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GEODYNAMICS & TECTONOPHYSICS PUBLISHED BY THE INSTITUTE OF THE EARTH’S CRUST SIBERIAN BRANCH OF RUSSIAN ACADEMY OF SCIENCES 2015 VOLUME 6 ISSUE 3 PAGES 387–408 ISSN 2078-502X http://dx.doi.org/10.5800/GT-2015-6-3-0187 GENETICSOURCESANDTECTONOPHYSICALREGULARITIESOF S.I.Sherman InstituteoftheEarth’sCrust,SiberianBranchofRAS,Irkutsk,Russia Abstract:Thepaperpresentsthefirsttectonophysicalreconstructionofinitialdivisibilityoftheprotolithosphereasa resultofconvectioninthecoolingprimitivemantle.Initialdivisionoftheprotolithosphereintoseparatemasses,i.e. prototypesoftheblocks,andtheirsizearepredeterminedbytheemergingRayleigh‐Benardconvectioncells.Instu‐ diesofgeologyandgeodynamics,theRayleigh‐Benardconvectioncellswerefirstreferredtoasafactortoexplainthe formationofinitialcontinentalcores.ConsideringtheRayleigh‐Benardcellsandtheirstructuralrelicscanhelpclarify initialdivisibilityoftheprotolithosphereandtheoriginofthemajorlithosphericplates,i.e.prototypesofcontinents. Inouropinion,theinitialmega‐scaleblockstructureoftheprotolithosphereandtheemerginglithospherewerepre‐ determinedbytheRayleigh‐Benardcellsastheywerepreservedintheemerginglithosphereandtheirlowerbounda‐ riescorrespondedtothecore‐mantleboundary,i.e.oneofthemajordiscontinuitiesoftheplanet.Ourtheoreticales‐ timationsareingoodagreementwiththenumberandsizesoftheEarth'stheorizedfirstsupercontinents,Vaalbara andUr. Inourtectonophysicaldiscussionoftheformationofthelithosphericblockstructure,weanalyzeindetailthemap ofmodernlithosphericplates[Bird,2003]incombinationwiththematerialsfrom[Shermanetal.,2000].Inthehie‐ rarchyoftheblockscomprisingthecontemporarylithosphere,whichsizesarewidelyvariable,twogroupsofblocks areclearlydistinguished.Thefirstgroupincludesmegablockswiththeaveragegeometricsizeabove6500km.Their formationisrelatedtoconvectionintheEarthmantleatthepresentstageofthegeodynamicevolutionoftheEarth, aswellasatallthepreviousstages,includingtheearliestone,whentheprotolithosphereemerged.Thesecondgroup includesmedium‐sizedblockswiththeaveragegeometricsizeoflessthan4500kmandthosewithminimumsizes, suchasrocklumps.Theyreflectprimarilythedegradationofmegablocksasaresultoftheirdestructionduetohigh stressesinexcessofthetensilestrengthofthemedium.Thisgroupmayalsoincludeblockswhichformationisrelated toconvectionintheuppermantlelayer,asthenosphere.Therearegroundstoassumethatthroughthevastinterme‐ diateintervalofgeologictime,includingsupercyclesofKenorlend,Rodin,andandparticallyPangea,theformationof thelargelithosphericblockswascontrolledbyconvection,andlateron,theywere'fragmented'underthephysical lawsofdestructionofsolidbodies.However,itisdifficulttoclearlydistinguishbetweentheprocessesthatpredeter‐ minethehierarchyofformationoftheblockstructuresofvariousorigins–sizesofancientlithosphericblockscannot beestimatedunambiguously. Thus, mantle convection is a genetic endogenous source of initial divisibility of the cooling upper cover of the Earthandmegablockdivisibilityofthelithosphereinthesubsequentandrecentgeodynamicdevelopmentstages.At thepresentstage,regularpatternsofthelithosphericblockdivisibilityofvariousscalesareobservedatallthehie‐ rarchic levels. The areas of the lithospheric megaplates result from regular changes of convective processes in the mantle,whichinfluencedtheformationofplatesandplatekinematics.Fragmentationofthemegaplatesintosmaller onesisaresultofdestructionofthesolidlithosphereunderthephysicallawsofdestructionofsolidbodiesunderthe impactofhighstresses. Keywords:lithosphere,tectonicplates,blocks,convection,destruction,tectonophysics,divisibilityofthelithosphere, Rayleigh‐Benardcells,continents Discussion DIVISIBILITYOFTHELITHOSPHEREINTOBLOCKSOFVARIOUSRANKSAT DIFFERENTSTAGESOFITSFORMATION:TECTONOPHYSICALANALYSIS RecommendedbyE.V.Sklyarov For citation: Sherman S.I. 2015. Genetic sources and tectonophysical regularities of divisibility of the lithosphere into blocks of various ranks at different stages of its formation: tectonophysical analysis. Geodynamics&Tectonophysics6(3),387–408.doi:10.5800/GT‐2015‐6‐3‐0187. 387 S.I. Sherman: Genetic sources and tectonophysical regularities of divisibility of the lithosphere… ГЕНЕТИЧЕСКИЕИСТОЧНИКИИТЕКТОНОФИЗИЧЕСКИЕ ЗАКОНОМЕРНОСТИРАЗНОРАНГОВОЙБЛОКОВОЙДЕЛИМОСТИ ЛИТОСФЕРЫНАРАЗЛИЧНЫХЭТАПАХЕЕФОРМИРОВАНИЯ: ТЕКТОНОФИЗИЧЕСКИЙАНАЛИЗ С.И.Шерман ИнститутземнойкоpыCОPАН,Иpкутcк,Россия Аннотация: Впервые проводится тектонофизическая реконструкция формирования первичной делимости протолитосферыврезультатеконвекцииостывающейпримитивноймантии.Формирующиесявнейконвек‐ тивныеячеиРэлея‐Бенарапредопределяютразмерыпервичногоразделенияпротолитосферынаотдельные массы–прообразыблоков.ЯчеиРэлея‐Бенараневпервыеиспользуютсявгеологииигеодинамике.Первона‐ чально на них ссылались для объяснения формирования первичных континентальных ядер. Обращение к ячеямРэлея‐Бенараиихструктурнымреликтамспособствуетпониманиютого,какзарождаетсяпервичная делимостьпротолитосферы,котораятрансформируетсявкрупныелитосферныеплиты–прообразыконти‐ нентов.ИменноконсервирующиесявформирующейсялитосфереячеиРэлея‐Бенара,нижняяграницакото‐ рыхкорреспондироваласоднимизглавныхразделовпланеты–границейядра,–предопределилипервона‐ чальнуюмегамасштабнуюблоковуюструктурупротолитосферыиформирующейсялитосферы.Проведенные теоретические оценки сопоставлены и хорошо согласуются с количеством и размерами площадей первых гипотетическихконтинентальныхструктур–суперконтинентовВаальбараиУра. Продолжениетектонофизическогоразбораформированияблоковойструктурылитосферыреализованона детальноманализекартысовременныхлитосферныхплит[Bird,2003]спривлечениемфактическихматериа‐ лов[Shermanetal.,2000].ВширокойпоразмерамплощадейиерархииблоковвсовременнойлитосфереЗемли отчетливо выделяются две группы. Первая – мегаблоки, среднегеометрический размер которых превышает 6500км.ИхформированиенасовременномэтапегеодинамическогоразвитияЗемли,атакженавсехпредше‐ ствующих,втомчислеинасамомраннем,призарождениипротолитосферысвязаносконвекционнымипро‐ цессамивмантииЗемли.Втораягруппа–блокисосреднегеометрическимразмеромменее4500км,вплотьдо минимального,соответствующегокусковатостигорныхпород,отражают,преждевсего,деструкциюмегабло‐ ков в результате их разрушения под действием высоких внутренних напряжений, превышающих предел прочности среды. В этой же группе могут быть блоки, формирование которых также связано с конвекцией, охватывающейверхниймантийныйуровень–астеносферу.Можнопредполагать,чтовгромадномпромежу‐ точном интервале геологического времени, охватывающем суперциклы Кенорленд, Родинию и, частично, Пангею,формированиекрупныхлитосферныхблоковконтролировалоськонвекцией,аихдальнейшее«дроб‐ ление»регулировалосьфизическимизаконамиразрушениятвердыхтел.Однакочеткуюграницумеждупро‐ цессами,определяющимииерархиюформированияблоковыхструктурразногогенезисавпрошедшиевреме‐ на,провеститрудноиз‐занеопределенностиразмеровлитосферныхблоковдалекогопрошлого. Такимобразом,конвекциявмантииявляетсягенетическимэндогеннымисточникомпервичнойделимо‐ стиостывающейверхнейоболочкиЗемли,атакжемегаблоковойделимостисобственнолитосферывпосле‐ дующиеэтапыеегеодинамическогоразвития.Насовременномэтапезакономерностиразномасштабнойбло‐ ковойделимостилитосферыпрослеживаютсянавсехиерархическихуровнях.Площадимегаплитлитосферы –результатзакономерныхизмененийконвективныхпроцессоввмантиииихвоздействиянаформирование икинематикуплит;деструкциямегаплитнаменьшиепоплощадиблоки–результатзакономерногодробле‐ ниятвердыхтеллитосферыпривысокихнапряжениях. Ключевыеслова:литосфера,тектоническиеплиты,блоки,конвекция,деструкция,тектонофизика, делимостьлитосферы,ячеиРелея‐Бенара,континенты ItisnowevidentthatwithoutunderstandingtheEarth'sevolutionsincetheearlieststages whenthecoversofourplanetanditscontinentalcrustwereformed,itisdifficulttodetermine locationswherethemajornaturalresourcesareaccumulatedandtorevealhowvarious structuralelementsandawidevarietyofigneousrocksweregeneratedandcontinuetheirdevelopment. 