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Earth-Science Reviews 105 (2011) 1–24
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Earth-Science Reviews
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e a r s c i r ev
Supercontinents, mantle dynamics and plate tectonics: A perspective based on
conceptual vs. numerical models
Masaki Yoshida a,⁎, M. Santosh b
a
b
Institute for Research on Earth Evolution (IFREE), Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 2-15 Natsushima-cho, Yokosuka, Kanagawa 237-0061, Japan
Division of Interdisciplinary Science, Faculty of Science, Kochi University, Akebono-cho 2-5-1, Kochi 780-8520, Japan
a r t i c l e
i n f o
Article history:
Received 1 June 2010
Accepted 7 December 2010
Available online 14 December 2010
Keywords:
supercontinents
mantle dynamics
plate tectonics
Wilson Cycle
supercontinent cycle
numerical model
a b s t r a c t
The periodic assembly and dispersal of supercontinents through the history of the Earth had considerable
impact on mantle dynamics and surface processes. Here we synthesize some of the conceptual models on
supercontinent amalgamation and disruption and combine it with recent information from numerical studies
to provide a unified approach in understanding Wilson Cycle and supercontinent cycle. Plate tectonic models
predict that superdownwelling along multiple subduction zones might provide an effective mechanism to
pull together dispersed continental fragments into a closely packed assembly. The recycled subducted
material 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 fragment
the supercontinent. Geological evidence related to the disruption of two major supercontinents (Columbia
and Gondwana) attest to the involvement of plumes. The re-assembly of dispersed continental fragments
after 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 through
Pacific-type or Atlantic-type processes. The timescales of the assembly and dispersion of supercontinents have
varied through the Earth history, and appear to be closely linked with the processes and duration of
superplume genesis. The widely held view that the volume of continental crust has increased over time has
been challenged in recent works and current models propose that plate tectonics creates and destroys Earth's
continental crust with more crust being destroyed than created. The creation–destruction balance changes
over a supercontinent cycle, with a higher crustal growth through magmatic influx during supercontinent
break-up as compared to the tectonic erosion and sediment-trapped subduction in convergent margins
associated with supercontinent assembly which erodes the continental crust. Ongoing subduction erosion
also occurs at the leading edges of dispersing plates, which also contributes to crustal destruction, although
this is only a temporary process. The previous numerical studies of mantle convection suggested that there is a
significant feedback between mantle convection and continental drift. The process of assembly of
supercontinents induces a temperature increase beneath the supercontinent due to the thermal insulating
effect. Such thermal insulation leads to a planetary-scale reorganization of mantle flow and results in longestwavelength thermal heterogeneity in the mantle, i.e., degree-one convection in three-dimensional spherical
geometry. The formation of degree-one convection seems to be integral to the emergence of periodic
supercontinent cycles. The rifting and breakup of supercontinental assemblies may be caused by either
tensional stress due to the thermal insulating effect, or large-scale partial melting resulting from the flow
reorganization and consequent temperature increase beneath the supercontinent. Supercontinent breakup
has also been correlated with the temperature increase due to upwelling plumes originating from the deeper
lower mantle or CMB as a return flow of plate subduction occurring at supercontinental margins. The active
mantle plumes from the CMB may disrupt the regularity of supercontinent cycles. Two end-member scenarios
can be envisaged for the mantle convection cycle. One is that mantle convection with dispersing continental
blocks has a short-wavelength structure, or close to degree-two structure as the present Earth, and when a
supercontinent forms, mantle convection evolves into degree-one structure. Another is that mantle
convection with dispersing continental blocks has a degree-one structure, and when a supercontinent
forms, mantle convection evolves into degree-two structure. In the case of the former model, it would take
longer time to form a supercontinent, because continental blocks would be trapped by different downwellings
thus inhibiting collision. Although most of the numerical studies have assumed the continent/supercontinent
⁎ Corresponding author. Tel.: + 81 46 867 9814; fax: +81 46 867 9315.
E-mail address: [email protected] (M. Yoshida).
0012-8252/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.earscirev.2010.12.002
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 of
models, a more recent numerical study allows the modeling of mobile, deformable continents, including
oceanic plates, and successfully reproduces continental drift similar to the processes and timescales envisaged
in Wilson Cycle.
© 2010 Elsevier B.V. All rights reserved.
Contents
1.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.
Supercontinent cycle and Wilson Cycle . . . . . . . . . . . . . .
3.
Supercontinent cycle and mantle convection . . . . . . . . . . .
4.
Thermal and mechanical interaction between continent and mantle
5.
Formation of degree-one mantle structure . . . . . . . . . . . . .
6.
Long-wavelength thermal structure in the mantle . . . . . . . . .
7.
Timescale of the supercontinent assembly . . . . . . . . . . . . .
8.
Supercontinent breakup . . . . . . . . . . . . . . . . . . . . .
9.
Stability and longevity of the continent . . . . . . . . . . . . . .
10.
Origin and growth of the continental crust . . . . . . . . . . . .
11.
A preliminary Wilson Cycle model . . . . . . . . . . . . . . . .
12.
Continents and plate tectonics . . . . . . . . . . . . . . . . . .
13.
Next supercontinent . . . . . . . . . . . . . . . . . . . . . . .
14.
Summary and conclusion . . . . . . . . . . . . . . . . . . . . .
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction
The history of growth, evolution and dispersion of supercontinents
on the globe through time has received considerable attention in the
recent years, particularly with respect to the impact of the assembly
and dispersion of continental fragments on mantle dynamics, surface
processes and life evolution (for a recent compilation, see Santosh and
Zhao, 2009, and papers therein). A recent synthesis of the various
conceptual models suggests that supercontinent tectonics in relation
to mantle dynamics provides a key to evaluate the history of evolution
and destruction of the continental crust, to understand the history of
life, and to trace the major surface environmental changes of our
planet (Santosh, 2010b). The postulated Neo-Archean continental
assemblies (e.g., Rogers and Santosh, 2004; Eriksson et al., 2009) and
the increasing evidence for the Paleo-Mesoproterozoic supercontinent 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 and
Lieberman, 2008), among other proposed supercontinents, support
the notion that global cycles of continental reorganization have
occurred throughout Earth's history (Worsley et al., 1984; Nance et al.,
1986).
Seismic tomographic images suggest that the Earth's mantle
structure is characterized by different modes of flow: (1) Subducting
plates mainly beneath the Circum-Pacific region, some of which are
stagnated at the 660 km phase boundary (i.e., spinel to perovskite
+ magnesiowüstite phase transition boundary), whereas others
penetrate into the deeper lower mantle (e.g., Fukao, 1992; van der
Hilst et al., 1997; Fukao et al., 2001; Zhao, 2004); (2) Large-scale,
broad upwelling-plumes beneath the South Africa–South Atlantic and
South Pacific regions (e.g., Fukao, 1992; Masters et al., 2000; Mégnin
and Romanowicz, 2000; Ritsema and van Heijst, 2000); (3) Smallscale, localized upwelling-plumes originating from the core–mantle
boundary (CMB) or 660 km phase boundary, which were detected
mainly by the recent highly-resolved tomographic model (e.g., Wolfe
et al., 1997; Montelli et al., 2004, 2006; Wolfe et al., 2009).
Geochemical evidence and geodynamic models support this global
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view of mantle structure, although several models with various
compositional heterogeneities have also been proposed (see review
by Tackley, 2000a, 2007). On the other hand, a continent/supercontinent 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 and mechanical interaction between
the continental drift and mantle convection has not been, however,
fully resolved.
The numerical studies of mantle convection have markedly
progressed toward the realization of seismic tomography images of
mantle structure and a better understanding of geodynamic mechanisms in accordance with the advancement in numerical modeling
techniques as well as the increase of computational power and
resource. The mantle convection theory is comprehensively summarized by several papers and textbooks (e.g., McKenzie et al., 1974;
Jarvis and McKenzie, 1980; Christensen, 1984; Busse, 1989; Schmeling, 1989; Davies, 1999; Schubert et al., 2001; Turcotte and Schubert,
2002; Ricard, 2007). A review of mantle convection studies and the
numerical simulation techniques used are beyond the scope of this
paper, and can be found in the several textbooks and papers with
broader 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, numerical
studies performed in the 80s–90s mainly by using two-dimensional
(2-D) model with continents/supercontinents are carefully reviewed
in the textbook by Schubert et al. (2001). The relationship between
the supercontinent and mantle convection processes is clarified in a
review by Condie (2001) from the viewpoint of geology and
geochronology. However, there have been very little attempts so far
to link the geophysical numerical models and the geological and
tectonic conceptual models to understand the history of plate
tectonics, Wilson Cycle and supercontinent cycle. Furthermore, it is
important to link these models with the actual surface geological
records, and the quantitative geophysical data from various types of
geophysical surveys. In the recent years, several numerical models of
mantle convection have addressed the assembly and breakup of
supercontinents using three-dimensional (3-D) models. This paper
M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
aims to synthesize the salient results from these studies in an attempt
to provide a unified approach in evaluating the numerical studies and
speculative geodynamic models to better constrain the mechanism of
formation 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 periodic
assembly and dispersal of continental fragments, the term Wilson
Cycle (after J. Tuzo Wilson, the pioneer who laid the base for the
modern concept of plate tectonics; Dewey and Spall, 1975) has been
used to explain the periodic opening and closing of ocean basins
(Wilson, 1966). In a simple sense, supercontinent cycle and Wilson
Cycle are complimentary because fragmentation of supercontinents
opens new ocean basins and amalgamation of supercontinents leads
to the closure of ocean basins. However, supercontinent cycles involve
more complex processes that occur during the assembly of multiple
continental fragments of various ages including ancient cratons
together with accreted terranes. This is in contrast to the rather
simple components in Wilson Cycle involving the production and
destruction of ocean floor, with the oldest oceanic crust on the planet
aged more than 200 Ma. Among various distinctions between the two
cycles, one important aspect is the time interval, with a shorter time
span for the Wilson Cycle as against a much longer time span in which
supercontinent cycle operates.
