supercontinents, mantle dynamics and plate tectonics: a ... · supercontinents, mantle dynamics and...

Earth-Science Reviews 105 (2011) 1–24

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Supercontinents, mantle dynamics and plate tectonics: A perspective based onconceptual vs. numerical models

Masaki Yoshida a,⁎, M. Santosh b

a Institute for Research on Earth Evolution (IFREE), Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 2-15 Natsushima-cho, Yokosuka, Kanagawa 237-0061, Japanb Division of Interdisciplinary Science, Faculty of Science, Kochi University, Akebono-cho 2-5-1, Kochi 780-8520, Japan

⁎ Corresponding author. Tel.: +81 46 867 9814; fax:E-mail address: [email protected] (M. Yoshid

0012-8252/$ – see front matter © 2010 Elsevier B.V. Aldoi:10.1016/j.earscirev.2010.12.002

a b s t r a c t
a r t i c l e i n f o
Article history:Received 1 June 2010Accepted 7 December 2010Available online 14 December 2010

Keywords:supercontinentsmantle dynamicsplate tectonicsWilson Cyclesupercontinent cyclenumerical model

The periodic assembly and dispersal of supercontinents through the history of the Earth had considerableimpact on mantle dynamics and surface processes. Here we synthesize some of the conceptual models onsupercontinent amalgamation and disruption and combine it with recent information from numerical studiesto provide a unified approach in understanding Wilson Cycle and supercontinent cycle. Plate tectonic modelspredict that superdownwelling along multiple subduction zones might provide an effective mechanism topull together dispersed continental fragments into a closely packed assembly. The recycled subductedmaterial that accumulates at the mantle transition zone and sinks down into the core–mantle boundary(CMB) provides the potential fuel for the generation of plumes and superplumes which ultimately fragmentthe supercontinent. Geological evidence related to the disruption of two major supercontinents (Columbiaand Gondwana) attest to the involvement of plumes. The re-assembly of dispersed continental fragmentsafter the breakup of a supercontinent occurs through complex processes involving ‘introversion’,‘extroversion’ or a combination of both, with the closure of the intervening ocean occurring throughPacific-type or Atlantic-type processes. The timescales of the assembly and dispersion of supercontinents havevaried through the Earth history, and appear to be closely linked with the processes and duration ofsuperplume genesis. The widely held view that the volume of continental crust has increased over time hasbeen challenged in recent works and current models propose that plate tectonics creates and destroys Earth'scontinental crust with more crust being destroyed than created. The creation–destruction balance changesover a supercontinent cycle, with a higher crustal growth through magmatic influx during supercontinentbreak-up as compared to the tectonic erosion and sediment-trapped subduction in convergent marginsassociated with supercontinent assembly which erodes the continental crust. Ongoing subduction erosionalso occurs at the leading edges of dispersing plates, which also contributes to crustal destruction, althoughthis is only a temporary process. The previous numerical studies of mantle convection suggested that there is asignificant feedback between mantle convection and continental drift. The process of assembly ofsupercontinents induces a temperature increase beneath the supercontinent due to the thermal insulatingeffect. Such thermal insulation leads to a planetary-scale reorganization of mantle flow and results in longest-wavelength thermal heterogeneity in the mantle, i.e., degree-one convection in three-dimensional sphericalgeometry. The formation of degree-one convection seems to be integral to the emergence of periodicsupercontinent cycles. The rifting and breakup of supercontinental assemblies may be caused by eithertensional stress due to the thermal insulating effect, or large-scale partial melting resulting from the flowreorganization and consequent temperature increase beneath the supercontinent. Supercontinent breakuphas also been correlated with the temperature increase due to upwelling plumes originating from the deeperlower mantle or CMB as a return flow of plate subduction occurring at supercontinental margins. The activemantle plumes from the CMBmay disrupt the regularity of supercontinent cycles. Two end-member scenarioscan be envisaged for the mantle convection cycle. One is that mantle convection with dispersing continentalblocks has a short-wavelength structure, or close to degree-two structure as the present Earth, and when asupercontinent forms, mantle convection evolves into degree-one structure. Another is that mantleconvection with dispersing continental blocks has a degree-one structure, and when a supercontinentforms, mantle convection evolves into degree-two structure. In the case of the former model, it would takelonger time to form a supercontinent, because continental blocks would be trapped by different downwellingsthus inhibiting collision. Although most of the numerical studies have assumed the continent/supercontinent

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2 M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24

to be rigid or nondeformable body mainly because of numerical limitations as well as a simplification ofmodels, a more recent numerical study allows the modeling of mobile, deformable continents, includingoceanic plates, and successfully reproduces continental drift similar to the processes and timescales envisagedin Wilson Cycle.

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Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22. Supercontinent cycle and Wilson Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33. Supercontinent cycle and mantle convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34. Thermal and mechanical interaction between continent and mantle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65. Formation of degree-one mantle structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76. Long-wavelength thermal structure in the mantle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97. Timescale of the supercontinent assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118. Supercontinent breakup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129. Stability and longevity of the continent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

10. Origin and growth of the continental crust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1411. A preliminary Wilson Cycle model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1512. Continents and plate tectonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1613. Next supercontinent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1914. Summary and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1. Introduction

The history of growth, evolution and dispersion of supercontinentson the globe through time has received considerable attention in therecent years, particularly with respect to the impact of the assemblyand dispersion of continental fragments on mantle dynamics, surfaceprocesses and life evolution (for a recent compilation, see Santosh andZhao, 2009, and papers therein). A recent synthesis of the variousconceptual models suggests that supercontinent tectonics in relationtomantle dynamics provides a key to evaluate the history of evolutionand destruction of the continental crust, to understand the history oflife, and to trace the major surface environmental changes of ourplanet (Santosh, 2010b). The postulated Neo-Archean continentalassemblies (e.g., Rogers and Santosh, 2004; Eriksson et al., 2009) andthe increasing evidence for the Paleo-Mesoproterozoic superconti-nent Columbia (Meert, 2002; Rogers and Santosh, 2002; Zhao et al.,2002; Rogers and Santosh, 2009), Neoproterozoic Rodinia (Dalziel,1991; Hoffman, 1991; Z.X. Li et al., 2008) and Late Neoproterozoic–Cambrian Gondwana (Collins and Pisarevsky, 2005; Meert andLieberman, 2008), among other proposed supercontinents, supportthe notion that global cycles of continental reorganization haveoccurred throughout Earth's history (Worsley et al., 1984; Nance et al.,1986).

Seismic tomographic images suggest that the Earth's mantlestructure is characterized by different modes of flow: (1) Subductingplates mainly beneath the Circum-Pacific region, some of which arestagnated at the 660 km phase boundary (i.e., spinel to perovskite+magnesiowüstite phase transition boundary), whereas otherspenetrate into the deeper lower mantle (e.g., Fukao, 1992; van derHilst et al., 1997; Fukao et al., 2001; Zhao, 2004); (2) Large-scale,broad upwelling-plumes beneath the South Africa–South Atlantic andSouth Pacific regions (e.g., Fukao, 1992; Masters et al., 2000; Mégninand Romanowicz, 2000; Ritsema and van Heijst, 2000); (3) Small-scale, localized upwelling-plumes originating from the core–mantleboundary (CMB) or 660 km phase boundary, which were detectedmainly by the recent highly-resolved tomographic model (e.g., Wolfeet al., 1997; Montelli et al., 2004, 2006; Wolfe et al., 2009).Geochemical evidence and geodynamic models support this global

view of mantle structure, although several models with variouscompositional heterogeneities have also been proposed (see reviewby Tackley, 2000a, 2007). On the other hand, a continent/supercon-tinent is isolated from the convecting mantle in terms of the rheology,composition, large radiogenic internal heating production (e.g.,Schubert et al., 2001), and the longevity over geologic time (e.g.,Carlson et al., 2005). The thermal andmechanical interaction betweenthe continental drift and mantle convection has not been, however,fully resolved.

The numerical studies of mantle convection have markedlyprogressed toward the realization of seismic tomography images ofmantle structure and a better understanding of geodynamic mecha-nisms in accordance with the advancement in numerical modelingtechniques as well as the increase of computational power andresource. The mantle convection theory is comprehensively summa-rized by several papers and textbooks (e.g., McKenzie et al., 1974;Jarvis and McKenzie, 1980; Christensen, 1984; Busse, 1989; Schmel-ing, 1989; Davies, 1999; Schubert et al., 2001; Turcotte and Schubert,2002; Ricard, 2007). A review of mantle convection studies and thenumerical simulation techniques used are beyond the scope of thispaper, and can be found in the several textbooks and papers withbroader view and perspective (e.g., Richards and Davies, 1992;Tackley, 2000a; Schubert et al., 2001; Ricard, 2007; Zhong et al.,2007b; Ismail-Zadeh and Tackley, 2010). In particular, numericalstudies performed in the 80s–90s mainly by using two-dimensional(2-D) model with continents/supercontinents are carefully reviewedin the textbook by Schubert et al. (2001). The relationship betweenthe supercontinent and mantle convection processes is clarified in areview by Condie (2001) from the viewpoint of geology andgeochronology. However, there have been very little attempts so farto link the geophysical numerical models and the geological andtectonic conceptual models to understand the history of platetectonics, Wilson Cycle and supercontinent cycle. Furthermore, it isimportant to link these models with the actual surface geologicalrecords, and the quantitative geophysical data from various types ofgeophysical surveys. In the recent years, several numerical models ofmantle convection have addressed the assembly and breakup ofsupercontinents using three-dimensional (3-D) models. This paper

3M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24

aims to synthesize the salient results from these studies in an attemptto provide a unified approach in evaluating the numerical studies andspeculative geodynamic models to better constrain the mechanism offormation and disruption of supercontinents.

2. Supercontinent cycle and Wilson Cycle

Whereas the term supercontinent cycle (Worsley et al., 1984,1986; Nance et al., 1988; Unrug, 1992) describes the periodicassembly and dispersal of continental fragments, the term WilsonCycle (after J. Tuzo Wilson, the pioneer who laid the base for themodern concept of plate tectonics; Dewey and Spall, 1975) has beenused to explain the periodic opening and closing of ocean basins(Wilson, 1966). In a simple sense, supercontinent cycle and WilsonCycle are complimentary because fragmentation of supercontinentsopens new ocean basins and amalgamation of supercontinents leadsto the closure of ocean basins. However, supercontinent cycles involvemore complex processes that occur during the assembly of multiplecontinental fragments of various ages including ancient cratonstogether with accreted terranes. This is in contrast to the rathersimple components in Wilson Cycle involving the production anddestruction of ocean floor, with the oldest oceanic crust on the planetaged more than 200 Ma. Among various distinctions between the twocycles, one important aspect is the time interval, with a shorter timespan for theWilson Cycle as against a much longer time span in whichsupercontinent cycle operates.

Whereas this aspect still remains vague, several complex processesassociated with supercontinent cycles have been proposed, involving‘introversion’ and ‘extroversion’ of continental fragments rifted from aprevious supercontinent, and sometimes even a combination of thesetwoprocesses (Murphy andNance, 2005;Murphyet al., 2009).Hoffman(1991) proposed the concept of ‘inside-out’ process as a mechanism ofassembling crustal fragments after the breakup of an earlier supercon-tinent. If the supercontinent was rifted on one side to bear a passivemargin such as in the case of the Atlantic Ocean, then the opposite sidebecomesa consumingboundary along the continents, suchas in the caseof the Pacific margin. With time, the Pacific Ocean would shrink andfinally close by thepassive collision of two continents to generate a largecontinental mass. In the case of Atlantic, initially both continentalmargins are passive, and later turn to active margins, and finally shrinkin size and totally disappear. If introversion occurs in this case, theAtlantic would close. On the other hand, duringmuch of the Mesozoic–Cenozoic the Indian Ocean has had two different types of marginssimultaneously in operation, active and passive, transporting thenorthern continental margin of Gondwana by the Atlantic-type processand amalgamating the rifted continents to the southern margin of Asiaby the Pacific-type process. Therefore, the Indian Ocean-type processillustrates simultaneous continental break up and continental amal-gamation exemplifying ‘inside-in’ mechanism (Murphy and Nance,2003, 2005). Similar simultaneous rifting and accretion on differentmargins were also proposed in the case of the Paleoproterozoicsupercontinent Columbia by Rogers and Santosh (2002). The Tethyanprocess started at least by the Triassic to Permian time and operatedsimultaneously with the Pacific process to the east. Subsequently,double-sided subduction started to define the frontier of the futuresupercontinent (Maruyama et al., 2007). Thus, the Tethyan region is anexample for the ‘inside-in’ reassembly of supercontinents (Hoffman,1991;Murphy andNance, 2003, 2005;Murphy et al., 2009)whereas thePacific region is related to the ‘inside-out’ configuration. Thus, theprocess of completion of a supercontinentwould involve a combinationof both introversion and extroversion (Fig. 1a–e). Such a combinationoperated in the case of Rodinia assembly, and is also implied in theprediction of the amalgamation of the future supercontinent Amasia(see Maruyama et al., 2007; Santosh et al., 2009).

