Downloaded by guest on October 1, 2021 pee seieti h evsvns fmlntsa many at mylonites of pervasiveness the in litho- evident ductile the as of portion sphere, strongest the in weakening explain offset to sufficiently could 19) margin (18, passive facilitate collapse. and damage lithosphere the subduct. grain of stiffening and thermal to detach due to weak- sediment accumulated margin that ening and proposed the (14) 16) Bercovici allow weakening and 15, to Mulyukova enough require lithosphere (5, still the margin these of sagging, although the 17), with at collapse, (13, associated loading its stretching stress trigger or to tensile to invoked rifting, example, margin been and buoy- passive for have negative the strongest mechanisms including, of weaken Various its action and/or 14). the at 13, load under 5, also deform (4, and to is ancy heaviest, likely it coldest, least oldest, unstable, thus is gravitationally lithosphere mar- the most passive where while are subduction However, (where gins margins. corre- trenches continental the ocean with of deep occurs) basin because existing ocean appealing, many opening is of mar- lation margin, an passive continental of at a lithosphere plume–lithosphere subduction abuts oceanic or the of where 6–11) initiation gins, The (4, faults (12). zones subduction transform interaction fracture new from preexisting nucleating a on key are example, or initiating There function for is for planets. including, tectonics and zone, terrestrial mechanisms plate (4–6) other possible not why is geosciences various apparently lithosphere and in but strong how enigmas Earth, cold major understanding a for subduc- in the to mechanisms How sustained of primary (1–3). and one the mantle initiated of Earth’s is tion one the and cooling convectively tectonics plate for T margins passive collapse. thereby margin sinking, passive and bending facilitating y. to is greatly million weak that but lithosphere 100 forcing the lateral about in to viscosity strong after anisotropic to lithosphere lead of bands and These portion oriented, mix- large vertically of a become bands develop, basin, occupy can ocean weakening opening stress an and the compressive in ing lateral push by With ridge lithosphere. and by gra- the imposed compositional heterogeneity in stress by petrological of both state with driven associated is mixing dients Such lithospheric occurs. in phases rocks damage mineral lithospheric between Grain mixing considerable collapse. where enhanced margin for is passive allow facilitate accu- and can weakening and damage Spontaneous grain necessary. the therefore mulated sink- of are weakening and mechanical margin weight of means own passive lithosphere Some its mantle. ocean under the cold into bending ing old, from the it prohibit of prob- should strength is floor the collapse sea margin because where locations passive lematic margins, Such favored margins. passive the continental at understand- of abuts is One in triggering tectonics. mysteries subduction plate key for has the Earth of why 2020) the 1, one ing June into review is plates for initiated (received lithospheric 2020 cold mantle—is 10, 2018. of December in approved sinking elected and Sciences subduction—the MN, of How Minneapolis, Academy Minnesota, National of the University of Kohlstedt, members L. by David Articles by Inaugural Edited of series special the of part is article This a Bercovici David damage and through mixing margins grain passive of demise and Evolution PNAS eateto at lntr cecs aeUiest,NwHvn T06511 CT Haven, New University, Yale Sciences, Planetary & Earth of Department h ri-aaemcaimhsbe rvosyproposed previously been has mechanism grain-damage The ltsi osdrdbt n ftemi rvn forces driving main the of tectonic heavy one and both cold, considered old, is of subduction, plates or sinking, he 01Vl 1 o e2011247118 4 No. 118 Vol. 2021 | subduction a,1 n liaMulyukova Elvira and | ri damage grain a alzdgan ln h te iea’ ri onais(58), boundaries grain recrys- mineral’s mineral’s other one the Mixing of along research. grains transport active tallized mechanical of from matter a arise still could is unlikely) is cavitation weak lithospheric developing in role het- unique zones. plays mantle and likely in units, important mineralogical mixing an between of mixing evolution i.e., the minerals erogeneity, where Thus, to relative unmixed. 58) 49, remain 40–42, been 34, weaken- indeed (29, and mechanisms has deformation ing different phases significantly mineral grain induce to of suppressing shown pro- Mixing and by healing. comminution ways, and (18). two and growth in damage reduction localization grain grain-size enhance moting accumu- to and acts the (54–57) pinning via Thus, dislocations) dynamic subgrains of facilitates of possibly lation formation pinning (43–45, (i.e., creep Zener recrystallization diffusion Moreover, permanent 53). in 51, medium growth the grain the suppressing of keeping in role migration and important grain-boundary an plays the phase) which blocks other mix (in and phase phases pinning mineral Zener olivine these that one where as suggests observation especially such This and (40–53). phases, peridotite, where mineralogical in mantle pyroxene multiple lithospheric the are in there 24–35) form 19, and typically mylonites (18, boundary theoretical ultramylonites and Plate of studies. number scale (36–42) a observational planetary of and and subject the global been the have for important at are processes mylonites understanding in occurring shear physics and (20–23). grain-scale reduction The deformation grain-size intense extreme with of correlated review). localization indication for 19, an ref. are (see Mylonites belts deformation and boundaries plate ulse aur 8 2021. 18, January Published doi:10.1073/pnas.2011247118/-/DCSupplemental at online information supporting contains article This 1 the under Published Submission.y Direct PNAS theory, a is the article This developed interest.y competing project, no paper.y declare the the authors wrote The conceived and graphics, and E.M. model numerical and the developed D.B. contributions: Author owo orsodnemyb drse.Eal [email protected] Email: addressed. be may correspondence whom To ad nteltopeeta aiiaesbuto initiation. subduction facilitate that lithosphere the weak a generate in in and bands damage stresses and compressive mixing induce Horizontal margin other. passive each miner- with where mix occurs mostly als and in lithosphere diminish the in stress weakens damage under size, Grain grains mineral sink. whereby col- to rocks, stiff mantle too then be litho- cold should but That however, founders. sphere, passive, and heavy the and or cold mantle, gets near-surface lithosphere, when immobile when occurs there, collapse once Margin formed lapsed. was they margin implies a the which remains margin, ocean– initiates the continent at subduction trenches engine along how occurs the often Yet, is Subduction mystery. mantle tectonics. Earth’s plate the into of floor sea of Subduction Significance o ieasi oi tt i thg rsue (where pressures high at mix state solid a in minerals How NSlicense.y PNAS https://doi.org/10.1073/pnas.2011247118 . y https://www.pnas.org/lookup/suppl/ | f9 of 1