Whereas this aspect still remains vague, several complex processes
associated with supercontinent cycles have been proposed, involving
‘introversion’ and ‘extroversion’ of continental fragments rifted from a
previous supercontinent, and sometimes even a combination of these
two processes (Murphy and Nance, 2005; Murphy et al., 2009). Hoffman
(1991) proposed the concept of ‘inside-out’ process as a mechanism of
assembling crustal fragments after the breakup of an earlier supercontinent. If the supercontinent was rifted on one side to bear a passive
margin such as in the case of the Atlantic Ocean, then the opposite side
becomes a consuming boundary along the continents, such as in the case
of the Pacific margin. With time, the Pacific Ocean would shrink and
finally close by the passive collision of two continents to generate a large
continental mass. In the case of Atlantic, initially both continental
margins are passive, and later turn to active margins, and finally shrink
in size and totally disappear. If introversion occurs in this case, the
Atlantic would close. On the other hand, during much of the Mesozoic–
Cenozoic the Indian Ocean has had two different types of margins
simultaneously in operation, active and passive, transporting the
northern continental margin of Gondwana by the Atlantic-type process
and amalgamating the rifted continents to the southern margin of Asia
by the Pacific-type process. Therefore, the Indian Ocean-type process
illustrates simultaneous continental break up and continental amalgamation exemplifying ‘inside-in’ mechanism (Murphy and Nance,
2003, 2005). Similar simultaneous rifting and accretion on different
margins were also proposed in the case of the Paleoproterozoic
supercontinent Columbia by Rogers and Santosh (2002). The Tethyan
process started at least by the Triassic to Permian time and operated
simultaneously with the Pacific process to the east. Subsequently,
double-sided subduction started to define the frontier of the future
supercontinent (Maruyama et al., 2007). Thus, the Tethyan region is an
example for the ‘inside-in’ reassembly of supercontinents (Hoffman,
1991; Murphy and Nance, 2003, 2005; Murphy et al., 2009) whereas the
Pacific region is related to the ‘inside-out’ configuration. Thus, the
process of completion of a supercontinent would involve a combination
of both introversion and extroversion (Fig. 1a–e). Such a combination
operated in the case of Rodinia assembly, and is also implied in the
prediction 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 two
geodynamically distinct tracts of oceanic lithosphere generated
3
during the breakup of supercontinents: a relatively young interior
ocean floor that develops between the dispersing continents, and a
relatively old exterior ocean floor, which surrounded the supercontinent before breakup. The geologic and Sm/Nd isotopic record
synthesized in their study (Fig. 1f) suggests that supercontinents
may form by two end-member mechanisms: introversion, in which
interior ocean floor is preferentially subducted, and extroversion, in
which 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 by
slab avalanche events (Machetel and Weber, 1991; Honda et al., 1993;
Tackley et al., 1993), could occasionally overwhelm top–down
geodynamics, imposing a geoid high over a pre-existing geoid low
and causing the dispersing continents to reverse their directions to
produce an introverted supercontinent.
In another different model, Silver and Behn (2008) proposed two
modes of ocean closure during supercontinent formation which they
termed as P-type (Pacific type) and A-type (Atlantic type), a concept
broadly similar to the model proposed in Murphy and Nance (2003,
2005) and Murphy et al. (2009). When a supercontinent surrounded by
subduction zones begins rifting, the resulting continental breakup
creates an internal ocean. As the breakup continues, the size of the
internal ocean increases at the expense of the external ocean. In A-type
closure, the subduction begins at a passive margin of the internal ocean
and the internal ocean begins to close. In P-type closure, the internal
ocean continues to grow and becomes an enlarged ocean basin. When a
supercontinent is assembled through A-type closure, the internal ocean
closes, shutting down subduction zones in the internal ocean, while
subduction and sea-floor spreading in the external ocean continue. In Ptype closure, the external ocean closes, shutting down all subduction.
Silver and Behn (2008) suggested that A-type and P-type closures can be
distinguished by the age of former oceanic crustal material (such as
ophiolites) that is trapped in the suture zone along which the
supercontinent assembled. In the case of A-type closure, the age of the
oceanic material will be younger than that of breakup of the previous
supercontinent. This is because the subduction initiation postdates the
previous breakup. On the other hand, in the case of P type closure, the
oceanic crustal material can predate the breakup of the previous
supercontinent because subduction initiation predates the breakup.
Similar to the case of ‘introversion’ and ‘extroversion’ (Murphy and
Nance, 2003, 2005), the P-type and A-type closures represent two
endmember cases, and the actual mode of closure may likely involve a
combination of the two processes. According to Silver and Behn (2008),
the supercontinent Pangaea, which was formed by the closing of the
Iapetus Ocean, appears to have formed primarily by A-type closure. In
contrast, both the supercontinents Pannotia and Rodinia formed
primarily by P-type closure. Although the Paleoproterozoic supercontinent Columbia might have formed by A-type closure (Rogers and
Santosh, 2002, 2009), the available data are not adequate to draw a firm
conclusion.
3. Supercontinent cycle and mantle convection
One of the major challenges in earth sciences is to resolve the
thermal and mechanical feedback between mantle convection and
continental/supercontinental drift. A widely-accepted theory proposes
that a supercontinent thermally insulates the underlying mantle and
isolates it from subduction (i.e., ‘thermal blanket effect’), and eventually
breaks into pieces that move towards colder regions of mantle
downwellings (Anderson, 1982; Gurnis, 1988; Anderson, 1994).
Continental aggregation might lead to a re-organization of the
convective flow in the mantle and a positive temperature excursion
beneath the supercontinent (e.g., Yoshida et al., 1999; Coltice et al.,
2009). Fig. 2 illustrates an example of the time evolution of mantle
convection with a rigid, undeformable supercontinent that covers 30%
of the total surface and 250 km thickness from the surface boundary in
4
M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
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 are
organized by the ‘old’ supercontinent (‘old’ in Fig. 2), and upwelling
plumes dominate beneath the old supercontinent, while downwelling
plumes dominate beneath the antipodes. Subsequently, at the elapsed
time of 0 Myr, we instantaneously imposed a ‘new’ supercontinent
(‘new’ in Fig. 2) on the antipodes of the old supercontinent where
downwelling plumes dominate. After the set of supercontinent, the
downwellings beneath the supercontinent tend to become weak and
are not discernable at ~32 Myr. A new upwelling plume occurs at
~92 Myr, and the mantle temperature beneath the supercontinent
tends to increase due to the thermal insulation effect (see Section 4). The
large-scale horizontal mantle flow beneath the supercontinent, including the high temperatures, swept the downwelling into the antipodes
and induced a planetary-scale flow in the whole mantle for b200 Myr.
M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
5
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 circumference
ratio 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. Orange
lid 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 in
this 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. In
this 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 radiogenic
heating 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 new
supercontinent, as the elapsed time passes. Fig. 3 illustrates a cartoon
showing the time series of mantle reorganization by the amalgamation
of supercontinent. The fragments of the supercontinent would migrate
to a downwelling flow of the mantle. The mantle beneath the
supercontinent warms up by the thermal blanket effect, and the largescale, hotter flow emerges from beneath the supercontinent to
subcontinental regions (i.e., oceanic lithosphere). This large-scale flow
in the shallower mantle produces large-scale (planetary-scale) flow via
the deeper mantle. Eventually, the bottom thermal boundary layer is
perturbed by this return flow and then the upwelling plumes are
concentrated beneath the supercontinent.
Continental rafts impose their own wavelength on mantle
convection by impeding downwelling below them (Gurnis, 1988).
Thus, the assembly of supercontinents would force larger scales of
convection and drive the underlying mantle towards higher temperature. Some models consider that the extensive subduction associated
with the assembly of supercontinents involves the transport of large
volumes of oceanic as well as continental materials into the deep
mantle, and that some of these recycled materials act as fuel to
generate mantle plumes which rise up and eventually disintegrate the
supercontinents (e.g., Maruyama et al., 2007). Although models on
the assembly and disruption of supercontinents are diverse, most of
the studies emphasize the implications of supercontinent tectonics on
Fig. 3. A cartoon showing the time series of mantle reorganization by the existence of amalgamation of supercontinent.
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M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
the rheological properties of the mantle, which in turn control the
major geological processes in our planet (Karato, 2010a).
Based on the topology of Y-shaped triple junctions in major
supercontinental assemblies, Santosh et al. (2009) recognized two
distinct categories of subduction zones on the globe: the CircumPacific subduction zone and the Tethyan subduction zone. In the
randomly distributed subduction zones on the surface of the earth, the
low temperature and dense subducted material sinks down to the
bottom of the mantle (e.g., Maruyama et al., 2007; Fukao et al., 2009).
In the scenario where the subduction is double-sided, the triangular
regions with Y-shaped topology selectively refrigerate the underlying
mantle, reducing the temperature and turn down the temperature in
these domains as compared to the surrounding regions. The Y-shaped
domains also accelerate the refrigeration through larger amounts of
subduction and thus promote stronger downwelling as compared to
other regions of the mantle. Once this process is initiated, a runaway
growth of a region characterized by cold downwelling starts to
develop, producing a zone of super-downwelling to pull together the
continental material on the surface into a tight assembly. The
‘maximum close packing’ of continental fragments within supercontinents suggested by Rogers and Santosh (2004) can be explained
through this process.
The continental lithosphere exhibits a general behavior that is
almost decoupled from the convecting mantle and the motion of the
oceanic plates because the material constituting this lithosphere is
less dense than that of the mantle and oceanic lithosphere and is less
deformable than that of the mantle. It thus acts as an assemblage of
fairly rigid bodies ‘floating’ on the top of the mantle. In numerical
studies of mantle convection, this allows the continent to be modeled
as a nondeformable, highly viscous lid (HVL) or a rigid cap. A number
of previous studies have addressed the effects of supercontinents on
the dynamics and structure of the mantle using 2-D models (Gurnis,
1988, 1990; Gurnis and Zhong, 1991; Lowman and Jarvis, 1993; Zhong
and 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 convection
with a rigid supercontinent (Gurnis, 1988) presents crucial results.
His 2-D rectangle model has presented crucial results on the dynamic
feedback between the mantle and continent/supercontinent. In his
model, a supercontinent and the dispersing continental fragments
from it can migrate in accordance with the horizontal velocity of the
mantle beneath the supercontinent. The supercontinent that is
initially located above an upwelling mantle plume in the welldeveloped convection breaks up, with its fragments migrating to a
downwelling mantle plume, where they reassemble. They eventually
reassemble at a site of the downwelling mantle plume. When the
downwelling plume waning from the bottom of the supercontinent,
the colder mantle beneath the supercontinent is replaced by the
hotter mantle with a new upwelling plume as an initial thermal
structure before the breakup of the old supercontinent. Such a
periodic supercontinental cycle and the formation of long-wavelength
thermal structures during the cycle have also been observed in 2-D
cylindrical models with wide model parameters (Gurnis and Zhong,
1991; Zhong and Gurnis, 1993).
The flow reorganization of mantle due to the existence of the
supercontinent is carefully examined by Lowman and Jarvis (1993,
1995) using 2-D Cartesian box models with various model parameters
such as an aspect ratio of box, the thermal diffusivity and thickness of the
continent, and a radiogenic internal heating ratio of mantle. They have
concluded that the flow reorganization appears prominently in a model
with a wider and thicker supercontinent and smaller thermal diffusivity
of lid, higher continental crustal heating, and lower radiogenic internal
heating of mantle. Lowman and Jarvis (1996) incorporated rigidly
moving continental blocks with a finite thickness in a 2-D Cartesian
mantle convection model. They suggested that stresses generated by
flow reorganization below the aggregated continents are sufficient to
produce continental rifting, and that the subduction of oceanic plates at
the margins of a thick continental plate may be the key event in
triggering the subsequent continental breakup.
