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The distribution of seafloor ages determines fundamental characteristics of Earth such as sea level, ocean chemistry, tectonic forces, and heat loss from the mantle. The present-day distribution suggests that subduction affects lithosphere of all ages, but this is at odds with the theory of thermal convection that predicts that subduction should happen once a critical age has been reached. We used spherical models of mantle convection to show that plate-like behavior and continents cause the seafloor area-age distribution to be representative of present-day Earth. The distribution varies in time with the creation and destruction of new plate boundaries. Our simulations suggest that the ocean floor production rate previously reached peaks that were twice the present-day value.
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DOI: 10.1126/science.1219120
, 335 (2012);336 Science et al.N. Coltice
Dynamic Causes of the Relation Between Area and Age of the Ocean
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(where ris the dislocation density) for the hot-
pressed and the compressively deformed specimens
for the representative 12- and 101-s oscillation
periods, which intercept the Q
axis at ~ 0.035
and 0.07 respectively, reflect contributions from
intergranular relaxation processes, such as grain-
boundary sliding, in the fine-grained (3 to 6 mm)
polycrystalline olivines of this study. The additional
dissipation, attributable to dislocation damping, was
approximately Q
= 0.024 × r(mm
) at a 101-s
period for the compressively pre-deformed mate-
rials. Thus, dislocation damping may account for
about 25% of the dissipation measured in the fine-
grained (3.1 mm) hot-pressed specimen 6585.
In order to assess the relative contributions of
these two dissipation mechanisms for the larger
grain sizes expected of Earths mantle, we used
the previously mentioned JF model (16), describ-
ing the behavior of undeformed, essentially dry
and melt-free polycrystalline olivine (including
H6585), of average dislocation density ~0.1 mm
This model, evaluated under laboratory conditions
of 0.2 GPa and 1100°C and at the experimental
periods near 12 and 101 s for representative upper-
mantle grain sizes of 1 and 10 mm, yields values
of Q
between 0.0065 and 0.0115 (Fig. 3, inset).
Such dissipation is largely due to intergranular re-
laxation rather than dislocation damping. For com-
pressively pre-deformed olivine tested at a 101-s
period, comparable levels of dissipation would
be expected from dislocation damping alone for
upper-mantle dislocation densities of 0.3 to
0.5 mm
. The torsionally pre-deformed speci-
men (T0436) of the present study, with a popula-
tion of dislocations similarly favorably oriented for
glide, displayed much higher levels of dislocation
damping than did compressively pre-deformed
materials of comparable dislocation density. We
conclude therefore that dislocation damping asso-
ciated with typical upper-mantle dislocation den-
sities (~0.01 to 0.1 mm
)(10,23) may contribute
comparably with grain-boundaryrelated dissipa-
tion (with associated shear wave dispersion), es-
pecially in regions of Earths upper mantle that
are subject to relatively high prevailing (or fossil)
deviatoric stress sand consequently high dis-
location density (11), and for shear waves with
propagation/polarization directions that provide
high resolved shear stress for dislocation glide.
Deformation in and beneath the oceanic litho-
sphere spreading away from a mid-ocean ridge in-
volves simple shear in the vertical plane parallel
to the spreading direction. This shear, if accom-
plished by glide on the dominant [100](010) slip
system of olivine, will tend to result in rotation
of the (010) planes of individual olivine crystals
toward the horizontal so that [100] is preferen-
tially aligned with the spreading direction. A
crystallographic preferred orientation of this type,
commonly measured in mantle xenoliths, provides
the accepted explanation of the azimuthal anisot-
ropy of compressional (P
) wave speed (6,24,25).
This fabric provides favorable average V
, shear wave velocity with horizontal polar-
ization; V
, shear wave velocity with vertical
polarization) in transversely isotropic seismolog-
ical wave speed models (26) that account for the
discrepancy between Rayleigh and Love surface
wave velocities (27). This fabric offers optimal av-
erage resolved shear stress for [100](010) dislo-
cation glide for the geometry of the simple shear
stress field controlling ongoing tectonic deforma-
tion beneath the oceanic plate. The same stress
field applies to vertically travelling shear waves
polarized parallel to the direction of plate motion
direction. Accordingly, we predict that these seis-
mic waves should be most strongly attenuated by
dislocation glide in the suboceanic mantle.
Our data demonstrate that strain-energy dis-
sipation (and shear modulus dispersion) associ-
ated with grain-boundary relaxation phenomena
are augmented by the effects of dislocation re-
laxation. The relaxation strength is expected to
vary linearly with the dislocation density, and in
turn with the magnitude of the fossil/prevailing
stress field as rºs
(11). However, only in rel-
atively cool parts of the lithosphere is a high dislo-
cation density, reflecting a high fossil stress, likely
to survive the process of static dislocation recovery.
Under these circumstances, the relevant tectonic
settings of high potential for dislocation damping
will be regions in the lower lithosphere and as-
thenosphere, where olivine is or was deformed via
(steady-state) dislocation creep. These regions in-
clude suboceanic mantle, deep-lithosphere shear
zones, and the material immediately above and
beneath an actively subducting slab.