EARTH, ATMOSPHERIC, INAUGURAL ARTICLE AND PLANETARY SCIENCES or through dissolution of one mineral and precipitation of it at Model Summary the other mineral’s grain-boundary junctions (41, 42, 49). These Our theoretical model builds on the theory for diffusive grain mechanisms are both limited by element diffusion and similarly mixing and damage (34) and the model of grain-size evolution in driven by imposed stresses. Bercovici and Mulyukova (34) pro- passive margins (14), with some adaptations; it is fully developed posed a theory whereby grain mixing itself is a form of diffusion and explained in SI Appendix, but summarized briefly here. of one mineral through the other, with diffusivity governed by Our model system is composed of three physical processes at the imposed state of stress. Such diffusive mixing between min- three different length scales; these involve 1) thermal diffusion eral phases promotes grain damage and weakening, specifically in a cooling, thickening lithosphere; 2) diffusion of petrologi- in the mixing regions; these zones correspond well to observa- cal heterogeneity through grain or phase mixing (i.e., mixing of tions of well-mixed mylonites and ultramylonites separating the olivine and pyroxene grains); and 3) mineral grain-size evolution larger-grained units of a single mineral phase (43–45, 53). via the competition between surface-tension–driven coarsening Mulyukova and Bercovici (14) demonstrated that an already and deformation-induced damage. The length scales for varia- well-mixed lithosphere leads to significant weakening by grain tions of temperature and ridge-push stress are referred to as the damage to facilitate passive margin collapse. Here we propose macroscopic scale and are much longer than the length scales for that petrological heterogeneity in an unmixed lithosphere may grain-mixing diffusion of petrological heterogeneity, referred to lead to mylonitic zones of extreme weakness at the boundaries as the mesoscopic scale, which, in turn, is larger than the grain between mineral phases, at the centimeter scale (Fig. 1). Accu- scale (Fig. 1). At physical conditions representative of Earth’s mulation of these weak zones by stress-driven grain mixing and lithosphere, the thermal diffusion length scale is LT = 112 km, grain damage may promote sufficient lithospheric weakening to the grain-mixing diffusion length scale is LG = 15 cm, and the facilitate passive margin collapse. Here we explore this hypoth- grain-size length scale is Rf = 360 µm (see SI Appendix for a esis in a model of the lithosphere in an opening ocean basin detailed discussion). undergoing simple ridge-push stress, which is compressive in the At the macroscopic scale, the imposed dimensionless tem- direction of plate motion. We show that diffusive grain mixing perature and ridge-push stress fields in the lithosphere of the is driven in the direction of compressive stress, which leads to widening ocean basin are for a half-space cooling model, as vertically aligned weak bands where mineral phases mix. These adapted from Dahlen (59): bands are predicted to exist in an envelope between a thin layer   of brittle lithosphere and crust near the surface and uniformly ΠGZ Θ = Θm − (Θm − Θs ) erfc − √ [1a] weakened and warmer material at depth; this envelope extends t across much of the thickness of the lithosphere by a passive mar- r t 2 2  Π Z  gin age of about 100 My. While the banded weak zones are not −ΠGZ /t G τN = e + ΠGZ erfc − √ [1b] uniformly weak, they lead to anisotropic lithospheric strength π t that is stiff to lateral forcing like ridge push, but susceptible to vertical shear and bending associated with negative buoyancy (14), where erfc is the complementary error function; Θ = and subduction initiation, thereby priming the collapse of passive T /Tref in which T is temperature (in kelvins) and Tref = margins. 1,000 K is a reference temperature typical of the midlithosphere;

Fig. 1. Conceptual sketch of the model setting, showing a spreading ocean basin and passive margin and the direction of ridge-push stress. Three model scales are indicated: the macroscopic scale of the lithosphere and ocean basin, the mesoscopic scale of the petrological heterogeneity (showing two phases, green and blue, in an unmixed conglomerate of olivine and pyroxene), and finally the grain scale at which grain size evolves and phase mixing is driven by compressive stress (which causes dilation of grain boundaries that are oriented parallel to the compressive direction and constriction on orthogonal grain boundaries, as indicated by the red arrows in Right Inset) and occurs by subgrains of one phase migrating mechanically or chemically along the other phase’s grain boundaries (green arrows, Right Inset).

2 of 9 | PNAS Bercovici and Mulyukova https://doi.org/10.1073/pnas.2011247118 Evolution and demise of passive margins through grain mixing and damage Downloaded by guest on October 1, 2021 Downloaded by guest on October 1, 2021 vlto n eieo asv agn hog ri iigaddamage and mixing grain through margins passive of demise and Evolution Mulyukova and Bercovici scale length grain-diffusion the by (normalized L vary stress and nor- age); margin (and motion spreading stress); of direction by the malized in compressive is respectively; temperatures, face Θ duteti o tesiflecsganmxn ifso (SI diffusion minor grain-mixing a influences with stress (34) Appendix): how Mulyukova evolution and in grain-size Bercovici adjustment equations and from dimensionless mixing adapted pin- coupled grain are Zener The grain stress-driven through scale. their diffusive other grain of of each the evolution on at the effect ning, and their scale diffusive including mesoscopic model sizes, pyrox- the we and olivine at scale, (nominally phases ene) macroscopic mineral two the of and mixing at grain variables stress and of ature definitions for 2 and 1 parameters.) Tables (See and uniform. alization effectively are stress Appendix and temperature of scale scale, grain-mixing the at stress L and temperature in diffusion); variations thermal to thus diffusion grain-scale and of ratio (the number G G m gis h akrpo h ihshr’ hnigtemper- changing lithosphere’s the of backdrop the Against ); cu nyoe etsof depths over only occur 1 = Π G .5 t ∂ = ∂ ∂φ ∂ ∂ R stm nraie yatmsaeo a of timescale a by (normalized time is ∂ Π t o ealddsuso fsae n nondimension- and scales of discussion detailed for and L r t t i G G τ ˜ = = = Z /L Z 70 = τ + Θ p qr stemcocpcdphoe hc temperature which over depth macroscopic the is T sdphnraie by normalized depth is N C η R s stesur oto h ri-ifso Prandtl grain-diffusion the of root square the is i Γφ(1 q ∂ C ∂ i p 0 = Z −1 I Independent T variables Dependent aibefactors Variable x P,caatrsi fmxmmrdepush ridge maximum of characteristic MPa, −1 be1 iesols variables Dimensionless 1. able i K b a D τ Θ t (x Z Z r R φ D C C η  Quantities .3 N − I i i i − I i , φ(1 − z D ) r h iesols ateadsur- and mantle dimensionless the are D φ)K I − i r R 2 φ)K i 2 η τ Z a N r siae sn h aeilpoete from properties material the using estimated are 2 Z