4. Thermal and mechanical interaction between continent
and mantle
The thermal and mechanical interaction between mantle and
continent/supercontinent would significantly affect the evolution of
the Earth's mantle. The question as to whether the temperature
increase beneath the supercontinent due to the thermal insulating
effect of the supercontinent (Anderson, 1982) aids continental rifting
and breakup is not clear in geodynamics. The subsequent mantle
reorganization that has been hypothesized to occur in response to
thermal insulating effect is probably one cause of continental breakup
and dispersal (Gurnis, 1988). The concept of thermal blanket
envisages the breakup of supercontinents through radiogenic heating
(e.g., Gurnis, 1988). Granites contain higher K, U and Th compared to
mantle peridotite. Recent studies recognize that substantial volume of
arc crust of granitic composition is subducted during the assembly of
supercontinents through arc subduction, sediment trapped subduction and tectonic erosion. This tonalite–trondhjemite–granodiorite
(TTG) material is dragged down and is thought to accumulate in the
mantle transition zone (Senshu et al., 2009). It is possible that the
radiogenic elements in the subducted TTG crust heat up the overlying
mantle with time to initiate continental rifting and dispersion leading
to the opening of oceans. Komabayashi et al. (2009) performed phase
assemblage analysis in the system mid-oceanic ridge basalt (MORB)–
anorthosite–TTG down to the CMB conditions. Their results show that
all these materials can be subducted even up to the CMB leading to the
development of a compositional stratification in the D” layer.
Numerical modeling studies, however, have not yet considered the
higher radiogenic heating rate through subduction of continental
crust. Maruyama et al. (2007) proposed that the exothermic reaction
during the perovskite and post-perovskite phase transition heats up
the cold materials accumulating at the CMB and leads to the formation
of superplumes which rise up and disintegrate the supercontinent.
Effects of thermal insulation by the supercontinent on the mantle
convection are so far investigated by the previous numerical models
of mantle convection. They have revealed that horizontal flow due to
temperature differences between the supercontinent and the rest of
the ‘oceanic’ region produces the large-scale flow in the mantle and
large upwelling plumes originating from the CMB beneath the
supercontinent (Gurnis, 1988; Gurnis and Zhong, 1991; Zhong and
Gurnis, 1993; Nakakuki et al., 1997; Yoshida et al., 1999; Honda et al.,
2000; Phillips and Bunge, 2005, 2007; Yoshida, 2010b) (see also
Fig. 2). It appears that the temperature increase by the thermal
insulation effect sustains for long geological timescales when
radiogenic internal heating in the mantle is considered (Yoshida
et al., 1999; Honda et al., 2000). The thermal insulating effects and
flow reorganization of mantle may cause ‘global mantle warming’ and
large-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 major
role in warming the bottom of the supercontinent. The temperature
increases beneath the supercontinent may be caused by upwelling
plumes originating from the CMB as a return flow of plate subduction
occurring at supercontinental margins (Zhong et al., 2007a).
Nakakuki et al. (1997) investigated the effects of a combined
system of highly-viscous continental lid and subcontinental regions
(i.e., ocean) using a 2-D, long aspect-ratio Cartesian model with
M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
multiple phase transitions at 410 km and 660 km and depthdependent properties (i.e., viscosity, thermal expansivity, and thermal
conductivity). They showed that beneath the ocean, thermal
boundary layer at the CMB is suppressed by the large-scale flow in
the highly-viscous lower mantle, whereas beneath the continental lid,
a thickened boundary layer developed at the CMB. The large-sized
upwelling plumes developed in the lower mantle are concentrated
beneath the continental lid. When the position of continental lid and
ocean is switched instantaneously during the simulation, the
upwelling plumes are concentrated beneath the newly-positioned
continental lid due to the mantle flow reorganization. This 2-D
numerical model suggests that there is a greater tendency that the
supercontinent enhances the longest-wavelength thermal structure
in the mantle.
During the amalgamation of continental fragments, the subducted
oceanic lithosphere of intervening oceans either moves down to the
deep mantle or is flattened, becoming stronger as stagnant slabs in the
mantle transition zone between ca. 410 and 660 km depth (Fukao et
al., 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 of
these stagnant slabs sink down into the deep mantle and accumulate
at the CMB. Zhao (2004) synthesized a P-wave tomographic image for
the Western Pacific region, along a transect covering Beijing to Tokyo,
where about 1200 km-long stagnant slabs are seen floating in the
mantle transition zone. The image shows the presence of a high Pwave velocity anomaly close to the bottom of the mantle and
immediately above the CMB which has been interpreted as a ‘slab
graveyard’ (Richards and Engebretson, 1992).
The recycled oceanic lithosphere at the CMB contributes potential
fuel for generating superplumes (Maruyama et al., 2007) which rise
from the core–mantle interface to the uppermost mantle, penetrating
the mantle transition zone and eventually giving rise to hot spot (e.g.,
Maruyama et al., 2007). Highly resolved seismic tomography models
clarify the configuration and amplitude of the velocity anomaly of two
superplumes beneath Southern Africa–Southern Atlantic Ocean and
Southern Pacific. For instance, Ritsema et al. (1999) observed that
beneath Southern Africa–Southern Atlantic Ocean the low-velocity
anomaly extends from the CMB into the upper mantle and has an
average velocity that is ~ 1% lower than normal mantle. Meanwhile,
Suetsugu et al. (2009) observed that beneath Southern Pacific, the
low-velocity anomaly extends 1000 km above CMB and has an
average velocity that is ~0.5% lower than normal mantle and smallscale low-velocity anomaly originating at the 1000 km-depth or
660 km phase boundary.
Multiple subduction zones promote the rapid amalgamation of
continental fragments into supercontinents and also act as major
zones of material flux into the deep mantle transporting substantial
volume of trench sediments and arc crust through sediment
subduction and tectonic erosion (e.g., Santosh et al., 2009; Yamamoto
et al., 2009; Santosh, 2010a). Due to buoyancy, the subducted TTG
material is stacked in the mid mantle region and may not sink down to
deeper levels.
5. Formation of degree-one mantle structure
With the advancement in numerical modeling techniques as well as
the enhancement in computational power and resource, it is now
possible to simulate the highly-resolved 3-D spherical-shell mantle
convection model with lateral variation of viscosity and realistic
rheology (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 of
supercontinents on the dynamics and structure of the mantle in 3-D
spherical-shell geometry (Yoshida et al., 1999; Phillips and Bunge, 2005;
Coltice et al., 2007; Phillips and Bunge, 2007; Zhong et al., 2007a;
Trubitsyn et al., 2008; Zhang et al., 2009; Yoshida, 2010b).
7
In general, a mantle convection planform with short-wavelength
structures and a large number of downwellings may not lead to the
assembly of supercontinents because continental blocks would be
trapped by different downwellings thus inhibiting collision. When the
continental blocks are smaller than the wavelength of mantle flow, it
takes a longer time for them to form the supercontinent (Phillips and
Bunge, 2007; Zhang et al., 2009) (see also Section 7 for the timescale
of supercontinent assembly). Thus, long-wavelength convection is
preferred for effective close packing of continental fragments into a
supercontinent assembly. Both Rodinia and Pangea are considered to
have been largely surrounded by subduction zones (Maruyama et al.,
2007) which suggests the presence of major downwellings and
upwellings, and leading to kinematic models of supercontinent cycles
which require mantle convection of very long-wavelengths at
spherical harmonic degree one or degree two (e.g., Monin, 1991;
Evans, 2003). The present-day mantle is predominated by degree-two
structures that include the seismically fast, cold anomalies around
Circum-Pacific and two large seismically slow, hot anomalies beneath
Africa and Pacific (Section 4), translated into one cold downwelling
zone and two hot upwelling zones (e.g., Maruyama et al., 2007).
A mantle convection model with a supercontinent in Earth-like 3D spherical-shell geometry was proposed for the first time by Yoshida
et al. (1999). They modeled the supercontinent as an elongated-diskshaped HVL with a thickness of 200 km, covering 30% of the total
surface, and imposed it on well-developed, isoviscous mantle
convection with the short-wavelength thermal heterogeneity. The
mantle is heated externally from the core and internally by radiogenic
elements. Their results show that the presence of a supercontinent
with the HVL produces large-scale horizontal mantle flow, thereby
reorganizing the thermal structure of the mantle interior. Large-scale
upwelling plumes arising from the CMB beneath the supercontinent
are observed and the thermal structure dominated by the spherical
harmonic degree of one (i.e., degree-one convection) develops in the
mantle (Yoshida et al., 1999; Yoshida, 2010b).
Fig. 4 illustrates a result of 3-D spherical-shell mantle convection
model with a rigid, spatially fixed HVL. The mantle is considered
realistic convection vigor and a temperature-dependent rheology. The
viscosity contrast between the HVL and surrounding mantle is fixed at
102. The result reveals that the very short-wavelength structure is
reorganized by a degree-one structure for ~ 500 Myr due to the
existence of the supercontinent. Yoshida (2010b) proposed that largescale upwelling plumes produce tensional stresses within the
supercontinent with a stress magnitude of the order of 10 MPa,
irrespective of model parameters studied here, which is comparable
to the strength of the Earth's continent, and thus may be responsible
for the subsequent continental rifting and breakup, as previously
suggested by the 2-D model of Lowman and Jarvis (1996).
It is quite important that the formation of degree-one convection
found in Yoshida et al. (1999) may be closely related to the periodicity
of supercontinent cycles. Phillips and Bunge (2005) have succeeded in
modeling the nondeformable HVL freely floating over the surface by a
torque balance method (i.e., calculating Euler poles through force
balance and applying repulsive forces to prevent overlap) with a 3-D
spherical-shell model and have reproduced the supercontinent cycles
in the limited geophysical situations. They demonstrated that degreeone convection that develops after the setup of the disk-shaped rigid
cap forms in cases for (1) convection models without a viscosity
increase at the 660 km phase boundary and purely basal heating (i.e.,
no radiogenic internal heating), and (2) convection models with a
viscosity increase at the 660 km. The broad, active upwelling plumes
due to the highly viscous lower mantle and strong heating from the
CMB might trigger the formation of the longest-wavelength thermal
structure in the mantle when the supercontinent is imposed. Such
upwelling plumes from the CMB have also been envisaged in recent
conceptual models (e.g., Maruyama et al., 2007). When degree-one
convection is established, the dispersing continental fragments
8
M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
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 and
purple 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 the
position 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). The
white sphere indicates the bottom of mantle (i.e., core–mantle boundary). The supercontinent is 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 viscous lithosphere) and hottest bottom surface
boundary (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 Earthlike timescale. The details of numerical methodology and model parameters are found in the work of Yoshida (2010b).
migrate towards the antipodal downwelling plumes and reassemble
to form a new supercontinent. A subsequent study by Phillips and
Bunge (2007) demonstrated that active upwelling plumes caused by
the significant basal heat flow from the core disrupt the periodicity of
supercontinental cycles. They suggest that the periodic supercontinent cycles are unlikely to occur in the history of Earth.