1.INTRODUCTION Initial divisibility of the Earth protolithosphere, i.e. the cooling outer hard cover of the planet, and its transformationwithtimeintolithosphericblockshave 388 AcademicianM.I.Kuz'min[2014,p.626] not been properly studied yet in terms of the geody‐ namicsoffaulting,andtectonicregularitiesindivisibi‐ lityofthelithosphericblocksofvariousranksstillneed to be clarified. In the outer cover of the Earth, initial divisibility of the protolithosphere was due to cooling Geodynamics & Tectonophysics 2015 Volume 6 Issue 3 Pages 387–408 oftheprimitivemantleasaresultofheat‐gravitational convectionmanifestedbyRayleigh–Bénardcells.Inthis study, we assess tectonophysical conditions for the generationofsuchcellsandestimatepotentialsizesof the cells and amounts of primary proto‐lithospheric coolingmassesasprototypesoftheblocks.Ourestima‐ tionsareconsistentwiththereconstructedfirstsuper‐ continental cycles of the geodynamic evolution of the Earth. The block divisibility of the recent continental lithosphere is analysed in detail with reference to the map of present tectonic plates and blocks of the litho‐ sphere and the cumulative plate count according to [Bird, 2003]. In addition to the data from [Bird, 2003] whichmainlycover megaplatesandblocksofmedium sizes,weanalysetheparametersspecifiedin[Sherman et al., 2000] for medium‐ and small‐size blocks resul‐ ting from destruction of megaplates and blocks of the continental lithosphere. We propose regression equa‐ tions describing divisibility of the continental litho‐ sphereintoblocksinawidescalerange,frommedium‐ to small‐sized blocks and rock fragments in outcrops. Such fragments result from destruction of medium‐ and small‐sized blocks of the 'solid' lithosphere which takes place when internal stresses exceed the rock breakdown point, as described by exponential func‐ tions. The occurrence of megablocks is related to mantle convection at the early stage of the evolution of the protolithosphere and subsequent stages of its trans‐ formation into the lithosphere through the global su‐ per‐cycles of the geodynamic evolution of the Earth. The scale and organization of mantle convection are factorsthatpredeterminedivisibilityofthelithosphere intomegablocksthroughalltherecentstagesofitsde‐ velopment,includingthepresentstage. 2.THEPRIMARYHOTCOVEROFTHEEARTH, ITSCOMPOSITIONANDTHICKNESS One of the most recent theoretical reviews of the early stages in the evolution of the Solar System and the geological history of the Earth was published by M.I. Kuz'min [2014] who rightly notes that the global academicgeologicalcommunityischallengedtoestima‐ tethetimewhenthefirstcontinentalcrustwasformed on the Earth. He develops the concepts co‐authored withV.V.Yarmolyuk[Yarmolyuk,Kuz’min,2012]onthe formation of the outer and deep covers of the Earth, mantle processes and their impacts on the occurrence ofsurfacestructures,igneousrocksandores. Thereview[Kuz’min,2014]isbasedonthelatestda‐ ta on the origin of the Solar System and formation of the first continental rocks on the Earth, which contain zircon,theoldestmineralsofardatedontheEarth.Itis assumedthattheSolarSystemformedfromagas‐and‐ dust nebula 4.568 Ga ago. The continental crust was gradually growing from its recorded peak size (4.25 Ga)till4.1Ga,i.e.completionofthefirsteoninEarth's history,theHadean.Itseemstobeacriticalmilestone intheearlygeologicalhistoryoftheEarth,followedby theArchaenhistory[Kuz'min,2014]–intensivecooling oftheoutercoveroftheEarthcommencedinthisperi‐ od.Theheatflowwassupportedbytheinnersupplyof heatgeneratedduetogravitationalcompressionofthe planetwhileitssolidbodywasformed[Schubertetal., 2001]. The estimated average temperatures of the mantle range from 1250–1350 °С to 1400 °С, and a roughly estimated temperature of the cooling Earth is 0 °С. In thepresentstage,themaximumtemperatureoftheas‐ thenospheretopisabout1350–1400°С,andthistem‐ perature level is supported by various endogenous heatsourcesoftheEarthandcompensatesheatlosses causedbycooling.AttheearlystageoftheEarthevolu‐ tion, temperatures range from 0°С (or slightly above 0°С) at the Earth's surface to ~1350–1400 °С at the depthlevelswhereattemperaturechangesintheperi‐ odofcoolingarelesssignificantduetoheatinflux.Un‐ der this assumption, the cover can be viewed as a gradually cooling low‐viscous fluid body comprising the lower and upper layers which temperatures are significantlydifferent.Atthefirststagewhentheouter coveroftheEarthwasformed,convectionwasthema‐ jormechanismofheatenergydissipation.Itcanbeas‐ sumed that convection commenced in the pre‐Kat‐ archean eon and is underway until now, while the volumes and forms of convective flows have signifi‐ cantlychangedwithtime.Thistimeperiodagreeswith the maximum age of about 4.1 Ga determined in [Kuz’min,2014]forthestartofthedevelopmentofthe protolithosphere that converted with time into the lithospherewhichdevelopmentiscontinued. By its initial composition, the cooling upper cover of the Earth corresponds to the so‐called primitive mantle,asevidencedbythecompositionofchondrites, i.e.stony(non‐metallic)meteorites.Thebulkcomposi‐ tion of the primitive mantle is similar to the silicate coveroftheEarthwhichwasformedoftheprotoplanet materialafterthecorehadseparated[Hofmann,1997]. It is noteworthy that variaitons in the composition of the primitive mantle do not influence estimations of temperatures at the lower boundaries of the primary mantlemassesatthecoolingsurfaceoftheEarth. Physical parameters and the composition of the primitive mantle changed in the post‐Archean period [Vrevsky et al., 2010] including several large cycles of thegeodynamicdevelopmentoftheEarth,whichwere also related to mantle convection. By the Archean pe‐ riod,theEarth'scrustwascompletelyformed,andthe upper boundary of the mantle convection processes wentdownintotheEarthinteriorbydozensofkilome‐ 389 S.I. Sherman: Genetic sources and tectonophysical regularities of divisibility of the lithosphere… tres [Artemieva, 2011]. Responses of the upper solid partofthelithosphereasarheologicalbodytoexternal impacts,especiallyexternalloadingatdifferentveloci‐ ties, became different. In the former convective medi‐ um,convectioninthecoolingupperlayerofthequasi‐ fluidwasreplacedbyheatconduction/diffusioninthe solid body. Studies of destruction of solid bodies and rank‐variable fracturing and faulting are reported in many papers, including [Peive, 1990; Sherman et al., 1991,1992,1994;Seminsky,2003;Sherman,2002,2012, 2014a, 2014b; and others], and it is established that physical laws of deformation and destruction of solid bodiesareapplicable. A major challenge is to analyse, in a retrospective, the origin and initial formation of structures in the coolingprotolithospherewhichphysicalpropertiesare assumed similar to those of the cooling low‐viscous quasi‐liquidmass.Insuchamedium,themaximumdis‐ sipation of energy was ensured by convection of va‐ rious types, from structurally organized (Rayleigh– Bénard cells) to chaotic.This long‐term process in the uppercoveroftheEarthhaditsregularfeaturesdueto convectiveflowsofthemegamassthatwascoolingit. Thetotalthicknessofthecoolingmassoftheprimitive mantle can be assumed at 2900 km as the outer core boundaryislocatedatthisdepth.Belowwereviewhy‐ drodynamic regularities in convection of cooling low‐ viscous materials and relic structures which are im‐ portant for reconstructing the paleogeodynamic set‐ tings of the distant past and estimating probable di‐ mensionsoftheprimaryblocks. 3.KEYREGULARITIESINTHEFORMATIONOFCONVECTIVE CELLSINCOOLINGLOW‐VISCOUSMATERIALSANDRELIC STRUCTURES It is most reasonable to believe that energy in the cooling low‐viscous medium is dissipated by mantle convection that is most common manifested by Ray‐ leigh–Bénard cells. The cooling surface of the Earth is assumedtobehaveasthecoolinglow‐viscousmedium much time before the Katarchean. Convection is gene‐ rally reviewed below as a prerequisite for an assess‐ ment of conditions for initial divisibility of the outer coveroftheprotolithosphere. Generalconvectionequation.Theonsetofconvection occurs when the Rayleigh number reaches some criti‐ cal value. The Rayleigh number, Ra is a dimensionless number predetermining the behaviour of gas, fluid or massofaverylowviscosityataspecifiedtemperature gradient. When the Rayleigh number exceeds its criti‐ cal value, the equilibrium of the cooling fluid is dis‐ turbed, which leads to the occurrence of convection flowsandbifurcation.Thebifurcationpointisthecriti‐ calvalueoftheRayleighnumber: 390 Ra Δ , 1 wheregisthegravityacceleration;Listhesizeofthe fluid area; Δ is the difference of temperatures at the surface and the lower layer of the fluid; is the kine‐ maticviscosityofthefluid; istheheatconductivityof the fluid; is the coefficient of thermal expansion of thefluid. IftheRavalueissmall,convectiondoesnotstart.If valuesofRaareaverage,conditionsarefavourablefor heatconvection.ChaosoccursathighvaluesofRa.Va‐ luesofRadependoncombinationsofallotherparame‐ tersinequation1.However,consideringcoolingofthe primitive mantle in the model discussed here, the dif‐ ference of temperatures and thickness of the cooling layerarethemainparameters.Itshouldbenotedthat patternsofconvectivecellsaresignificantlydependent ondimensionsofthecoolingarea.Insuchcases,anad‐ ditionalparameterneedstobeintroduced–aspectra‐ tio,G[Getling,1998]: G=L/h, (2) whereLishorizontalsizeofanarea(foracircularsec‐ tion,itcorrespondstoaradius);hisverticalsizeofthe area. TheGrashof(Gr)andPrandtl(Pr)numbersarealso widelyusedinstudiesofRayleigh–Bénardcells,butnot inthisreview. Inthebelowdiscussionofthenaturalconditions,we refertocaseswithlargevaluesofG.Horizontalprojec‐ tionsofcellsarecalledplanforms.Theplanformsmay significantlyvarydependingonparametersoftheme‐ dium.Planformsofthecellswhicharetypicalobserved in the experimental and natural settings are reviewed below. Planformsofconvectivecells,andphysicalconditions for their formation and stability. Three types of cell planforms are typically observed in the experiments [Getling, 1998]: two‐dimensional bars, hexagonal cells andsquare/rectangularcells(Fig.1). AsshowninFig.1a,2Dbarsareorientedalongaxis ХandparalleltoaxisУ(x‐bars)orviceversa,andacell is formed by a pair of neighbouring bars that occupy theentirespatialinterval.Inthebars,fluidcirculatesin verticalplaneX,Zaswellasintheoppositedirections. Hexagonal cells (Fig. 1, b) are composed by the su‐ perpositionofthreesystemsofbarswhicharelocated at angles 2π/3 to each other. Such cells are characte‐ rised by periodicity in directions of axes Х and У and invariant in case of rotation by an angle of 60°. A he‐ xagonal cell is classified in l‐type in liquid convection cases(Fig.1,b–l)org‐typeingasconvectioncases(Fig. 1, b–g) with regard to a velocity vector, i.e. depending onwhethertheliquidisascendinginthecentralpartof Geodynamics & Tectonophysics 2015 Volume 6 Issue 3 Pages 387–408 Fig.1.Schematicsofconvectivecells:a–2Dbars;b–hexagonalcellsofl‐andg‐types(accordingto[Getling,1998]). Рис.1. Схематическое изображение конвективных ячеек: a – двумерные валы; b – шестиугольные ячейки l‐ и g‐типа(по[Getling,1998]). thecellorgasisdescending,which,initsturn,isrela‐ ted to the temperature dependence from the viscosity of the medium. As known, with higher temperatures, viscosity of fluids decreases, while viscosity of gases increases. A velocity vector depends on a sign of deri‐ vativedγ/dTwhichisnegativeforliquidsandpositive forgases.Intheascendingconvectiveflow,themateri‐ al is always warmer than in the descending flow. Re‐ spectively, the liquid viscosity in the central parts of l‐cells is lower, while the gas viscosity in the central partsofg‐cellsishigher.Circulationtendstofollowthe direction where the viscosity is lower in the centre of the cell. The stability of circulation trends, as well as theunchangeabilityofstationaryflowsofbarsinrela‐ tiontovariationsofdefiningparametersareestimated in a wide range of Rayleigh and Prandtl numbers, ta‐ king into account k=2π/λ, i.e. the number of waves of lengthλper2πradians,orthenumberofspatialinter‐ valsofwavesperon2πradians. Square cells form systems which directions are ro‐ tatedbyaπ/4anglewithrespecttothecoordinatesys‐ tem(X,Y). Cell planforms are significantly influenced by even minor changes in the physical conditions of the medi‐ um and variations of its parameters included in the generalequationofconvection(see Equation1).Two‐ dimensionalbarsarethemainformofstationarycon‐ vective structures produced by thermal‐gravitational or thermocapillary convection mechanisms. In case of thermal‐gravitational convection, the scale of flow can increase depending on ΔТ and G (see Equations 1 and 2). For the geological interpretation of the significance of cellular structures developing in cooling masses of the primitive mantle material, two facts are of im‐ portance: (1) relic structures, such as boundaries of cellularstructuresinthecoolingprotolithosphere,and subsequently,intheupperpartofthelithosphere,and (2) relic masses of the deep mantle material, which were delivered into the Earth's upper horizons and cooledinzonesofinter‐cellboundaries,i.e.relicstruc‐ tures at the boundaries of the primary cellular for‐ mations. Specialists in the laws of Rayleigh–Bénard convection believe that two groups of boundaries in theEarth'supperhorizonsareofimportance:bounda‐ riesbetweenconvectivecellsandborderlinesbetween orderly fragment‐textures with different orientations of the bars, which comprise a more complex pattern (Fig.2). Themostsignificantstructuralboundariesarelines bordering fragments‐textures with different orienta‐ tions of the bars [Getling, 1998]. The duration of their existence predetermines the stability of stationary convectionflowsandthegeologicalsignificanceofcon‐ vection.Accordingto[Clever,Busse,1996],thehexago‐ nalcellscanbestableatPr≥1.2andRa≥3000.IfPr≤10, thestabilityareaofthehexagoncellslookslikeaband stretching from smaller to larger Ra values. If the 391 S.I. Sherman: Genetic sources and tectonophysical regularities of divisibility of the lithosphere… Fig.2.Defectsofbarstructures(linesshowboundariesofbars):a–dislocation;b–disclination(singularitiesofthefocus typearebelow);c–structuralboundary(accordingto[Getling,1998]). Рис. 2. Дефекты валиковых структур (линии соответствуют границам валов): a – дислокация; b – дисклинации (внизусингулярноститипафокуса);c–структурнаяграница(по[Getling,1998]). Prandtlnumbersarelargerthan10,theareaofstable hexagoncellsisdisturbed.IntheexperimentswithRa <3000,nostablehexagonsarerecorded. The area of stable square cells is wider and covers the range of Ra from 4000 to 50000 with Pr varying from 2.5 to 16. When approaching the specified mini‐ mum value, the stability area narrows and becomes undetectablewhenPr=2.5[Busse,Clever,1998]. The material conveyed by the convective flows is hardening in places where the flows begin to move downward due to lower temperatures. Solidification takes place at the walls of thermal convection cells. Thus, when the vertical walls of the cells (i.e. surfaces of basalt prisms) are solidified, thermal convection continues inside the prisms until complete solidifica‐ tionofallthelavacomponents.AphotoinFig.3shows the tops of basalt pillars with sagging centres of the columnswhichwerethelasttocoolandsolidify. Based on the brief review of convective planforms and conditions of their formation, it is possible to re‐ vealacommonpatternofconvectionprocessestaking place during cooling of the homogeneous medium. In space and time, convection is manifested by a highly orderedflowofcoolingquasi‐liquidmasses.Thestabi‐ lity area is wide. As the area occupied by the flow is narrowing, stability is reduced as the characteristic scale of inhomogeneity of the structure is reducing [Getling,1998]. In standard experimental conditions, Rayleigh– Bénard convection cells occupy the entire thickness of the cooling layer, and their typical horizontal size is 392 comparabletotheverticalsizeorslightlyexceedsit.In the majority of problems solved by geodynamics, it is assumedthatconvectioncellsoccupytheentiremantle orpartiallyoccupythelayeroroccurbetweenthelayers [Kirdyashkin, Dobretsov, 1991; Dobretsov et al., 2001; Trubitsyn V.P., Trubitsyn A.P., 2014]. In such conditions, the main factor predetermining convection is viscosity ofthemedium,whichisincludedinequationsofinterre‐ latedRayleigh,GrashofandPrandtlnumbers.Itcansig‐ nificantly increase or decrease their values and change the stability of convection accordingly. When viscosity varies by two or three orders (which may take place in the cooling upper part of the protolithosphere), the mainviscositygradientisinthetopmostlayer,wherein viscosityisincreasingrelativelyfasterthaninthelower layers,andahardcoveristhusformed.Convectiongoes downward. Moreover, in the discussed cases of ascen‐ ding convection, the cooling masses drift towards bor‐ dersofthecellsandsubsideduetogravity,whichleads tosimultaneousthickeningoftheemergingverticalbor‐ derzone(i.e.aplane),whichsubstanceismoreviscous. As the process develops further, such planes create fa‐ vourableconditionsforinitialfaultingofthelithosphere, and the lithospheric plates and large blocks are thus borderedbyfaultsthatarestableintime. As a result of gradual cooling, a protective cap is formedoverthecoolingmass.Astheprocessdevelops, the solid cap becomes thicker. The merger of the two descendingcoolingflowsleadstofurtherthickeningof theemergingcap,andthepartitionbetweenemerging blocksofthelithosphereisthusfixed. Geodynamics & Tectonophysics 2015 Volume 6 Issue 3 Pages 387–408 4.THEORIGINOFTHEFIRSTLARGESTLOCALSTRUCTURES INTHEPROTOLITHOSPHEREASVIEWEDUNDERTHE CONCEPTOFCONVECTIONINTHECOOLINGPRIMITIVE MANTLE:ATECTONOPHYSICALAPPROACHTO PALEOGEODYNAMICRECONSTRUCTIONS Fig.3.Solidifiedconvectionflowsofbasaltlavawith'sag‐ ging'surfacesinthecentresofcells[Shumilov,2009]. Рис. 3. Застывшие конвекционные потоки базальто‐ вой лавы с «проседанием» поверхностей в центрах ячей[Shumilov,2009]. Over time, the cap thickens and evolves into the brittle part of the lithosphere, while convection flows continue to function in the mantle and gradually drift tothelowerhypsometriclevels.Theabove‐mentioned processes take place as the equilibrium of the convec‐ tionsystemunderthecapisdisturbedduetochanges oftemperatureandviscositygradients.Conditionsthat are favourable for convection are now found at larger depths,andheatenergydissipationisfacilitated.Inthis time period, the dominating convection occupying the entiremantlemaybeeitherreplacedbyconvectionin twolayersoroccurinamorecomplicatedpattern. Regardlessoftheirplanforms,theRayleigh–Bénard