variables i τ τ  N N X n  ∂ ∂ ∂φ ∂ +1 i sterdeps tes which stress, ridge-push the is φ x x hs ttegrain-mixing the at thus, 1;  φ  i 2  ! L a T . Since . τ N n eocpcposition Mesoscopic Interface ri-ifso coefficient Grain-diffusion coefficient compliance creep Diffusion Dislocation ig-uhstress Ridge-push Temperature Time depth Macroscopic ee inn factor pinning Zener nefc ogns rrdu fcraueFnto of Function curvature of radius or roughness Interface Phase hs o fraction vol 1 Phase ri-onaydmg ubr phase number, damage Grain-boundary nefc oreignumber coarsening Interface phase of number Grain-coarsening factor area Interface +1 + 0 My 100 Π b R i τ engansize grain mean G i m N 2 aaenumber damage   re opinecoefficient compliance creep then 1, passive [2b] [2a] Definition [2c] SI al S1. Table Parameters T of by that is to normalized evolution roughness grain-size (also interface coupling phases factor pinning two Zener the The between interface the by and malized phase minor the likewise, of olivine); (nominally and phase lithosphere) the in pyroxene lithosphere by normalized the also of (and over, reference ridge the of from frame away moving the First, in here. ones coordinate key spatial few a highlight we All be2 iesols Parameters Dimensionless 2. able D C C m q p Γ D f E c Π n Quantities 1 a I i G f , i I iesols uniisaedfie nTbe n ,but 2, and 1 Tables in defined are quantities dimensionless , E al S1. Table Appendix, SI 2 φ b , , ν ≡ E g φ i 1 r siae sn h aeilpoete from properties material the using estimated are R stevlm rcino h io hs (nominally phase minor the of fraction volume the is f ri-onaydmg number, damage Grain-boundary nefc-oreignme at number Interface-coarsening Grain-coarsening ifso re ri-ieexponent grain-size creep Diffusion exponent Interface-coarsening exponent Grain-coarsening coefficient work Grain-diffusion nefc aaenme at number damage Interface aaefato parameters fraction Damage re n oreignraie 4 5 24 45, 64, normalized coarsening and Creep coefficient pinning Zener qaero fgrain-diffusion of root Square ilcto re tesexponent stress creep Dislocation i ); phase ciainenergies activation number Prandtl at Z r i T sterdu fcraueo ogns of roughness or curvature of radius the is 1 = 0 = i ucinof Function ucinof Function of func. ucinof Function ucinof Function K b a D D C η C at , I i ,0 K 1,000 = = = oe n equations and Notes I i − = = = = = R e 3φ(1 e Definition b T C C tanh D D −E −E 2 0 R ¯ I i e e 2−m I i hto h ao hs bt nor- (both phase major the of that a −E b −E (Θ Z (Θ − ubr phase number, f f , 2 2 −  g g −1 t /f /f φ) (Θ (Θ https://doi.org/10.1073/pnas.2011247118 e Eq. see ; 1 x x Z x φ, c −1) 1 −1) 1 1 − −1 , , , (1 ,

z z z t R − 1 Θ Θ , , , −1) −1) i (Eq. − 1−Θ 1−Θ t t t , m ν m ν R φ r −Θ (Eq. (Eq. (Eq. −Θ φ 1 (Eq. ≡ ν ν (x i 1b) 1a T s ν s ν stema ri size grain mean the is ) φ 0 2c) 2b) 2a) R , r 2 3) T z 2 i i 2 0 sta ftemajor the of that is )  stemesoscopic the is 10 yia values Typical PNAS 1.34 −10 L IAppendix, SI G 10 0.87 10 , .More- ). 10 10 10 3.5 × 3 4 2 3 −2 | 4 3 3 10 −1 3 R −6 [3] f9 of 10 , f ).

EARTH, ATMOSPHERIC, INAUGURAL ARTICLE AND PLANETARY SCIENCES (SI Appendix and ref. 34, appendix B). The quantities a and Heterogeneity is introduced at a given time t0 with the same b are the dislocation and diffusion creep rheological compli- initial condition in φ, at different temperatures, from the cold ance (inverse viscosity) factors, respectively; both quantities are near surface, to the hotter depths closer to the underlying man- dependent on temperature Θ in that viscosity increases as the tle. (A statistical analysis of the effect of varying this initial material gets colder (see Tables 1 and 2 and SI Appendix for a condition is provided in SI Appendix.) In reality, we expect het- detailed discussion). erogeneity to be mostly introduced to the base of the lithosphere Eq. 2a is a diffusion model for grain mixing driven by the at hotter temperatures; however, we track the evolution of het- imposed compressive stress τN acting on the boundary between erogeneity at various temperatures to gauge the extent to which petrological phases and effectively squeezing grains of one phase it diffuses away, partially mixes, or is frozen in place. into the other (Fig. 1). Contrasts in petrological composition are Heterogeneity introduced at a time t0 and temperature T0 (or represented by ∇φ, and mixing occurs where this gradient is dimensionless temperature Θ0) remains at a fixed macroscopic in the direction of compressive stress. Since ridge-push stress is depth Z = −H, given by Eq. 4 (see Materials and Methods); these compressive and horizontal, grain-mixing diffusion (right side of initial conditions thereafter determine the changing temperature Eq. 2a) is only in the x direction (i.e., only horizontal gradients in and stress according to Eq. 1. Given the evolving background φ influence diffusion). (We also briefly consider slab-pull stresses temperature and stress field at this depth, we determine the below for comparison, in which case the compressive stresses and changes in φ, Ri , and r from Eq. 2 over a patch of meso- gradients in φ are in the vertical z direction.) The grain diffusiv- scopic space moving with the lithosphere, in the domain given ity coefficient K allows for faster mixing for smaller grains and by −2 ≤ x, z, ≤ +2. These cases are integrated to steady state or higher temperatures (Tables 1 and 2) and its functional form is quasi-steady state (see Materials and Methods and SI Appendix somewhat agnostic about whether it describes either a mechani- for details), after which we can assume the structures undergo lit- cal or a dissolution mechanism for grain mixing (see SI Appendix tle further change against the cooling background (unless newly for details). introduced heterogeneity is imprinted over the top of them at The grain-damage equations Eqs. 2b and 2c describe how a much later time). We analyze the evolution of heterogeneity the evolution of grain sizes in each phase Ri and the interface with φ, microstructure with the mean grain-size R¯ = φR1 + (1 − roughness r are governed by the competition between surface- φ)R2, and strength with the normalized viscosity µˆ or, conversely, −1 tension–driven coarsening (terms proportional to Ci and CI ) the compliance µˆ given by Eq. 5. Moreover, we can infer the and comminution driven by damage associated with deforma- bulk volume fraction of material that is at least 10 times weaker tional work (terms proportional to Di and DI ) (18, 34). The than the strongest material Φwz given by Eq. 7. factors Ci and CI are the grain and interface coarsening numbers, For a given time t0 and relatively low initial temperature respectively, and Di and DI are the grain and interface dam- T0 or Θ0 and associated depth Z = −H, grain-mixing diffusion age numbers, respectively; these quantities are also dependent is extremely slow and little happens in the system other than on temperature Θ (Tables 1 and 2 and SI Appendix). The evo- gradual coarsening of grains and associated strengthening. The lution of the interface roughness r (Eq. 2c) occurs only where minimum and maximum values of both the mean grain size R¯ phases mix, i.e., in which φ is neither 0 nor 1 (given the factor and the normalized mean viscosity µˆ remain roughly equal, show- η ∝ φ(1 − φ); Table 1). The term proportional to Γ represents ing that the medium remains strong, and thus the fraction of work on the interface during diffusive grain mixing, which acts weak material Φwz = 0 (Fig. 2 A and D). to increase interface area; for ridge push, this work is also pro- At moderate initial temperatures for a given t0, grain-mixing portional to the imposed stress and horizontal gradients in φ (SI diffusion becomes more significant, displaying finite-width mixed Appendix and ref. 34). zones between the monophase units, which develop into small- grain–sized, vertically oriented weak bands. The minimum and Results maximum R¯ and µˆ diverge widely, showing large contrasts in While the model system has various intrinsic complexities, our grain size and viscosity between the mixed and unmixed regions. goal is to examine how lithological or petrological heterogene- Moreover, the volume fraction of weak zones Φwz grows to 50% ity, i.e., poorly mixed conglomerates of monophase units (each or more, before the temperature drops enough to decelerate the unit composed of many tectonites or large grains), mix diffusively system’s evolution. With the vertical orientation of weak bands, across their common interface under the applied ridge-push the material becomes rheologically anisotropic, i.e., more sus- stress. The two-phase mixed regions are the locus of Zener ceptible to vertical shear than horizontal shear (see Fig. 2 B pinning and thus experience both decreased coarsening and and E, green arrows, which indicate the principal directions of enhanced grain-size reduction and induced weakening. How anisotropy). and the extent to which these zones of grain mixing, damage, and At relatively high initial temperatures, grain diffusion becomes weakening develop depend on the stress, temperature, depth, rapid, with pervasive mixing that laterally erases much of the and age of the lithosphere. (Model solution diagnostics are sum- originally introduced petrological heterogeneity. Although the marized in Materials and Methods and described in detail in SI minimum and maximum R¯ and µˆ widely diverge, the area of Appendix.) small-grained, weak material dominates, with only small islands of strength remaining; the fraction of weak zones Φwz → 100% Passive Margins and Ridge Push. As the ocean basin with passive (Fig. 2 C and F). margins grows, the lithosphere away from the spreading center We specifically identify the initial temperature and associated 1 thickens with time. Lithospheric growth is necessarily supplied depth DT for which Φwz ≈ /2 (Fig. 2 B and E), over a range of by the broad upwelling of underlying mantle material (rising in initial times t0= 1, 25, 50, 75, and 100 My. The 50% volume frac- response to the global subduction flux into the mantle; see ref. 3), tion marks the peak in effective anisotropy due to the vertically and thus mantle heterogeneity is continuously introduced into banded weak zones (see SI Appendix for detailed discussion). the lithosphere, primarily through its base. We thus consider Moreover, the depth Z = −DT is near the transition to pervasive how such lithospheric heterogeneity evolves (i.e., as ridge-push mixing and weakness (e.g., see Fig. 2B vs. Fig. 2C and Fig. 2E stress drives grain mixing, damage, and weakening) after being vs. Fig. 2F, in which each pair is separated by a few kilometers). introduced, at all ages from 1 My after the opening of the basin Thus, Z = −DT marks both peak anisotropy and the base of the (chosen to exclude the region of melting and crustal produc- banded zone. tion at the ridge axis) to the typical maximum basin age of Although new petrological heterogeneity is introduced in each around 100 My. model run with the same initial condition in φ, it is, in reality,