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Acknowledgments: We thank H. Kokkonen, C. Saint, H. Miller,
and F. Brink for experimental help and D. Kohlstedt for
allowing us to use his laboratory at the University of
Minnesota. The Australian government (an Endeavor
International Postgraduate Research Scholarship), a Mervyn
and Katalin Paterson Fellowship (Research School of Earth
SciencesAustralian National University), and NASA grant
NNX11AF58G supported this work. We thank three anonymous
reviewers for helping to improve the manuscript. The raw data
are available in the supplementary materials.
Supplementary Materials
Materials and Methods
Figs. S1 to S4
Databases S1 to S5
References (2937)
22 December 2011; accepted 20 March 2012
Dynamic Causes of the Relation Between
Area and Age of the Ocean Floor
N. Coltice,
*T. Rolf,
P. J. Tackley,
S. Labrosse
The distribution of seafloor ages determines fundamental characteristics of Earth such as sea
level, ocean chemistry, tectonic forces, and heat loss from the mantle. The present-day distribution
suggests that subduction affects lithosphere of all ages, but this is at odds with the theory of thermal
convection that predicts that subduction should happen once a critical age has been reached. We used
spherical models of mantle convection to show that plate-like behavior and continents cause the
seafloor area-age distribution to be representative of present-day Earth. The distribution varies in time
with the creation and destruction of new plate boundaries. Our simulations suggest that the ocean
floor production rate previously reached peaks that were twice the present-day value.
The distribution of ages of the ocean floor is
a first-order observation that determines
the evolution of Earths surface and inte-
rior (1). Because heat flow and bathymetry direct-
ly depend on the age of the ocean floor (2), a shift
in the area-age distribution profoundly modifies
Earths cooling (3), sea level (4,5), and conse-
quently global climate (6,7). The characterization SCIENCE VOL 336 20 APRIL 2012 335
on June 15, 2012www.sciencemag.orgDownloaded from
of the age of the ocean floor has shown that its
present-day area per unit age decreases roughly
linearly with increasing age (8,9), defining a
function triangular in shape (Fig. 1A) for which a
common expression is
dt ¼C01
where A(t) is the area of ocean floor that is
younger than age t,C
is the rate of generation
of new ocean floor, and t
is the age of the
oldest seafloor [where present-day C
and t
are 3.01 km
and 180 million years (My),
respectively, and C
/2) is the total oceanic
If such a distribution were to define a steady
state, it would result from a constant production
of ocean floor for the past 180 My combined with
a consumption of seafloor, with a probability in-
dependent of its age (1,10). However, an evolv-
ing crustal production could explain the variance
of the data equally well (11) and one-dimensional
(1D) models provide a good fit to the present-day
observations as long as spreading rates have varied
(12). Indeed, seafloor spreading reconstructions
have shown variations of ocean floor production,
essentially through creation of mid-ocean ridges
after the breakup of Pangea (1315). As a conse-
quence, the distribution has differed from the
triangular shape we observe today (12,15).
The dynamic origin of the area-age distribu-
tion is a subject of debate, because subduction of
young and buoyant seafloor seems at odds with
the principles of convection that predict insta-
bilities of the top boundary layer occurring for
old and cooled material only. Continents may
geometrically impose subduction of seafloor in-
dependently of the age (3), but other mechanisms
could also reduce the dependence of subduction
on seafloor age. Most of them involve rheolog-
ical complexities of plates such as plate bending
(16) and dehydration stiffening (17). However,
simulations of mantle convection have never pre-
dicted any consistent triangular area-age distri-
bution, thereby failing to satisfy an elementary
geological constraint on mantle dynamics.
We performed 3D spherical mantle convec-
tion simulations introducing minimal complexity
to study the causes of the triangular area-age
distributions (18). In the following models, we
varied the number of continents (for a constant
surface fraction of 30%) and the rheology (iso-
viscous or inducing plate-like behavior). In these
simulations, we calculated synthetic ages for the
ocean floor from the computed local heat flow by
means of the half-space cooling approximation
(18), which is a very good approximation for a
mantle convection model (3). However, the synthet-
Laboratoire de Géologie de Lyon, Université Lyon 1; Ecole
Normale Supérieure de Lyon; Université de Lyon; CNRS, 69100
Villeurbanne, France.
Institut Universitaire de France.
stitute of Geophysics, ETH Zürich, 8092 Zürich, Switzerland.
*To whom correspondence should be addressed. E-mail:
0 40 80 120 160 200
Age (Ma)
Area per unit age (km2 yr-1)
40 80 120 160 200
Age (Ma)
40 80 120 160 200
Age (Ma)
6 continents
6 continents
3 continents
1 continent
Fig. 1. (A) Distribution of area versus age (Ma, millions of years ago) of the ocean floor on the present-day
Earth from (9). (B) Time-averaged distribution computed in 3D spherical simulations implementing
continents (red) or plate-like behavior (black) over 5 billion years. (C) Time-averaged distribution computed
in 3D spherical simulations implementing continents (their cumulative area is 30% of the total) and plate-
like behavior. The model with plumes (purple) has 15% of core heating generating hot plumes. The straight
dashed line in each panel represents the best triangular fit for the present-day distribution. The error bars
show the standard deviation of the distribution.