In another recent work, Murphy et al. (2009) discussed the twogeodynamically distinct tracts of oceanic lithosphere generated

during the breakup of supercontinents: a relatively young interiorocean floor that develops between the dispersing continents, and arelatively old exterior ocean floor, which surrounded the supercon-tinent before breakup. The geologic and Sm/Nd isotopic recordsynthesized in their study (Fig. 1f) suggests that supercontinentsmay form by two end-member mechanisms: introversion, in whichinterior ocean floor is preferentially subducted, and extroversion, inwhich exterior ocean floor is preferentially subducted. Murphy et al.(2009) speculated that ‘superplumes’ (Larson, 1991; Fukao et al.,1994; Maruyama, 1994; Maruyama et al., 2007), perhaps driven byslab avalanche events (Machetel andWeber, 1991; Honda et al., 1993;Tackley et al., 1993), could occasionally overwhelm top–downgeodynamics, imposing a geoid high over a pre-existing geoid lowand causing the dispersing continents to reverse their directions toproduce an introverted supercontinent.

In another different model, Silver and Behn (2008) proposed twomodes of ocean closure during supercontinent formation which theytermed as P-type (Pacific type) and A-type (Atlantic type), a conceptbroadly similar to the model proposed in Murphy and Nance (2003,2005) andMurphy et al. (2009).When a supercontinent surrounded bysubduction zones begins rifting, the resulting continental breakupcreates an internal ocean. As the breakup continues, the size of theinternal ocean increases at the expense of the external ocean. In A-typeclosure, the subduction begins at a passive margin of the internal oceanand the internal ocean begins to close. In P-type closure, the internalocean continues to grow and becomes an enlarged ocean basin.When asupercontinent is assembled through A-type closure, the internal oceancloses, shutting down subduction zones in the internal ocean, whilesubduction and sea-floor spreading in the external ocean continue. In P-type closure, the external ocean closes, shutting down all subduction.Silver andBehn(2008) suggested thatA-typeandP-type closures canbedistinguished by the age of former oceanic crustal material (such asophiolites) that is trapped in the suture zone along which thesupercontinent assembled. In the case of A-type closure, the age of theoceanic material will be younger than that of breakup of the previoussupercontinent. This is because the subduction initiation postdates theprevious breakup. On the other hand, in the case of P type closure, theoceanic crustal material can predate the breakup of the previoussupercontinent because subduction initiation predates the breakup.

Similar to the case of ‘introversion’ and ‘extroversion’ (Murphy andNance, 2003, 2005), the P-type and A-type closures represent twoendmember cases, and the actual mode of closure may likely involve acombination of the two processes. According to Silver and Behn (2008),the supercontinent Pangaea, which was formed by the closing of theIapetus Ocean, appears to have formed primarily by A-type closure. Incontrast, both the supercontinents Pannotia and Rodinia formedprimarily by P-type closure. Although the Paleoproterozoic supercon-tinent Columbia might have formed by A-type closure (Rogers andSantosh, 2002, 2009), the available data are not adequate to draw a firmconclusion.

3. Supercontinent cycle and mantle convection

One of the major challenges in earth sciences is to resolve thethermal and mechanical feedback between mantle convection andcontinental/supercontinental drift. A widely-accepted theory proposesthat a supercontinent thermally insulates the underlying mantle andisolates it from subduction (i.e., ‘thermal blanket effect’), and eventuallybreaks into pieces that move towards colder regions of mantledownwellings (Anderson, 1982; Gurnis, 1988; Anderson, 1994).Continental aggregation might lead to a re-organization of theconvective flow in the mantle and a positive temperature excursionbeneath the supercontinent (e.g., Yoshida et al., 1999; Coltice et al.,2009). Fig. 2 illustrates an example of the time evolution of mantleconvection with a rigid, undeformable supercontinent that covers 30%of the total surface and 250 km thickness from the surface boundary in

Fig. 1. (a–e) Stages of breakup and assembly of supercontinents through ‘introversion’, ‘extroversion’ or a combination of both introversion and extroversion as discussed in the text(after Murphy and Nance, 2005). (f) Schematic representation of the Sm/Nd isotopic evolution of oceanic lithosphere from the interior and exterior oceans (from Murphy et al.,2009). The depleted mantle ages for the interior ocean (TI) are younger than the time of supercontinent breakup (TR). Whereas in the case of exterior ocean (TE) the ages are older.Relative to the breakup of Rodinia supercontinent, the Mozambique Ocean is an exterior ocean; relative to the breakup of Pannotia, the Iapetus and Rheic Oceans are interior oceans.


2-D spherical-shell geometry. Initially, the mantle convections areorganized by the ‘old’ supercontinent (‘old’ in Fig. 2), and upwellingplumes dominate beneath the old supercontinent, while downwellingplumes dominate beneath the antipodes. Subsequently, at the elapsedtime of 0 Myr, we instantaneously imposed a ‘new’ supercontinent(‘new’ in Fig. 2) on the antipodes of the old supercontinent wheredownwelling plumes dominate. After the set of supercontinent, the

downwellings beneath the supercontinent tend to become weak andare not discernable at ~32 Myr. A new upwelling plume occurs at~92 Myr, and the mantle temperature beneath the supercontinenttends to increase due to the thermal insulation effect (see Section4). Thelarge-scale horizontal mantle flow beneath the supercontinent, includ-ing the high temperatures, swept the downwelling into the antipodesand induced a planetary-scale flow in the whole mantle for b200 Myr.

image of Fig.�1

Fig. 2. Time sequence of mantle convection with a rigid, highly viscous supercontinent in two-dimensional spherical-shell geometry with a thickness of 2867 km. The circumferenceratio between the inner and outer shell is considered to be the ratio of the area between the CMB and top surface boundary of the Earth. Color contour shows the temperature. Orangelid indicates the position of the supercontinent with a thickness of 250 km, covering 30% of total surface area (note that for clarify, the supercontinent is set out on the outer surface inthis illustration). ‘Old’ and ‘new’ indicate an old and new supercontinent: the new supercontinent is instantaneously imposed on the antipodes of the ‘old’ supercontinent at 0 Myr. Inthis model, realistic Rayleigh number (5.9×107) is considered in the mantle which is heated from the bottom and internally heated by the radiogenic elements. The radiogenicheating rate of mantle materials are 8.0×10−12 W/kg, which is close to the value at 2 Ga (Turcotte and Schubert, 2002).


Eventually the upwelling plumes tend to dominate beneath the newsupercontinent, as the elapsed time passes. Fig. 3 illustrates a cartoonshowing the time series of mantle reorganization by the amalgamationof supercontinent. The fragments of the supercontinent would migrateto a downwelling flow of the mantle. The mantle beneath thesupercontinent warms up by the thermal blanket effect, and the large-scale, hotter flow emerges from beneath the supercontinent tosubcontinental regions (i.e., oceanic lithosphere). This large-scale flowin the shallower mantle produces large-scale (planetary-scale) flow viathe deeper mantle. Eventually, the bottom thermal boundary layer isperturbed by this return flow and then the upwelling plumes areconcentrated beneath the supercontinent.

Fig. 3. A cartoon showing the time series of mantle reorganiza

Continental rafts impose their own wavelength on mantleconvection by impeding downwelling below them (Gurnis, 1988).Thus, the assembly of supercontinents would force larger scales ofconvection and drive the underlying mantle towards higher temper-ature. Somemodels consider that the extensive subduction associatedwith the assembly of supercontinents involves the transport of largevolumes of oceanic as well as continental materials into the deepmantle, and that some of these recycled materials act as fuel togeneratemantle plumes which rise up and eventually disintegrate thesupercontinents (e.g., Maruyama et al., 2007). Although models onthe assembly and disruption of supercontinents are diverse, most ofthe studies emphasize the implications of supercontinent tectonics on

tion by the existence of amalgamation of supercontinent.

image of Fig.�2

image of Fig.�3


the rheological properties of the mantle, which in turn control themajor geological processes in our planet (Karato, 2010a).

Based on the topology of Y-shaped triple junctions in majorsupercontinental assemblies, Santosh et al. (2009) recognized twodistinct categories of subduction zones on the globe: the Circum-Pacific subduction zone and the Tethyan subduction zone. In therandomly distributed subduction zones on the surface of the earth, thelow temperature and dense subducted material sinks down to thebottom of the mantle (e.g., Maruyama et al., 2007; Fukao et al., 2009).In the scenario where the subduction is double-sided, the triangularregions with Y-shaped topology selectively refrigerate the underlyingmantle, reducing the temperature and turn down the temperature inthese domains as compared to the surrounding regions. The Y-shapeddomains also accelerate the refrigeration through larger amounts ofsubduction and thus promote stronger downwelling as compared toother regions of the mantle. Once this process is initiated, a runawaygrowth of a region characterized by cold downwelling starts todevelop, producing a zone of super-downwelling to pull together thecontinental material on the surface into a tight assembly. The‘maximum close packing’ of continental fragments within super-continents suggested by Rogers and Santosh (2004) can be explainedthrough this process.

The continental lithosphere exhibits a general behavior that isalmost decoupled from the convecting mantle and the motion of theoceanic plates because the material constituting this lithosphere isless dense than that of the mantle and oceanic lithosphere and is lessdeformable than that of the mantle. It thus acts as an assemblage offairly rigid bodies ‘floating’ on the top of the mantle. In numericalstudies of mantle convection, this allows the continent to be modeledas a nondeformable, highly viscous lid (HVL) or a rigid cap. A numberof previous studies have addressed the effects of supercontinents onthe dynamics and structure of the mantle using 2-D models (Gurnis,1988, 1990; Gurnis and Zhong, 1991; Lowman and Jarvis, 1993; Zhongand Gurnis, 1993; Lowman and Jarvis, 1995, 1996; Nakakuki et al.,1997; Trubitsyn et al., 2006) and 3-D Cartesian/spherical-shell models(Trubitsyn and Rykov, 1995; Lowman and Gable, 1999; Yoshida et al.,1999; Honda et al., 2000; Trubitsyn and Rykov, 2001; Coltice et al.,2007; Zhong et al., 2007a; Trubitsyn et al., 2008; Coltice et al., 2009;Phillips and Coltice, 2010; Yoshida, 2010b).

A pioneering work with a numerically modeled mantle convectionwith a rigid supercontinent (Gurnis, 1988) presents crucial results.His 2-D rectangle model has presented crucial results on the dynamicfeedback between the mantle and continent/supercontinent. In hismodel, a supercontinent and the dispersing continental fragmentsfrom it can migrate in accordance with the horizontal velocity of themantle beneath the supercontinent. The supercontinent that isinitially located above an upwelling mantle plume in the well-developed convection breaks up, with its fragments migrating to adownwelling mantle plume, where they reassemble. They eventuallyreassemble at a site of the downwelling mantle plume. When thedownwelling plume waning from the bottom of the supercontinent,the colder mantle beneath the supercontinent is replaced by thehotter mantle with a new upwelling plume as an initial thermalstructure before the breakup of the old supercontinent. Such aperiodic supercontinental cycle and the formation of long-wavelengththermal structures during the cycle have also been observed in 2-Dcylindrical models with wide model parameters (Gurnis and Zhong,1991; Zhong and Gurnis, 1993).

The flow reorganization of mantle due to the existence of thesupercontinent is carefully examined by Lowman and Jarvis (1993,1995) using 2-D Cartesian box models with various model parameterssuchasanaspect ratio ofbox, the thermal diffusivity and thicknessof thecontinent, and a radiogenic internal heating ratio of mantle. They haveconcluded that the flow reorganization appears prominently in amodelwith awider and thicker supercontinent and smaller thermal diffusivityof lid, higher continental crustal heating, and lower radiogenic internal

heating of mantle. Lowman and Jarvis (1996) incorporated rigidlymoving continental blocks with a finite thickness in a 2-D Cartesianmantle convection model. They suggested that stresses generated byflow reorganization below the aggregated continents are sufficient toproduce continental rifting, and that the subduction of oceanic plates atthe margins of a thick continental plate may be the key event intriggering the subsequent continental breakup.