cellsgiveevidencethatconvectionnon‐equilibriumcan be asource of order.In comparison withthehomoge‐ neous hot mass, convective cells (regardless of their forms)canberegardedashighlyorganizedstructures facilitatingthedissipationofenergyandtheformation of other, more stable forms in the cooling mantle. In thisregard,thesystemremainsopenandcontinuesto givetheentropy. Based on the above, cooling of the pre‐Katarchean Earth's surface can be analysed with an assumption thattheenergyofthehotlow‐viscousbodydissipated by thermal‐gravitational convection. In this case, the Rayleigh–Bénard cells can be viewed as initial struc‐ tures in the cooling mantle of the Earth, and bounda‐ ries between the cells were the first to get solidified and thus predetermined the contours of the future huge masses/blocks of the protolithosphere, which werethebasisofVaalbaraand,maybe,othertheorized firstsupercontinentsoftheEarth. In this study, a tectonophysical approach is pro‐ posed to analyse initial divisibility of the protolitho‐ sphere. The origin of the primary local structures / blocksisrelatedtocoolingoftheEarth'ssurfacelayer composed by hot low‐viscous masses of the primitive mantle.Insuchamedium,arelativelyefficient wayof heat dissipation is convection that is structurally ar‐ rangedinRayleigh–Bénardcells.Theirrelics,i.e.proto‐ continents, can be regarded as residual structures giving evidence of intitial atectonic divisibility of the protolithosphere.Inthisassumption,lawsoftheirfor‐ mationaredeterminedbythelawsofconvection. Thecoolingupperlayercoveredtheentireprimary surface of our planet. Its thickness was limited by the outer boundary of the almost completely formed core which was located at a depth of about 2900 km. It is knownthattheevolutionofconvectionanditspatterns are significantly influenced by dimensions (diameter and depth) of the area involved in convection (see Equation 2). For circular cross‐sections in the experi‐ ments, the horizontal size of convection cells corre‐ sponds to the depth of the layer wherein convection takes place. Original convection experiments are de‐ scribedinthebookbyN.L.Dobretsovetal.[2001]who estimated the minimum horizontal size of convection cells in the lower mantle: “As follows from results of theexperimentsandtheclassicallawsofconvection,a cellcanbestableifitstransversesizeisonlybyafactor of1.8times(orless)largerthanitsthickness”(p.161). Therefore, when convection takes place in a rather thick layer, a pattern of convection cells is compatible with the thickness of the layer. In our study of the mega‐scalecase,thehorizontalsizeofthelayersubject toconvectionismuchlargerthanitsverticalsize,and thelayercanthusbeconsideredasacoolingflatbody. The radius of the first round‐shaped convective cells can amount to 2900–3000 km, and the distance be‐ tween the emerging cooling boundaries of areas with descending masses (i.e. cell diameter) can be about 6000km.Inthiscase,thecelldiametercanbenumeri‐ callysimilartotheradiusofthecoolingEarth,andthe cell area can be determined as the area of a spherical segment(Ss=2πRh,whereRistheEarthradius,andhis thethicknessofthecoolinglayer,i.e.R/2).Itamounts to πR2 or about 3 steradians1. The total area of the Earthsurfaceis4πR2(or4πΩ).Underidealconditions, 1 Steradian,sr(Ω)asolidangleatthecentreofaspheresubtending asectiononthesurfaceequalinareatothesquareoftheradiusof thesphere. 393 S.I. Sherman: Genetic sources and tectonophysical regularities of divisibility of the lithosphere… Fig. 4. Principal scheme of Rayleigh‐Benard cells on the sphericalsurface. Рис.4.ПринципиальнаясхемаконвективныхячейРэ‐ лея‐Бенаранасфере. as a maximum, four mega‐large convective cells with an average area of about three steradians can form in thecoolinguppercoveroftheEarth.Itshouldbenoted thattheboundaryofthebottomsurfacesofthecellsis the outer core of the Earth, which square area is four timessmallerthanthatoftheEarthsurface.Asthearea ofthebottomsurfacesofthecellsisrestricted,thecells cannot achieve their potential maximum area on the surface. If a minimum surface area of a cell is one steradian,12cellsasamaximumcanformattheEarth surface. Therefore, the total number of the primary cellspredeterminingtheinitialdivisibilityoftheemer‐ ging protolithosphere can range between 3–4 (mini‐ mum)to12(maximum)(Fig.4). Paleogeodynamic reconstructions shows that the firstsupercontinentVaalbara(2.8–3.6Ga)consistedof two major structures, i.e. protocontinents/cratons Kaapval and Pilbara [Hazen, 2012], which reflect the divisibility of the already solid protolithosphere and, may be, the divisibility of the emerging lithosphere. Theconceptthatconvectiontookplaceintheprimitive mantleattheveryearlystagesoftheprotolithosphere is not denied, although not widely discussed in the press [Nebel et al., 2014]. An acceptable argument is proposed by I. Artemieva and B. Mooney [2001] who considerthe'thermal'ageoftheArcheanformationsof theEarth. 394 There are grounds to state that convective proces‐ ses in the Earth's mantle played the major role and were the basic criterion for the formation of the first largest block structures of the protolithosphere and alsoforsubsequenttransformationsofsuchblocksinto the lithospheric structures. According to the recon‐ structions, after Vaalbara supercontinent reconstruct‐ ted Ura (about 3 Ga) and younger Kenorland (2100– 2700 Ma), Columbia (1500–1800 Ma), Rodinia (750– 1050 Ma) and Pangea (200–300 Ma) supercontinents [Lietal.,2008;Lubnina,2011;Hazen,2012].About200 mln years ago, Pangea broke apart to form Laurasia and Gondwana, i.e. groups of the southern and north‐ ern continents, respectively. The lithospheric mega‐ blockshavenotbeencompletelyformedanddestruct‐ edyet,andtheseprocessesarestillongoingatthepre‐ sentstagethatistransitionaltotheformationofanew supercontinent. In the long‐term geological history of the Earth, the number and dimensions of the litho‐ spheric plates, which were actively involved in super cycles, were variable, but the blocks and plates per se have never disappeared completely (!). Since the Ar‐ chean,theseintegrallargebodieshavebeensubjectto manygeodynamiccatastrophesandreconstructions[Li et al., 2008], and their initial masses were partially 'lost'insomeofthegeodynamiccycles,regainedinthe others,convertedintothesixmajorlithosphericplates and survived! Strongly metamorphosed rocks of the Archaeanageareobservedinhugeareasofthesixcon‐ tinental lithospheric plates (Africa, Antarctica, North America,Eurasia,AustraliaandSouthAmerica). It is challenging to conduct a proper mathematical analysis of changes in the number of the lithospheric platesandtheirareasfromonesupercycletoanother. The major cycles in the geodynamic evolution of the Earth and corresponding lithospheric plates of dif‐ ferent shapes and kinematics are revealed by paleo‐ geodynamic reconstructions. The lithospheric plates canprovideforstablemantleconvectionatRa≤106,but it becomes unsteady at Ra≥107 [Getling, 1998]. In re‐ sponse to changes in the convection pattern, the sys‐ tem of interacting lithospheric plates has to readjust itself.Numericalsolutionsofequationsofenergy,mass and momentum transfer suggest that mantle convec‐ tion takes place while a set of plates is self‐generated. According to [Trubitsyn V.P., Trubitsyn A.P., 2014], “the set of plates is inevitably generated, without requiring any additional boundary and initial condi‐ tions” (p. 146). The foregoing explains why the Earth has been subject to numerous transformations, inclu‐ ding the catastrophic ones, in the natural course of its geodynamicevolution.Isthisnotaproofofthelawof self‐organized criticality which is discussed in [Bak, 1996]? Obviously, mantle convection has been the major long‐term genetic source providing for the cyclic geo‐ Geodynamics & Tectonophysics 2015 Volume 6 Issue 3 Pages 387–408 dynamicdevelopmentoftheentirelithosphereandits mega‐blockpattern. In this regard, results of studies by P. Bird and co‐ authors[Bird,1988,1998,2003;Bird,Rosenstock,1984; Birdetal.,2002]arenoteworthy–thehierarchyofthe lithospheric plates and blocks is mathematically ana‐ lyzed and the cumulative‐number/area distribution is established. In our study, their results are comple‐ mentedbyexperimentaldatapublishedin[Shermanet al., 2000] (Table) and compared with other quantified information on the formation of plates and the fault‐ block structure of the lithosphere which vary in ranks atthepresentstageofdevelopment.Weapplytectono‐ physicalmethodstoanalysethehierarchyofthelitho‐ spheric plates and blocks with regard to their square areasatthepresentstageofthegeodynamicevolution of the lithosphere. The analysis is aimed at identifica‐ tionofgeneticsourcesandpatternsofthelithosphere blockdivisibilityatvarioushierarchicallevelsindiffe‐ rentstagesofthelithosphereevolution. 