Area-age distributions Isochron maps
0 40 80 120 160 200
e (Ma)
0 40 80 120 160 200
Age (Ma)
0 40 80 120 160 200
Age (Ma)
Area per unit age (km2 yr-1)Area per unit age (km2 yr-1)Area per unit age (km2 yr-1)
Fig. 2. Snapshots of the distribution of the area versus age of the ocean floor along with the cor-
responding best triangular fit in dashed lines (left) and maps of synthetic isochrons (right) computed in
the 3D spherical convection models. The gray areas on the maps represent the continents, the white lines
are the positions of the downwellings, and the age contours are plotted at 10-My intervals. (Aand B)An
example corresponding to a triangular distribution (with three continents covering respectively 15%,
10%, and 5% of the surface). (Cand D) An example for a flat distribution (one supercontinent). (Eand F)
An example for a skewed distribution (six continents covering 5% of the surface each).
on June 15, 2012www.sciencemag.orgDownloaded from
ic ages can be biased in regions of downwellings
and in diffuse zones of extension or compression
where heat transport is more complex.
Convection simulations integrated over 5 bil-
lion years generated time-averaged distributions
of the area versus synthetic age of ocean floor.
For the model with six continents (each covering
5% of the surface area) but without plate-like
behavior (i.e., the viscosity is constant for each
material), the synthetic area-age distribution is
not triangular but the area decreases with age
faster than exponentially (Fig. 1B). As previously
observed, this is typical of internally heated con-
vection (3,19). The area-age distribution for the
model without continents but with plate-like be-
havior is also not triangular (Fig. 1B); it displays
a skewed plateau. The plateau expresses the fact
that young and hot material is not entrained in
subduction and only the lithosphere that has
reached a certain age (here, around 60 My) can
be subducted. These distributions are consistent
with those already computed in models without
continents and in cartesian geometry (3).
When plate-like behavior and continents are
combined, the average area-age distribution is
close to a triangular shape with an approximately
linear decrease of the area with increasing age
and a present-day production of seafloor slightly
larger than the observed present-day value (Fig.
1C). The averaged synthetic distributions given
by the convection models with continents and
plate-like behavior are in good agreement with
the observed triangular distribution for the present-
day Earth and with a 1D distribution correspond-
ing to a model with a subduction probability
depending on the square root of age (12). Simu-
lations with different numbers and sizes of con-
tinental blocks, with and without a reasonable
amount of core heating (15% of the total heat
flow), yield results with very little differences.
Within the course of a simulation, the area-age
distribution is mostly triangular but evolves with
the birth of new plate boundaries and the vanish-
ing of others. When the distribution is triangular
(Fig. 2A), ridge-like structures with youngocean
floor end at triple junctions and regions of trans-
form motion (Fig. 2B). The downwellings here
are mostly located on the edges of the continents.
Several of the ridge-like structures are cut by down-
wellings, highlighting the sinking of youngma-
terial in these models. Here, continents seem to act
as a geometrical constraint that imposes the location
of downwellings at the continent-ocean boundary.
A first type of nontriangular distribution (Fig.
2C) is relatively flat with a smaller value for the
production of new ocean floor (t
is about the
same as for the triangular shape), where down-
wellings are not all located on the edges of the
continents (Fig. 2D). Such a distribution is more
likely encountered in simulations with few con-
tinents (one or two), rather than with many. This
distribution is close to that observed with plate-
like behavior and without continents described
above. Hence, a flat distribution could occur when
the geometrical influence of the continents on the
location of downwellings is minimal and when the
flow is self-organized so that ocean floor is free to
reach a critical buoyancy before starting to sink.
A second type of nontriangular distribution,
observed in all the simulations at times where new
plate boundaries are generated (Fig. 2E), has two
characteristics: a large production of new ocean
floor (here almost twice the time-averaged one)
and a relative skewness. In this snapshot, ridge-
like structures dominate and are very irregular.
Fig. 4. (Aand B) Evolution of the average spectral heterogeneity of the temperature field in (A) the
supercontinent case and (B) the six-continent case, corresponding to the evolution depicted in Fig. 3.
Shown are powers of the first six harmonic degrees in a logarithmic scale, depth-averaged over the upper
mantle. For each point in time, the spectrum is normalized separately with the maximum spectral power
occurring at this time. The color scale corresponds to the normalized power.
10 1 continent
6 continents
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Elapsed time (My)
Production rate of
new ocean floor (km2 yr -1)Oceanic heat flow (TW)
Fig. 3. Production rate of new ocean floor (top) and oceanic heat flow (bottom) as a function of elapsed
time in models with the supercontinent covering 30% of the surface (black) and with six continents each
covering 5% of the surface (red). The average productions are 4.91 km year
with one continent and
4.55 km year
with six continents, with standard deviations of 1.59 km year
and 0.97 km year
respectively. The transit time t
of 85 My is used for the scaling (18). The averages of the heat flow are
38.2 TW with one continent and 39.3 TW with six continents, with standard deviations of 4.8 TW (12%)
and 2.8 TW (7%), respectively. The vertical dashed lines illustrate the points in time represented in Fig. 2C
and Fig. 2E. The distributions computed over the time period give the average distributions in Fig. 1C. SCIENCE VOL 336 20 APRIL 2012 337
on June 15, 2012www.sciencemag.orgDownloaded from
They are formed in response to the onset of new
cold instabilities. They develop and a reorganization
of the flow takes place to progressively produce a
more triangular distribution. Variations in the shape
of the distribution with time are consistent with
reconstructions for the past 150 My (12,14,15).