4. Thermal and mechanical interaction between continentand mantle

The thermal and mechanical interaction between mantle andcontinent/supercontinent would significantly affect the evolution ofthe Earth's mantle. The question as to whether the temperatureincrease beneath the supercontinent due to the thermal insulatingeffect of the supercontinent (Anderson, 1982) aids continental riftingand breakup is not clear in geodynamics. The subsequent mantlereorganization that has been hypothesized to occur in response tothermal insulating effect is probably one cause of continental breakupand dispersal (Gurnis, 1988). The concept of thermal blanketenvisages the breakup of supercontinents through radiogenic heating(e.g., Gurnis, 1988). Granites contain higher K, U and Th compared tomantle peridotite. Recent studies recognize that substantial volume ofarc crust of granitic composition is subducted during the assembly ofsupercontinents through arc subduction, sediment trapped subduc-tion and tectonic erosion. This tonalite–trondhjemite–granodiorite(TTG) material is dragged down and is thought to accumulate in themantle transition zone (Senshu et al., 2009). It is possible that theradiogenic elements in the subducted TTG crust heat up the overlyingmantle with time to initiate continental rifting and dispersion leadingto the opening of oceans. Komabayashi et al. (2009) performed phaseassemblage analysis in the system mid-oceanic ridge basalt (MORB)–anorthosite–TTG down to the CMB conditions. Their results show thatall thesematerials can be subducted even up to the CMB leading to thedevelopment of a compositional stratification in the D” layer.Numerical modeling studies, however, have not yet considered thehigher radiogenic heating rate through subduction of continentalcrust. Maruyama et al. (2007) proposed that the exothermic reactionduring the perovskite and post-perovskite phase transition heats upthe coldmaterials accumulating at the CMB and leads to the formationof superplumes which rise up and disintegrate the supercontinent.

Effects of thermal insulation by the supercontinent on the mantleconvection are so far investigated by the previous numerical modelsof mantle convection. They have revealed that horizontal flow due totemperature differences between the supercontinent and the rest ofthe ‘oceanic’ region produces the large-scale flow in the mantle andlarge upwelling plumes originating from the CMB beneath thesupercontinent (Gurnis, 1988; Gurnis and Zhong, 1991; Zhong andGurnis, 1993; Nakakuki et al., 1997; Yoshida et al., 1999; Honda et al.,2000; Phillips and Bunge, 2005, 2007; Yoshida, 2010b) (see alsoFig. 2). It appears that the temperature increase by the thermalinsulation effect sustains for long geological timescales whenradiogenic internal heating in the mantle is considered (Yoshidaet al., 1999; Honda et al., 2000). The thermal insulating effects andflow reorganization of mantle may cause ‘global mantle warming’ andlarge-scale partial melting beneath the supercontinent (Coltice et al.,2007, 2009) (Section 8). On the other hand, Lowman and Gable(1999) have suggested that, rather than the thermal insulating effect,the cessation of subduction beneath a supercontinent plays a majorrole in warming the bottom of the supercontinent. The temperatureincreases beneath the supercontinent may be caused by upwellingplumes originating from the CMB as a return flow of plate subductionoccurring at supercontinental margins (Zhong et al., 2007a).

Nakakuki et al. (1997) investigated the effects of a combinedsystem of highly-viscous continental lid and subcontinental regions(i.e., ocean) using a 2-D, long aspect-ratio Cartesian model with


multiple phase transitions at 410 km and 660 km and depth-dependent properties (i.e., viscosity, thermal expansivity, and thermalconductivity). They showed that beneath the ocean, thermalboundary layer at the CMB is suppressed by the large-scale flow inthe highly-viscous lower mantle, whereas beneath the continental lid,a thickened boundary layer developed at the CMB. The large-sizedupwelling plumes developed in the lower mantle are concentratedbeneath the continental lid. When the position of continental lid andocean is switched instantaneously during the simulation, theupwelling plumes are concentrated beneath the newly-positionedcontinental lid due to the mantle flow reorganization. This 2-Dnumerical model suggests that there is a greater tendency that thesupercontinent enhances the longest-wavelength thermal structurein the mantle.

During the amalgamation of continental fragments, the subductedoceanic lithosphere of intervening oceans either moves down to thedeepmantle or is flattened, becoming stronger as stagnant slabs in themantle transition zone between ca. 410 and 660 km depth (Fukao etal., 1992; van der Hilst et al., 1997; Fukao et al., 2001; Grand, 2002;Zhao, 2004; C. Li et al., 2008; Fukao et al., 2009; Zhao, 2009). Blobs ofthese stagnant slabs sink down into the deep mantle and accumulateat the CMB. Zhao (2004) synthesized a P-wave tomographic image forthe Western Pacific region, along a transect covering Beijing to Tokyo,where about 1200 km-long stagnant slabs are seen floating in themantle transition zone. The image shows the presence of a high P-wave velocity anomaly close to the bottom of the mantle andimmediately above the CMB which has been interpreted as a ‘slabgraveyard’ (Richards and Engebretson, 1992).

The recycled oceanic lithosphere at the CMB contributes potentialfuel for generating superplumes (Maruyama et al., 2007) which risefrom the core–mantle interface to the uppermost mantle, penetratingthe mantle transition zone and eventually giving rise to hot spot (e.g.,Maruyama et al., 2007). Highly resolved seismic tomography modelsclarify the configuration and amplitude of the velocity anomaly of twosuperplumes beneath Southern Africa–Southern Atlantic Ocean andSouthern Pacific. For instance, Ritsema et al. (1999) observed thatbeneath Southern Africa–Southern Atlantic Ocean the low-velocityanomaly extends from the CMB into the upper mantle and has anaverage velocity that is ~1% lower than normal mantle. Meanwhile,Suetsugu et al. (2009) observed that beneath Southern Pacific, thelow-velocity anomaly extends 1000 km above CMB and has anaverage velocity that is ~0.5% lower than normal mantle and small-scale low-velocity anomaly originating at the 1000 km-depth or660 km phase boundary.

Multiple subduction zones promote the rapid amalgamation ofcontinental fragments into supercontinents and also act as majorzones of material flux into the deep mantle transporting substantialvolume of trench sediments and arc crust through sedimentsubduction and tectonic erosion (e.g., Santosh et al., 2009; Yamamotoet al., 2009; Santosh, 2010a). Due to buoyancy, the subducted TTGmaterial is stacked in themidmantle region andmay not sink down todeeper levels.

5. Formation of degree-one mantle structure

With the advancement in numerical modeling techniques as well asthe enhancement in computational power and resource, it is nowpossible to simulate the highly-resolved 3-D spherical-shell mantleconvection model with lateral variation of viscosity and realisticrheology (i.e., temperature- and/or strain-rate dependent rheology)(Zhong et al., 2000; Richards et al., 2001; Yoshida and Kageyama, 2004).Several previous studies have attempted to characterize the effects ofsupercontinents on the dynamics and structure of the mantle in 3-Dspherical-shell geometry (Yoshida et al., 1999; Phillips andBunge, 2005;Coltice et al., 2007; Phillips and Bunge, 2007; Zhong et al., 2007a;Trubitsyn et al., 2008; Zhang et al., 2009; Yoshida, 2010b).

In general, a mantle convection planform with short-wavelengthstructures and a large number of downwellings may not lead to theassembly of supercontinents because continental blocks would betrapped by different downwellings thus inhibiting collision.When thecontinental blocks are smaller than the wavelength of mantle flow, ittakes a longer time for them to form the supercontinent (Phillips andBunge, 2007; Zhang et al., 2009) (see also Section 7 for the timescaleof supercontinent assembly). Thus, long-wavelength convection ispreferred for effective close packing of continental fragments into asupercontinent assembly. Both Rodinia and Pangea are considered tohave been largely surrounded by subduction zones (Maruyama et al.,2007) which suggests the presence of major downwellings andupwellings, and leading to kinematic models of supercontinent cycleswhich require mantle convection of very long-wavelengths atspherical harmonic degree one or degree two (e.g., Monin, 1991;Evans, 2003). The present-daymantle is predominated by degree-twostructures that include the seismically fast, cold anomalies aroundCircum-Pacific and two large seismically slow, hot anomalies beneathAfrica and Pacific (Section 4), translated into one cold downwellingzone and two hot upwelling zones (e.g., Maruyama et al., 2007).

A mantle convection model with a supercontinent in Earth-like 3-D spherical-shell geometry was proposed for the first time by Yoshidaet al. (1999). They modeled the supercontinent as an elongated-disk-shaped HVL with a thickness of 200 km, covering 30% of the totalsurface, and imposed it on well-developed, isoviscous mantleconvection with the short-wavelength thermal heterogeneity. Themantle is heated externally from the core and internally by radiogenicelements. Their results show that the presence of a supercontinentwith the HVL produces large-scale horizontal mantle flow, therebyreorganizing the thermal structure of the mantle interior. Large-scaleupwelling plumes arising from the CMB beneath the supercontinentare observed and the thermal structure dominated by the sphericalharmonic degree of one (i.e., degree-one convection) develops in themantle (Yoshida et al., 1999; Yoshida, 2010b).

Fig. 4 illustrates a result of 3-D spherical-shell mantle convectionmodel with a rigid, spatially fixed HVL. The mantle is consideredrealistic convection vigor and a temperature-dependent rheology. Theviscosity contrast between the HVL and surrounding mantle is fixed at102. The result reveals that the very short-wavelength structure isreorganized by a degree-one structure for ~500 Myr due to theexistence of the supercontinent. Yoshida (2010b) proposed that large-scale upwelling plumes produce tensional stresses within thesupercontinent with a stress magnitude of the order of 10 MPa,irrespective of model parameters studied here, which is comparableto the strength of the Earth's continent, and thus may be responsiblefor the subsequent continental rifting and breakup, as previouslysuggested by the 2-D model of Lowman and Jarvis (1996).

It is quite important that the formation of degree-one convectionfound in Yoshida et al. (1999)may be closely related to the periodicityof supercontinent cycles. Phillips and Bunge (2005) have succeeded inmodeling the nondeformable HVL freely floating over the surface by atorque balance method (i.e., calculating Euler poles through forcebalance and applying repulsive forces to prevent overlap) with a 3-Dspherical-shell model and have reproduced the supercontinent cyclesin the limited geophysical situations. They demonstrated that degree-one convection that develops after the setup of the disk-shaped rigidcap forms in cases for (1) convection models without a viscosityincrease at the 660 km phase boundary and purely basal heating (i.e.,no radiogenic internal heating), and (2) convection models with aviscosity increase at the 660 km. The broad, active upwelling plumesdue to the highly viscous lower mantle and strong heating from theCMB might trigger the formation of the longest-wavelength thermalstructure in the mantle when the supercontinent is imposed. Suchupwelling plumes from the CMB have also been envisaged in recentconceptual models (e.g., Maruyama et al., 2007). When degree-oneconvection is established, the dispersing continental fragments

Fig. 4. Time sequence of mantle convection with a rigid, highly viscous supercontinent in three-dimensional spherical-shell geometry with a thickness of 2867 km. The blue andpurple isosurfaces of the temperature anomaly δT (i.e., the deviation from horizontally averaged temperature at each depth) indicate−250 K and +250 K, and orange indicates theposition of elongated disk-shaped supercontinent with a thickness of 250 km, covering 30% of total surface area (note that for clarity, the supercontinent is largely transparent). Thewhite sphere indicates the bottom of mantle (i.e., core–mantle boundary). The supercontinent is instantaneously imposed on the well-developed mantle convection withtemperature-dependent rheology. The viscosity contrast between the coldest upper surface boundary (i.e., uppermost part of high viscous lithosphere) and hottest bottom surfaceboundary (i.e., core–mantle boundary) is 102. The viscosity of supercontinent is 102 times larger than the surrounding ‘oceanic’ lithosphere. The elapsed times are scaled by an Earth-like timescale. The details of numerical methodology and model parameters are found in the work of Yoshida (2010b).


migrate towards the antipodal downwelling plumes and reassembleto form a new supercontinent. A subsequent study by Phillips andBunge (2007) demonstrated that active upwelling plumes caused bythe significant basal heat flow from the core disrupt the periodicity ofsupercontinental cycles. They suggest that the periodic superconti-nent cycles are unlikely to occur in the history of Earth.