We note here that degree-one convection is observed when
supercontinent is not imposed in the mantle convection with
temperature-dependent rheology. The viscosity of mantle materials
strongly depends on the temperature, pressure, and composition,
among other parameters (e.g., Karato, 2008). It has been accepted that
mantle convection patterns with temperature-dependent rheology
are classified into three regimes from the 2-D convection studies
(Solomatov, 1995; Solomatov and Moresi, 1997). Recent advances on
computational techniques and resources facilitate the numerical
simulation of 3-D spherical mantle convection with strong temperature-dependence of viscosity (e.g., Yoshida and Kageyama, 2004;
McNamara and Zhong, 2005a; Roberts and Zhong, 2006; Yoshida and
Kageyama, 2006; Zhong et al., 2007a; Yoshida, 2008). Fig. 5a
illustrates a regime diagram for mantle convection with purely basal
heating (i.e., no internal heating rate) and with a linearized viscosity
form (i.e., η ∝ exp(ET), where η is the viscosity and E is the activation
energy that controls the degree of viscosity's temperature (T)dependence) (Yoshida and Kageyama, 2006).
The degree-one convection has been produced by some numerical
models that considered temperature-dependent rheologies. When
internal heating is included with moderately temperature-dependent
viscosity, degree-one convection occurs (McNamara and Zhong,
2005a). On the other hand, Yoshida and Kageyama (2006) have
shown that degree-one convection occurs even without internal
heating when temperature-dependence of the viscosity is moderately
strong. This degree-one convection pattern belongs to the ‘sluggishlid regime’ (Solomatov, 1993) or ‘transitional regime’ (Solomatov,
1995), in which the moderately highly viscous layer around the top
surface boundary slowly moves with less Rayleigh–Taylor instability
and eventually sinks into the mantle, and the resultant mantle
convection has longest-wavelength thermal structure. Considering
the Rayleigh number of the Earth's mantle and the viscosity contrast
between the lithosphere and underlying mantle, the Earth's mantle
presumably falls into sluggish-lid or ‘stagnant-lid’ regimes (orange
box in Fig. 4a). In the stagnant-lid regime, a deformable, immobile lid
develops near the surface boundary of mantle convection. In order to
let the surface plate-like motion, we need to impose the visco-plastic
rheology (see Section 12).
Degree-one convection is found in mantle convection with a more
realistic 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 internal
heating) (Yoshida, 2008) (Fig. 5b–c), and high internal heating
(McNamara and Zhong, 2005a) modes. Therefore there is a highly
possibility that degree-one convection is one of the basic structure of
mantle convection without the surface heterogeneities such as
continent and plate motions. However, as reported by Yoshida
(2008), it seems that the geophysically relevant degree-two convection with sheet-like downwellings (i.e., Circum-Pacific subduction
zone) and two upwelling plumes (i.e., superplumes) is not observed
in the mantle convection model with real convective vigor and
without the surface heterogeneities.
On the basis of a previous numerical result that a supercontinent
spends most of the time over the cold, downwelling mantle (Gurnis
and Zhong, 1991), Zhong et al. (2007a) considered in their 3-D
spherical model that the continental fragments migrate towards the
downwellings in degree-one mantle convection and settle into the
downwellings for a certain period of time. When a disk-shaped HVL is
imposed on well-organized degree-one convection, the oceanic
material begins to subduct at a margin of the HVL and downwellings
beneath the supercontinent eventually vanishes. Subsequently, new
upwelling plumes tend to originate at the CMB for a short timescale
(~50 Myr) and the degree-two thermal structure with old and new
upwellings develops in the mantle (see Zhong et al., 2007a for
details). Following their scenario, when the continental fragments
fully disperse on the Earth so that the mantle does not 'feel' the
existence of continents, the degree-two pattern may go back to
degree-one structure. However it has not been resolved yet whether
or not mantle convection is dominated by degree-one when plate
motions and continental drift continuously occur throughout out the
Earth's history. There is a possibility that the present-day degree-2
pattern is realized both by the history of plate motions and large-scale
thermochemical upwelling plumes (McNamara and Zhong, 2005b).
The thermochemical upwelling plumes or thermochemical piles
stratified in the deep lower mantle, reproduced in the mantle
convection model (Tackley, 1998; Kellogg et al., 1999; McNamara
M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
9
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-shell
models 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 (dashed
curve) 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 see
Yoshida and Kageyama (2006) and papers herein. Dashed line shows the approximate boundaries that separate the three convection regimes. An orange box indicates a parameter
range 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 and
104, 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 the
temperature 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 superplumes
beneath South Atlantic–South Africa and South Pacific regions
(Larson, 1991; Maruyama, 1994; Maruyama et al., 2007). The
thermochemical piles with abundance of radioactive elements
produces ‘superswells’ i.e., the broadly elevated topography at the
earth's surface (McNutt, 1998).
6. Long-wavelength thermal structure in the mantle
The longer thermal structures in the mantle may shorten the
period of supercontinent cycle, because continental blocks would
smoothly drift on the Earth's surface without being inhibited by
upwelling and downwelling plumes. Theoretical and numerical
studies on dynamics of planetary mantle convection demonstrate
that the effects of depth- or pressure-dependent properties such as
viscosity and thermal expansion coefficient (or thermal expansivity)
contribute to the predominance of the long-wavelength thermal
structure in the planetary mantle, because they reduce convective
vigor effectively (Schubert et al. (2001); Yuen et al. (2007)). Since the
mid-1990s, several numerical models of mantle convection within a
3-D geometry have investigated the effects of depth-dependent
viscosity 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 the
other hand, high pressure experiments of mantle rocks have recently
proposed a substantial decrease in the thermal expansion coefficient
with depth. Katsura et al. (2009) suggested on the basis of their
experiments that the thermal expansion coefficient of MgSiO3
perovskite generally decreases with increasing pressure and that
the Anderson–Grüneisen parameter (Anderson, 1967; Birch, 1968),
δT, of MgSiO3 perovskite is 6.5. As for the comparison of this δT with δT
derived from the previous high-pressure experiments for various
mantle rocks, see, for instance, Katsura et al. (2009) and Schubert et al.
(2001). The decrease in the thermal expansivity with pressure is
expected to reduce the buoyancy force of mantle convection in the
deep mantle. Furthermore, it is expected to offset the adiabatic
temperature gradient because the degree of adiabatic heating/cooling
is linearly proportional to the thermal expansivity (e.g., Jarvis and
McKenzie, 1980).
Here we attempt a simulation of the mantle convection models
with both the depth-dependent viscosity and thermal expansivity.
Fig. 6a and b shows the depth profiles of viscosity and thermal
expansivity, respectively, used in the simulation. The parameters used
here are V which controls the maximum viscosity contrast and δT
which controls the thermal expansivity contrast across the mantle.
We considered a viscosity profile with different viscosity contrast
10
M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
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 and
δT (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. The
cross 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 is
250 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 number
within 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 and
Yuen, 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 the
dissipation 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 internal
heating 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).
M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
across the mantle (Fig. 6a). The peak viscosity is assumed to be located
at the depth of 2000 km, in accordance with the results obtained by
the 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 viscosity
below depths of 2000 km, including at the hot thermal boundary
layer, decreases because of the temperature dependence of viscosity.
In the present study, we investigate the cases with V = 0, ln 30, and ln
100; the range of these values was selected on the basis of post-glacial
rebound analyses (e.g., Lambeck and Johnston, 1998; Peltier, 1998)
and geoid inversion studies (e.g., King, 1995). Meanwhile, as for the
thermal expansivity, we test the cases with both the ‘classical’ value of
δT = 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 expansivity
contrasts between the top and bottom surfaces are ~ 0.2 and ~ 0.04,
respectively (Fig. 6b).
The results of the numerical calculations for the nine cases
representing different combinations of V = 0, ln 30, ln 100 and
δT = 0, 3, and 6.5 are presented in Fig. 6c–n. For each case, calculations
were repeated until the output parameters such as root-mean square
velocity 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 short
wavelengths and numerous upwelling and downwelling plumes that
exist in the mantle after the statistically steady state was reached
(Fig. 6c and l). This well-developed convection pattern from the first
case was used as the starting scenario for the calculations for the other
eight cases.
We first focus on the effect of depth-dependent viscosity on the
convection pattern. Fig. 6c, d, and e shows the cases with V = 0, ln 30,
and ln 100, respectively, and a constant thermal expansivity. Even
when the highest viscosity contrast is imposed (i.e., V = ln 100), the
convection pattern shows a quite short wavelength thermal structure
(Fig. 6e). This convection pattern is quite different from those with a
viscosity profile with a step-increase of viscosity at 660 km and
without the gradual decrease of the viscosity below 2000-km depth
(Bunge et al., 1996; Zhong et al., 2000): The convection pattern shifts
to larger wavelengths and is re-organized into well-established
convection cells with stable large-sized upwelling plumes originating
at 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 that
the number of large-sized upwelling plumes is reduced with
increasing δT. When δT = 6.5 is considered (Fig. 6i and m), the
convection pattern drastically changes compared with the case where
δT = 3 (Fig. 6f). The convection pattern shifts to larger wavelengths
and is re-organized into well-established convection cells with two
stable 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 decrease
with increasing δT. The large-sized upwelling plumes are increased in
width by the effect of depth-dependent viscosity. We note that with
increasing δT, downwelling plumes tend to effectively ‘subduct’ into
the deep lower mantle. This implies that in the real Earth, the largely
reduced thermal expansivity with depth facilitates the subduction of
plates into the deep lower mantle and resultant large-scale flow
circulations in the whole mantle (e.g., van der Hilst et al., 1997) (for
instance, ‘M’ in Fig. 6m). Depth-dependent viscosity alone does not
produce such a large-scale mantle circulation, even when the largest
viscosity contrast is considered (Fig. 6e).
As stated in Section 5, the temperature-dependent viscosity also
leads to the long-wavelength structure because of reduced thermal
instability in the shallow part of the mantle (Fig. 5), while the depthdependent properties lead to a long-wavelength structure because of
the reduced thermal instability at the bottom of the mantle. There
11
may be some other factors that define the long-wavelength thermal
structure in the mantle. For instance, theoretical and numerical
analyses demonstrate that the low-viscosity asthenosphere (channel)
wedged between the highly viscous lithosphere and underlying
mantle 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 mantle
beneath the Hawaii (e.g., Wolfe et al., 2009) and Iceland (e.g.,
Bijwaard and Spakman, 1999) hotspots have been detected by seismic
tomography studies. However, in general, the origin of the Earth's
hotspot plumes remains a controversial issue in geodynamics. The
large-sized upwelling plumes observed in Fig. 6, which have been
quite steady during the geological timescale, may be one of the
important keys that could resolve the question regarding the origin of
the isolated plumes, regardless of whether convection in the deep
mantle is dominated by compositional driving force or not. The largely
reduced thermal expansivity in the deep mantle may allow the
thermo-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 and
δT = 6.5 (Fig. 6i and n) is similar to the Earth's convection pattern
characterized by two large-scale upwellings like Earth's superplumes
beneath the South Pacific and South Atlantic–South Africa and one
‘great-circle’-downwelling in the Circum-Pacific, even when the
mantle convection studied here is purely dominated by the thermal
buoyancy. It seems that such great-circle-downwelling is also
observed in the models with relatively weak temperature-dependent
viscosity and relatively low yield stress (van Heck and Tackley, 2008;
Yoshida, 2008). The planetary-scale, long downwelling like the
Circum-Pacific subduction zone are selfconsistently reproduced by
the mantle convection model even with more realistic geophysical
conditions (see Section 12).