5.RECENTHIERARCHICDIVISIBILITYOFTHEFAULT‐BLOCK STRUCTUREOFTHELITHOSPHERE:TECTONOPHYSICAL ANALYSIS The subject of our analysis and the basis of further reconstructionsisthemapoflithosphericblocksofthe Earth which is published in [Bird, 2003] (Fig. 5). Its mainoriginalfeaturesare(1)thepatternoftheplates onthepresentsurfaceoftheEarth,and(2)calculations of plate areas in steradians (Table). To analyse ratios between areas and boundaries of the lithospheric plates, P. Bird showed them on the map close to each otherinanarbitraryreconstruction(nomore!–S.Sh.) of the 'intact' surface of the Earth. His map shows 52 plates of various ranks, including ‘Manus microplate’ which area is the smallest (0.0002 sr, see Table). An‐ otherspecificfeatureofthemapistheuseofsteradian, a dimensionless unit to estimate areas of plates and blocks, thus avoiding some skewing in quantitative comparisons of plates and blocks located at different latitudesofthesphere.Usingthismethod,P.Birdpre‐ sentedindigitalformaglobalsetofboundariesofthe present lithospheric plates and blocks of various sizes and ranks and estimated plate sizes. He established a mathematical regularity in the abrupt, non‐uniform decrease of plate areas on the present Earth's sphere (columns2and3inTable).InFigure6,thecumulative platecountasafunctionofplateareasinsteradiansis showninthebilogarithmeticscale. BasedonTable(Nos.1–52,column3)supplemented bydatafrom[Bird,1988,1998,2003;Bird,Rosenstock, 1984;Birdetal.,2002],regressionequationsshowthat areas of the plates and blocks are decreasing with in‐ creasing numbers in the hierarchy, i.e. with transition from mega structures to regional and local ones (Fig. 6). The detailed interpretation of the plot is given in [Bird, 2003], and a brief is given in the figure caption (Fig. 6). The main regression line based on the data fromTablehastwobends. AccordingtoP.Bird[2003],whenplottedwithloga‐ rithmicscales,theplatesofareasbetween0.002and1 steradian (from the relatively small Jian Fernandes plate,JZtothelargeSouthAmericaplate,SA)occurin numbersthatroughlyobeyapowerlaw: (cumulativecount)N~7(steradians)–1/3 orN≈7Ω–1/3. (3) This equation clearly reflects the scale relationship between the increase in the number of plates and a proportionalreductionintheirareas.Thisischaracter‐ isticofplateswhichareasaresmallerthanonesteradi‐ an,i.e.plateswithanaveragelateralsizeofabout4000 km(seeTable). For a more detailed tectonophysical analysis of the relationships between sizes of the lithospheric plates and blocks, the data published by P. Bird are supple‐ mented by results of similar studies focused on intra‐ continental areas [Sherman et al., 2000]. The consoli‐ dated database provides for analyses of tectonophysi‐ cal regularities in the block divisibility of the present 'solid' lithosphere. For now, seven major lithospheric plates (Nos. 1 to 7 in Table) are outside the scope of analysis and considered below in the closing state‐ ments.Thesemajorplatesareviewedasoriginalindi‐ cators of the initial and subsequent stages of litho‐ sphere divisibility, and it seems more reasonable to considerthemafterreviewingand'excluding'quantita‐ tivedataonplatesdominatinginnumberinotherhie‐ rarchiclevels. Table consolidates three data sets – [Bird, 2003] (Nos.1to52,columns1,2and3),[Cheremnykh,1998] and [Sherman et al., 2000] (Nos. 53 to 225) and thus providesforamoredetailedconsiderationoftheratios ofareasofmedium‐andsmall‐sizedlithosphericplates from[Bird,2003]andtheratiosofareasofcontinental lithosphericblocksfromotherpublications.Foranade‐ quate comparison of plate areas in different hierar‐ chicallevels,theareascalculatedinsteradiansarecon‐ verted to measurement system SI and given in square kilometres and corresponding characteristic linear di‐ mensions (columns 4 and 5, Table). In the recalcula‐ tions, it is assumed that the Earth's radius is R=6371 km, and the equation from [Sadovsky et al., 1987; Sadovsky, Pisarenko, 1991] is used to calculate linear dimensionsLbandplate/blockareas,Sb: . (4) Regressionequationsarecalculatedforcomparative analysesofthethreeabove‐mentioneddatasets: 395 S.I. Sherman: Genetic sources and tectonophysical regularities of divisibility of the lithosphere… Fig.5.LithosphericplatesmappedbyP.Bird[Bird,2003]. The52platesofhismodelPB2002areshownwithcontrastingcolours.Two‐letterplateidentifiersareexplainedinTable.The13cross‐ hatchedareasare‘orogens’inwhichanEulerianplatemodelisnotexpectedtobeaccurate.Labelsofsmallplatesandorogensareoffset (withleaderlines)forclarity.Mercatorprojection. Рис.5.КарталитосферныхплитпоП.Бёрду[Bird,2003]. Цветом выделены 52 плиты по модели РВ2002. Наименование плит дано двойными буквами в соответствии с таблицей. За‐ штрихованныеквадратнойсеткойплощади13районовсоответствуют«орогенам»,длякоторыхмодельвращениявокругЭйле‐ ровых полюсов не совсем точна. Двухбуквенное наименование мелких плит вынесено за их границы. Карта дана в проекции Меркатора. (1)RegressionbyP.Bird,initsmiddlepartshowing areasfromJianFernandesplate(JZ)toSouthAmerica plate(SA),i.e.frommega‐tomedium‐sizedplatesand blocks (Nos. 8 to 52, Table; equation 3 (in sr), and Nc=2259.3L–0.67(5)(symbol1inFig.7); (2) Regression for the additional data on medium‐ and small‐sized blocks (Nos. 53 to 225, Table; Nc=7049.1L–0.91 (6) (symbol 2 in Fig. 7). An important indicatorisaninclinationangleoftheregressioncurve. Equation 6 differs from Equation 5 by an increase of theinclinationangle.TakingintoaccountthatEquation 6isbasedonnumerousdatafromgeologicalandstruc‐ tural maps of continents in various scales, it can be notedthat'small‐sized'blocksaremorenumerousthat 'large'ones.Thisisalogicalconsequencefollowingthe ratioofdataobtainedbydirectfieldobservationsthat always record more small blocks on sites than large ones.Thesameisvalidforevenrockoutcropsandevi‐ dencedbytheplotfrom[Bird,2003](seeFig.6)atthe secondbendoftheregressionline; 396 (3) Regression for the consolidated data on plates and blocks of different characteristic sizes (No. 8 to 225,Table;Nc=3080.8L–0.72 (7)(symbol3inFig.7).Re‐ gression(7)showsasignificantlysmoothedtransition fromsmall‐sizedlithosphericblockstointra‐continen‐ talblocksdivisibility. Ingeneral,equations3,5,6and7aresimilar,which suggeststhatthefragmentationof'solid'rocksfollows a physically uniform pattern, and, in more general terms,thereisatectonophysicallawofthefault‐block divisibility of the lithosphere which is valid for litho‐ spheric blocks of a wide range of areas, from blocks whichsizeiscompatiblewithNorthandSouthAmerica continents, i.e. nearly as big as lithospheric plates, to lumpofrocksobservedonsmalloutcroppedsites. With account of our detailed studies of fault‐block continental lithosphere structures of different ranks andinviewoftheidentityofthephysicsoftheprocess andthesimilarityofmathematicalequations5,6and7, we construct a continuation of the regression curve Geodynamics & Tectonophysics 2015 Volume 6 Issue 3 Pages 387–408 Areasanddimensionsoflithosphericplatesandblocks Параметрыплощадейиразмеровлитосферныхплитиблоковлитосферы # Namesofplatesandblocks 53 54 55 56 57 58 59 60 61 Angara‐Ilim‐9 Angara‐Ilim‐13 Angara‐Ilim‐3 Angara‐Ilim‐12 Prisayan‐Enisei‐2 Baikal‐Patom‐3 Angara‐Ilim Mirny Stanovoy 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 Pacific Africa Antarctica NorthAmerica Eurasia Australia SouthAmerica Somalia Nazca India Sunda PhilippineSea Amur Arabia Okhotsk Caribbean Cocos Yangtze Scotia Caroline NorthAndes Altiplano BandaSea NewHebrides Anatolia BirdsHead Burma Kermadec Woodlark Mariana MoluccaSea NorthBismarck Timor Okinawa AegeanSea SouthBismarck Panama JuandeFuca Tonga BalmoralReef Sandwich Easter ConwayReef SolomonSea Niuafo’ou Maoke Rivera JuanFernandez Shetland Futuna Galapagos Manus Identifiers PA AF AN NA EU AU SA SO NC IN SU PS AM AR OK CA CO YA SC CL ND AP BS NH AT BH BU KE WL MA MS NB TI ON AS SB PM JF TO BR SW EA CR SS NI MO RI JZ SL FT GP MN IA9 IA13 IA3 IA12 IPЕ2 IIIBP3 IA7 IM1 IV1 Area,steradian 2.57685 1.44065 1.43268 1.36559 1.1963 1.13294 1.03045 0.47192 0.39669 0.30637 0.21967 0.13409 0.13066 0.12082 0.07482 0.07304 0.07223 0.05425 0.0419 0.03765 0.02394 0.0205 0.01715 0.01585 0.01418 0.01295 0.0127 0.01245 0.01116 0.01037 0.0103 0.00956 0.0087 0.00802 0.00793 0.00762 0.00674 0.00632 0.00625 0.00481 0.00454 0.00411 0.00356 0.00317 0.00306 0.00284 0.00249 0.00241 0.00178 0.00079 0.00036 0.0002 Area,km2 104593416 58475466 58151967 55428808 48557388 45985628 41825596 19155063 16101505 12435448 8916326 5442665 5303442 4904040 3036917 2964667 2931790 2201988 1700706 1528200 971716 832087.6 696112.3 643345.8 575561.1 525635.9 515488.4 505341 452980.4 420914.6 418073.3 388037 353129.9 325528.9 321875.9 309293.1 273574.2 256526.5 253685.3 195236.2 184277 166823.4 144499.1 128669.2 124204.3 115274.6 101068.2 97821.03 72249.56 32065.82 14612.27 8117.928 47520 34120 33620 31430 28100 27450 27380 