The shape of the distribution may have evolved
from flat-like, when Pangea was barely splitting,
to a skewed distribution after the birth of new
ridges (15), ultimately transforming to the present-
day triangular shape with dispersed continents.
Like the shape of the area-age distribution,
the rate of production of new ocean floor (youn-
ger than 10 My) in the mantle convection mod-
els varies with time (Fig. 3). Fluctuations are
moderate32% and 21% of the mean value
for the supercontinent and six-continent cases,
respectivelybut they can reach 100% at times,
doubling or halving the production of new ocean
floor. The strongest variations occur on a time
scale of 500 million years, which corresponds to
the time scale of flow reorganization through the
onset of new plate boundaries. The peaks of pro-
duction are generally correlated with the gener-
ation of new plate boundaries and peaks in heat
flow (like the configuration in Fig. 2F). The fluc-
tuations are stronger with one continent than with
six continents. Many small continents make the
flow adopt a smaller wavelength, so that a change
in plate organization has a smaller contribution
to the total (Fig. 4). The smaller wavelength im-
poses a higher time-averaged heat flow than for
the supercontinent case (20). The magnitudes
and time scales of the computed variations of
the production of new ocean floor are compara-
ble to those extracted from seafloor spreading
reconstructions (12,13).
Our models provide a fundamental basis for
realistically simulating Earths mantle convection.
Although they have relatively low Rayleigh num-
bers and simplified parameters for the interior of
the mantle, they show that plate-like behavior and
the presence of continents are the two necessary
ingredients to build a model in which young
seafloor is subducted like on Earth. Continents
constrain the location and geometry of the down-
wellings that cool Earths mantle. When subduc-
tion is confined at an ocean-continent boundary,
convection forces the subduction of very young
seafloor. Such a situation is favored by continen-
tal growth and dispersal. The distribution of sea-
floor age is a primary observation that should
be used as a diagnostic when simulating Earths
mantle, predicting the long-term cooling of Earth,
the fluctuations of sea level caused by tectonics
(21) that ultimately condition climate change on
geological time scales.
References and Notes
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12. T. Becker, C. Conrad, B. Buffett, R. Müller, Earth Planet.
Sci. Lett. 278, 233 (2009).
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687 (2009).
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C. Heine, Science 319, 1357 (2008).
Acknowledgments: We thank R. D. Müller and T. W. Becker
for fruitful reviews. Supported by Institut Universitaire de France
and ANR grant DynBMO (Dynamique de locéan de magma
basal) ANR-08-JCJC-0084-01 (N.C. and S.L.) and by Crystal2Plate,
a FP-7 funded Marie Curie action under grant agreement
PITN-GA-2008-215353 (T.R.). Supercomputing resources were
provided by ETH and the Swiss Supercomputer Centre (CSCS).
Supplementary Materials
Materials and Methods
Data File and Codes
References (2227)
13 January 2012; accepted 21 March 2012
A Segmentation Clock with
Two-Segment Periodicity in Insects
Andres F. Sarrazin,*Andrew D. Peel,Michalis Averof
Vertebrate segmentation relies on a mechanism characterized by oscillating gene expression. Whether
this mechanism is used by other segmented animals has been controversial. Rigorous proof of cyclic
expression during arthropod segmentation has been lacking. We find that the segmentation gene
odd-skipped (Tc-odd) oscillates with a two-segment periodicity in the beetle Tribolium castaneum.By
bisectingembryosandculturingthetwohalvesover different time intervals, we demonstrate that
Tc-odd cycles with a period of about 95 minutes at 30°C. Using live imaging and cell tracking in green
fluorescent proteinexpressing embryos, we can exclude that cell movements explain this dynamic
expression. Our results show that molecular oscillators represent a common feature of segmentation in
divergent animals and help reconcile the contrasting paradigms of insect and vertebrate segmentation.
Many animals generate body segments se-
quentially from a posterior region known
asthegrowthzone(1,2). Whether there
are common mechanisms underlying this process of
segmentation in disparate segmented animals, such
as vertebrates, annelids, and arthropods, has been
intensely debated (38). A role for molecular os-
cillators in segmentation was initially proposed
on theoretical grounds by Cooke and Zeeman (9).
Their clock and wavefrontmodel explained how
the temporal periodicity of a clock could be trans-
lated into a repetitive spatial pattern during sequen-
tial segmentation. Subsequent studies showed that
oscillating patterns of gene expression sweeping
through the growth zone play a key role in verte-
brate segmentation (1013).
A number of studies have indicated that an
equivalent segmentation clock may operate in the
presegmental zone of arthropods (35,14,15).
These studies revealed changing patterns of gene
expression in the presegmental zone of an insect,
a centipede, and a spider. They also showed that
disrupting Notch signaling, which is an important
element of the vertebrate segmentation clock
(13,16), leads to defects in segmentation in some
of these species. These results have been inter-
preted by some researchers as evidence that a
common mechanism for segmentation was in-
herited by vertebrates and arthropods from a
segmented common ancestor.