4 of 9 | PNAS Bercovici and Mulyukova https://doi.org/10.1073/pnas.2011247118 Evolution and demise of passive margins through grain mixing and damage Downloaded by guest on October 1, 2021 Downloaded by guest on October 1, 2021 pe Left size (Upper of grain stage final the show fraction volume phase The initial the with introduced is heterogeneity 2. Fig. nie oewudrmi nhne ntikessneits strong since the thickness below; in from unchanged zone at pervasively remain banded inception the would the heterogeneity times, zone to receive later adding unmixed to At cools, continue it all. would unlikely as zone at is weak if depths and My more shallow heterogeneity, mixed 3 at much new to strong little evolve and 1 with to unmixed way at was that middepths what remain and cool to likely at more be banded is tem- likely was cooler the will What of My because peratures. banding some 3 vertical later, undergo years and will million which 1 few of a between heterogeneity new lithosphere by the overprinted the of near and of weakened base mixing and base mixed the pervasive well the was more at what the Thus, mantle occurs. where weakening the also from is which entrained lithosphere, be to likely most the Appendix hence cooling; to with comparison Z viscosity for creep shown is diffusion (B–F (dashed) frames than line faster unity stiffens The (see which indicated (green). exists are material it compliance strongest the the if size maximum than in banding, grain weaker anisotropy field-boundary of effective times the orientation of 10 delineating average degree least the and at fabric is indicates the that arrow and long (strongest), Right the minimum (Lower where the arrows, is black green material), by (weakest maximum the is vlto n eieo asv agn hog ri iigaddamage and mixing grain through margins passive of demise and Evolution Mulyukova and Bercovici sonhr sapstv ubr;adfia time final and number); positive a as here (shown D A t 0 − ueia ouin o ae tdfeetdepths different at cases for solutions Numerical T . 0 oe Left (Lower minimum; is blue and maximum, is yellow where R, µ ¯ ˆ hri ilcto re ly oeipratrl. bv ahfae h nta n nltemperatures, final and initial the frame, each Above role.) important more a plays creep dislocation wherein ) ar ie,frames (i.e., pairs uvsfor curves fec rm) eso h ieeouino iiu n aiu of maximum and minimum of evolution time the show we frame), each of t 0 1 = y hs h einweebnigoccurs banding where region the Thus, My. A safce ytenraiain h ytmi ndfuincepbttevsoiyi omlzdb h ilcto re value, creep dislocation the by normalized is viscosity the but creep diffusion in is system the normalization; the by affected is A–F hwcssitgae owr osed rqaised tt setx o xlnto) h lt ihnec frame each within plots The explanation). for text (see state quasi-steady or steady to forward integrated cases show ) h ouefato ftemnrphase minor the of fraction volume the ) R f dse-otd,gvnb Eq. by given (dashed-dotted), t f E B r niae.Dtiso h ueia ouin n nta odtoson conditions initial and solutions numerical the of Details indicated. are Z triga nta times initial at starting , φ 0 o aho these of each For . ssonfrcmaio to comparison for shown is 6, opineo nes omlzdviscosity normalized inverse or compliance ) φ µ ˆ ie ekzn) loigtebne oet rwsc that such grow to is zone heterogeneity banded the pervasively by times, allowing warmer zone), later the weak through mixed At (primarily remains thick. mar- added zone passive continuously km strong the this 10 until assume frozen can (or approximately be we perpetuity will collapses); in strength possibly high depths gin and shallower mixing at no of in zone the thus and the into introduced is heterogeneity new lithosphere. growing as time with thickens etsi ewe h initial the between in depths tutr Fg ) tsol entdtetastosa these they at variations; transitions strength the in noted trends be estimated should represent It depths 3). (Fig. a structure in bands weak accumulated pe Right (Upper (blue); 1 to (green) 0 from going pyroxene), (e.g., ausapa odces tltrtms hsi ncnrs oteother the to contrast in is this times; later at decrease to appear values pcfial,tetasto et is depth transition the Specifically, t 0 t 0 100 = t = 0 y(A–C My 1 and R ¯ φ My, 0 bak and (black) hr r he ifrn nta temperatures initial different three are there , and ) D T ≈ IAppendix SI t 0 F C hs ya g f10M,the My, 100 of age an by Thus, km. 70 Nt httebhvo ftemnmmand minimum the of behavior the that (Note R. ¯ µ = ˆ 5M (D–F My 75 bu)advlm fraction volume and (blue) D tikaiorpclyweak anisotropically 60-km-thick T https://doi.org/10.1073/pnas.2011247118 o ealddsuso) naddition In discussion). detailed for ≈ ,a hc h aepetrological same the which at ), 0km 10 µ Φ ˆ −1 wz D T si prahs1 h line The 1. approaches it as (Eq. T ≈ 0 and and 0km 10 ,weelgtcopper light where 5), φ T 0km 70 r icse in discussed are f h xddepth fixed the ; Φ at PNAS wz T t 0 fmaterial of 0 h mean the ) ilhave will (columns). 1 = | f9 of 5 My, SI