We note here that degree-one convection is observed whensupercontinent is not imposed in the mantle convection withtemperature-dependent rheology. The viscosity of mantle materialsstrongly depends on the temperature, pressure, and composition,among other parameters (e.g., Karato, 2008). It has been accepted thatmantle convection patterns with temperature-dependent rheologyare classified into three regimes from the 2-D convection studies(Solomatov, 1995; Solomatov and Moresi, 1997). Recent advances oncomputational techniques and resources facilitate the numericalsimulation of 3-D spherical mantle convection with strong temper-ature-dependence of viscosity (e.g., Yoshida and Kageyama, 2004;McNamara and Zhong, 2005a; Roberts and Zhong, 2006; Yoshida andKageyama, 2006; Zhong et al., 2007a; Yoshida, 2008). Fig. 5aillustrates a regime diagram for mantle convection with purely basalheating (i.e., no internal heating rate) and with a linearized viscosityform (i.e., η∝exp(ET), where η is the viscosity and E is the activationenergy that controls the degree of viscosity's temperature (T)-dependence) (Yoshida and Kageyama, 2006).

The degree-one convection has been produced by some numericalmodels that considered temperature-dependent rheologies. Wheninternal heating is included with moderately temperature-dependentviscosity, degree-one convection occurs (McNamara and Zhong,2005a). On the other hand, Yoshida and Kageyama (2006) haveshown that degree-one convection occurs even without internalheating when temperature-dependence of the viscosity is moderatelystrong. This degree-one convection pattern belongs to the ‘sluggish-lid regime’ (Solomatov, 1993) or ‘transitional regime’ (Solomatov,1995), in which the moderately highly viscous layer around the topsurface boundary slowly moves with less Rayleigh–Taylor instabilityand eventually sinks into the mantle, and the resultant mantleconvection has longest-wavelength thermal structure. Consideringthe Rayleigh number of the Earth's mantle and the viscosity contrastbetween the lithosphere and underlying mantle, the Earth's mantlepresumably falls into sluggish-lid or ‘stagnant-lid’ regimes (orangebox in Fig. 4a). In the stagnant-lid regime, a deformable, immobile lid

develops near the surface boundary of mantle convection. In order tolet the surface plate-like motion, we need to impose the visco-plasticrheology (see Section 12).

Degree-one convection is found in mantle convection with a morerealistic viscosity form (i.e., Arrhenius-type form, η∝exp(E/T)) and/or with three end-member heating modes, i.e., purely basal heating(i.e., no internal heating rate), mixed heating (i.e., basal and internalheating) (Yoshida, 2008) (Fig. 5b–c), and high internal heating(McNamara and Zhong, 2005a) modes. Therefore there is a highlypossibility that degree-one convection is one of the basic structure ofmantle convection without the surface heterogeneities such ascontinent and plate motions. However, as reported by Yoshida(2008), it seems that the geophysically relevant degree-two convec-tion with sheet-like downwellings (i.e., Circum-Pacific subductionzone) and two upwelling plumes (i.e., superplumes) is not observedin the mantle convection model with real convective vigor andwithout the surface heterogeneities.

On the basis of a previous numerical result that a supercontinentspends most of the time over the cold, downwelling mantle (Gurnisand Zhong, 1991), Zhong et al. (2007a) considered in their 3-Dspherical model that the continental fragments migrate towards thedownwellings in degree-one mantle convection and settle into thedownwellings for a certain period of time. When a disk-shaped HVL isimposed on well-organized degree-one convection, the oceanicmaterial begins to subduct at a margin of the HVL and downwellingsbeneath the supercontinent eventually vanishes. Subsequently, newupwelling plumes tend to originate at the CMB for a short timescale(~50 Myr) and the degree-two thermal structure with old and newupwellings develops in the mantle (see Zhong et al., 2007a fordetails). Following their scenario, when the continental fragmentsfully disperse on the Earth so that the mantle does not 'feel' theexistence of continents, the degree-two pattern may go back todegree-one structure. However it has not been resolved yet whetheror not mantle convection is dominated by degree-one when platemotions and continental drift continuously occur throughout out theEarth's history. There is a possibility that the present-day degree-2pattern is realized both by the history of plate motions and large-scalethermochemical upwelling plumes (McNamara and Zhong, 2005b).The thermochemical upwelling plumes or thermochemical pilesstratified in the deep lower mantle, reproduced in the mantleconvection model (Tackley, 1998; Kellogg et al., 1999; McNamara

image of Fig.�4

Fig. 5. (a) Regime diagram showing three convection regimes with a linearized viscosity form and with varying Rayleigh number (Rabot) and the viscosity contrast across the shell(γ); the mobile-lid (circles), the sluggish-lid regime (triangles), and the stagnant-lid regimes (squares). Solid, open, and shaded symbols show the results from 3-D spherical-shellmodels by Yoshida and Kageyama (2006) and Ratcliff et al. (1997), and a 3-D Cartesian box model by Trompert and Hansen (1998b), respectively. The regime boundary (dashedcurve) between convection regime and no-convection regime is referred with the reviews by Schubert et al. (2001). For the definitions of three regimes, see text, and also seeYoshida and Kageyama (2006) and papers herein. Dashed line shows the approximate boundaries that separate the three convection regimes. An orange box indicates a parameterrange appropriate to the Earth's mantle. (b–c) Snapshots of convection pattern with an Arrhenius-type viscosity form and with weak and moderate viscosity contrasts (γ=102 and104, respectively). The convection models with (b) purely basal heating and (c) mixed (i.e., basal and internal) heating modes are shown. The blue and yellow isosurfaces of thetemperature anomaly indicate colder and hotter regions. For cases with γ=104 (degree-one convection) cross sections of mantle temperature are shown.


and Zhong, 2005b), are expected to be a part of the superplumesbeneath South Atlantic–South Africa and South Pacific regions(Larson, 1991; Maruyama, 1994; Maruyama et al., 2007). Thethermochemical piles with abundance of radioactive elementsproduces ‘superswells’ i.e., the broadly elevated topography at theearth's surface (McNutt, 1998).

6. Long-wavelength thermal structure in the mantle

The longer thermal structures in the mantle may shorten theperiod of supercontinent cycle, because continental blocks wouldsmoothly drift on the Earth's surface without being inhibited byupwelling and downwelling plumes. Theoretical and numericalstudies on dynamics of planetary mantle convection demonstratethat the effects of depth- or pressure-dependent properties such asviscosity and thermal expansion coefficient (or thermal expansivity)contribute to the predominance of the long-wavelength thermalstructure in the planetary mantle, because they reduce convectivevigor effectively (Schubert et al. (2001); Yuen et al. (2007)). Since themid-1990s, several numerical models of mantle convection within a3-D geometry have investigated the effects of depth-dependentviscosity on the mantle convection pattern with real convective vigor(Zhang and Yuen, 1995; Bunge and Richards, 1996; Bunge et al., 1996;

Tackley, 1996; Zhang and Yuen, 1996; Bunge et al., 1997). On theother hand, high pressure experiments of mantle rocks have recentlyproposed a substantial decrease in the thermal expansion coefficientwith depth. Katsura et al. (2009) suggested on the basis of theirexperiments that the thermal expansion coefficient of MgSiO3

perovskite generally decreases with increasing pressure and thatthe Anderson–Grüneisen parameter (Anderson, 1967; Birch, 1968),δT, of MgSiO3 perovskite is 6.5. As for the comparison of this δT with δTderived from the previous high-pressure experiments for variousmantle rocks, see, for instance, Katsura et al. (2009) and Schubert et al.(2001). The decrease in the thermal expansivity with pressure isexpected to reduce the buoyancy force of mantle convection in thedeep mantle. Furthermore, it is expected to offset the adiabatictemperature gradient because the degree of adiabatic heating/coolingis linearly proportional to the thermal expansivity (e.g., Jarvis andMcKenzie, 1980).

Here we attempt a simulation of the mantle convection modelswith both the depth-dependent viscosity and thermal expansivity.Fig. 6a and b shows the depth profiles of viscosity and thermalexpansivity, respectively, used in the simulation. The parameters usedhere are V which controls the maximum viscosity contrast and δTwhich controls the thermal expansivity contrast across the mantle.We considered a viscosity profile with different viscosity contrast

image of Fig.�5

Fig. 6. Depth profiles of (a) viscosity and (b) thermal expansivity variations used in the model. (a) Dotted, thin, and thick lines represent V=0, ln 30, and ln 100, respectively. (b)Dotted, thin, and thick lines represent δT=0, 3, and 6.5, respectively. (c–k) Plan views of temperature field at middle depth of mantle (1433 km) for different combinations of V andδT (see the values embedded in the figure). (l–n) Cross sections of temperature and velocity fields for three cases that correspond to plan views of (c), (i), and (k), respectively. Thecross sections are cut along the great circles drawn by dashed lines marked 'A'–'D', 'E'–'H' and 'I'–'L' in the corresponding plan views. The contour interval in the temperature plots is250 K. The viscosity and thermal expansivity are fixed at 3×1021 Pa s and 3×10−5 K−1 at the top surface boundary. The mantle is modeled as a fluid with an infinite Prandtl numberwithin a 3-D spherical shell geometry with a thickness of 2867 km, and that it is heated from the bottom and from within. An extended-Boussinesq approximation (Christensen andYuen, 1985) is applied to the mantle fluid. Free-slip, impermeable, and isothermal conditions are imposed on the top and bottom boundaries. The Rayleigh number and thedissipation number are 1.91×107 and 0.67. The dimensionless internal heating production rate per unit mass due to radioactive decay is 9.19, which corresponds to the internalheating rate at the present day (3.50×10−12 W/kg) on the basis of the abundance of the radioactive elements in chondritic meteorite (Turcotte and Schubert, 2002).


image of Fig.�6


across themantle (Fig. 6a). The peak viscosity is assumed to be locatedat the depth of 2000 km, in accordance with the results obtained bythe joint inversion of convection and glacial isostatic adjustment data(Mitrovica and Forte, 2004) and other studies (Ricard and Wuming,1991; Forte and Mitrovica, 2001). It is assumed that the viscositybelow depths of 2000 km, including at the hot thermal boundarylayer, decreases because of the temperature dependence of viscosity.In the present study, we investigate the cases with V=0, ln 30, and ln100; the range of these values was selected on the basis of post-glacialrebound analyses (e.g., Lambeck and Johnston, 1998; Peltier, 1998)and geoid inversion studies (e.g., King, 1995). Meanwhile, as for thethermal expansivity, we test the cases with both the ‘classical’ value ofδT=3 used in the previous numerical studies (e.g., Anderson, 1987;Zhang and Yuen, 1987; Hansen et al., 1993; Hansen and Yuen, 1994)and a ‘new’ value of δT=6.5. The resultant thermal expansivitycontrasts between the top and bottom surfaces are ~0.2 and ~0.04,respectively (Fig. 6b).

The results of the numerical calculations for the nine casesrepresenting different combinations of V=0, ln 30, ln 100 andδT=0, 3, and 6.5 are presented in Fig. 6c–n. For each case, calculationswere repeated until the output parameters such as root-mean squarevelocity in the mantle, volume-averaged temperature in the mantle,and top and bottom heat fluxes reached a statistically steady-state.The case with the constant viscosity and thermal expansivity (i.e.,V=0 and δT=0) shows the thermal structure with quite shortwavelengths and numerous upwelling and downwelling plumes thatexist in the mantle after the statistically steady state was reached(Fig. 6c and l). This well-developed convection pattern from the firstcase was used as the starting scenario for the calculations for the othereight cases.

We first focus on the effect of depth-dependent viscosity on theconvection pattern. Fig. 6c, d, and e shows the cases with V=0, ln 30,and ln 100, respectively, and a constant thermal expansivity. Evenwhen the highest viscosity contrast is imposed (i.e., V=ln 100), theconvection pattern shows a quite short wavelength thermal structure(Fig. 6e). This convection pattern is quite different from those with aviscosity profile with a step-increase of viscosity at 660 km andwithout the gradual decrease of the viscosity below 2000-km depth(Bunge et al., 1996; Zhong et al., 2000): The convection pattern shiftsto larger wavelengths and is re-organized into well-establishedconvection cells with stable large-sized upwelling plumes originatingat the CMB and sheet-like plumes downwelling from the top surface.