However, several doubts remain regarding
this interpretation. First, Notch signaling is known
to be involved in many other developmental pro-
cesses, such as specification of the presegmental
zone. These diverse functions may provide al-
ternative explanations for segmentation defects
(8,17,18). Second, cycling expression patterns
have been inferred from in situ hybridization
stainings on fixed embryos and comparison of
similarly staged embryos. However, embryo-to-
embryo variation and difficulty in accurately
staging embryos (relative to the speed of segment
formation) limits the reliability of this approach.
Moreover, it has not yet been proven that these
dynamic expression patterns reflect intracellu-
lar changes in gene expression, rather than cell
movements. Thus, there is no rigorous demon-
stration that cyclic waves of expression are sweep-
ing through the growth zone of arthropods. We use
embryo culture and live imaging in the insect
Tri bo lium ca sta ne um to address these issues.
Institute of Molecular Biology and Biotechnology (IMBB),
Foundation for Research and Technology Hellas (FORTH),
Nikolaou Plastira 100, GR-70013 Heraklio, Crete, Greece.
*Present address: Instituto de Química, Pontificia Universidad
Católica de Valparaíso, Casilla 4059, Valparaiso, Chile.
These authors contributed equally to this work.
To whom correspondence should be addressed. E-mail:
20 APRIL 2012 VOL 336 SCIENCE www.sciencemag.org338
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... We build a time-dependent model of O-LIP volume using theDoucet et al. (2020) oceanic mantle plume occurrence record by summing plume occurrences over a 180 Myr sliding window (to account for the residence time of seafloor;Coltice et al., 2012) so that the number of O-LIPs at a given time is equal to:N OLIP (t) =t−180 Myr t n OLIP where t is time. The mean present-day O-LIP volume is multiplied by the O-LIP count in the record to estimate O-LIP volume (V O −LIP ) through time. ...
The sedimentary rock record suggests that global sea levels may have fluctuated by hundreds of meters throughout Phanerozoic times. Long-term (10–80 Myr) sea level change can be inferred from paleogeographic reconstructions and stratigraphic methods can be used to estimate sea level change over 1–10 Myr in tectonically quiescent regions assumed to be stable. Plate tectonic reconstructions and mantle flow models make it possible to isolate, quantify and estimate the contribution of different solid Earth mechanisms to sea level change through time, including: the volume of water deeper than mid-oceanic ridges, mantle dynamic topography, marine sedimentation, oceanic large igneous province emplacement, deep-water cycle, volume above oceanic trenches and changes in continental area. Although these processes are intrinsically linked, their impact on sea level change is rarely studied in combination, and time-dependent models of long-term eustasy from tectonic and geodynamic processes are in their infancy. Here we couple plate tectonic reconstructions with time-dependent models of past mantle flow and develop a new holistic framework to model sea level change that accounts for the main solid Earth drivers of eustatic rise and fall. We present the first model of the effect of individual solid Earth mechanisms on eustatic change over the past 560 Myr, including time-dependent continental and oceanic dynamic topography, volume above oceanic trenches and changing continental slope. Our results are consistent with the Cretaceous highstand and Paleozoic and early Mesozoic lowstands deduced from stratigraphy, provided that the deep-water cycle contributed ∼240 m of sea level drop since 250 Myr. We find that changes in the volume of water below the depth of mid-ocean ridges are not balanced by changes in the volume of water above subduction zones or by global dynamic topography. Our results confirm that a young seafloor decreased the volume of water below the depth of ridges and contributed +280 m [+90/−0 m] to a sea level high at approximately 120 Ma, and show that changes in dynamic topography were the primary driver (−320 m [+80/−60 m]) of lowering sea level between ∼240–160 Ma when Pangea was assembled. Predicted sea level changes by up to −220/+470 m when Panthalassan mid-ocean ridge spreading rates are varied between 50 mm/yr and 200 mm/yr. We compute sea level estimates for two alternative global tectonic reconstructions and while the results differ (by ∼150 m) between 250-560 Ma, both suggest a sea level fall during Pangea assembly (between ∼380-320 Ma) that is consistent with published constraints.
... However, existing reconstructions only provide estimates of global surface heat flow variations since 230 Ma, a period that adequately captures Pangea breakup, but not the earlier stages of supercontinent assembly. Early conceptual models for this "supercontinent cycle" (Worsley et al., 1985;Worsley et al., 1986;Nance et al., 1986) postulated that the age-area distribution of the oceanic lithosphere ( Fig. 1c) should vary through the different phases of this cycle, and this notion has since been reinforced by results from numerical geodynamic models (Coltice et al., 2012) and the construction and analysis of paleo-seafloor age grids (Müller et al., 2016;Karlsen et al., 2020). Thus, in order to derive a representative value of the long-term oceanic heat flow, it may be necessary to compute a time-averaged value across a wider swath of time, approximating a full supercontinent cycle. ...
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Earth’s heat budget is strongly influenced by spatial and temporal variations in surface heat flow caused by plate tectonic cycles. Here we use a novel set of paleo-seafloor age grids extending back to the mid-Paleozoic to infer spatiotemporal variations in surface heat loss. The time-averaged oceanic heat flow is 36.6 TW, or ~25% greater than present-day. Our thermal budget for the mantle indicates that 149 K/Gyr of cooling occurred over this period, consistent with geochemical estimates of mantle cooling for the past 1 Gyr. Our analysis also suggests sustained rapid cooling of the Pacific mantle hemisphere, which may have cooled ~50 K more than its African counterpart since 400 Ma. The extra heat released from the Pacific mantle may have been trapped there by the earlier long-lived supercontinent Rodinia (~1.1-0.7 Ga), and the Pacific mantle may still be hotter than the African mantle today.