25113 24000 Averagegeometric size,km 10227.09 7646.925 7625.744 7445.053 6968.313 6781.27 6467.271 4376.65 4012.668 3526.393 2986.022 2332.952 2302.92 2214.507 1742.675 1721.821 1712.247 1483.91 1304.111 1236.204 985.7566 912.1884 834.3335 802.0884 758.6574 725.0075 717.9752 710.8734 673.0382 648.7793 646.5859 622.9261 594.2473 570.5514 567.341 556.1412 523.0432 506.4845 503.6718 441.8554 429.2749 408.4402 380.1304 358.7048 352.4263 339.5211 317.9123 312.7635 268.7928 179.0693 120.8812 90.09955 218 185 183 177 168 166 165 158 155 397 S.I. Sherman: Genetic sources and tectonophysical regularities of divisibility of the lithosphere… C ontinuationofTable П р о д о л ж е н и е т а б л и ц ы # 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 398 Namesofplatesandblocks Angara‐Ilim Angara‐Ilim Prisayan‐Enisei Aldan Angara‐Ilim Selenga‐Yablonovy Mirny Mirny Barguzin Selenga‐Yablonovy Angara‐Ilim Aldan Baikal‐Patom Mirny EastSayan Selenga‐Yablonovy Mirny Selenga‐Yablonovy Stanovoy Aldan Tunguska Barguzin(IIIБ2) Mirny Mirny Aldan Selenga‐Yablonovy Angara‐Ilim Aldan Baikal‐Patom Selenga‐Yablonovy Khentei‐Dauria Mirny Barguzin Angara‐Ilim EastSayan EastTransbaikalie Barguzin Selenga‐Yablonovy Stanovoy Mirny Selenga‐Yablonovy Angara‐Ilim Angara‐Ilim Sayan‐Altai Selenga‐Yablonovy Stanovoy Mirny Mirny Baikal‐Patom Selenga‐Yablonovy EastSayan Selenga‐Yablonovy Baikal‐Patom Sayan‐Altai Barguzin Barguzin Baikal‐Patom Stanovoy EastTransbaikalie Mirny Barguzin Baikal‐Patom Identifiers IA11 IA5 IPЕ1 II1 IA10 IIISYa18 IM21 IM25 IIIB3 IIISYa15 IA15 II2 IIIBP1 IM11 IIIES2 IIISYa5 IM7 IIISya21 IV2 II6 IT1 IIIB2 IM5 IM23 II5 IIISYa19 IA1 II16 IIIBP6 IIISYa13 VKhD2 IM2 IIIB13 IA4 IIIES10 VET3 IIIB5 IIISYa4 IV10 IM9 IIISYa20 IA16 IA8 IIISA3 IIISYa16 IV7 IM3 IM14 IIIBP4 IIISYa23 IIIES9 IIISYa14 IIIBP11 IIISA2 IIIB1 IIIB11 IIIBP12 IV8 VET1 IM6 IIIB19 IIIBP2 Area,steradian Area,km2 23790 21770 20700 20680 18940 17730 17480 17300 17060 16780 16380 16370 15700 15340 15500 15200 14820 14810 14580 14360 13900 13875 13800 13460 13400 13470 13280 13150 13320 13200 13260 13053 12700 12470 12400 12100 11700 11600 11450 11170 11220 11020 10570 10320 10260 10300 9800 9730 9800 9420 9190 9200 8900 8530 8490 8550 8500 8530 8600 8250 8100 8100 Averagegeometric size,km 154 148 144 144 138 133 132 131 131 129 128 128 125 124 124 123 122 122 121 119 118 118 117 116 116 116 115 115 115 115 115 114 113 112 111 110 108 108 107 106 106 105 103 101 101 101 99 99 99 97 96 96 94 92 92 92 92 92 92 91 90 90 Geodynamics & Tectonophysics 2015 Volume 6 Issue 3 Pages 387–408 C ontinuationofTable П р о д о л ж е н и е т а б л и ц ы # 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 Namesofplatesandblocks Selenga‐Yablonovy Selenga‐Yablonovy Barguzin Baikal‐Patom Aldan Aldan Angara‐Ilim Barguzin Baikal‐Patom Selenga‐Yablonovy Barguzin EastSayan Barguzin Baikal‐Patom EastTransbaikalie Dzhida Khentei‐Dauria EastTransbaikalie EastTransbaikalie Angara‐Ilim Mirny Aldan Barguzin Mirny Barguzin Baikal‐Patom Selenga‐Yablonovy Selenga‐Yablonovy Baikal‐Patom Dzhida Mirny Stanovoy Stanovoy Barguzin Barguzin Stanovoy Angara‐Ilim Aldan Aldan Stanovoy Mirny Pribaikalskyfaultzone Stanovoy EastTransbaikalie Angara‐Ilim EastSayan Baikal‐Patom Mirny Aldan Barguzin Mirny Baikal‐Patom Selenga‐Yablonovy EastTransbaikalie EastTransbaikalie Barguzin Stanovoy EastTransbaikalie Aldan Barguzin Stanovoy EastTransbaikalie Identifiers IIISYa24 IIISYa7 IIIB7 IIIBP5 II9 II18 IA14 IIIB21 IIIBP15 IIISYa9 IIIB23 IIIES12 IIIB15 IIIBP7 VET20 (IIID1) (VKhD1) (VET16) (VET17) (IA2) (IM24) (II13) (IIIB10) (IM4) (IIIB14) (IIIBP8) (IIISYa11) (IIISYa12) (IIIBP9) (IIID2) (IM22) (IV13) (IV14) (IIIB12) (IIIB22) (IV5) (IA18) (II8) (II17) (IV6) (IM16) VET8 IA6 IIIES8 IIIBP13 IM13 II12 IIIB20 IM26 IIIBP10 IIISYa8 VET12 VET15 IIIB8 IV4 VET13 II10 IIIB24 IV12 VET7 Area,steradian Area,km2 8080 8000 7700 7600 7315 7400 7180 7200 7200 7300 6850 6750 6750 6700 6800 6600 6500 6500 6500 6400 6400 6075 6000 5800 5800 5850 5800 5800 5625 5600 5300 5380 5140 5100 5000 5000 4900 4855 4700 4700 4490 4500 4500 4500 4350 4400 4275 4040 4050 4150 4040 4000 4000 4000 4000 3800 3800 3800 3740 3600 3590 3590 Averagegeometric size,km 90 89 88 87 86 86 85 85 85 85 83 82 82 82 82 81 81 81 81 80 80 78 77 76 76 76 76 76 75 75 73 73 72 71 71 71 70 69 69 69 67 67 67 67 66 66 65 64 64 64 63 63 63 63 63 62 62 62 61 60 60 60 399 S.I. Sherman: Genetic sources and tectonophysical regularities of divisibility of the lithosphere… EndofTable Окончаниетаблицы # 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 Namesofplatesandblocks Aldan(II11) Baikal‐Patom Aldan EastTransbaikalie EastTransbaikalie Aldan EastSayan EastSayan Barguzin Stanovoy Angara‐Ilim Mirny Mirny EastSayan EastSayan Barguzin Selenga‐Yablonovy Khentei‐Dauria EastTransbaikalie Mirny EastSayan Selenga‐Yablonovy Khentei‐Dauria EastSayan Selenga‐Yablonovy Selenga‐Yablonovy Mirny Barguzin EastSayan Barguzin Mirny Selenga‐Yablonovy Mirny Barguzin Barguzin EastTransbaikalie EastTransbaikalie Mirny Mirny EastTransbaikalie Identifiers Area,steradian II11 IIIBP14 II15 VET4 VET21 II14 IIIES11 IIIES6 IIIB16 IV11 IA17 IM10 IM15 IIIES7 IIIES13 IIIB4 IIISYa17 VKhD4 VET9 IM17 IIIES3 IIISYa1 VKhD3 IIIES4 IIISYa22 IIISYa3 IM18 IIIB9 IIIES5 IIIB17 IM27 IIISYa10 IM8 IIIB6 IIIB18 VET5 VET11 IM19 IM12 VET10 Area,km2 3350 3350 3200 3300 3230 3100 3000 2900 2900 2900 2680 2690 2690 2700 2700 2700 2700 2690 2690 2470 2475 2400 2400 2250 2240 2100 2000 1800 1700 1600 1570 1500 1390 1300 1200 1100 1100 898 540 494 Averagegeometric size,km 58 58 57 57 57 56 55 54 54 54 52 52 52 52 52 52 52 52 52 50 50 49 49 47 47 46 45 42 41 40 39 39 37 36 35 33 33 30 23 22 N o t e s.Thetableconsolidatesthefollowingdata:Nos.1to52–from[Bird,2003]withrecalculationforareaandlinearsizes;Nos.53to 225–accordingto[Cheremnykh,1998;Shermanetal.,2000].Namesofthelargestplatesareboldprinted;thegenerallawsofdestructionof solid bodies do not apply to such plates. Names and two‐letter identifiers of megablocks correspond to [Bird, 2003]. Names of regional blocksarefromthecataloguebyA.V.Cheremnykh. П р и м е ч а н и е. Данные с № 1 по 52 – по [Bird, 2003] с пересчетом на площадные и линейные меры; с № 53–225 – по [Cheremnykh, 1998; Sherman et al., 2000]. Жирным шрифтом выделены самые крупные литосферные плиты, не вписывающиеся в общиезакономерностидеструкциитвердоготела.Названиямегаблоковсоответствуюткарте[Bird,2003],названиярегиональных блоковданыпоавторскомукаталогуА.В.Черемных. derived from equation 3 (Fig. 7) in the direction that hasbeensubstantiatedbyP.Bird(seeFig.6).Thetwo regression lines based on equations 3 and 7 have the same physical meaning in bilogarithmical scales, and theirmiddlepartsareidenticalinFigure6andgeneral‐ ly similar in Figure 7. The regression lines and the equations reflect destruction patterns of the 'solid' lithosphereinawidevarietyofscales. 400 The area estimations obtained by different methods provide for well‐reasoned general conclusions concer‐ ning regular patterns of the block destruction of the Earth's lithosphere at specified hierarchical levels. The reviewedresultscomplementeachotherandextendour knowledgeofdestructionofthelithosphereasthesolid coveroftheEarth.Itisnowreasonabletobrieflyreview theknownlawsofdestructionofsolidbodies,i.e.rocks. Geodynamics & Tectonophysics 2015 Volume 6 Issue 3 Pages 387–408 Fig.6.Numberofplatesplottedasafunctionofarea[Bird,2003,fig.19]. CurvePB2002(green)referstothemodelinFig.7.Arelativelysteadyslopeofthecurveforplateareasbetween0.002and1steradian suggestsapowerlawrelationshipbetweenthenumberofplatesandtheirminimumsize.Flatteningintheleftsegmentofthecurveisdue tothemodelincompleteness,i.e.therearemanyplatesofsmallersizeswhicharenotincludedinmodelPB2002.Anabruptvariationof theslopeintherightsegmentofthecurvesuggeststhatverylargeplatesarelimitedintheirareabecauseofthefiniteareaoftheEarth, andperhapsalsobymantleconvectiontractions. Рис.6.Графиквзаимосвязиколичестваплиткакфункцииихплощади(по[Bird,2003,fig.19]). КриваяРВ2002(зеленыйцвет)отражаетситуациюподаннымрисунка7.Относительнопостоянныйнаклонкривоймеждугра‐ ницамиплощадей0.002и1.000стерадианотражаетвзаимоотношениямеждучисломплитиихминимальнымразмером.Изме‐ нениеугланаклонавлевойчастиграфикаотражаетнедостаточноечислонаблюдений,тоестьимеютсяещеболеемелкие,не учтенныевавторскоймоделиблоки.Резкоеизменениеугланаклонавправойчастиграфикапоказывает,чтокрупныеплиты ограниченывсвоихразмерахконечнойплощадьюЗемли,атакже,возможно,конвекционнымимантийнымипотоками. 