EARTH, ATMOSPHERIC, INAUGURAL ARTICLE AND PLANETARY SCIENCES Fig. 3. Summary figure of solutions. Gray contours symbolize isotherms in a cooling half-space model of ocean lithosphere. The circles show the location of DT (at which the weak band volume fraction is Φwz ≈ 0.5) for five cases in which mantle heterogeneity (symbolized by rising blue-green stipple below the lithosphere) is introduced at times t0 = 1, 25, 50, 75, and 100 My (the solution at t0 = 90 My with a + symbol is for the isothermal test case discussed in SI Appendix). The thick green curves bound the envelope in which weak bands accumulate; below this region the material is more uniformly weakened as in the model by Mulyukova and Bercovici (14); above this envelope the material is cold and remains poorly mixed, coarse grained, and strong, but also likely subject to brittle failure. Insets are sample solutions within each domain of (Top) little mixing and high strength, (Middle) vertical weak bands, and (Bottom) uniform weakness; these frames are taken from Fig. 2 for the cases with t0 = 75 My. Just like the grenadier fish, the snapshots of microstructure are not to scale.

will of course vary slightly depending on initial conditions in ure regime and thus exert little influence on the net strength φ (see SI Appendix for a statistical analysis of the initial con- of the lithosphere. Below the banded zone, grain damage pro- ditions), as well as the choice of dimensionless factors and motes uniform and isotropic weakness, thus also reducing the material properties, some of which remain the subject of active resistance to negative buoyancy, as proposed by Mulyukova and investigation. Bercovici (14). The 60-km-thick weak-banded zone comprises a significant The susceptibility to negative buoyancy and subduction portion of the lithosphere beneath the 100-My-old passive mar- depends on the absolute reduction in lithospheric strength. In gin. While the banded region is not uniformly low viscosity, its particular, if the mean lithospheric viscosity of about 1025Pa s anisotropic fabric is vertically aligned, making the lithosphere (e.g., refs. 60 and 61, which are consistent with laboratory rheo- more susceptible to vertical shear or bending stresses associ- logical laws at about 1,000 K temperature) is reduced to ambient ated with subduction initiation. Above the banded zone, the upper mantle viscosity of 1021Pa s, then the lithosphere has no 10-km cold, unmixed layer is likely to be in the brittle fail- more resistance to negative buoyancy and convective forces than

Fig. 4. Horizontal profiles of the compliance (inverse viscosity) field µˆ−1 for the example of Fig. 2E. The two profile locations are marked by the blue lines in the compliance field (Left); the variations in compliance across grain-mixed weak zones are shown in the two frames (Right) with mesoscopic depth z indicated (compliance is also normalized by the minimum value, as noted on the vertical axis).

6 of 9 | PNAS Bercovici and Mulyukova https://doi.org/10.1073/pnas.2011247118 Evolution and demise of passive margins through grain mixing and damage Downloaded by guest on October 1, 2021 Downloaded by guest on October 1, 2021 vlto n eieo asv agn hog ri iigaddamage as, and magnitude mixing grain of through order margins same passive the of demise of and although Evolution than, larger Mulyukova is and Bercovici pull slab general, in conservative; be to and comparison of (63). sake push the ridge for stress ridge-push the see i.5. Fig. from depths, and temperatures com- of The range to (14). larger weakening mixing allow a without processes over damage damage occur inferred grain and also grain-mixing of as margin, bined model passive push a a weak- ridge near in accumulated lithosphere by an the driven predicts of damage, basins, ening ocean and of mixing opening grain during of model Our Conclusion and Discussion the effect). enhance mixing that turn, vertical in lithosphere would, the (which in heterogeneity drive shear elongate to to would promote weak continue possibly to but but pull slab, motion, slab and plate permit plate would the this along shear; tension horizontal in strong is sphere lead pull see slab respectively; alignment, and Appendix horizontal push and ridge vertical sam- that to large shows robustly a conditions for aligned initial alignment horizontally band of of ple predominantly analysis are statistical (A that 5). (Fig. bands weak to ing ver- fraction with Eqs. volume associated in is is derivatives diffusion stress grain-scale tical compressive case, of this direction In the vertical. thus and rollback) complexities horizontally without slab sense, geometry like ideal 2D an simple in a assuming is, (i.e., pull tensile slab weak-zone particu- of stress In and driving significantly. the change mixing lar, may diffusive lithosphere initiated the of is in Pull. nature evolution subduction Slab the which and established, after and collapse, Collapse margin Postmargin passive on ing Comment Brief and A buoyancy for negative ripe own therefore its is instability. under lithosphere convective collapse cold margin old, passive shear the vertical deflection; for particularly and values, mantle a ambient 1/4 present to viscosity about zones is weak shear (see banded laminae) to ratio the the viscosity normal true to of the weak parallel of ratio laminated that and the of normal fraction, (i.e., viscosity volume viscosity anisotropic 50% an uniformly with almost For are about zones volume 4). is the (Fig. of ratio 50% this weak fill that age, and bands late weak strong a the about between at typically ratio structure is model banded viscosity our The in regions (62). weak mantle the does IAppendix SI 2a aea i.2for 2 Fig. as Same and o eal. nti ae h addrgo ftelitho- the of region banded the case, this In details.) for iigte eoe rmrl etcl lead- vertical, primarily becomes then Mixing 2c. o eal)adcnrsigtesse’ vlto fudrsa ulvru ig uh eetesa ulsrs ssteuladopst to opposite and equal set is stress pull slab the Here push. ridge versus pull slab under if evolution system’s the contrasting and details) for t 0 = 5M ae,btfradfeetrno nta odto gvnb admnme eeao vuiom ihseed= with “v5uniform” generator number random a by (given condition initial random different a for but cases, 75-My IAppendix SI 10 ∂φ/∂ 4 euto nlithospheric in reduction z nta of instead 10 o eal) Thus details). for 4 o10 to 4 × 5 ∂φ/∂ o the For . 10 Follow- 4 and , x SI in n,a rpsdb u oe,wudas eueazimuthal reduce also band- would Vertical model, (67). our spreading by vis- fault- of proposed from normal direction Pacific, as fabric brittle the the ing, deformation-induced in deeper in strain reduced to that cous to attributed to leading reduc- been 50% relative ing has roughly anisotropy subduc- this a no azimuthal and displays has margins, in which passive tion only lithosphere, and basin deformation-induced tion Atlantic radial of to development The contribute the fabric. and would hor- shearing plate facilitate and izontal Pacific structures laminate the with associated for inferred anisotropy viscosity model in our banding by petrologi- by Horizontal scat- sheared mantle (66). by to heterogeneity attributed implied upper are cal structures anisotropy the laminate radial of and and the tering 65), shearing (64, in to motion fabric plate due deformation-induced direction to azimuthal plate, particular, spreading attributed in Pacific is zones; the subduction of anisotropy with studies replete rea- seismic is are in which basin estab- structures established ocean with shear well basin an horizontal sonably a in Indeed, in subduction. fabric fabric lished vertical horizontal and with subduction banding, without to due sphere of direction the ori- become in horizontally motion. weakening plate would become reduced entail bands mixing would weak which of col- ented, resulting direction the margin and the passive vertical stresses, for subduction slab-pull of establishment conditions and the and collapse the associated margin After establish bending lapse. damage and readily grain and shear mixing can phase vertical oriented Thus, initiation. vertically to Although subduction its with susceptible uniformly. weak, uniformly or is not bands lithosphere fabric is the vertical region banded of in the most weakened thus, be weakness; would uniform by thin The underlain the bands. margin, roughly roughly weak passive be a 100-My-old aligned would a sep- vertically region be at of strong would that, zone these predicts thick and model 14), a cold ref. by shallow by arated predicted homogeneously thin deep (as a a region and failure) weak maintain In brittle to stress. subject would (likely ridge-push layer lithosphere pre- under occurs the when it bands uniform, general, where not vertical places is in In damage dominantly and lithosphere. mixing lower by the weakening into and depths shallow h oe rdcsefcieaiorpcsrnt ntelitho- the in strength anisotropic effective predicts model The tikrgo fwa ad,wihi itself is which bands, weak of region km-thick 60 https://doi.org/10.1073/pnas.2011247118 0km 10 hc n neli by underlain and thick PNAS | f9 of 7 3;