Focusing next on the cases with V=0 (Fig. 6c, f, and i), we find thatthe number of large-sized upwelling plumes is reduced withincreasing δT. When δT=6.5 is considered (Fig. 6i and m), theconvection pattern drastically changes compared with the case whereδT=3 (Fig. 6f). The convection pattern shifts to larger wavelengthsand is re-organized into well-established convection cells with twostable large-sized upwelling plumes and a ‘great-circle’ downwelling.Also, when other values of V (V=ln 30 and ln 100) are considered,there is a tendency for the number of upwelling plumes to decreasewith increasing δT. The large-sized upwelling plumes are increased inwidth by the effect of depth-dependent viscosity. We note that withincreasing δT, downwelling plumes tend to effectively ‘subduct’ intothe deep lower mantle. This implies that in the real Earth, the largelyreduced thermal expansivity with depth facilitates the subduction ofplates into the deep lower mantle and resultant large-scale flowcirculations in the whole mantle (e.g., van der Hilst et al., 1997) (forinstance, ‘M’ in Fig. 6m). Depth-dependent viscosity alone does notproduce such a large-scale mantle circulation, even when the largestviscosity contrast is considered (Fig. 6e).

As stated in Section 5, the temperature-dependent viscosity alsoleads to the long-wavelength structure because of reduced thermalinstability in the shallow part of the mantle (Fig. 5), while the depth-dependent properties lead to a long-wavelength structure because ofthe reduced thermal instability at the bottom of the mantle. There

may be some other factors that define the long-wavelength thermalstructure in the mantle. For instance, theoretical and numericalanalyses demonstrate that the low-viscosity asthenosphere (channel)wedged between the highly viscous lithosphere and underlyingmantle promotes a long wavelength flow in the mantle (Busse et al.,2006; Lenardic et al., 2006; Höink and Lenardic, 2008).

Single, spatially-isolated plumes rising from the deep mantlebeneath the Hawaii (e.g., Wolfe et al., 2009) and Iceland (e.g.,Bijwaard and Spakman, 1999) hotspots have been detected by seismictomography studies. However, in general, the origin of the Earth'shotspot plumes remains a controversial issue in geodynamics. Thelarge-sized upwelling plumes observed in Fig. 6, which have beenquite steady during the geological timescale, may be one of theimportant keys that could resolve the question regarding the origin ofthe isolated plumes, regardless of whether convection in the deepmantle is dominated by compositional driving force or not. The largelyreduced thermal expansivity in the deep mantle may allow thethermo-chemical ‘megaplume’ (Tackley, 1998) or thermochemical‘dome’ or ‘piles’ (Tackley, 1998; Davaille, 1999; Kellogg et al., 1999;Tackley, 2000a; Davaille et al., 2002; Jellinek and Manga, 2002;Tackley, 2002; Jellinek and Manga, 2004; McNamara and Zhong,2005b) to be more stable.

The degree-two convection pattern for the case with V=0 andδT=6.5 (Fig. 6i and n) is similar to the Earth's convection patterncharacterized by two large-scale upwellings like Earth's superplumesbeneath the South Pacific and South Atlantic–South Africa and one‘great-circle’-downwelling in the Circum-Pacific, even when themantle convection studied here is purely dominated by the thermalbuoyancy. It seems that such great-circle-downwelling is alsoobserved in the models with relatively weak temperature-dependentviscosity and relatively low yield stress (van Heck and Tackley, 2008;Yoshida, 2008). The planetary-scale, long downwelling like theCircum-Pacific subduction zone are selfconsistently reproduced bythe mantle convection model even with more realistic geophysicalconditions (see Section 12).

7. Timescale of the supercontinent assembly

Although it is well established that supercontinent cycles operatedthroughout the Earth history, the timescales of their assembly anddispersal are not well-constrained. A stable configuration is hypoth-esized for Columbia between 1800 and 1500 Ma (Meert, 2002) whichassigns a time gap of 450–500 Myr prior between the breakup ofColumbia and the assembly of Rodinia. On the other hand, if we takeinto consideration the hypothetical supercontinent Pannotia at ca.600 Ma (Dalziel, 1991), it leaves only 150 Myr between the birth ofthis supercontinent and the demise of Rodinia and 300 Myr before theformation of the subsequent supercontinent Pangea. Senshu et al.(2009) evaluated the history of supercontinents based on a number ofparameters such as the surface configuration based on paleogeo-graphic reconstructions, super downwelling events as suggested bythe rapid amalgamation of the majority of continents, and mantledynamics. These parameters predict that the only supercontinent thatwas assembled within a short period of timewas the Paleoproterozoicsupercontinent Columbia. Although Gondwana and Pangea assem-blies do not tally with this predictedmodel in Senshu et al. (2009) andwere therefore considered together by these authors, these assem-blies have distinct mountain building events and clearly representtwo different supercontinental assemblies. In a speculative model,Senshu et al. (2009) suggested that the precise time when a youngertrue supercontinent might have existed in terms of mantle dynamicsis around 340 Ma. According to their model, the lifespan of super-continents becomes longer in the younger Earth, a phenomenonassigned to a decrease in the rate of heat generation of the subductedTTG materials with time. However, this model requires further


evaluation as there is more subduction erosion with time, and thisfactor outweighs the decreasing heat production.

Numerical models with mobile continents/supercontinents canaddress the timescale of the assembly of supercontinents. Phillips andBunge (2007) demonstrated that using a 3-D spherical-shell modelwith isoviscous mantle, three pieces of continental fragments whosesize broadly corresponds to 10% of thewhole surface of the globe, tendto assemble for an interval of 300–500 Myr, which is comparable to orshorter than the actual supercontinental cycles, 500–700 Myr (e.g.,Silver and Behn, 2008). Zhang et al. (2009) demonstrated that using a3-D spherical-shell model with temperature-dependent rheology anddeformable continents, continents assemble to form a supercontinentfor ~250–650 Myr that depends on the wavelength of mantlestructure. This timescale also seems to be comparable to or shorterthan the actual supercontinental cycles.

Because the timescales obtained from numerical simulationmodels depend on model parameters that control flow speed (inparticular, rheological parameters), it is difficult for us to preciselycompare the timescales of the assembly of supercontinents obtainedby different numerical models with the actual supercontinent cycles.However, the regularity of the assembly of supercontinents can beresolved by the numerical simulation. One of the outstandingproblems in this context is that the effects of the size of supercon-tinent on the behavior of mantle convection and supercontinentcycles. Phillips and Bunge (2007) have shown that when sixcontinental fragments whose size is 5% of the whole surface of theEarth are considered, a much larger time interval (~1500 Myr) isrequired to form the supercontinent. This implies that the size ofsupercontinents/continental fragments significantly affects the time-scale of supercontinent cycles.

There is a possibility that the timescale of supercontinent cyclesmay be closely related to the timescale of generation of strongupwelling plumes from the deep mantle. Previous numericalsimulation models suggest that the timescale of the plume generationand resulting mantle reorganization is much shorter than that of theactual supercontinent cycle. Yoshida et al. (1999) and Honda et al.(2000) have concluded that using an isoviscous mantle model, well-developed upwelling plumes originate from the CMB beneath thehighly viscous supercontinent over a timescale of 200–400 Myr whenreal convection vigor is considered in the model. This timescale maybe shorter than the actual supercontinent cycles. However, if thistimescale is rescaled by the Earth timescale using a typical speed ofmotion of Earth's plates, the duration may be further shortened by afactor of two or three, that is, ~50–100 Myr. On the other hand, Zhonget al. (2007a) concluded that using a temperature- and depth-dependent viscosity model, the transition from degree-one convec-tion to degree-two convection is observed with a timescale of~50 Myr. This implies that mantle reorganization may occur withina short time after a supercontinent is assembled.

8. Supercontinent breakup

A related topic of ongoing discussion is whether the initiation ofcontinental breakup is caused by active rifting initiated by mantleplumes originating in the deep mantle (e.g., Morgan, 1983; Richardset al., 1989, 1991; Storey, 1995; Dalziel et al., 2000; Condie, 2004), bypassive rifting associated with a pre-existing weak zone (e.g., Ruppel,1995) or by a combination of both these phenomena. Some geologicalevidence does not support a plume origin for the breakup of Pangea(e.g., McBride, 1991; McHone, 2000). Coltice et al. (2007) tested thehypothesis that the assembly of supercontinents would force a large-scale thermal structure and therefore drive the underlying mantle tohigher temperatures by using a numerical model. The position of thecontinents was fixed and an equilibrium temperature field wascomputed by stacking the temperature fields over several billion yearsin order to obtain a statistical steady state. Their results show that the

sub-continental lithospheric mantle temperature correlates inverselywith the number of continents. Thus, with a single supercontinent, theconvection planform is dominated by spherical harmonic degree oneand the temperatures are 100 K higher than those with dispersedcontinents. Even when the convective parameters were changed, thelarge temperature excursion observed in the supercontinent config-uration is maintained. The convection modeling in an internallyheated mantle by Coltice et al. (2007) led them to conclude that theassembly of continents into supercontinents would naturally lead to‘global mantle warming’ without the involvement of hot activeplumes. However, this model is considered as one of the two endmember models to explain the formation of continental flood basaltsthat occur over a supercontinent which are characterized by wide anddiffusive magmatism and a lower rate of magma supply. The otherendmembermodel relates to plume-derived continental flood basaltsthat are characterized by a very brief and high rate of magma supplyover a restricted and radiating area followed by continuous hotspotactivity.

A robust example for plume-related mafic magmatism whichultimately broke-up the globe's first coherent supercontinent (Co-lumbia) has been evaluated by Hou et al. (2008). They synthesizeddata on the 1.3–1.2 Ga fan-shaped Mackenzie dyke swarm and othersimilar aged dyke swarms in the Canadian Shield which constitute thesub-swarms of a Late Mesoproterozoic giant radiating dyke swarm.These dyke swarms also correlate with the Late Mesoproterozoicmafic dyke swarms in Australia and East Antarctica which constituteadditional sub-swarms of the giant radiating dyke swarm. Hou et al.(2008) proposed a Late Mesoproterozoic mantle plume at the focalarea of the giant radiating dyke swarm between North America andthe landmass comprising West Australia–East Antarctica (see also,Ernst and Buchan, 2003). They suggested that this mantle plumetriggered the continuous extension at ca. 1.3–1.2 Ga and voluminousmafic magma emplacement, which extended into much of theColumbia supercontinent, and led to its final fragmentation. It mustbe noted that rifts started developing in the Columbia assemblyimmediately after its amalgamation as indicated by the emplacementof several suits of mafic dykes in various constituent fragments of thisPaleoproterozoic supercontinent (Rogers and Santosh, 2009). Aprotracted event of mafic magmatism during the Paleoproterozoicand early Mesoproterozoic recorded from this continental assemblywould probably relate to a global mantle warming process, asenvisaged in the model of Coltice et al. (2007). However, the ultimatefragmentation of the supercontinent in the latest Mesoproterozoicprobably involved plume-related activity as indicated by theformation of radiating giant dyke swarms and voluminous maficmagmatism. The fragmentation history of Columbia might thusrepresent a combination of prolonged global warming and incipientrifting culminating in a plume-triggered final fragmentation. Wetherefore propose that the two endmembermodels of supercontinentbreak-up (global mantle warming and plume activity) might haveoperated in conjunction in the case of at least some of thesupercontinents in Earth history.

A specific case of supercontinent break-upwas evaluated by Storey(1995) with regard to the disintegration of the Gondwana supercon-tinent which started at about 180 Ma ago. The magmatic and tectonicsignatures along the proto-Pacific margin of Gondwana recordimportant changes in subduction zone forces during its initialfragmentation. The absence of subduction along the Neotethyanmargin of Gondwana, together with the observation that initial riftformed at right angles to the active subduction margin as demon-strated by Storey (1995) suggest a potential active role for mantleplumes in the initial separation of the East and West blocks of thesupercontinent. The initial plume-related magmatism is representedby the ca. 182 Ma Karoo province and the final breakup is constrainedat ca. 156 Ma. The large extent of magmatic provinces also suggeststhat the Gondwana supercontinent was underlain by a broad shallow


region of higher temperature, rather than a single plume. Althoughnot considered as a mantle plume, this anomaly is broadly similar tothe thermal blanket effect (Anderson, 1982, 1994). Storey (1995)concluded that either a plume point source or a regional heat anomalycould have weakened the Gondwana lithosphere leading to the highmagma production rates and local rifting leading to the fragmentationof the supercontinent into the East and West Gondwana blocks. Insummary, the role of plumes in initiating the disintegration ofsupercontinents is emphasized in the case of Gondwana also. Similarmodels involving the role of mantle plumes have also been proposedfor the fragmentation of the Neoproterozoic supercontinent Rodinia(Maruyama et al., 2007 and references therein) and Pangea (Isozaki,2009) with significant implications on surface environment and lifehistory of the planet.