7. Timescale of the supercontinent assembly
Although it is well established that supercontinent cycles operated
throughout the Earth history, the timescales of their assembly and
dispersal are not well-constrained. A stable configuration is hypothesized for Columbia between 1800 and 1500 Ma (Meert, 2002) which
assigns a time gap of 450–500 Myr prior between the breakup of
Columbia and the assembly of Rodinia. On the other hand, if we take
into consideration the hypothetical supercontinent Pannotia at ca.
600 Ma (Dalziel, 1991), it leaves only 150 Myr between the birth of
this supercontinent and the demise of Rodinia and 300 Myr before the
formation of the subsequent supercontinent Pangea. Senshu et al.
(2009) evaluated the history of supercontinents based on a number of
parameters such as the surface configuration based on paleogeographic reconstructions, super downwelling events as suggested by
the rapid amalgamation of the majority of continents, and mantle
dynamics. These parameters predict that the only supercontinent that
was assembled within a short period of time was the Paleoproterozoic
supercontinent Columbia. Although Gondwana and Pangea assemblies do not tally with this predicted model in Senshu et al. (2009) and
were therefore considered together by these authors, these assemblies have distinct mountain building events and clearly represent
two different supercontinental assemblies. In a speculative model,
Senshu et al. (2009) suggested that the precise time when a younger
true supercontinent might have existed in terms of mantle dynamics
is around 340 Ma. According to their model, the lifespan of supercontinents becomes longer in the younger Earth, a phenomenon
assigned to a decrease in the rate of heat generation of the subducted
TTG materials with time. However, this model requires further
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M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
evaluation as there is more subduction erosion with time, and this
factor outweighs the decreasing heat production.
Numerical models with mobile continents/supercontinents can
address the timescale of the assembly of supercontinents. Phillips and
Bunge (2007) demonstrated that using a 3-D spherical-shell model
with isoviscous mantle, three pieces of continental fragments whose
size broadly corresponds to 10% of the whole surface of the globe, tend
to assemble for an interval of 300–500 Myr, which is comparable to or
shorter than the actual supercontinental cycles, 500–700 Myr (e.g.,
Silver and Behn, 2008). Zhang et al. (2009) demonstrated that using a
3-D spherical-shell model with temperature-dependent rheology and
deformable continents, continents assemble to form a supercontinent
for ~ 250–650 Myr that depends on the wavelength of mantle
structure. This timescale also seems to be comparable to or shorter
than the actual supercontinental cycles.
Because the timescales obtained from numerical simulation
models depend on model parameters that control flow speed (in
particular, rheological parameters), it is difficult for us to precisely
compare the timescales of the assembly of supercontinents obtained
by different numerical models with the actual supercontinent cycles.
However, the regularity of the assembly of supercontinents can be
resolved by the numerical simulation. One of the outstanding
problems in this context is that the effects of the size of supercontinent on the behavior of mantle convection and supercontinent
cycles. Phillips and Bunge (2007) have shown that when six
continental fragments whose size is 5% of the whole surface of the
Earth are considered, a much larger time interval (~ 1500 Myr) is
required to form the supercontinent. This implies that the size of
supercontinents/continental fragments significantly affects the timescale of supercontinent cycles.
There is a possibility that the timescale of supercontinent cycles
may be closely related to the timescale of generation of strong
upwelling plumes from the deep mantle. Previous numerical
simulation models suggest that the timescale of the plume generation
and resulting mantle reorganization is much shorter than that of the
actual supercontinent cycle. Yoshida et al. (1999) and Honda et al.
(2000) have concluded that using an isoviscous mantle model, welldeveloped upwelling plumes originate from the CMB beneath the
highly viscous supercontinent over a timescale of 200–400 Myr when
real convection vigor is considered in the model. This timescale may
be shorter than the actual supercontinent cycles. However, if this
timescale is rescaled by the Earth timescale using a typical speed of
motion of Earth's plates, the duration may be further shortened by a
factor of two or three, that is, ~ 50–100 Myr. On the other hand, Zhong
et al. (2007a) concluded that using a temperature- and depthdependent viscosity model, the transition from degree-one convection to degree-two convection is observed with a timescale of
~ 50 Myr. This implies that mantle reorganization may occur within
a short time after a supercontinent is assembled.
8. Supercontinent breakup
A related topic of ongoing discussion is whether the initiation of
continental breakup is caused by active rifting initiated by mantle
plumes originating in the deep mantle (e.g., Morgan, 1983; Richards
et al., 1989, 1991; Storey, 1995; Dalziel et al., 2000; Condie, 2004), by
passive rifting associated with a pre-existing weak zone (e.g., Ruppel,
1995) or by a combination of both these phenomena. Some geological
evidence does not support a plume origin for the breakup of Pangea
(e.g., McBride, 1991; McHone, 2000). Coltice et al. (2007) tested the
hypothesis that the assembly of supercontinents would force a largescale thermal structure and therefore drive the underlying mantle to
higher temperatures by using a numerical model. The position of the
continents was fixed and an equilibrium temperature field was
computed by stacking the temperature fields over several billion years
in order to obtain a statistical steady state. Their results show that the
sub-continental lithospheric mantle temperature correlates inversely
with the number of continents. Thus, with a single supercontinent, the
convection planform is dominated by spherical harmonic degree one
and the temperatures are 100 K higher than those with dispersed
continents. Even when the convective parameters were changed, the
large temperature excursion observed in the supercontinent configuration is maintained. The convection modeling in an internally
heated mantle by Coltice et al. (2007) led them to conclude that the
assembly of continents into supercontinents would naturally lead to
‘global mantle warming’ without the involvement of hot active
plumes. However, this model is considered as one of the two end
member models to explain the formation of continental flood basalts
that occur over a supercontinent which are characterized by wide and
diffusive magmatism and a lower rate of magma supply. The other
end member model relates to plume-derived continental flood basalts
that are characterized by a very brief and high rate of magma supply
over a restricted and radiating area followed by continuous hotspot
activity.
A robust example for plume-related mafic magmatism which
ultimately broke-up the globe's first coherent supercontinent (Columbia) has been evaluated by Hou et al. (2008). They synthesized
data on the 1.3–1.2 Ga fan-shaped Mackenzie dyke swarm and other
similar aged dyke swarms in the Canadian Shield which constitute the
sub-swarms of a Late Mesoproterozoic giant radiating dyke swarm.
These dyke swarms also correlate with the Late Mesoproterozoic
mafic dyke swarms in Australia and East Antarctica which constitute
additional sub-swarms of the giant radiating dyke swarm. Hou et al.
(2008) proposed a Late Mesoproterozoic mantle plume at the focal
area of the giant radiating dyke swarm between North America and
the landmass comprising West Australia–East Antarctica (see also,
Ernst and Buchan, 2003). They suggested that this mantle plume
triggered the continuous extension at ca. 1.3–1.2 Ga and voluminous
mafic magma emplacement, which extended into much of the
Columbia supercontinent, and led to its final fragmentation. It must
be noted that rifts started developing in the Columbia assembly
immediately after its amalgamation as indicated by the emplacement
of several suits of mafic dykes in various constituent fragments of this
Paleoproterozoic supercontinent (Rogers and Santosh, 2009). A
protracted event of mafic magmatism during the Paleoproterozoic
and early Mesoproterozoic recorded from this continental assembly
would probably relate to a global mantle warming process, as
envisaged in the model of Coltice et al. (2007). However, the ultimate
fragmentation of the supercontinent in the latest Mesoproterozoic
probably involved plume-related activity as indicated by the
formation of radiating giant dyke swarms and voluminous mafic
magmatism. The fragmentation history of Columbia might thus
represent a combination of prolonged global warming and incipient
rifting culminating in a plume-triggered final fragmentation. We
therefore propose that the two end member models of supercontinent
break-up (global mantle warming and plume activity) might have
operated in conjunction in the case of at least some of the
supercontinents in Earth history.
A specific case of supercontinent break-up was evaluated by Storey
(1995) with regard to the disintegration of the Gondwana supercontinent which started at about 180 Ma ago. The magmatic and tectonic
signatures along the proto-Pacific margin of Gondwana record
important changes in subduction zone forces during its initial
fragmentation. The absence of subduction along the Neotethyan
margin of Gondwana, together with the observation that initial rift
formed at right angles to the active subduction margin as demonstrated by Storey (1995) suggest a potential active role for mantle
plumes in the initial separation of the East and West blocks of the
supercontinent. The initial plume-related magmatism is represented
by the ca. 182 Ma Karoo province and the final breakup is constrained
at ca. 156 Ma. The large extent of magmatic provinces also suggests
that the Gondwana supercontinent was underlain by a broad shallow
M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
region of higher temperature, rather than a single plume. Although
not considered as a mantle plume, this anomaly is broadly similar to
the thermal blanket effect (Anderson, 1982, 1994). Storey (1995)
concluded that either a plume point source or a regional heat anomaly
could have weakened the Gondwana lithosphere leading to the high
magma production rates and local rifting leading to the fragmentation
of the supercontinent into the East and West Gondwana blocks. In
summary, the role of plumes in initiating the disintegration of
supercontinents is emphasized in the case of Gondwana also. Similar
models involving the role of mantle plumes have also been proposed
for 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 life
history of the planet.
9. Stability and longevity of the continent
Based on information from heat flow, geochemistry and the
relative delay times of seismic waves in different settings, Jordan
(1975) proposed the ‘tectosphere’ (highly depleted relatively low
density upper mantle layer) model, in which a zone moves with the
motion of the plate lying beneath the old continental shields and is
expected to be up to 400 km thick. The depth to which the
tectospheric mantle extends is still a hotly debated topic, although
most tomographic images of the cratons show high velocity roots
13
extending to at least 200 km depth, and in some cases to depths
greater than 300 km (Grand, 2002; Gung et al., 2003; Romanowicz,
2009) (Fig. 7). The tectosphere, also known as continental keel or
cratonic root, is thus a rigid, cold and chemically distinct raft that
supports the continental crust (Jordan, 1988) and occurs only beneath
old cratons. With time, this keel is extensively eroded by younger
magmatic and subduction-erosion processes as in the case of the
North China Craton (Kusky et al., 2007; Santosh, 2010a).
The longevity of the continental root in the geological timescale is
closely related to the rheological properties (i.e., viscosity and strainrate of materials) not only of the continental root itself but also of the
surrounding mantle. As the viscosity contrast between the continental
root and oceanic upper mantle (including low-viscosity asthenosphere) is larger, it takes longer time for the continental root to cause
Rayleigh–Taylor instability (at the bottom of the keel) or convective
erosion (mainly at the subduction zone) and to be involved into the
surrounding mantle. It has been accepted that the continental root is
depleted in volatile elements due to a high degree of partial melting in
which case it is dehydrated, and has high viscosity (Pollack, 1986;
Karato, 2008, 2010b). However, considering the plausible values of
the degree of water content and activation volume of dry olivine, the
viscosity of continental roots is likely to be no more than the order of
1021 Pa s, even when the combined effects of differences in temperature and water content on the viscosity are considered (Karato,
2010b). The viscosity of continental roots may be two or three orders
Fig. 7. Distribution of tectosphere defined by S-wave tomography (Grand, 2002). Note the selective occurrence of high velocity anomaly under cratons older than 2.0 Ga and
downward thinning of tectosphere. Maximum depths are about 300 km. The continental crust is only about one tenth of the continental keel.
