dep h (and age) o low- (0–30◦), mid- (30–60◦), and high-angle (60–90◦)
dip classes o slip bands. The dashed g ey lines se e as e e ence o he equencies o low-, mid-,
and high-angle dip classes in he ideal case o andomly o ien ed slip bands, aking in o accoun
he e ec s de i ed om Rema ks 1 and 2.