... • Mantle convection models with prescribed weak zones as plate boundaries (Davies, 1989;Puster et al., 1995;Zhong and Gurnis, 1995;Zhong SJ et al., 2000). iv) Internally driven forcing with self-nucleated shear zone • Passive margin collapse: triggered by hydrous upwelling (van der Lee et al., 2008), or by sedimentary loading (Fyfe and Leonardos, 1977;Cloetingh et al., 1989;Regenauer-Lieb et al., 2001); • Plume injection (Ueda et al., 2008;Burov and Cloetingh, 2010;Gerya et al., 2015;Davaille et al., 2017); • Plume induced mantle traction (Lu et al., 2015); • Suction from sinking slab (Baes et al., 2018); • Continent push (Marques et al., 2013;Rey et al., 2014); • Small-scale convection (Solomatov, 2004); • Transient mantle flow with damage and inheritance (Bercovici and Ricard, 2014); • Initiation of global network of rifts due to thermal expansiondriven fracturing (Tang et al., 2020); • Mantle convection models with self-organized plate behavior (e.g., Tackley, 2000a, b, c;Zhong SJ et al., 2007;Rolf and Tackley, 2011;Coltice et al., 2012;Rolf et al., 2012Rolf et al., , 2018Tackley, 2014, 2016;Lourenço et al., 2016;Ballmer et al., 2017;Nakagawa and Iwamori, 2017), some of which have shown self-consistent subduction polarity reversal (Crameri and Tackley, 2014) and plate reorganization (Mallard et al., 2016;Coltice et al., 2019). ...
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Key Points: We raise a "paradox of the first SI", a situation that appears to require existing subduction before the start of the first subduction, and review state-of-the-art SI models with a focus on evaluating their suitability in explaining the onset of plate tectonics. q We re-investigate plate driving mechanisms and conclude that mantle drag may be more important than previously thought, which may be the missing driving force that can resolve the "paradox of the first SI". q We propose a composite driving mechanism, one that is compatible with present-day Earth and may also be applicable to broader geodynamic settings. q Citation: Lu, G., Zhao, L., Chen, L., Wan, B. and Wu, F. Y. (2021). Reviewing subduction initiation and the origin of plate tectonics: What do we learn from present-day Earth?. Earth Planet. Phys., 5(2), 1-18. http://doi. Abstract: The theory of plate tectonics came together in the 1960s, achieving wide acceptance after 1968. Since then it has been the most successful framework for investigations of Earth's evolution. Subduction of the oceanic lithosphere, as the engine that drives plate tectonics, has played a key role in the theory. However, one of the biggest unanswered questions in Earth science is how the first subduction was initiated, and hence how plate tectonics began. The main challenge is how the strong lithosphere could break and bend if plate tectonics-related weakness and slab-pull force were both absent. In this work we review state-of-the-art subduction initiation (SI) models with a focus on their prerequisites and related driving mechanisms. We note that the plume-lithosphere-interaction and mantle-convection models do not rely on the operation of existing plate tectonics and thus may be capable of explaining the first SI. Re-investigation of plate-driving mechanisms reveals that mantle drag may be the missing driving force for surface plates, capable of triggering initiation of the first subduction. We propose a composite driving mechanism, suggesting that plate tectonics may be driven by both subducting slabs and convection currents in the mantle. We also discuss and try to answer the following question: Why has plate tectonics been observed only on Earth?
... To capture the dynamics of the Earth's interior and its surface expression, we solve for the equations of conservation of mass, momentum, and energy and for the advection of different material compositions. Temperature, pressure, velocity flow, and composition solutions are found in dimensionless space and have to be scaled in order to be compared to Earth dynamics (for nondimensional equations and governing parameters, description of the initial conditions, and scaling procedure, see supporting information; Coltice et al., 2012;Müller et al., 2016;Turcotte & Schubert, 2002). ...
Relative plate motions during continental rifting result from the interplay of local with far-field forces. Here, we study the dynamics of rifting and breakup using large-scale numerical simulations of mantle convection with self-consistent evolution of plate boundaries. We show that continental separation follows a characteristic evolution with four distinctive phases: (1) An initial slow rifting phase with low divergence velocities and maximum tensional stresses, (2) a syn-rift speed-up phase featuring an abrupt increase of extension rate with a simultaneous drop of tensional stress, (3) the breakup phase with inception of fast seafloor spreading and (4) a deceleration phase occurring in most but not all models where extensional velocities decrease. We find that the speed-up during rifting is compensated by subduction acceleration or subduction initiation even in distant localities. Our study illustrates new links between local rift dynamics, plate motions and subduction kinematics during times of continental separation.