6.GENETICSOURCESOFTHELITHOSPHERE DIVISIBILITYOFVARIOUSRANKS ItcanbestatedthatEquation7anditsspecificvari‐ ants(seeFig.7)aresufficienttofullydescriberelative‐ lysmalllithosphericplatesandintraplateblocksofthe 'solid'lithosphereupto rocklumps. Theexperimental methods have yielded similar equations that mathe‐ maticallyreflectthephysicsofdestructionofsolidbo‐ dies in a wide range of scales (from a medium‐size block which size amounts to a few thousand kilome‐ tres,toarockfragmentwhichdiameterisadozencen‐ timetres),andtherearegroundtostatethattheblock divisibilityofthelithospherefollowslawsofself‐simi‐ larity.Inthephysicsofdestructionofsolidandviscoe‐ lastic bodies, self‐similarity patterns have been noted longagoatdifferentscalelevels.However,self‐simila‐ rityinaverywidespectrumofhierarchicallevels,from centimetrestomegasizes,hasnotbeenconsideredyet, andthispaperisthefirstattemptinthisrespect. Based on results of independent studies, A.N. Kol‐ mogorov [1941] and A.F. Filippov [1962] established thatrocksaresubjecttofragmentationaccordingtothe law of destruction of solid bodies, and the following exponentialexpressionislinearincoordinateslgNand lgL: lgN=f(lgL), (8), where L is the sample's arbitrary size, and N is the numberofsamples. This conclusion includes the above‐described em‐ pirical relationships that refer to large‐size objects, suchaslithosphereblocksofvariousranksand,partly, 401 S.I. Sherman: Genetic sources and tectonophysical regularities of divisibility of the lithosphere… Fig.7.Curvesofrelationshipsbetweenmediumlateraldimensionsoflithosphericplatesandblocks:1–accordingto[Bird, 2003];2–accordingto[Cheremnykh,1998;Shermanetal.,2000];3–integratedregressionlinebasedondata(1)and(2); 4–extrapolatedregressionlineaccordingtoequation1;5–extrapolatedregressionlineaccordingtoequation3.3.Nc – rowoflithosphericplatesandblocksbyaveragecharacteristicsizesL,km(analoguestoreconstructionsbyP.Birdinstera‐ dians). Рис. 7. Графики взаимосвязи средних поперечных размеров плит и блоков литосферы по: 1 – по данным [Bird, 2003];2–поданным[Cheremnykh,1998;Shermanetal.,2000];3–совмещеннаялиниярегрессииподанным[1и2]; 4 – экстраполяция линии регрессии по данным уравнения (1); 5 – экстраполяция линии регрессии по данным уравнения(3).Nc–последовательностьлитосферныхплитиблоковвпорядкеувеличенияусредненныххарактер‐ ныхразмеровL,км(поаналогииспостроениямиП.Бёрдавстерадианах). faults in the upper brittle layer of the lithosphere, whichcrosseachothertoformthecorrespondinghier‐ archic group of the fault‐block structures of the solid coveroftheEarth[Sherman,1977;Shermanetal.,2000, 2004; Seminsky, 2001, 2003; and many others]. Obvi‐ ously, this property mitigates issues related to 'buck‐ ling' of the regression lines at the boundaries of Juan Fernandez (JZ) and Shetland (SL) plates (0.00241 and 0.00178 sr, respectively). Buckling occurs due to the lack of quantitative data. In our study, this issue is completely eliminated after the additional data are supplemented(Table). Itcanthusbestatedthatdeformationanddestruc‐ tion of the Earth's solid cover under the influence of external loads take place according to a regular pat‐ tern.Fromcertainhierarchicallevels,residualdestruc‐ tion (in the form of blocks varying in ranks) is distri‐ butedinaccordancewiththecharacteristicsizesofthe blocks and their number, as described by Equation 7. 402 Theregressionisbucklingatthetransitionfrommedi‐ um‐sizedplatestolargeones(seeFig.6and7)dueto otherreasons. In terms of physics, buckling of the regression line showingthehierarchyofplatesizesversusplateareas (seeFig.6and7)isrelatedtosourcesofrank‐variable destruction of the lithosphere as a solid body. The buckle occurs abruptly at the transition from a few very large lithospheric plates to medium‐sized plates and small blocks that are statistically abundant. The regressioncurveisbuckledfromaverysteepangletoa moregentleoneattheboundarybetweenSouthAme‐ rica(areaof1.03sr)andSomaliplates(areaof0.47sr). Ajumpoccurswhenthesquareareaisdoubled.Forsix largeplates(Africa,Antarctica,NorthAmerica,Eurasia, Australia and South America; data on Pacific plate are nottakenintoaccount),theregressioncurveisasteep, almostverticalline.Theirareasarenearlysimilarand almost unchangeable. Naturally, they are governed by Geodynamics & Tectonophysics 2015 Volume 6 Issue 3 Pages 387–408 another law of formation of solid lithospheric masses, whichisnotconsistentwiththelawsofdestructionof solid bodies. In this respect, P. Bird [2003] also notes thatthefactthatlargeplatesareclearlyestablishedis indicative of a very weak dependence of plate areas fromanyquantitativeparameters,exceptfortheEarth radius. When the Earth radius is used as a natural in‐ dependentunittomeasuresolidanglesinsteradians,it is clearly revealed that very large areas of the above‐ mentionedsixplates(Pacificplateisanexception)are almost similar. According to P. Bird [2003], typical areas of the large lithospheric plates correlate with mantle convection: “….this characteristic size seems more consistent with whole mantle convection than with layered convection”. Indeed, the formation of the largestblocks(i.e.primarylithosphericplatesoriginat‐ ingatthestagewhentheprotolithospherewasformed andlaterperiods)ismoreinlinewithmantleconvec‐ tionthandestructionofthesolidbody.Theauthorfully shares these assumptions by P. Bird as they are sup‐ portedbyalltheabovediscusseddata,argumentsand tectonophysicalcalculations. As shown by the analysis of areas of the rank‐ variable present lithospheric plates (see Table), the totalareaofthesevenlargestplates(lessthan14%of the total number of plates) is about 10.15 steradians, and they occupy almost 81 % of the entire surface of theEarth.Theareaofthesixcontinentalplates(Africa, Antarctica,NorthAmerica,Eurasia,AustraliaandSouth America) is more than 60 % of the planet's surface area.TheyarewelltracedinthehistoryofPangeaand less evidently in the more distant past. Through the history of the Earth, these huge integral bodies were subject to numerous geodynamic catastrophes and transformations.Some ofthemlost muchoftheinitial mass, others completely 'disappeared' in the mantle, whilesomeoftheplateshavegrowninsize.Therefore, fromonesuper‐continentalcycletoanother,thelitho‐ sphericblocksdifferinnumberandkinematics.Based on the available data, it is impossible to state for sure which of them were formed before the Archaean and arestillinplace,andwhichofthemweremoreorless transformed.Itischallengingtorestorethe genesisof structural relics in the cooling medium of the proto‐ lithosphere and those in the lithosphere medium with referencetotheverydistantpast.Itisaninverseprob‐ lem with unambiguous solutions. As a definite and in‐ disputable conclusion cannot be drawn, one can only assumethatconvectionisthemostprobableandbetter argumented physical process that took place when the low‐viscous medium of the protolithosphere was cooling down to form large masses in the first hypo‐ thetical(?)supercyclesofVaalbaraandUr,and,finally, convection can be viewed as a mechanism predeter‐ miningthepresentshapeoftheEarth'scontinents.Itis most probable that the megablocks were fragmented in the similar pattern in Kenorlend and later super‐ cycles.However,basedontheavailablematerials,itis possible only to justify the block structure of the pre‐ sentstage. ItisreasonableheretoquotethebookbyN.L.Dob‐ retsovetal.[2001]:“InthehistoryoftheEarth,convec‐ tionintwolayerswasreplacedbyconvectionintheen‐ tire mantle and vice versa, and this might have taken placeseveraltimes…Therefore,itismostlikelythatin theEarth'shistory,convectionintheentiremantlewas replaced by two‐layer convection. Another possible scenario is more complicated: about 2.5 Ga ago, two‐ layerconvectionwasreplacedbyconvectionintheen‐ tiremantle[Maruyama,1994];afteraperiodofonebil‐ lionyears,two‐layerconvectionoccurredagain[Honda, 1995],and,finally,atransitionbacktoconvectioninthe entire mantle took place in the past 150‐100 Ma [Tru‐ bitsyn, Rykov, 2000]” (p. 111). Convection predeter‐ minesthemajorcyclesinthegeodynamicsoftheEarth and fragmentation of the lithosphere into megablocks. The latter are destructed under the physical laws of destructionofsolidrocks.Currently,destructionofthe lithosphereisactivelycontinuedinseismiczonesofthe continental lithosphere and zones of subduction and spreadingatthemarginsofthelithosphericblocks. 7.DISCUSSION PublicationsonconvectionintheEarth'smantleand its role in global geodynamic processes are quite nu‐ merous. In the majority of papers, recent geodynamic processes are considered with an assumption that the evolution of convection in the mantle and astheno‐ spheretookplaceintwo‐orthree‐layerormorecom‐ plicatedpatterns[Lobkovsky,1988;Lobkovsky,Kotelkin, 2000; Lobkovsky et al., 2004; Rykov, Trubitsyn, 1994a, 1994b;Trompert,Hansen,1988;Trubitsyn,Rykov,2002; TrubitsynV.P.,TrubitsynA.P.,2014].Mantleconvection wasdiscussedinanumberofpublicationsmanyyears ago, the most famous of which are [Pekeris, 1935; Molnaretal.,1979]. Accordingto[Molnaretal.,1979],largesizesofcon‐ tinental plates are related to convection in the entire mantle,andhorizontaldimensionsoftheplatedepend onthedepthoftheconvectiveprocess.Theiranalysisis based on the proportional change in the length of the subduction zone on the surface and the velocity of its sinking which depends on heat assimilation in the ab‐ senceofabarrierattheborderwiththelowermantle. Thetwo‐layerconvectionintheEarthmantleisde‐ scribedbyL.P.ZonenshainandM.I.Kuz’min[1993]and reconstructedinaworld‐knownschemebyS.Maruya‐ ma[1994]. To sum up this very brief information on the two‐ layer models of convection in the Earth mantle, it is 403 S.I. Sherman: Genetic sources and tectonophysical regularities of divisibility of the lithosphere… worthy to refer again to the book by N.L. Dobretsov et al.