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M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
larger than that of the surrounding asthenosphere with orders of
1018–1019 Pa s, on the basis of postglacial rebound analyses (e.g., Bills
and May, 1987; Okuno and Nakada, 2001) and tectonic observations
(e.g., Gordon, 2000). The resultant viscosity contrast between
continental root and the surrounding mantle is, therefore, 102–103,
and the assumption of continents as highly viscous bodies made in the
numerical models discussed above seems reasonable. In a recent
study based on the Kaapval craton of southern Africa, Peslier et al.
(2010) concluded that the deep roots of cratons are protected by a
layer of unusually dry minerals, and provide sufficient viscosity
contrast with underlying asthenosphere.
Geochemical studies have revealed that the continental lithospheres (or cratonic root) beneath some of the old cratons have
survived for periods more than 3 billion years in spite of later tectonic
disturbance (Carlson et al., 2005). However, the numerical model
with HVL described in the previous section cannot address the
mechanism for stability and longevity of the cratonic lithosphere,
because the model supercontinent does not deform by the convection
force with time. In contrast, in some numerical studies, a continent is
modeled as a highly viscous, compositionally buoyant fluid in a 2D
Cartesian model (e.g., Doin et al., 1997; Lenardic and Moresi, 1999;
Shapiro et al., 1999; Lenardic et al., 2003). One of their significant
observations is that continental roots must be 1000 times as viscous as
the surrounding mantle in order to stabilize the roots with
compositionally buoyant materials over geological timescales (Doin
et al., 1997; Lenardic and Moresi, 1999). This viscosity contrast is in
the range of that obtained by the mineral physics described above.
Lenardic et al. (2003) presented a 2-D numerical model with three
chemically distinct materials: continental crust, continental mantle
lithosphere and bulk mantle. The visco-plastic rheology is imposed in
the oceanic lithosphere to realize the plate boundary and plate
motion. They concluded that a high yield stress for cratonic
lithosphere relative to the oceanic lithosphere is found to be an
effective and robust means for providing tectonic stability of cratonic
crust and the relative longevity of deep cratonic lithosphere. They also
suggested that the degree of yield stress variations between cratonic
and oceanic lithosphere required for the stability and longevity can be
decreased if cratons are bordered by continental lithosphere that has a
relatively low yield stress (i.e., mobile belt). This means that the
mobile belts protect cratons from being deformed for certain periods
of geologic timescale.
The longevity of cratonic lithosphere has not been investigated by
a 3-D numerical model so far. Yoshida (2010a) demonstrated for the
first time that using a 3-D spherical-shell model, the deformable and
mobile continental lithosphere is stable only for b1 billion years, that
is, the continental materials tend to gradually merge into the oceanic
plates and underlying mantle with time, when the viscosity contrast
between cratonic lithosphere and surrounding oceanic plates is 102
(see Section 11 for details of this result). However, their previous
model (Lenardic et al., 2003; Yoshida, 2010a) did not consider the
origin and growth of continental crust.
10. Origin and growth of the continental crust
Continental growth occurs predominantly through the addition of
juvenile crust by arc magmas (e.g., Rapp and Watson, 1995; Nair and
Chacko, 2008; Windley and Garde, 2009). In the early history of the
Earth, the parallel collision of intra-oceanic arcs was an important
process to build embryonic continents (e.g., Santosh et al., 2009;
Windley and Garde, 2009). Recent studies from Archean terranes in
different parts of the world have offered important clues for the
process of amalgamation of composite arcs (Komiya et al., 2002,
Santosh et al., 2009 and references therein). A modern analogue for
the Archean process is the western Pacific domain where 60–70% of
island arcs are concentrated in the oceanic domain. Archean TTG
magmatic suites represent the oldest coherent pieces of felsic
continental crust. In a recent study, Nair and Chacko (2008) presented
results from long-duration dehydration melting experiments which
suggest melting depths of N48 km. This result is consistent with the
early crustal evolution models which propose melting at the base of
oceanic crust or oceanic plateaus to explain the origin of early Archean
continental crust. Under the high Archean geothermal gradient, the
subducted oceanic crust would melt to produce TTG. The model
proposed by Nair and Chacko (2008) differs from earlier models of
subduction initiation in that the subduction of oceanic lithosphere
occurs through the protomantle lithosphere at the base of the newly
formed oceanic plateau crust. Their model can thus effectively explain
the origin of subduction systems, TTG, TTG-mafic and/or ultramafic
magma association, stabilization of continental crust and the broadly
coeval formation of cratons and their lithospheric roots.
It is now generally understood that plate tectonics not only creates
but also destroys Earth's continental crust, both occurring mostly at
subduction zones, the former by arc magmatic creation and the latter
by subduction removal (Stern, 2008; Stern and Scholl, 2010) (Fig. 8).
Since subduction zones are the only major routes through which
material is returned to great depths within the Earth, the mass flux
through convergent plate margins has received considerable attention in recent studies particularly to evaluate the origin and growth of
the continental crust. Clift and Vannucchi (2004) classified convergent plate margins into those showing long-term landward retreat of
the trench and those dominated by accretion of sediments from the
subducting plate. They proposed that tectonic erosion is favored in
regions where convergence rates exceed 6 ± 0.1 cm yr− 1 and where
the sedimentary cover is less than 1 km. In regions of slow
convergence (b 7.6 cm yr− 1) and/or trench sediment thickness
exceed 1 km, preferential accretion occurs. Large volumes of continental crust are subducted at both erosive and accretionary margins.
At present, creation and destruction of continental crust are either
in balance (ca. 3.2 km3 yr− 1) or more crust is being destroyed than
created. The creation–destruction balance changes over a supercontinent cycle, with crustal growth being greatest during supercontinent
break-up due to high magmatic flux at new arcs and crustal
destruction being greatest during supercontinent amalgamation due
to subduction of continental material and increased sediment flux due
to orogenic uplift (Stern and Scholl, 2010). Ongoing subduction
erosion also occurs at the leading edges of dispersing plates, which
also contributes to crustal destruction, although this is only a
temporary process. The widely held view that the volume of
continental crust has increased over time through plate tectonic
activity (e.g., Hurley and Rand, 1969) has thus been challenged, with
the possibility that the volume has in fact decreased.
The mechanism of crust production and growth should be
incorporated in a future numerical model in order to test the concept
that plate tectonics creates and destroys continental crust with time,
and also to evaluate whether more volume of crust is being destroyed
than that is being created as suggested in some recent works
discussed above. Such a study can also test whether the geologically
suggested episodic emergence of supercontinents is realized in the
numerical model. The thermal effect of accumulation of continental
crust with compositionally buoyant materials on mantle convection
has been previously evaluated in a series of papers (Lenardic and
Kaula, 1994, 1995, 1996; Lenardic, 1997; Moresi and Lenardic, 1997;
Lenardic, 1998; Moresi and Lenardic, 1999). Convective overturn of
the mantle causes chemically light crust to thicken above the mantle
downwelling and surface heat flux above the thick crust is lower than
that above the mantle (Lenardic and Kaula, 1995). A number of such
studies are carefully reviewed in Schubert et al. (2001).
Walzer and Hendel (2008) performed simulations of mantle
convection with the growth of a continent using a 3-D spherical-shell
model with real convective vigor (i.e., Rayleigh number), temperature- and pressure dependent rheologies, and viscoplastic yield stress
(i.e., maximum of rupture strength) of the lithosphere to induce the
M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
15
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 not
artificially imposed on the convection model in contrast to models
discussed in previous sections and temporally evolved with mantle
convection by considering the chemical differentiation and redistribution of incompatible elements, U, Th, and K. The distribution of
radiogenic elements in the mantle is represented by the tracer
particles. In their model, chemical differentiation generates the
depleted MORB mantle from the primordial mantle, if the conditions
for partial melting are fulfilled, and a large amount of the
differentiated primordial mantle is assumed to produce the new
continental crust with higher abundances of incompatible elements
(see, Walzer and Hendel, 2008, for the details of methodology). With a
wide range of parameter space for convective vigor and yield stress of
the lithosphere, their result supports evidence that continental crust
has grown progressively with time in an episodic manner (Condie,
1998). However, the creation–destruction balance of continental crust
is not presented in their work. Despite this, among mantle convection
models proposed so far, this work has produced the first realistic
distributions of continents.
11. A preliminary Wilson Cycle model
A 3-D mantle convection model with mobile and deformable
continents and visco-plastic oceanic plates has not been proposed so
far, primarily because of the difficulty to accurately solve the
advection of a chemically distinct body (i.e., continent/supercontinent) without numerical diffusion (i.e., artifact diffusion). In particular, serious hurdles remained for simulations that attempted tectonic
processes occurring over geological timescales. Overcoming this
difficulty, Yoshida (2010a) has recently presented a new numerical
model of mantle convection with a deformable, mobile continental
lithosphere within 3-D regional spherical-shell geometry (Fig. 9). In
this preliminary model, a supercontinent is instantaneously imposed
on well-developed mantle convection. The supercontinent has a
spherical-square-shaped cratonic lithosphere with a uniform thickness of 250 km (dark orange regions in Fig. 9), which is comparable to
the tectosphere thickness inferred from seismological analysis and
geodynamic evidence (Section 9). It covers ~ 30% of the total surface
area of the model domain, and is initially separated into four pieces by
the weak (low-viscosity) continental margins (WCMs; light orange
regions in Fig. 9). In order to ensure the conservation of the
continental materials, a process of advection with approximately
zero chemical diffusion is solved by a kind of tracer particle method
(e.g., Christensen and Hofmann, 1994). A viscosity increase due to the
660-km phase transition is assumed to be 30 on the basis of the results
of postglacial rebound analyses (Mitrovica and Forte, 1997; Lambeck
and Johnston, 1998; Peltier, 1998). The maximum viscosity contrast
between the continents and the oceanic lithosphere is 102 at the top
surface boundary, which is within the range predicted from
rheological experiments for dehydrated continental root materials
relative to a reference mantle (Hirth and Kohlstedt, 1996; Karato,
2010b; Peslier et al., 2010) (Section 9). The viscosity contrast between
the cratonic lithosphere and the WCM is fixed at ~ 101.5. The viscoplastic oceanic lithosphere and the associated subduction of oceanic
plates are incorporated in this model.