EARTH, ATMOSPHERIC, INAUGURAL ARTICLE AND PLANETARY SCIENCES aτ n−1 + b P φ /Rm 1  b P φ /Rm  anisotropy by a similar fraction since only the stronger, large- µˆ−1 = i i i = 1 + i i i , [5] aτ n−1 + b/Rm 2 aτ n−1 grained regions would be susceptible to dislocation creep and f deformation-induced fabric, and these regions would occupy about 50% of the rock volume. Moreover, the vertical weak where  b 1/m bands would facilitate vertical shear, partially offsetting the R = [6] f aτ n−1 azimuthal anisotropy due to horizontal shear. The proposed effects of weakening by grain damage and mixing in passive is the evolving dimensionless field boundary grain size; this normalization and active margins might be further tested with studies of seis- partially excludes the effect of background thermal stiffening. We also track ¯ mic anisotropy and petrological heterogeneity, as well as field the minimum and maximum values of R and normalized viscosity µˆ and the studies of ophiolitic mylonites in past and present subduction net volume fraction of weak-zone material ZZ environments. 1 1 h −1 −1 i Φwz = sign(µˆ − 10 min(µˆ )) + 1 dxdz, [7] ∆A ∆ 2 Materials and Methods A A complete development of the model is provided in SI Appendix; however, where ∆A is the area of the mesoscopic domain. The principal directions here we summarize some of the key diagnostics presented in Results. of the anisotropic strength (green arrows in the images of compliance) are The macroscopic model equations for lithospheric temperature and determined by an eigenvector analysis of the fabric tensor F = (∇U)(∇U), −1 ridge-push stress given in Eq. 1 are initiated with a dimensionless tempera- where U = log10(µˆ ), with the principal direction vectors also scaled by the ture Θ0 at dimensionless initial time t0 and fixed macroscopic depth Z = −H, minimum and maximum viscosities. See SI Appendix for a detailed analysis which is defined according to Eq. 1a as of anisotropic strength and fabric directions. In each case we integrate the system forward to steady or quasi-steady √   t0 −1 Θm − Θ0 state, specifically when the grain size R¯ and volume fraction of weak zones H = erfc [4] ΠG Θm − Θs Φwz plateau. Temperature Θ evolves at a different rate for each initial time t0, and thus we integrate the model forward√ so that most calculations have at which future temperature and the ridge-push stress are determined by approximately the same increment in t (except for the case starting at Eq. 1. The dimensional depth is HLG, as indicated in Figs. 2, 3, and 5. The t0 = 1 My). We integrate five cases over the following time intervals: 1) t = system of equations in Eq. 2 is solved numerically in the mesoscopic domain 1 to 3 My, 2) t = 25 to 28 My, 3) t = 50 to 54.2 My, 4) t = 75 to 80.1 My, and −2 ≤ (x, z) ≤ +2, in the frame of reference of the moving lithosphere, start- 5) t = 100 to 105.9 My. Fig. 2 shows only cases with t0 = 1 and 75 My, since ing with the same petrological heterogeneity φ = φ0(x, z) at time t0; factors other cases are qualitatively alike. Fig. 3, however, includes all five cases dependent on the macroscopic depth Z and governed by Eq. 1 are con- (indicated by circles). sidered uniform over the mesoscopic domain. A complete description of the numerical solution methods, as well as the setup and analysis of initial Data Availability. There are no new observational data underlying this conditions, is provided in SI Appendix. Solutions are analyzed using the vol- work. ¯ ume fraction φ, mean grain size R = φR1 + (1 − φ)R2, and normalized mean compliance or inverse viscosity ACKNOWLEDGMENTS. Support was provided by NSF Grant EAR-1853184.