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Plain Language Summary The question of whether the speeds of tectonic plates vary over time is controversial but has big‐picture implications for our understanding of the forces inside the Earth that drive the plates, the role of volcanoes in controlling climate change over millions of years, and the rise and fall of sea level. At mid‐ocean ridges, two plates move apart, and the volcanic rocks that comprise the ocean crust are created. Magnetic minerals in the rocks record their age of formation and therefore the relative speeds of the diverging plates. However, this record is incomplete because seafloor is destroyed at subduction zones. We used the preserved seafloor magnetic record to calculate diverging plate speeds over the past 19 million years. We find that the relative plate speed at almost all divergent plate boundaries has slowed down, with a major inflection point at 15–16 Myr. As a result, the rate at which new ocean crust is created also slowed down, by roughly 35%. We speculate that there is not a single explanation for the nearly global slowdown in plate speeds but rather several unrelated tectonic events, such as the emergence of the Andes.
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The presence of offsets, appearing at intervals ranging from 10s to 100s of kilometres, is a distinct characteristic of constructive tectonic plate margins. By comparison, boundaries associated with subduction exhibit uninterrupted continuity. Here, we present global mantle convection calculations that result in a mobile lithosphere featuring dynamically derived plate boundaries exhibiting a contrasting superficial structure which distinguishes convergence and divergence. Implementing a yield-stress that governs the viscosity in the lithosphere, spreading boundaries at the top of a vigorously convecting mantle form as divergent linear segments regularly offset by similar length zones that correlate with a large degree of shear but comparatively minimal divergence. Analogous offset segments do not emerge in the boundaries associated with surface convergence. Comparing the similarity in the morphologies of the model plate margins to the Earth’s plate boundaries demonstrates that transform-like offsets are a result of stress induced weakness in the lithosphere owing to passive rupturing.
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Plain Language Summary Earth's interior is cooling because its rate of heat loss exceeds its rate of internal heat production. Heat loss happens at the Earth's surface and is highly variable, with thick continents providing strong insulation to Earth's interior and thin seafloor allowing more rapid heat transfer. Using models for how the continents and oceanic plates have moved for the past 400 million years, we reconstructed the history of heat loss from Earth's interior. We find that heat loss was on average 25% higher in the past than it is today, which implies more rapid overall cooling than expected. We also find that the Pacific side of the world has lost heat at a much faster rate than the African side. This is partly due to positioning of continental landmasses, including the supercontinent Pangea, on the African side for most of the past 400 million years. By contrast, the oceans on the Pacific side offered “poor insulation” that led to ∼50 °C more cooling of the Pacific mantle compared to its African counterpart. The extra heat lost from the Pacific side may have been trapped there by Rodinia, an older, long‐lived supercontinent that covered the Pacific mantle about one billion years ago.
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Strain localization in the lithosphere and the formation, evolution, and maintenance of resulting plate boundaries play a crucial role in plate tectonics and thermo-chemical mantle convection. Previously activated lithospheric deformation zones often appear to maintain a “memory” of weakening, leading to tectonic inheritance within plate reorganizations including the Wilson cycle. Different mechanisms have been proposed to explain such strain localization, but it remains unclear which operate on what spatio-temporal scales, and how to best incorporate them in large-scale mantle convection models. Here, we analyze two candidates, 1), grain-size sensitive rheology and, 2), damage-style parameterizations of yield stress which are sometimes used to approximate the former. Grain-size reduction due to dynamic recrystallization can drive localization in the ductile domain, and grain growth provides a time-dependent rheological hardening component potentially enabling the preservation of rheological heterogeneities. We compare the dynamic weakening and hardening effects as well as the timescales of strength evolution for a composite rheology including grain-size dynamics with a pseudo-plastic rheology including damage- (or “strain”-) dependent weakening. We explore the implications of different proposed grain-size evolution laws, and test to which extent strain-dependent rheologies can mimic the weakening and hardening effects of the more complex micro-physical behavior. Such an analysis helps to better understand the parallels and differences between various strainlocalization modeling approaches used in different tectonics and geodynamics communities. More importantly, our results contribute to efforts to identify the key ingredients of strainlocalization and damage hysteresis within plate tectonics and how to represent those in planetary-scale modeling.
Geochemical constraints on mantle temperature indicate a regular decrease by around 250 K since 3 Ga. However, models of Earth’s cooling that rely on scaling laws for thermal convection without strong plates are facing a thermal runaway backwards in time, due to the power-law dependence of heat loss on temperature. To explore the effect of surface dynamics on Earth’s cooling rate, we build a 2D temperature-dependent model of plate tectonics that relies on a force balance for each plate and on Earth- like parameterized behaviors for the motion, creation and disappearance of plate boundaries. While our model predicts the expected thermal runaway if plate boundaries are fixed, we obtain an average cooling rate consistent with geochemical estimates if the geometry of plate tectonics evolves through time. For a warmer mantle in the past, plates are faster but also larger (and less numerous) so that the average seafloor age and resulting heat flux always remain moderate. The predicted decrease in the number of plates backwards in time is in good agreement with recent plate reconstructions over the last 400 Myr. Our model also gives plate speed and subduction area flux consistent with these reconstructions. We finally compare the effect of parameters controlling mantle viscosity and individual plate speeds to the effect of localized surface processes, such as oceanization and subduction initiation. We infer that studies of Earth’s thermal history should focus on surface processes as they appear to be key control parameters.