9. Stability and longevity of the continent

Based on information from heat flow, geochemistry and therelative delay times of seismic waves in different settings, Jordan(1975) proposed the ‘tectosphere’ (highly depleted relatively lowdensity upper mantle layer) model, in which a zone moves with themotion of the plate lying beneath the old continental shields and isexpected to be up to 400 km thick. The depth to which thetectospheric mantle extends is still a hotly debated topic, althoughmost tomographic images of the cratons show high velocity roots

Fig. 7. Distribution of tectosphere defined by S-wave tomography (Grand, 2002). Note thdownward thinning of tectosphere. Maximum depths are about 300 km. The continental cr

extending to at least 200 km depth, and in some cases to depthsgreater than 300 km (Grand, 2002; Gung et al., 2003; Romanowicz,2009) (Fig. 7). The tectosphere, also known as continental keel orcratonic root, is thus a rigid, cold and chemically distinct raft thatsupports the continental crust (Jordan, 1988) and occurs only beneathold cratons. With time, this keel is extensively eroded by youngermagmatic and subduction-erosion processes as in the case of theNorth China Craton (Kusky et al., 2007; Santosh, 2010a).

The longevity of the continental root in the geological timescale isclosely related to the rheological properties (i.e., viscosity and strain-rate of materials) not only of the continental root itself but also of thesurroundingmantle. As the viscosity contrast between the continentalroot and oceanic upper mantle (including low-viscosity astheno-sphere) is larger, it takes longer time for the continental root to causeRayleigh–Taylor instability (at the bottom of the keel) or convectiveerosion (mainly at the subduction zone) and to be involved into thesurrounding mantle. It has been accepted that the continental root isdepleted in volatile elements due to a high degree of partial melting inwhich case it is dehydrated, and has high viscosity (Pollack, 1986;Karato, 2008, 2010b). However, considering the plausible values ofthe degree of water content and activation volume of dry olivine, theviscosity of continental roots is likely to be no more than the order of1021 Pa s, even when the combined effects of differences in temper-ature and water content on the viscosity are considered (Karato,2010b). The viscosity of continental roots may be two or three orders

e selective occurrence of high velocity anomaly under cratons older than 2.0 Ga andust is only about one tenth of the continental keel.

image of Fig.�7


larger than that of the surrounding asthenosphere with orders of1018–1019 Pa s, on the basis of postglacial rebound analyses (e.g., Billsand May, 1987; Okuno and Nakada, 2001) and tectonic observations(e.g., Gordon, 2000). The resultant viscosity contrast betweencontinental root and the surrounding mantle is, therefore, 102–103,and the assumption of continents as highly viscous bodiesmade in thenumerical models discussed above seems reasonable. In a recentstudy based on the Kaapval craton of southern Africa, Peslier et al.(2010) concluded that the deep roots of cratons are protected by alayer of unusually dry minerals, and provide sufficient viscositycontrast with underlying asthenosphere.

Geochemical studies have revealed that the continental litho-spheres (or cratonic root) beneath some of the old cratons havesurvived for periods more than 3 billion years in spite of later tectonicdisturbance (Carlson et al., 2005). However, the numerical modelwith HVL described in the previous section cannot address themechanism for stability and longevity of the cratonic lithosphere,because the model supercontinent does not deform by the convectionforce with time. In contrast, in some numerical studies, a continent ismodeled as a highly viscous, compositionally buoyant fluid in a 2DCartesian model (e.g., Doin et al., 1997; Lenardic and Moresi, 1999;Shapiro et al., 1999; Lenardic et al., 2003). One of their significantobservations is that continental rootsmust be 1000 times as viscous asthe surrounding mantle in order to stabilize the roots withcompositionally buoyant materials over geological timescales (Doinet al., 1997; Lenardic and Moresi, 1999). This viscosity contrast is inthe range of that obtained by the mineral physics described above.

Lenardic et al. (2003) presented a 2-D numerical model with threechemically distinct materials: continental crust, continental mantlelithosphere and bulk mantle. The visco-plastic rheology is imposed inthe oceanic lithosphere to realize the plate boundary and platemotion. They concluded that a high yield stress for cratoniclithosphere relative to the oceanic lithosphere is found to be aneffective and robust means for providing tectonic stability of cratoniccrust and the relative longevity of deep cratonic lithosphere. They alsosuggested that the degree of yield stress variations between cratonicand oceanic lithosphere required for the stability and longevity can bedecreased if cratons are bordered by continental lithosphere that has arelatively low yield stress (i.e., mobile belt). This means that themobile belts protect cratons from being deformed for certain periodsof geologic timescale.

The longevity of cratonic lithosphere has not been investigated bya 3-D numerical model so far. Yoshida (2010a) demonstrated for thefirst time that using a 3-D spherical-shell model, the deformable andmobile continental lithosphere is stable only for b1 billion years, thatis, the continental materials tend to gradually merge into the oceanicplates and underlying mantle with time, when the viscosity contrastbetween cratonic lithosphere and surrounding oceanic plates is 102

(see Section 11 for details of this result). However, their previousmodel (Lenardic et al., 2003; Yoshida, 2010a) did not consider theorigin and growth of continental crust.

10. Origin and growth of the continental crust

Continental growth occurs predominantly through the addition ofjuvenile crust by arc magmas (e.g., Rapp and Watson, 1995; Nair andChacko, 2008; Windley and Garde, 2009). In the early history of theEarth, the parallel collision of intra-oceanic arcs was an importantprocess to build embryonic continents (e.g., Santosh et al., 2009;Windley and Garde, 2009). Recent studies from Archean terranes indifferent parts of the world have offered important clues for theprocess of amalgamation of composite arcs (Komiya et al., 2002,Santosh et al., 2009 and references therein). A modern analogue forthe Archean process is the western Pacific domain where 60–70% ofisland arcs are concentrated in the oceanic domain. Archean TTGmagmatic suites represent the oldest coherent pieces of felsic

continental crust. In a recent study, Nair and Chacko (2008) presentedresults from long-duration dehydration melting experiments whichsuggest melting depths of N48 km. This result is consistent with theearly crustal evolution models which propose melting at the base ofoceanic crust or oceanic plateaus to explain the origin of early Archeancontinental crust. Under the high Archean geothermal gradient, thesubducted oceanic crust would melt to produce TTG. The modelproposed by Nair and Chacko (2008) differs from earlier models ofsubduction initiation in that the subduction of oceanic lithosphereoccurs through the protomantle lithosphere at the base of the newlyformed oceanic plateau crust. Their model can thus effectively explainthe origin of subduction systems, TTG, TTG-mafic and/or ultramaficmagma association, stabilization of continental crust and the broadlycoeval formation of cratons and their lithospheric roots.

It is now generally understood that plate tectonics not only createsbut also destroys Earth's continental crust, both occurring mostly atsubduction zones, the former by arc magmatic creation and the latterby subduction removal (Stern, 2008; Stern and Scholl, 2010) (Fig. 8).Since subduction zones are the only major routes through whichmaterial is returned to great depths within the Earth, the mass fluxthrough convergent plate margins has received considerable atten-tion in recent studies particularly to evaluate the origin and growth ofthe continental crust. Clift and Vannucchi (2004) classified conver-gent plate margins into those showing long-term landward retreat ofthe trench and those dominated by accretion of sediments from thesubducting plate. They proposed that tectonic erosion is favored inregions where convergence rates exceed 6±0.1 cm yr−1 and wherethe sedimentary cover is less than 1 km. In regions of slowconvergence (b7.6 cm yr−1) and/or trench sediment thicknessexceed 1 km, preferential accretion occurs. Large volumes of conti-nental crust are subducted at both erosive and accretionary margins.

At present, creation and destruction of continental crust are eitherin balance (ca. 3.2 km3yr−1) or more crust is being destroyed thancreated. The creation–destruction balance changes over a supercon-tinent cycle, with crustal growth being greatest during supercontinentbreak-up due to high magmatic flux at new arcs and crustaldestruction being greatest during supercontinent amalgamation dueto subduction of continental material and increased sediment flux dueto orogenic uplift (Stern and Scholl, 2010). Ongoing subductionerosion also occurs at the leading edges of dispersing plates, whichalso contributes to crustal destruction, although this is only atemporary process. The widely held view that the volume ofcontinental crust has increased over time through plate tectonicactivity (e.g., Hurley and Rand, 1969) has thus been challenged, withthe possibility that the volume has in fact decreased.

The mechanism of crust production and growth should beincorporated in a future numerical model in order to test the conceptthat plate tectonics creates and destroys continental crust with time,and also to evaluate whether more volume of crust is being destroyedthan that is being created as suggested in some recent worksdiscussed above. Such a study can also test whether the geologicallysuggested episodic emergence of supercontinents is realized in thenumerical model. The thermal effect of accumulation of continentalcrust with compositionally buoyant materials on mantle convectionhas been previously evaluated in a series of papers (Lenardic andKaula, 1994, 1995, 1996; Lenardic, 1997; Moresi and Lenardic, 1997;Lenardic, 1998; Moresi and Lenardic, 1999). Convective overturn ofthe mantle causes chemically light crust to thicken above the mantledownwelling and surface heat flux above the thick crust is lower thanthat above the mantle (Lenardic and Kaula, 1995). A number of suchstudies are carefully reviewed in Schubert et al. (2001).

Walzer and Hendel (2008) performed simulations of mantleconvection with the growth of a continent using a 3-D spherical-shellmodel with real convective vigor (i.e., Rayleigh number), tempera-ture- and pressure dependent rheologies, and viscoplastic yield stress(i.e., maximum of rupture strength) of the lithosphere to induce the

Fig. 8. Cartoon illustrating tectonic erosion and sediment trapped subduction (compiled after Clift et al., 2009; Senshu et al., 2009).


plate-like motion in the lithosphere. Their modeled continent was notartificially imposed on the convection model in contrast to modelsdiscussed in previous sections and temporally evolved with mantleconvection by considering the chemical differentiation and redistri-bution of incompatible elements, U, Th, and K. The distribution ofradiogenic elements in the mantle is represented by the tracerparticles. In their model, chemical differentiation generates thedepleted MORB mantle from the primordial mantle, if the conditionsfor partial melting are fulfilled, and a large amount of thedifferentiated primordial mantle is assumed to produce the newcontinental crust with higher abundances of incompatible elements(see,Walzer and Hendel, 2008, for the details of methodology).With awide range of parameter space for convective vigor and yield stress ofthe lithosphere, their result supports evidence that continental crusthas grown progressively with time in an episodic manner (Condie,1998). However, the creation–destruction balance of continental crustis not presented in their work. Despite this, among mantle convectionmodels proposed so far, this work has produced the first realisticdistributions of continents.

11. A preliminary Wilson Cycle model

A 3-D mantle convection model with mobile and deformablecontinents and visco-plastic oceanic plates has not been proposed sofar, primarily because of the difficulty to accurately solve theadvection of a chemically distinct body (i.e., continent/superconti-nent) without numerical diffusion (i.e., artifact diffusion). In partic-ular, serious hurdles remained for simulations that attempted tectonicprocesses occurring over geological timescales. Overcoming thisdifficulty, Yoshida (2010a) has recently presented a new numericalmodel of mantle convection with a deformable, mobile continentallithosphere within 3-D regional spherical-shell geometry (Fig. 9). Inthis preliminary model, a supercontinent is instantaneously imposedon well-developed mantle convection. The supercontinent has aspherical-square-shaped cratonic lithosphere with a uniform thick-ness of 250 km (dark orange regions in Fig. 9), which is comparable tothe tectosphere thickness inferred from seismological analysis andgeodynamic evidence (Section 9). It covers ~30% of the total surfacearea of the model domain, and is initially separated into four pieces bythe weak (low-viscosity) continental margins (WCMs; light orangeregions in Fig. 9). In order to ensure the conservation of thecontinental materials, a process of advection with approximatelyzero chemical diffusion is solved by a kind of tracer particle method(e.g., Christensen and Hofmann, 1994). A viscosity increase due to the660-kmphase transition is assumed to be 30 on the basis of the results

of postglacial rebound analyses (Mitrovica and Forte, 1997; Lambeckand Johnston, 1998; Peltier, 1998). The maximum viscosity contrastbetween the continents and the oceanic lithosphere is 102 at the topsurface boundary, which is within the range predicted fromrheological experiments for dehydrated continental root materialsrelative to a reference mantle (Hirth and Kohlstedt, 1996; Karato,2010b; Peslier et al., 2010) (Section 9). The viscosity contrast betweenthe cratonic lithosphere and the WCM is fixed at ~101.5. The visco-plastic oceanic lithosphere and the associated subduction of oceanicplates are incorporated in this model.