Earth-like continental drift and the characteristic thermal interaction between the mantle and a continent are observed in this
preliminary numerical model (Fig. 9). By ca. 100 Myr, the supercontinent begins to break up because of the tensional stress induced by
mantle upwelling, deforms with time because of the surrounding
convecting force, and gradually moves towards a side boundary of the
model domain (note that in this model, the continents reaching the
lateral boundary of the model domain appear at the opposite lateral
boundary due to the periodic boundary condition). Fig. 10 illustrates
an early stage of the composition-field (representing 1 for continental
material and 0 for oceanic material) and the corresponding temperature anomaly (i.e., the deviation from horizontally averaged
temperature at the same depth) δT at a shallower mantle (depth of
358 km) to observe the thermal insulating effect. The regional
upwelling plumes with high buoyancy and maximum temperature
anomaly of ≥+300 K originating from the CMB are remnants of the
initial thermal condition (indicated by arrows ‘A’ in Fig. 10), while
broad hot regions with a temperature anomaly of approximately
+100 K (‘B’ in Fig. 10) are due to the thermal insulating effect by the
existence of a supercontinent and the radioactive elements in the
mantle. The beginning of the continental breakup is likely to be
mainly responsible for the tensional force of these broad hot regions.
The tensional force generated by upwelling plumes may additionally
help the continental rift and breakup. The temperature anomaly of
+100 K generated by the thermal insulating effect observed here is
consistent with that proposed by Anderson (1982).
Fig. 9 shows that by ca. 150 Myr, Continent-A (or Continent-B) is
completely separate from Continent-C (or Continent-D), while
Continent-A relatively stays with Continent-B. All the continents
seem to maintain their positions around the lateral boundary of the
convection domain, as observed from the snapshots at 237 Myr. By
the time the large-scale upwelling plumes in the center of the
convection domain become weak by ca. 237 Myr, pieces of continent
tend 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
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M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
Fig. 9. Time sequence of mantle convection with deformable, mobile continents. The computational domain of mantle convection is confined to three-dimensional regional
spherical-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 and
purple 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 orange
isosurfaces 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 the
four continental fragments (named ‘A’ to ‘D’), surrounding by the weak (low-viscosity) continental margins (WCM) (light orange), and it instantaneously imposed on the welldeveloped mantle convection with temperature-dependent rheology. The viscosity contrast between the coldest upper surface boundary (i.e., uppermost part of high viscous
lithosphere) 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 methodology
and model parameters are found in the work of Yoshida (2010a).
seen from a snapshot at 322 Myr. And eventually, Continent-B and
Continent-D collide with each other by 375 Myr. A series of these
behaviors may mimic a Wilson Cycle, self-consistently reproduced by
the numerical model. Paleographic reconstruction models show that
the continental drift from the Rodinia supercontinent formed at
~ 900 Ma to the Pangea supercontinent formed at ~ 350 Ma is likely to
occur on the hemispheric scale of the Earth's surface, not the
planetary-scale, through the introversion process (Murphy and
Nance, 2003, 2005) or A-type ocean closure (Silver and Behn, 2008)
(Section 2). Thus, this mimicked Wilson Cycle observed in the
regional spherical-shell geometry may be relevant to the real Wilson
Cycle. Continental splitting and thinning, i.e., rift valley formation, that
occur in the first stage of the Wilson Cycle are also observed in this
model because the model allows a continent to laterally and radially
deform with the driving force of mantle convection. A continental
collision, the final stage of the Wilson Cycle, is observed after about
~ 375 Myr, which is broadly similar to the timescales for the actual
Wilson Cycles as inferred from geological criteria (Section 1).
This model presented here would represent an important step
towards formulating a more realistic model that could be used to
address many outstanding problems about the thermal and mechanical feedbacks between the mantle and continents, the cycle of
continental breakup and collision, the duration of a supercontinent,
the mechanism of continental drift, and the temporal evolution of the
Earth'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 present model (Figs. 9 and 10), because this model
allows a continent to laterally and radially deform with the driving
force of mantle convection. However this model used a relatively
simple rheology especially for the continental materials, and the
result does not answer the question of how supercontinents break
apart, because the weak zones are imposed a priori in a model
supercontinent (i.e., no yield mechanism in the continent). Nevertheless, among the 3-D models proposed so far, this model has the
largest potential to explain the Wilson Cycles documented from
geological and geochronological data.
12. Continents and plate tectonics
The upwelling and downwelling plumes, plate tectonics, and
continental drift are a part of the convecting system in the mantle. It is
considered that the flow scale that characterizes the upwelling
plumes is independent from the one that is characterized by plate
subduction. As stated in Section 1, the Earth's mantle structure has
different scale of downwellings (i.e., planetary-scale subduction of
plate) and upwellings (i.e., multi-scale upwelling plumes). In
particular, if the heat from the core is significantly small compared
with the heat production by radiogenic elements of mantle rocks
(Davies, 1988; Sleep, 1990), mantle plumes define only the secondary
flow compared to the main flow determined by the plate tectonics
(Davies, 1988, 1999), and therefore do not impart significant
influence on the global-scale plate motion. The formation and rapid
M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
17
Fig. 10. Early stage of the time evolution of mantle convection with supercontinents. The composition field (left panels) and the corresponding temperature anomaly δT (right
panels) 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 the
composition 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 regions
caused by the thermal insulating effect.
expansion of the Pacific and Indian oceanic plates in the Cretaceous
took place in the broadly low-velocity regions because they have not
been cooled or displaced by cold oceanic lithosphere for more than
200 Myr, and mantle plumes are not required to explain such a plate
formation and expansion (Anderson, 1994).
In contrast to the nearly independent relation between plates and
mantle plumes, the behavior of mantle plumes is closely linked with
the continental aggregation and breakup as stated in Section 8.
However, the mechanical interaction between continent/supercontinent and moving/subduction plates has been poorly understood in
geodynamics. Because continental fragments drift in accordance with
plate motions on the Earth, there should be a mechanical coupling
between continental drift and plate motions throughout the Earth's
history. Although the preliminary study by Yoshida (2010a) discussed
in Section 11 has considered the aspects of both mobile continents
and oceanic plates in numerical models, it is still one of the major
challenges in numerical studies of mantle convection to selfconsistently reproduce moving plates in 3-D space (e.g., Bercovici et
al., 2000). This is because the mechanisms for the generation of
narrow plate boundary and the associated plate motion are not
adequately clear in geodynamics (e.g., Bercovici, 1996, 1998;
Bercovici et al., 2000).
There is a high possibility that chemical and rheological heterogeneities due to moving plates, as well as drifting continent/supercontinent (Sections 4–5), give rise to the long-wavelength structure in the
3-D spherical mantle. Fig. 11 shows the results of mantle convection
with the oceanic plates but without continents/supercontinent. The
highly viscous oceanic lithosphere is damaged by imposing a yield stress
18
M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
(i.e., maximum limit of strength of oceanic lithosphere), which was
often used for the previous 2-D and 3-D mantle convection models (e.g.,
Moresi and Solomatov, 1998; Trompert and Hansen, 1998a). When the
yield stress is small, the oceanic lithosphere is highly damaged. When it
is large, the oceanic lithosphere is not substantially damaged (left panels
of Fig. 11). The plate-like behavior is obtained in a moderate yield stress
of around τy = 100 MPa (Tackley, 2000b; Richards et al., 2001; van Heck
and Tackley, 2008; Walzer and Hendel, 2008; Yoshida, 2008; Foley and
M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
Becker, 2009), which is almost determined by the convection stress.
When the yield stress is 100–125 MPa, narrow divergence and
convergence zones coexist in the lithosphere, and both of them are
comparable to the ‘spreading center’ and ‘trench’ of the Earth,
respectively. The Y-shaped subduction zone observed in the western
Pacific regions of the present-day Earth is also reproduced (see red
arrow in the map with τy = 100 MPa). Broadly deformed regions with
low-viscosity (for instance, ‘D’ in the map with τy = 100 MPa) may
correspond to the ‘diffuse plate boundary’ of the Earth's lithosphere
(Gordon and Stein, 1992; Gordon, 1998, 2000; Zatman et al., 2005). The
Earth's continental and oceanic plates are not uniformly rigid, in
contrast with the theory of plate tectonics that can be attributed to the
near rigidity of plates and narrow plate boundaries (Wilson, 1966;
McKenzie and Parker, 1967; Le Pichon, 1968; Morgan, 1968) and the
previous 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-wavelength
thermal structure organized by subducting ‘oceanic plates,’ when
the value of yield stress is moderate, 100–125 MPa (right panels of
Fig. 11). The results indicate that the subduction zones surrounding
the margins of the past supercontinents since the Palaeozoic era (i.e.,
Gondwana and Pangaea), as seen in some paleographic reconstructions (e.g., Collins, 2003), may be an inherent characteristic of mantle
convection only with thermally induced driving force, that is, without
any chemical heterogeneity like the compositionally distinct continent/supercontinent. The interplay between plate motions and
continental assembly–dispersal in the evolving mantle is not clear
in the numerical study at present. Future simulation studies should
focus on mantle convection models which take into account both the
continents/supercontinents and plate-tectonic motions.
A possible mechanical coupling between supercontinent cycle and
plate tectonics throughout the Earth's history is proposed with a
conceptual model by Silver and Behn (2008) (Section 2). They
hypothesized that drastic reductions or temporary cessations of plate
subduction (‘intermittent plate tectonics’) have occurred in situations
where a supercontinent forms primarily by external ocean closing and
the dispersing continental fragments assemble in the antipode of the
Earth. Namely, plate tectonics temporarily stops in the process of
continental assembly because all the subduction of the plates
diminishes at the continental margins. This external ocean closure
primarily occurred to form the supercontinent Rodinia at 900 Ma and
Pannotia at 650 Ma (Silver and Behn, 2008). However, in contrast to
their conceptual model, there may be a possibility that plate tectonics
temporarily stops by a change in the stress magnitude in the oceanic
lithosphere (i.e., lithospheric strength) in the process of the
mechanical interaction between drifting continent/supercontinent
and moving oceanic plates, because plate-like motion may occur in a
narrow range of the yield stress as shown in Fig. 11.
13. Next supercontinent
The formation of the future supercontinent is of broad interest not
only for earth scientists but also for the larger audience who are
interested in the future shape of the Earth. The name ‘Amasia’ has
19
been proposed for the next supercontinent (Hoffman, 1992). The
North American and Asiatic plates already fused along a zone of
uncertain nature through eastern Asia, and it is possible that the next
supercontinent will develop as more of the present continents collide
around the Asia–North America nucleus (Rogers and Santosh, 2004).
Part of this fusion might result from further accretion of Gondwana
blocks to southern Asia, perhaps by closure of the Indian Ocean. If
South America and Antarctica moved in a pattern that would accrete
them to Asia in about 500 Myr, then the next supercontinent would
reach its maximum packing at the same time in the cycle as previous
supercontinents. It has also been proposed that if modern subduction
in the Caribbean and Scotia arcs spreads along the Atlantic seaboard,
then convergence and destruction of the Atlantic Ocean would result
in a supercontinent termed as ‘Pangea Ultima’ (Scotese, 2000) that
would form by introversion (Murphy et al., 2009).
Maruyama et al. (2007) proposed a conceptual model which
argues that the Western Pacific Triangular Zone (WPTZ) is a potential
candidate for the frontier of a future supercontinent (Fig. 12).