1. D. Forsyth, S. Uyeda, On the relative importance of the driving forces of plate motion. 18. D. Bercovici, Y. Ricard, Mechanisms for the generation of plate tectonics by two-phase Geophys. J. R. Astron. Soc. 43, 163–200 (1975). grain-damage and pinning. Phys. Earth Planet. Int. 202-203, 27–55 (2012). 2. I. Wada, S. D. King, “Dyamics of subducting slabs: Numerical modeling and con- 19. E. Mulyukova, D. Bercovici, The generation of plate tectonics from grains to global straints from seismology, geoid, topography, geochemistry and petrology” in Treatise scales: A brief review. Tectonics 38, 4058–4076 (2019). on Geophysics, D. Bercovici, Ed. (Mantle Dynamics, Elsevier, ed. 2, 2015), vol. 7, pp. 20. S. H. White, S. E. Burrows, J. Carreras, N. D. Shaw, F. J. Humphreys, On mylonites in 339–392. ductile shear zones. J. Struct. Geol. 2, 175–187 (1980). 3. D. Bercovici, P. J. Tackley, Y. Ricard, “The generation of plate tectonics from mantle 21. D. Jin, S. I. Karato, M. Obata, Mechanisms of shear localization in the continental dynamics” in Treatise on Geophysics, D. Bercovici, Ed. (Mantle Dynamics, Elsevier, ed. lithosphere: Inference from the deformation microstructures of peridotites from the 2, 2015), vol. 7, pp. 271–318. Ivrea zone, northwestern Italy. J. Struct. Geol. 20, 195–209 (1998). 4. S. Mueller, R. J. Phillips, On the initiation of subduction. J. Geophys. Res. 96, 651–665 22. M. Furusho, K. Kanagawa, Reaction induced strain localization in a lherzo- (1991). lite mylonite from the Hidaka metamorphic belt of central Hokkaido, Japan. 5. K. Nikolaeva, T. V. Gerya, F. O. Marques, Subduction initiation at passive margins: Tectonophysics 313, 411–432 (1999). Numerical modeling. J. Geophys. Res. 115, B03406 (2010). 23. A. H. Dijkstra, M. R. Drury, R. L. M. Vissers, J. Newman, H. L. M. Van Roermund, Shear 6. F. Crameri et al., A transdisciplinary and community-driven database to unravel zones in the upper mantle: Evidence from alpine- and ophiolite-type peridotite subduction zone initiation. Nat. Commun. 11, 3750 (2020). massifs. Geol. Soc. Lond. Spec. Publ. 224, 11–24 (2004). 7. G. Toth, M. Gurnis, Dynamics of subduction initiation at preexisting fault zones. J. 24. J. Braun et al., A simple parameterization of strain localization in the ductile regime Geophys. Res. 103, 18053–18067 (1998). due to grain size reduction: A case study for olivine. J. Geophys. Res. Solid Earth 104, 8. J.-F. Lebrun, G. Lamarche, J.-Y. Collot, Subduction initiation at a strike-slip plate 25167–25181 (1999). boundary: The Cenozoic Pacific-Australian plate boundary, south of New Zealand. 25. L. G. J. Montesi,´ G. Hirth, Grain size evolution and the rheology of ductile shear zones: J. Geophys. Res. 108, 2453 (2003). From laboratory experiments to postseismic creep. Earth Planet Sci. Lett. 211, 97–110 9. C. E. Hall, M. Gurnis, M. Sdrolias, L. L. Lavier, R. D. Mueller, Catastrophic initiation of (2003). subduction following forced convergence across fracture zones. Earth Planet Sci. Lett. 26. D. Bercovici, Y. Ricard, Tectonic plate generation and two-phase damage: Void growth 212, 15–30 (2003). versus grainsize reduction. J. Geophys. Res. 110, B03401 (2005). 10. M. Gurnis, C. Hall, L. Lavier, Evolving force balance during incipient subduction. 27. D. Bercovici, Y. Ricard, Generation of plate tectonics with two-phase grain-damage G-cubed 5, Q07001 (2004). and pinning: Source–sink model and toroidal flow. Earth Planet Sci. Lett. 365, 275–288 11. R. J. Stern, Subduction initiation: Spontaneous and induced. Earth Planet Sci. Lett. (2013). 226, 275–292 (2004). 28. D. Bercovici, Y. Ricard, Plate tectonics, damage and inheritance. Nature 508, 513–516 12. T. V. Gerya, R. J. Stern, M. Baes, S. V. Sobolev, S. A. Whattam, Plate tectonics on (2014). the earth triggered by plume-induced subduction initiation. Nature 527, 221–225 29. D. Bercovici, Y. Ricard, Grain-damage hysteresis and plate-tectonic states. Phys. Earth (2015). Planet. Int. 253, 31–47 (2016). 13. S. Cloetingh, R. Wortel, N. J. Vlaar, “On the initiation of subduction zones” in Sub- 30. N. Austin, B. E. Paleowattmeters, A scaling relation for dynamically recrystallized duction Zones Part II, L. J. Ruff and H. Kanamori, Eds. (Birkhauser,¨ Basel, Switzerland, grain size. Geology 35, 343–346 (2007). 1989), pp. 7–25. 31. Y. Ricard, D. Bercovici, A continuum theory of grain size evolution and damage. J. 14. E. Mulyukova, D. Bercovici, Collapse of passive margins by lithospheric damage and Geophys. Res. 114, B01204 (2009). plunging grain size. Earth Planet Sci. Lett. 484, 341–352 (2018). 32. A. Rozel, Y. Ricard, D. Bercovici, A thermodynamically self-consistent damage equa- 15. D. V. Kemp, D. J. Stevenson, A tensile flexural model for the initiation of subduction. tion for grain size evolution during dynamic recrystallization. Geophys. J. Int. 184, Geophys. J. Int. 125, 73–94 (1996). 719–728 (2011). 16. D. Kiss, L. G. Candioti, T. Duretz, S. M. Schmalholz, Thermal softening induced 33. F. Gueydan, J. Precigout,´ L. G. J. Montesi,´ Strain weakening enables continental plate subduction initiation at a passive margin. Geophys. J. Int. 220, 2068–2073 tectonics. Tectonophysics 631, 189–196 (2014). (2019). 34. D. Bercovici, E. Mulyukova, A continuum model for phase mixing and grain-damage 17. K. Regenauer-Lieb, D. A. Yuen, J. Branlund, The initiation of subduction: Criticality by relevant to tectonic plate boundary evolution. Phys. Earth Planet. Int. 285, 23–44 addition of water?Science 294, 578–580 (2001). (2018).