Earth-like continental drift and the characteristic thermal interac-tion between the mantle and a continent are observed in thispreliminary numerical model (Fig. 9). By ca. 100 Myr, the supercon-tinent begins to break up because of the tensional stress induced bymantle upwelling, deforms with time because of the surroundingconvecting force, and gradually moves towards a side boundary of themodel domain (note that in this model, the continents reaching thelateral boundary of the model domain appear at the opposite lateralboundary due to the periodic boundary condition). Fig. 10 illustratesan early stage of the composition-field (representing 1 for continentalmaterial and 0 for oceanic material) and the corresponding temper-ature anomaly (i.e., the deviation from horizontally averagedtemperature at the same depth) δT at a shallower mantle (depth of358 km) to observe the thermal insulating effect. The regionalupwelling plumes with high buoyancy and maximum temperatureanomaly of ≥+300 K originating from the CMB are remnants of theinitial thermal condition (indicated by arrows ‘A’ in Fig. 10), whilebroad hot regions with a temperature anomaly of approximately+100 K (‘B’ in Fig. 10) are due to the thermal insulating effect by theexistence of a supercontinent and the radioactive elements in themantle. The beginning of the continental breakup is likely to bemainly responsible for the tensional force of these broad hot regions.The tensional force generated by upwelling plumes may additionallyhelp the continental rift and breakup. The temperature anomaly of+100 K generated by the thermal insulating effect observed here isconsistent with that proposed by Anderson (1982).

Fig. 9 shows that by ca. 150 Myr, Continent-A (or Continent-B) iscompletely separate from Continent-C (or Continent-D), whileContinent-A relatively stays with Continent-B. All the continentsseem to maintain their positions around the lateral boundary of theconvection domain, as observed from the snapshots at 237 Myr. Bythe time the large-scale upwelling plumes in the center of theconvection domain become weak by ca. 237 Myr, pieces of continenttend to go back to the central part of the model domain; for instance,Continent-B and Continent-D are about to collide with each other, as

image of Fig.�8

Fig. 9. Time sequence of mantle convection with deformable, mobile continents. The computational domain of mantle convection is confined to three-dimensional regionalspherical-shell geometry in spherical polar coordinates and has a thickness of 2867 km and a lateral extent of 90°×90° in the latitudinal and longitudinal directions. The blue andpurple isosurfaces of the temperature anomaly δT (i.e., the deviation from horizontally averaged temperature at each depth) indicate −250 K and +250 K, and the orangeisosurfaces indicate the position of continents. The white spherical surface indicates the bottom of the mantle (i.e., core–mantle boundary). The supercontinent is composed by thefour continental fragments (named ‘A’ to ‘D’), surrounding by the weak (low-viscosity) continental margins (WCM) (light orange), and it instantaneously imposed on the well-developed mantle convection with temperature-dependent rheology. The viscosity contrast between the coldest upper surface boundary (i.e., uppermost part of high viscouslithosphere) and hottest bottom surface boundary (i.e., core–mantle boundary) is 104. The elapsed times are scaled by an Earth-like timescale. The details of numerical methodologyand model parameters are found in the work of Yoshida (2010a).


seen from a snapshot at 322 Myr. And eventually, Continent-B andContinent-D collide with each other by 375 Myr. A series of thesebehaviors may mimic a Wilson Cycle, self-consistently reproduced bythe numerical model. Paleographic reconstruction models show thatthe continental drift from the Rodinia supercontinent formed at~900 Ma to the Pangea supercontinent formed at ~350 Ma is likely tooccur on the hemispheric scale of the Earth's surface, not theplanetary-scale, through the introversion process (Murphy andNance, 2003, 2005) or A-type ocean closure (Silver and Behn, 2008)(Section 2). Thus, this mimicked Wilson Cycle observed in theregional spherical-shell geometry may be relevant to the real WilsonCycle. Continental splitting and thinning, i.e., rift valley formation, thatoccur in the first stage of the Wilson Cycle are also observed in thismodel because the model allows a continent to laterally and radiallydeform with the driving force of mantle convection. A continentalcollision, the final stage of the Wilson Cycle, is observed after about~375 Myr, which is broadly similar to the timescales for the actualWilson Cycles as inferred from geological criteria (Section 1).

This model presented here would represent an important steptowards formulating a more realistic model that could be used toaddress many outstanding problems about the thermal and mechan-ical feedbacks between the mantle and continents, the cycle ofcontinental breakup and collision, the duration of a supercontinent,the mechanism of continental drift, and the temporal evolution of theEarth's mantle structure. The continental splitting and thinning (i.e.,rift valley formation) that occur in the first stage of the Wilson Cycle

are observed in the presentmodel (Figs. 9 and 10), because this modelallows a continent to laterally and radially deform with the drivingforce of mantle convection. However this model used a relativelysimple rheology especially for the continental materials, and theresult does not answer the question of how supercontinents breakapart, because the weak zones are imposed a priori in a modelsupercontinent (i.e., no yield mechanism in the continent). Never-theless, among the 3-D models proposed so far, this model has thelargest potential to explain the Wilson Cycles documented fromgeological and geochronological data.

12. Continents and plate tectonics

The upwelling and downwelling plumes, plate tectonics, andcontinental drift are a part of the convecting system in themantle. It isconsidered that the flow scale that characterizes the upwellingplumes is independent from the one that is characterized by platesubduction. As stated in Section 1, the Earth's mantle structure hasdifferent scale of downwellings (i.e., planetary-scale subduction ofplate) and upwellings (i.e., multi-scale upwelling plumes). Inparticular, if the heat from the core is significantly small comparedwith the heat production by radiogenic elements of mantle rocks(Davies, 1988; Sleep, 1990), mantle plumes define only the secondaryflow compared to the main flow determined by the plate tectonics(Davies, 1988, 1999), and therefore do not impart significantinfluence on the global-scale plate motion. The formation and rapid

image of Fig.�9

Fig. 10. Early stage of the time evolution of mantle convection with supercontinents. The composition field (left panels) and the corresponding temperature anomaly δT (rightpanels) at a shallower mantle (depth of 358 km). The composition field indicates 1 for the continent and 0 for oceanic plates. The surface velocity fields are superimposed on thecomposition field. Interval of line counters for δT is 100 K. The arrow ‘A’ indicates the hot upwelling plumes from the core–mantle boundary; ‘B’ indicates the broad hot regionscaused by the thermal insulating effect.


expansion of the Pacific and Indian oceanic plates in the Cretaceoustook place in the broadly low-velocity regions because they have notbeen cooled or displaced by cold oceanic lithosphere for more than200 Myr, and mantle plumes are not required to explain such a plateformation and expansion (Anderson, 1994).

In contrast to the nearly independent relation between plates andmantle plumes, the behavior of mantle plumes is closely linked withthe continental aggregation and breakup as stated in Section 8.However, the mechanical interaction between continent/superconti-nent and moving/subduction plates has been poorly understood ingeodynamics. Because continental fragments drift in accordance withplate motions on the Earth, there should be a mechanical couplingbetween continental drift and plate motions throughout the Earth'shistory. Although the preliminary study by Yoshida (2010a) discussed

in Section 11 has considered the aspects of both mobile continentsand oceanic plates in numerical models, it is still one of the majorchallenges in numerical studies of mantle convection to self-consistently reproduce moving plates in 3-D space (e.g., Bercovici etal., 2000). This is because the mechanisms for the generation ofnarrow plate boundary and the associated plate motion are notadequately clear in geodynamics (e.g., Bercovici, 1996, 1998;Bercovici et al., 2000).

There is a high possibility that chemical and rheological hetero-geneities due to moving plates, as well as drifting continent/supercon-tinent (Sections 4–5), give rise to the long-wavelength structure in the3-D spherical mantle. Fig. 11 shows the results of mantle convectionwith the oceanic plates but without continents/supercontinent. Thehighly viscous oceanic lithosphere is damagedby imposing a yield stress

image of Fig.�10


(i.e., maximum limit of strength of oceanic lithosphere), which wasoften used for the previous 2-D and 3-Dmantle convectionmodels (e.g.,Moresi and Solomatov, 1998; Trompert and Hansen, 1998a). When theyield stress is small, the oceanic lithosphere is highly damaged.When it

is large, the oceanic lithosphere is not substantially damaged (left panelsof Fig. 11). The plate-like behavior is obtained in amoderate yield stressof around τy=100 MPa (Tackley, 2000b; Richards et al., 2001; vanHeckand Tackley, 2008; Walzer and Hendel, 2008; Yoshida, 2008; Foley and

image of Fig.�11


Becker, 2009), which is almost determined by the convection stress.When the yield stress is 100–125 MPa, narrow divergence andconvergence zones coexist in the lithosphere, and both of them arecomparable to the ‘spreading center’ and ‘trench’ of the Earth,respectively. The Y-shaped subduction zone observed in the westernPacific regions of the present-day Earth is also reproduced (see redarrow in the map with τy=100 MPa). Broadly deformed regions withlow-viscosity (for instance, ‘D’ in the map with τy=100 MPa) maycorrespond to the ‘diffuse plate boundary’ of the Earth's lithosphere(Gordon and Stein, 1992; Gordon, 1998, 2000; Zatman et al., 2005). TheEarth's continental and oceanic plates are not uniformly rigid, incontrast with the theory of plate tectonics that can be attributed to thenear rigidity of plates and narrow plate boundaries (Wilson, 1966;McKenzie and Parker, 1967; Le Pichon, 1968; Morgan, 1968) and theprevious 3-D models for plate dynamics (Hager and O'Connell, 1979,1981; Zhong and Davies, 1999; Yoshida et al., 2001).

The resultant convection pattern shows a long-wavelengththermal structure organized by subducting ‘oceanic plates,’ whenthe value of yield stress is moderate, 100–125 MPa (right panels ofFig. 11). The results indicate that the subduction zones surroundingthe margins of the past supercontinents since the Palaeozoic era (i.e.,Gondwana and Pangaea), as seen in some paleographic reconstruc-tions (e.g., Collins, 2003), may be an inherent characteristic of mantleconvection only with thermally induced driving force, that is, withoutany chemical heterogeneity like the compositionally distinct conti-nent/supercontinent. The interplay between plate motions andcontinental assembly–dispersal in the evolving mantle is not clearin the numerical study at present. Future simulation studies shouldfocus on mantle convection models which take into account both thecontinents/supercontinents and plate-tectonic motions.

A possible mechanical coupling between supercontinent cycle andplate tectonics throughout the Earth's history is proposed with aconceptual model by Silver and Behn (2008) (Section 2). Theyhypothesized that drastic reductions or temporary cessations of platesubduction (‘intermittent plate tectonics’) have occurred in situationswhere a supercontinent forms primarily by external ocean closing andthe dispersing continental fragments assemble in the antipode of theEarth. Namely, plate tectonics temporarily stops in the process ofcontinental assembly because all the subduction of the platesdiminishes at the continental margins. This external ocean closureprimarily occurred to form the supercontinent Rodinia at 900 Ma andPannotia at 650 Ma (Silver and Behn, 2008). However, in contrast totheir conceptual model, there may be a possibility that plate tectonicstemporarily stops by a change in the stress magnitude in the oceaniclithosphere (i.e., lithospheric strength) in the process of themechanical interaction between drifting continent/supercontinentand moving oceanic plates, because plate-like motion may occur in anarrow range of the yield stress as shown in Fig. 11.