According to these authors, the presence of a double-sided subduction
zone in this region where the Pacific plate subducts under the WPTZ,
and the Indo-Australian plate subducts and collides locally against the
WPTZ would promote the assembly of continental fragments. This
concept was further elaborated recently by Santosh et al. (2009)
where they identified two major categories of subduction zones on
the globe based on Y-shaped trip junctions, termed as the CircumPacific Tethyan subduction zones (Section 3). The Circum-Pacific
subduction zone covers a length of over 20,000 to 30,000 km, and the
remaining 10,000 km zone lies within the northern margin of the
Indo-Australian plate starting from the junction of the Pacific
subduction zone to the East in New Zealand to Fiji region. The zone
continues to the west through Indonesia, Himalaya and Middle East
to the Mediterranean through Turkey and is finally connected to the
Mid Atlantic Ridge. The Tethyan subduction zone broadly covers the
zone along the northern margin of India and the Tethyan Ocean. The
past 200 million year history along this zone shows a series of
continent collision leading to the growth of Eurasia (cf. Metcalfe,
2006, in press), and must have also witnessed the subduction of
substantial volume of oceanic lithosphere. Along the eastern margin
of the Y-shaped subduction zone running from Kamchatka down to
New Zealand, the passive subduction of Pacific oceanic lithosphere is
speculated to continue, leading to the consumption of the oceanic
lithosphere deep in the mantle off North and South America. The
trench will then migrate to the west leading to a reduction in the size
of the Pacific Ocean with time. According this model, in another
250 Myr, the Pacific Ocean might vanish from the globe leading to the
assembly of Asia with the amalgam of North and South America.
Although the fate of Antarctica is not known, presumably this
continent will also join the amalgam in course of time through the
propagating westward trench along the northern margin of
Antarctica. Thus, the assembly of the future supercontinent Amasia
will be finally completed through Pacific ocean closure and
extroversion. However, this model faces the problem that the Pacific
superplume is situated in between. Also, alternate models of the
Atlantic Ocean closing first require evaluation.
Fig. 11. Snapshots of mantle convection with varying the magnitude of yield stress (τy; maximum rupture strength) of the lithosphere. Note that only the mechanism for plate-like
motion is considered, and continents/supercontinents are not imposed in this model. The degree-one component of toroidal velocity field that represents the rigid-body rotation is
subtracted from solutions at each simulation time-step. Left panel shows viscosity and velocity fields on the top surface of model domain. Blue and yellow show the higher and lower
viscosities, respectively. Right panel shows the corresponding isosurfaces of temperature anomaly. The blue and yellow isosurfaces of the temperature anomaly δT (i.e., the deviation
from horizontally averaged temperature at each depth) indicate − 250 K and + 250 K. The white sphere indicates the bottom of mantle (i.e., core–mantle boundary). The highly
viscous oceanic lithosphere is realized by the temperature-dependent rheology of mantle materials, and the plate-like motions in the oceanic lithosphere are realized by imposing
the moderate yield stresses (τy = 100 and 125 MPa): ‘S’ and ‘T’ indicate divergence and convergence zones in the lithosphere, i.e., correspond to the spreading center and trench in
the Earth. Broadly deformed regions with low-viscosity (for instance, ‘D’ in the map with τy = 100 MPa) may correspond to the ‘diffuse plate boundary’ in the Earth (Gordon, 1998).
A red arrow in the map with τy = 100 MPa shows the Y-shaped subduction zone. When the yield stress is lower (i.e., τy = 50 MPa), the lithosphere is highly ruptured, while it is
higher (i.e., 150 MPa), the lithosphere is not ruptured so much and the plate boundary is incompletely evolved. The details of numerical methodology and model settings are similar
to a previous study by Yoshida (2008), but the viscosity contrast between the coldest upper surface boundary (i.e., uppermost part of high viscous lithosphere) and hottest bottom
surface boundary (i.e., core–mantle boundary) is taken to be a higher value, 106. The Rayleigh number defined by the reference viscosity (1021 Pa s) is fixed at 5.72 × 106.
20
M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
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 a
double-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 upper
and 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 transition
zone, and formation of hydrous plumes at 410 km depth.
We will now examine how numerical simulations approach the
shape of the future globe in terms of supercontinent configurations.
As stated in Section 11, it is difficult for numerical simulations to
reproduce the continental drift on the 3-D spherical model because of
some limitations in the techniques currently employed. Nevertheless,
Trubitsyn et al. (2008) constructed a 3-D numerical model to realize
the continental drift from present to 100 Myr later and to predict a
configuration of future supercontinent. They consider continents as
thin rigid (non-deformable) spherical caps, the motion of which is
described by Euler's solid body equation (see Trubitsyn et al., 2008 for
the details of numerical methodology and model parameters used).
The model continents are arranged in a real distribution of continents
of the present Earth. The initial temperature condition of mantle is
given by the present mantle flow pattern estimated from a seismic
tomography model (that is, it has the Circum-Pacific subduction zone
and two superplumes in the Africa–Atlantic and the South Pacific
regions). Their simulation reveals that after 100 Myr, all continents
will be assembled in the southern hemisphere. Africa, Eurasia,
Australia, Antarctica and South America form a future supercontinent
around Antarctica, because the Y-shaped subduction zone in the
Western Pacific pulls the continents. According to the model, North
America will not be part of the future, probably because the tensional
force due to both the South Pacific and African superplumes prevents
North America from moving to the southern hemisphere and joining
the future supercontinent amalgam.
14. Summary and conclusion
A synthesis of some of the conceptual models on supercontinent
amalgamation and disruption, together with recent information from
M. Yoshida, M. Santosh / Earth-Science Reviews 105 (2011) 1–24
numerical studies, leads to a better understanding of the Wilson Cycle
and supercontinent cycle. The superdownwelling along multiple
subduction zones predicted in plate tectonic models might provide an
effective mechanism to pull together dispersed continental fragments
into a closely packed assembly. Plumes and superplumes which
breakup supercontinents are considered to be fueled by the recycled
subducted material that initially accumulates at the mantle transition
zone and ultimately sinks down into the CMB. The process of reassembly of dispersed continental fragments occurs through complex
processes involving ‘introversion’, ‘extroversion’ or a combination of
both, with the closure of the intervening ocean occurring through
Pacific-type or Atlantic-type processes. The timescales of the assembly
and dispersion of supercontinents have varied through the Earth
history, and appear to be closely linked with the processes and
duration of superplume genesis. It is now widely recognized that plate
tectonic processes lead to both creation and destruction of continental
crust. The production–destruction balance changes over a supercontinent cycle, with a higher crustal growth through magmatic influx
during supercontinent break-up as compared to the tectonic erosion
and sediment-trapped subduction in convergent margins associated
with supercontinent assembly which erodes the continental crust.
The link between deep mantle dynamics and lithospheric plate
motions emphasizes the periodic assembly and dispersal of supercontinents. Model relations between the Wilson Cycle and mantle
convection have a strong bearing on the ‘superplume’ hypothesis.
Despite the controversy surrounding the superplume concept, the
geophysical and geochemical tools at our disposal have aided in the
formulation of persuasive models on the role of superplumes. The
beginning of a consensus is visible in the various studies concerning
the origins of ‘hot spots’ and likely ‘superplume’ candidates. The
processes responsible for the formation and disruption of past
supercontinents and the hypothetical future supercontinent amalgam
have important bearing on future biotic evolution and climate change.
Often, unusual phenomena such as backarc basin propagation
occur associated with some of the subduction systems. There are also
conflicting interpretations of ‘proto-continents’ as drifted fragments
or terranes extruded from major continental collision. From the
geological point of view, certain specific rock types have been
considered as the signature of plumes, although similar rock types
also occur in alternate tectonic settings. Another case concerns
contiguous marginal basins which are considered as the products of
collision-induced lateral mantle flow. Although these may reflect
‘plate-driven’ lateral displacement of ductile upper mantle, they do
not negate the ‘super’ or ‘regular’ plume models. Whereas the Tethyan
collisions (Africa, India, and Australia) clearly share common
lithospheric indications, this does not necessarily apply to their
respective asthenospheric responses. They are probably similar in
kind but need to be compared and contrasted from geological
evidence within the erstwhile sutures between constituent Gondwana terranes.
The numerical studies reviewed herein suggest that there is a
significant feedback not only between mantle convection and
continental drift, but also between mantle convection and plate
motions. The process of assembly of supercontinents induces a
temperature increase due to the thermal insulating effect. 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 3-D spherical geometry. The
formation of degree-one convection seems to be integral to the
emergence of periodic supercontinent cycles. The rifting and breakup
of supercontinental assemblies may be caused by either tensional
stress due to the thermal insulating effect, or large-scale partial
melting due to the flow reorganization and the resultant temperature
increase beneath the supercontinent. Supercontinent breakup has
also been correlated with the temperature increase due to upwelling
plumes originating from the CMB as a return flow of plate subduction
21
occurring at supercontinental margins. The active mantle plumes
from the CMB seem to disrupt the regularity of supercontinent cycles.
If mantle convection with dispersed continental blocks is wellorganized degree-one structure owing to its temperature-dependent
rheology, the continental blocks may move to downwellings and form
a supercontinent. Although most of the numerical studies have
assumed the continent/supercontinent to be rigid or nondeformable
body mainly because of numerical limitations as well as a simplification of models, a more recent numerical study allows the modeling
of mobile, deformable continents, including oceanic plates, and
successfully reproduces continental drift similar to the processes
and timescales envisaged in Wilson Cycle.
On the basis of the numerical studies synthesized here, we can
draw two possible end-member scenarios of the mantle convection
cycle. One is that mantle convection with dispersing continental
blocks has a short-wavelength structure (or close to degree-two
structure as the present Earth), and when a supercontinent forms,
mantle convection evolves into degree-one structure. Another is the
degree-one to degree-two model (Section 5). As for the former model
(high-degrees to degree-one), it would take longer time to form a
supercontinent, because continental blocks would be trapped by
different downwellings thus inhibiting collision. The timescale of
mantle convection cycle may be, however, significantly affected by
the plate motion and subduction that stir mantle convection.
In order to better constrain some of the key topics covered in this
paper, the future studies based on numerical modeling need to
address the following aspects: (1) Thermal and mechanical interaction between continent/supercontinent and plate motion. (2) The
mechanism of formation of large-scale upwellings beneath the
supercontinent. (3) The mechanism of origin and growth of the
continental crust. (4) The mechanism of supercontinent breakup. (5)
The episodic growth of continental crust and supercontinent. (6) The
growth and destruction of continental crust both related to subduction zone processes. (7) The thermal and mechanical interaction
between supercontinent cycle and mantle convection during the
Earth's history, as well as the thermal and chemical evolution of
convecting mantle.
Acknowledgements
We thank Editor Prof. M.F.J. Flower and Reviewer Prof. J. Brendan
Murphy for their valuable suggestions and helpful comments. M.Y.
was supported by a Grant-in-Aid (No. 20740260) from the Ministry of
Education, Culture, Sports, Science and Technology, Japan.
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