8 of 9 | PNAS Bercovici and Mulyukova https://doi.org/10.1073/pnas.2011247118 Evolution and demise of passive margins through grain mixing and damage Downloaded by guest on October 1, 2021 Downloaded by guest on October 1, 2021 5 .Hreh .Lnkn,A br,A egr .H rda,Terl fscn phases second of role The rheological Brodhag, H. and S. Berger, Microstructural A. Ebert, Hirth, A. Linckens, G. J. Herwegh, Kelemen, M. naturally B. P. in 45. Warren, mechanisms M. deformation J. sensitive Skemer, size P. Grain 44. Hirth, G. Warren, M. J. 43. mechanisms of investigation Laboratory Kohlstedt, D. Zimmerman, M. Wiesman, H. 42. St H. strain Kohlstedt, high L. D. in Zimmerman, mixing E. phase M. via Tasaka, generation M. Ultramylonite 41. Skemer, P. weakening Cross, rheological in J. A. orthopyroxene of 40. Torsion Role Cai, localization: Z. strain Karato, S.-I. Reaction-induced Farla, Grobety, M. J. B. R. Burlini, 39. L. Piane, D. C. parti- 38. strain and deformation Large-strain Mackwell, S. Heidelbach, F. Bystricky, M. 37. bimin- in localisation Strain Burg, J.-P. Burlini, L. Kunze, K. Bystricky, M. Barnhoorn, A. 36. 35. 7 .Mk,T iaa .E imra,Iflec fmnrlfato nterheological the on fraction mineral of Influence Zimmerman, E. M. Hiraga, T. Miki, of T. properties rheological 47. the on fraction mineral of Influence Hiraga, T. Tasaka, M. 46. 9 .Tsk,M .Zmemn .L oltd,Relgclwaeigo lvn + olivine of weakening Rheological Kohlstedt, L. D. Zimmerman, E. M. Tasaka, M. 49. rheological the on fraction mineral of Influence Michibayashi, K. Hiraga, T. Tasaka, M. 48. vlto n eieo asv agn hog ri iigaddamage and mixing grain through margins passive of demise and Evolution Mulyukova and Bercovici .Mluoa .Broii omto fltopei ha oe:Efc of Effect zones: shear lithospheric of Formation Bercovici, D. Mulyukova, E. o otoln irsrcua vlto nplmnrlcrcs review. A rocks: polymineralic in Geol. evolution microstructural controlling for zone. shear mantle a of evolution peridotites. deformed aggregates. olivine+ferropericlase (2018). 20170417 in mixing phase mixing: for phase to due aggregates development. orthopyroxene (2017). Microstructural + 2. olivine Part of weakening logical experiments. recrystallization. dynamic (2013). 16355–16360 via lithosphere the of dolomite. on experiments olivine–magnesiow of Tectonophysics creep Dislocation rocks: polyphase in tioning aggregates. calcite–anhydrite synthetic Lett. of Sci. Planet deformation Earth Experimental rocks: eralic damage. grain (2017). two-phase on temperature rpriso oseieesaiedrn ri-iesniiecep .Deformation 2. creep: grain-size-sensitive experiments. during forsterite+enstatite of properties growth grain and size Grain laws. 1. creep: grain-size-sensitive during forsterite+enstatite rhprxn grgtsdet hs iig .Mcaia behavior. Mechanical Earth 1. Solid mixing: Res. phase to due aggregates orthopyroxene ultramylonite. of (2014). peridotite Application 840–857 on 119, 3. laws creep: flow sensitive and size growth grain grain during forsterite+enstatite of properties .Gohs e.SldEarth Solid Res. Geophys. J. 7815 (2011). 1728–1750 33, .Gohs e.SldEarth Solid Res. Geophys. J. .Gohs e.SldEarth Solid Res. Geophys. J. 1–3 (2006). 115–132 427, 5479 (2017). 7584–7596 122, 4–6 (2005). 748–763 240, at lntSi Lett. Sci. Planet Earth at lntSi Lett. Sci. Planet Earth 9039 (2013). 3970–3990 118, .Petrol. J. .Gohs e.SldEarth Solid Res. Geophys. J. 7415 (2017). 1744–1759 122, 9141 (2013). 3991–4012 118, 35 (2010). 43–53 51, 3–5 (2006). 438–450 248, hs at lnt Int. Planet. Earth Phys. 64 (2007). 36–46 256, rc al cd c.U .A. S. U. Sci. Acad. Natl. Proc. nt,R elrne,Rheo- Heilbronner, R. unitz, ¨ hls rn.R o.A Soc. R. Trans. Philos. .Gohs e.SldEarth Solid Res. Geophys. J. sieaggregates. ustite ¨ 7597–7612 122, 195–212 270, .Geophys. J. .Struct. J. 376, 110, 7 .B aet,D iarle .A oln,G it,S i,Mnl eomto dur- deformation Mantle Kim, S. Hirth, G. Collins, A. J. Lizarralde, D. Gaherty, B. J. petro- and 67. seismological of reconciliation the Toward Furumura, T. Kennett, N. L. B. 66. 5 .D en .Hrh .R EsnekI.Ipiain fgansz vlto nthe on evolution size grain of Implications II. .Elsenbeck Pacific R. the J. of Hirth, anisotropy G. Azimuthal Behn, Barruol, D. M. G. Priestley, 65. plate K. for Debayle, mechanism E. driving a Maggi, as A. force pull 64. super- slab net on the tectonics Quantifying plate Schellart, P. W. for conditions 63. The Landuyt, W. Bercovici, D. Foley, J. B. 62. lithosphere. oceanic the in stress of state ambient the and Isostasy Dahlen, formation. A. F. plate-boundary and 59. mixing phase damage, Grain Skemer, P. Bercovici, recrystallisation. D. dynamic On Ashby, 58. F. M. Derby, B. 57. in crystals minerals” in recrystallization single “Dynamic Lister, olivine S. G. of Means, D. recrystallization W. Urai, W. Dynamic J. Fujii, 56. T. Toriumi, M. single-crystalline Karato, of S. creep during 55. recrystallization Dynamic Poirier, P. J. Guillope, M. 54. M O. Herwegh, M. Linckens, J. 53. 1 .B at,G .Kre,M .Seke,Ltopeeflxr n h vlto of evolution the and flexure Lithosphere Steckler, lithosphere. S. M. viscoelastic Karner, a D. G. on Watts, basins B. A. sedimentary of 61. evolution The Beaumont, C. 60. in mixing phase and recrystallization Dynamic Skemer, P. Bruijn, C. H. R. Linckens, J. 52. M O. + Herwegh, M. olivine Linckens, of J. weakening 51. Rheological Kohlstedt, L. D. Zimmerman, E. M. Tasaka, M. 50. n lwsaorsraigcntandb bevtoso esi nstoyi the in anisotropy seismic of observations Atlantic. by western constrained spreading seafloor slow ing heterogeneity. lithosphere oceanic (2015). on perspectives logical (2009). esi tutr fteoencuprmantle. upper oceanic the of structure seismic region. tectonics. damage. with models (2012). convection 281–290 331-332, from Inferences earths: Geodyn. J. (American Eds. Heard, 166–199. C. pp. H. 1986), Hobbs, DC, E. Washington, B. Union, Geophysical Studies, Laboratory Deformation: Rock and creep. temperature high during study. experimental An halite: zones. shear mantle upper (2015). in 26–43 localization strain control phases eietr basins. sedimentary Soc. Astron. R. J. Geophys. Earth Solid Res. Geophys. deformation. peridotite. of deformed localization experimentally the in phases second of role Res. the Geophys. and zone shear tle volume orthopyroxene of Effects mixing: phase fraction. to due aggregates orthopyroxene at lntSi Lett. Sci. Planet Earth .Gohs e.SldEarth Solid Res. Geophys. J. epy.Rs Lett. Res. Geophys. 05 (2017). 40–55 108, 020(2011). B06210 116, at lntSi Lett. Sci. Planet Earth hls rn.R o.Ln.Sr A Ser. Lond. Soc. R. Trans. Philos. 8170 (1981). 7801–7807 86, 7–9 (1976). 471–497 55, 061(2004). L07611 31, 37 (2006). 53–71 250, nee,I ecli vlto faplmnrlcman- polymineralic a of Evolution Mercolli, I. untener, ¨ .Gohs e.SldEarth Solid Res. Geophys. J. nee,Salqatt u ag fethwminor effect—how large but quantity Small untener, ¨ epy.Rs Lett. Res. Geophys. 22J098 (2020). e2020JB019888 125, at lntSi Lett. Sci. Planet Earth 5–6 (2004). 255–265 228, https://doi.org/10.1073/pnas.2011247118 at lntSi Lett. Sci. Planet Earth cit Metall. Scripta 4–5 (1980). 649–652 7, 4–8 (1982). 249–281 305, 5756 (1979). 5557–5567 84, 3–4 (2014). 134–142 388, G-cubed at lntSi Lett. Sci. Planet Earth Tectonophysics 7–8 (1987). 879–884 21, PNAS 3129–3141 16, 178–189 282, | Mineral 9 f9 of 643, J. J.

EARTH, ATMOSPHERIC, INAUGURAL ARTICLE AND PLANETARY SCIENCES