13. Next supercontinent

The formation of the future supercontinent is of broad interest notonly for earth scientists but also for the larger audience who areinterested in the future shape of the Earth. The name ‘Amasia’ has

Fig. 11. Snapshots of mantle convection with varying the magnitude of yield stress (τy; maxmotion is considered, and continents/supercontinents are not imposed in this model. The desubtracted from solutions at each simulation time-step. Left panel shows viscosity and velociviscosities, respectively. Right panel shows the corresponding isosurfaces of temperature anofrom horizontally averaged temperature at each depth) indicate −250 K and +250 K. Theviscous oceanic lithosphere is realized by the temperature-dependent rheology of mantle mthe moderate yield stresses (τy=100 and 125 MPa): ‘S’ and ‘T’ indicate divergence and convthe Earth. Broadly deformed regions with low-viscosity (for instance, ‘D’ in the map with τy=A red arrow in the map with τy=100 MPa shows the Y-shaped subduction zone. When thhigher (i.e., 150 MPa), the lithosphere is not ruptured so much and the plate boundary is incoto a previous study by Yoshida (2008), but the viscosity contrast between the coldest uppersurface boundary (i.e., core–mantle boundary) is taken to be a higher value, 106. The Rayle

been proposed for the next supercontinent (Hoffman, 1992). TheNorth American and Asiatic plates already fused along a zone ofuncertain nature through eastern Asia, and it is possible that the nextsupercontinent will develop as more of the present continents collidearound the Asia–North America nucleus (Rogers and Santosh, 2004).Part of this fusion might result from further accretion of Gondwanablocks to southern Asia, perhaps by closure of the Indian Ocean. IfSouth America and Antarctica moved in a pattern that would accretethem to Asia in about 500 Myr, then the next supercontinent wouldreach its maximum packing at the same time in the cycle as previoussupercontinents. It has also been proposed that if modern subductionin the Caribbean and Scotia arcs spreads along the Atlantic seaboard,then convergence and destruction of the Atlantic Ocean would resultin a supercontinent termed as ‘Pangea Ultima’ (Scotese, 2000) thatwould form by introversion (Murphy et al., 2009).

Maruyama et al. (2007) proposed a conceptual model whichargues that the Western Pacific Triangular Zone (WPTZ) is a potentialcandidate for the frontier of a future supercontinent (Fig. 12).According to these authors, the presence of a double-sided subductionzone in this region where the Pacific plate subducts under the WPTZ,and the Indo-Australian plate subducts and collides locally against theWPTZ would promote the assembly of continental fragments. Thisconcept was further elaborated recently by Santosh et al. (2009)where they identified two major categories of subduction zones onthe globe based on Y-shaped trip junctions, termed as the Circum-Pacific Tethyan subduction zones (Section 3). The Circum-Pacificsubduction zone covers a length of over 20,000 to 30,000 km, and theremaining 10,000 km zone lies within the northern margin of theIndo-Australian plate starting from the junction of the Pacificsubduction zone to the East in New Zealand to Fiji region. The zonecontinues to the west through Indonesia, Himalaya and Middle Eastto the Mediterranean through Turkey and is finally connected to theMid Atlantic Ridge. The Tethyan subduction zone broadly covers thezone along the northern margin of India and the Tethyan Ocean. Thepast 200 million year history along this zone shows a series ofcontinent collision leading to the growth of Eurasia (cf. Metcalfe,2006, in press), and must have also witnessed the subduction ofsubstantial volume of oceanic lithosphere. Along the eastern marginof the Y-shaped subduction zone running from Kamchatka down toNew Zealand, the passive subduction of Pacific oceanic lithosphere isspeculated to continue, leading to the consumption of the oceaniclithosphere deep in the mantle off North and South America. Thetrench will thenmigrate to the west leading to a reduction in the sizeof the Pacific Ocean with time. According this model, in another250 Myr, the Pacific Oceanmight vanish from the globe leading to theassembly of Asia with the amalgam of North and South America.Although the fate of Antarctica is not known, presumably thiscontinent will also join the amalgam in course of time through thepropagating westward trench along the northern margin ofAntarctica. Thus, the assembly of the future supercontinent Amasiawill be finally completed through Pacific ocean closure andextroversion. However, this model faces the problem that the Pacificsuperplume is situated in between. Also, alternate models of theAtlantic Ocean closing first require evaluation.

imum rupture strength) of the lithosphere. Note that only the mechanism for plate-likegree-one component of toroidal velocity field that represents the rigid-body rotation isty fields on the top surface of model domain. Blue and yellow show the higher and lowermaly. The blue and yellow isosurfaces of the temperature anomaly δT (i.e., the deviationwhite sphere indicates the bottom of mantle (i.e., core–mantle boundary). The highlyaterials, and the plate-like motions in the oceanic lithosphere are realized by imposingergence zones in the lithosphere, i.e., correspond to the spreading center and trench in100 MPa) may correspond to the ‘diffuse plate boundary’ in the Earth (Gordon, 1998).

e yield stress is lower (i.e., τy=50 MPa), the lithosphere is highly ruptured, while it ismpletely evolved. The details of numerical methodology andmodel settings are similarsurface boundary (i.e., uppermost part of high viscous lithosphere) and hottest bottomigh number defined by the reference viscosity (1021 Pa s) is fixed at 5.72×106.

Fig. 12. Location of the western Pacific triangular zone (WPTZ), considered as the frontier of the future supercontinent (after Maruyama et al., 2007). East Asia is the location of adouble-sided subduction zone, where the old Pacific plate subducts from the east, and the Indo-Australia plate from the south. Due to subduction, and hence refrigeration, the upperand lower mantle here are the coldest mantle regions in the world. A schematic cross-section of WPTZ is shown below to illustrate the stagnant slabs, hydrous mantle transitionzone, and formation of hydrous plumes at 410 km depth.


We will now examine how numerical simulations approach theshape of the future globe in terms of supercontinent configurations.As stated in Section 11, it is difficult for numerical simulations toreproduce the continental drift on the 3-D spherical model because ofsome limitations in the techniques currently employed. Nevertheless,Trubitsyn et al. (2008) constructed a 3-D numerical model to realizethe continental drift from present to 100 Myr later and to predict aconfiguration of future supercontinent. They consider continents asthin rigid (non-deformable) spherical caps, the motion of which isdescribed by Euler's solid body equation (see Trubitsyn et al., 2008 forthe details of numerical methodology and model parameters used).The model continents are arranged in a real distribution of continentsof the present Earth. The initial temperature condition of mantle isgiven by the present mantle flow pattern estimated from a seismictomography model (that is, it has the Circum-Pacific subduction zone

and two superplumes in the Africa–Atlantic and the South Pacificregions). Their simulation reveals that after 100 Myr, all continentswill be assembled in the southern hemisphere. Africa, Eurasia,Australia, Antarctica and South America form a future supercontinentaround Antarctica, because the Y-shaped subduction zone in theWestern Pacific pulls the continents. According to the model, NorthAmerica will not be part of the future, probably because the tensionalforce due to both the South Pacific and African superplumes preventsNorth America from moving to the southern hemisphere and joiningthe future supercontinent amalgam.

14. Summary and conclusion

A synthesis of some of the conceptual models on supercontinentamalgamation and disruption, together with recent information from

image of Fig.�12


numerical studies, leads to a better understanding of theWilson Cycleand supercontinent cycle. The superdownwelling along multiplesubduction zones predicted in plate tectonic models might provide aneffective mechanism to pull together dispersed continental fragmentsinto a closely packed assembly. Plumes and superplumes whichbreakup supercontinents are considered to be fueled by the recycledsubducted material that initially accumulates at the mantle transitionzone and ultimately sinks down into the CMB. The process of re-assembly of dispersed continental fragments occurs through complexprocesses involving ‘introversion’, ‘extroversion’ or a combination ofboth, with the closure of the intervening ocean occurring throughPacific-type or Atlantic-type processes. The timescales of the assemblyand dispersion of supercontinents have varied through the Earthhistory, and appear to be closely linked with the processes andduration of superplume genesis. It is nowwidely recognized that platetectonic processes lead to both creation and destruction of continentalcrust. The production–destruction balance changes over a supercon-tinent cycle, with a higher crustal growth through magmatic influxduring supercontinent break-up as compared to the tectonic erosionand sediment-trapped subduction in convergent margins associatedwith supercontinent assembly which erodes the continental crust.

The link between deep mantle dynamics and lithospheric platemotions emphasizes the periodic assembly and dispersal of super-continents. Model relations between the Wilson Cycle and mantleconvection have a strong bearing on the ‘superplume’ hypothesis.Despite the controversy surrounding the superplume concept, thegeophysical and geochemical tools at our disposal have aided in theformulation of persuasive models on the role of superplumes. Thebeginning of a consensus is visible in the various studies concerningthe origins of ‘hot spots’ and likely ‘superplume’ candidates. Theprocesses responsible for the formation and disruption of pastsupercontinents and the hypothetical future supercontinent amalgamhave important bearing on future biotic evolution and climate change.

Often, unusual phenomena such as backarc basin propagationoccur associated with some of the subduction systems. There are alsoconflicting interpretations of ‘proto-continents’ as drifted fragmentsor terranes extruded from major continental collision. From thegeological point of view, certain specific rock types have beenconsidered as the signature of plumes, although similar rock typesalso occur in alternate tectonic settings. Another case concernscontiguous marginal basins which are considered as the products ofcollision-induced lateral mantle flow. Although these may reflect‘plate-driven’ lateral displacement of ductile upper mantle, they donot negate the ‘super’ or ‘regular’ plumemodels. Whereas the Tethyancollisions (Africa, India, and Australia) clearly share commonlithospheric indications, this does not necessarily apply to theirrespective asthenospheric responses. They are probably similar inkind but need to be compared and contrasted from geologicalevidence within the erstwhile sutures between constituent Gond-wana terranes.

The numerical studies reviewed herein suggest that there is asignificant feedback not only between mantle convection andcontinental drift, but also between mantle convection and platemotions. The process of assembly of supercontinents induces atemperature increase due to the thermal insulating effect. Suchthermal insulation leads to a planetary-scale reorganization of mantleflow and results in longest-wavelength thermal heterogeneity in themantle, i.e., degree-one convection in 3-D spherical geometry. Theformation of degree-one convection seems to be integral to theemergence of periodic supercontinent cycles. The rifting and breakupof supercontinental assemblies may be caused by either tensionalstress due to the thermal insulating effect, or large-scale partialmelting due to the flow reorganization and the resultant temperatureincrease beneath the supercontinent. Supercontinent breakup hasalso been correlated with the temperature increase due to upwellingplumes originating from the CMB as a return flow of plate subduction

occurring at supercontinental margins. The active mantle plumesfrom the CMB seem to disrupt the regularity of supercontinent cycles.If mantle convection with dispersed continental blocks is well-organized degree-one structure owing to its temperature-dependentrheology, the continental blocks maymove to downwellings and forma supercontinent. Although most of the numerical studies haveassumed the continent/supercontinent to be rigid or nondeformablebody mainly because of numerical limitations as well as a simplifi-cation of models, a more recent numerical study allows the modelingof mobile, deformable continents, including oceanic plates, andsuccessfully reproduces continental drift similar to the processesand timescales envisaged in Wilson Cycle.

On the basis of the numerical studies synthesized here, we candraw two possible end-member scenarios of the mantle convectioncycle. One is that mantle convection with dispersing continentalblocks has a short-wavelength structure (or close to degree-twostructure as the present Earth), and when a supercontinent forms,mantle convection evolves into degree-one structure. Another is thedegree-one to degree-twomodel (Section 5). As for the former model(high-degrees to degree-one), it would take longer time to form asupercontinent, because continental blocks would be trapped bydifferent downwellings thus inhibiting collision. The timescale ofmantle convection cycle may be, however, significantly affected bythe plate motion and subduction that stir mantle convection.

In order to better constrain some of the key topics covered in thispaper, the future studies based on numerical modeling need toaddress the following aspects: (1) Thermal and mechanical interac-tion between continent/supercontinent and plate motion. (2) Themechanism of formation of large-scale upwellings beneath thesupercontinent. (3) The mechanism of origin and growth of thecontinental crust. (4) The mechanism of supercontinent breakup. (5)The episodic growth of continental crust and supercontinent. (6) Thegrowth and destruction of continental crust both related to subduc-tion zone processes. (7) The thermal and mechanical interactionbetween supercontinent cycle and mantle convection during theEarth's history, as well as the thermal and chemical evolution ofconvecting mantle.

Acknowledgements

We thank Editor Prof. M.F.J. Flower and Reviewer Prof. J. BrendanMurphy for their valuable suggestions and helpful comments. M.Y.was supported by a Grant-in-Aid (No. 20740260) from theMinistry ofEducation, Culture, Sports, Science and Technology, Japan.

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