[2001]whogivemuchattentiontoconvectionasan important component of geodynamic processes. In their book, prior to the geodynamic analysis of pro‐ cesses in the mantle, asthenosphere and lithosphere, they provide a comprehensive description of the two mainmodelsofthermal‐gravitationalconvectionwhich provide the basis for a variety of geodynamic recon‐ structions. In the first model, convection take place in the entire mantle, from boundaries of the lithosphere base (30 to 100km) to the upper limit of the core (about2900km).Thesecondmodelshowsconvection intheupperandlowermantlewithoutanysignificant masstransferbetweenthetwolayers.In[Dobretsovet al., 2001], the authors focus on the complexity of geo‐ dynamicprocessesinthemantleanddiscusstheirevo‐ lution up to the present stage of the Earth develop‐ ment. The concept of two‐layer mantle convection is convincingly proved by results of many original expe‐ rimentsconductedbytheauthorswiththeuseofspe‐ cially designed installations [Kirdyashkin, Dobretsov, 1991; Dobretsov, Kirdyashkin, 1993]. Besides, they es‐ timated parameters of convection. Specifically, based on the video records, they revealed flow lines in the two‐layer fluid convection system and estimated hori‐ zontal and vertical velocities of the flows. Their very important observation is that convection flows above and below the interface go in different directions, and this is an evidence that vector directions of horizontal convection flows in the layers located one upon ano‐ therarenotinterrelated.Accordingto[Dobretsovetal., 2001],vectorsoftheverticalflowsaresimilar,andthis fact emphasises the major role of convection in the mantle which provides for dissipation of heat energy. Important are the digital parameters and vectors of flow velocities and cell sizes. In the bottom layer (whichisthicker),cellsizesareproportionaltothelay‐ er's thickness, and flow velocities are lower. In [Do‐ bretsov et al., 2001], the concept of the two‐layer con‐ vectionintheEarth'smantleiswellestablishedbythe experimentalandactualobservationdata.Nonetheless, the authors note: “In the majority of cases, the geo‐ chemicaldatasupportthetwo‐layerconvectionmodel, whilemuchgeophysicaldatamaybeinterpretedinfa‐ vourofconvectionintheentiremantle”(p.108). In [Trubitsyn V.P., Trubitsyn A.P., 2014], a digital model is described in detail to show that the present setofthelithosphericplatesisaresultoftheevolution of convection. It provides an insight into the possible mode of flows in the entire mantle, movements of the massesbetweentheupperandlowermantle,aswellas betweenthecentralandlaterallimitsoftheconvection cells.Usingequations,V.P.TrubitsynandA.P.Trubitsyn calculated temperature, viscosity and velocity of mantle convection flows generated by effective diffu‐ sion‐dislocation creeping in the absence of pseudo‐ 404 plastic deformation and in case of the very hard litho‐ sphere. In particular, their temperature distribution pattern shows that small cold descending flows, i.e. small‐scale convection, occur under the lithosphere. The estimated scheme of convection in the entire mantle in [Trubitsyn V.P., Trubitsyn A.P., 2014] is con‐ sistentwithourideasoftheprimarygeneticallyemer‐ ging block divisibility of the protolithosphere. In the initial state, the protolithosphere remains uniform at the surface, has a roughly constant thickness and in‐ creased quasi‐strength at the primary inter‐cell boun‐ daries whereat the viscosity of the medium is increa‐ singduetocoolingoftheprotolithosphere. Regretfully,initialdivisibilityoftheemergingupper solid cover of the Earth is taken into account by few researchersintheirestimations,whilesuchdivisibility is one of the most likely results of convection in the cooling protolithosphere. This is obviously due to the absence of direct geological materials and the lack of appropriate paleo‐reconstruction methods that can integrate geological, geophysical and geochemical da‐ tabases. As shown by our study, computational me‐ thodsarehelpful,toacertainextent,insolvingill‐con‐ ditioned inverse problems to reconstruct processes andstructuresofthedistantpast. The concept of the single‐layer convection, assu‐ ming that convection took place through the ½‐radius depth at the initial stage when the Earth lithosphere was formed, is acceptable and seems quite realistic, even though the literature is still insufficient on this subject. This justifies the author's efforts to clarify the origin of divisibility of the primary non‐solid, almost continuous cover of the Earth which evolution history includesperiodsofthePhanerozoicandcontemporary faultinginthelithosphereanditsfragmentationunder thelawsofdestructionofsolidbodies.Itcanbenoted in general that the upper cover of the Earth is subject to destruction in a regular pattern, from larger to smallermasses. 8.CONCLUSION This study is pioneering in tectonophysical recon‐ structionofinitialdivisibilityoftheprotolithosphereas a result of convection in the cooling primitive mantle. Initial division of the protolithosphere into separate masses,i.e.prototypesoftheblocks,andtheirsizewas predetermined by the emerging Rayleigh–Bénard con‐ vection cells. In studies of geology and geodynamics, the Rayleigh–Bénard convection cells were first re‐ ferred to as a factor to explain the formation of initial continental cores. Considering the Rayleigh–Bénard cells and their structural relics can help clarify initial divisibilityoftheprotolithosphereandtheoriginofthe majorlithosphericplates,i.e.prototypesofcontinents. Geodynamics & Tectonophysics 2015 Volume 6 Issue 3 Pages 387–408 Inouropinion,theinitialmega‐scaleblockstructureof the protolithosphere and the emerging lithosphere were predetermined by the Rayleigh–Bénard cells as they were preserved in the emerging lithosphere and their lower boundaries corresponded to the core‐ mantle boundary, i.e. one of the major discontinuities of the planet. Our theoretical estimations are in good agreement with the number and sizes of the Earth's theorizedfirstsupercontinents,VaalbaraandUr. In our tectonophysical discussion of the formation ofthelithosphericblockstructure,weanalyseindetail the map of modern lithospheric plates [Bird, 2003] in combination with the materials from [Sherman et al., 2000]. In the hierarchy of the blocks comprising the present lithosphere, which sizes are widely variable, twogroupsofblocksareclearlydistinguished.Thefirst groupincludesmegablockswiththeaveragegeometric sizeabove6500km.Theirformationisrelatedtocon‐ vectionintheEarthmantleatthepresentstageofthe geodynamicevolutionoftheEarth,aswellasatallthe previous stages, including the earliest one, when the protolithosphere emerged. The second group includes medium‐sized blocks with the average geometric size of less than 4500 km and those with minimum sizes, suchasrocklumps.Theyreflectprimarilythedegrada‐ tion of the megablocks as a result of their destruction due to high internal stresses in excess of the tensile strength of the medium. This group may also include blocks which formation is related to convection in the uppermantlelayer,asthenosphere.Therearegrounds to assume that through the vast intermediate interval of geologic time, including supercycles of Kenorlend, Rodin, and Pangea, the formation of the large litho‐ sphericblockswascontrolledbyconvection,andlater on, they were ‘fragmented’ under the physical laws of destruction of solid bodies. However, it is difficult to 10.REFERENCES clearly distinguish between the processes that prede‐ termine the hierarchy of formation of the block struc‐ tures of various origins – sizes of ancient lithospheric blockscannotbeestimatedunambiguously. 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Т. 34. № 4. С. 3–13]. Sherman, Semen I., Academician of the Russian Academy of Natural Sciences, Doctor of Geology and Mineralogy, Professor, Chief Researcher Institute of the Earth’s Crust, Siberian Branch of RAS 128 Lermontov street, Irkutsk 664033, Russia Tel.: (3952)428261; e-mail: [email protected] Шерман Семен Иойнович, академик Российской академии естественных наук, докт. геол.-мин. наук, профессор, г.н.с. Институт земной коры СО РАН 664033, Иркутск, ул. Лермонтова, 128, Россия Тел.: (3952)428261; e-mail: [email protected] 408