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Anisotropy of upper mantle physical properties results from lattice preferred orientation (LPO) of upper mantle minerals, in particular olivine. We use an anisotropic viscoplastic self-consistent (VPSC) and an equilibrium-based model to simulate the development of olivine LPO and, hence, of seismic anisotropy during deformation. Comparison of model predictions with olivine LPO of naturally and experimentally deformed peridotites shows that the best fit is obtained for VPSC models with relaxed strain compatibility. Slight differences between modeled and measured LPO may be ascribed to activation of dynamic recrystallization during experimental and natural deformation. In simple shear, for instance, experimental results suggest that dynamic recrystallization results in further reorientation of the LPO leading to parallelism between the main (010)[100] slip system and the macroscopic shear. Thus modeled simple shear LPOs are slightly misoriented relative to LPOs measured in natural and experimentally sheared peridotites. This misorientation is higher for equilibrium-based models. Yet seismic properties calculated using LPO simulated using either anisotropic VPSC or equilibrium-based models are similar to those of naturally deformed peridotites; errors in the prediction of the polarization direction of the fast S wave and of the fast propagation direction for P waves are usually
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For subduction to occur, plates must bend and slide past overriding plates along fault zones. Because the lithosphere is strong, significant energy is required for this deformation to occur, energy that could otherwise be spent deforming the mantle. We have developed a finite element representation of a subduction zone in which we parameterize the bending plate and the fault zone using a viscous rheology. By increasing the effective viscosity of either the plate or the fault zone, we can increase the rates of energy dissipation within these regions and thus decrease the velocity of a plate driven by a given slab buoyancy. We have developed a simple physical theory that predicts this slowing by estimating a convecting cell's total energy balance while taking into account the energy required by inelastic deformation of the bending slab and shearing of the fault zone. The energy required to bend the slab is proportional to the slab's viscosity and to the cube of the ratio of its thickness to its radius of curvature. The distribution of dissipation among the mantle, lithosphere, and fault zone causes the speed of a plate to depend on its horizontal length scale. Using the observation that Earth's plate velocities are not correlated to plate size, we can constrain the lithosphere viscosity to be between 50 and 200 times the mantle viscosity, with higher values required if the fault zone can support shear tractions  50 MPa over 300 km. These subduction zone strengths imply that the mantle, fault zone, and lithosphere dissipate about 30%, 10%, and 60% of a descending slab's potential energy release if the slab is 100 km thick. The lithospheric component is highly dependent on slab thickness; it is smaller for thin plates but may be large enough to prevent bending in slabs that can grow thicker than 100 km. $ubduction zone strength should be more stable than mantle viscosity to changes in mantle temperature, so the controlling influence of subduction zones could serve to stabilize plate velocities over time as the Earth cools. Because the "details" of convergent plate boundaries are so important to the dynamics of plate motion, numerical models of mantle flow should treat subduction zones in a realistic way.
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Concurrent changes in seawater chemistry, sea level, and climate since the mid-Cretaceous are thought to result from an ongoing decrease in the global rate of lithosphere production at ridges. The present-day area distribution of seafloor ages, however, is most easily explained if lithosphere production rates were nearly constant during the past 180 m.y. We examined spatial gradients of present-day seafloor ages and inferred ages for the subducted Farallon plate to construct a history of spreading rates in each major ocean basin since ca. 140 Ma, revealing dramatic Cenozoic events. Globally, seafloor spreading rates increased by ˜20% during the early Cenozoic due to an increase in plate speeds in the Pacific basin. Since then, subduction of the fast-spreading Pacific-Farallon ridge system has led to a 12% decrease in average global spreading rate and an 18% or more decrease in the total rate of lithosphere production by the most conservative estimates. These rapid changes during the Cenozoic defy models of steady-state seafloor formation, and demonstrate the time-dependent and evolving nature of plate tectonics on Earth.
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Previous mantle convection studies with continents have revealed a first-order influence of continents on mantle flow, as they affect convective wavelength and surface heat loss. In this study we present 3D spherical mantle convection models with self-consistent plate tectonics and a mobile, rheologically strong continent to gain insight into the effect of a lithospheric heterogeneity (continents vs. oceans) on plate-like behaviour. Model continents are simplified as Archaean cratons, which are thought to be mostly tectonically inactive since 2.5 Ga. Long-term stability of a craton can be achieved if viscosity and yield strength are sufficiently higher than for oceanic lithosphere, confirming results from previous 2D studies. Stable cratons affect the convective regime by thermal blanketing and stress focussing at the continental margins, which facilitates the formation of subduction zones by increasing convective stresses at the margins, which allows for plate tectonics at higher yield strength and leads to better agreement with the yield strength inferred from laboratory experiments. Depending on the lateral extent of the craton the critical strength can be increased by a factor of 2 compared to results with a homogeneous lithosphere. The resulting convective regime depends on the lateral extent of the craton and the thickness ratio of continental and oceanic lithosphere: for a given yield strength a larger ratio favours plate-like behaviour, while intermediate ratios tend towards an episodic and small ratios towards a stagnant lid regime.
The basic quantitative distinction between global oceanic ridge volume and the global rate of seafloor generation is made fully explicit. From this, the question of inversion over time from the former quantity into the latter is then posed using a generalized expression to approximate global subduction zone distribution. Two numerical methods are described. Then, assuming the hypothesis that long-term (108 yr) eustatic sealevel change is due primarily to changing ridge volume, an inversion of a widely cited Phanerozoic sealevel curve (Vail) is also presented. The approach taken here is expected to be of direct importance for quantitative models of the carbonate-silicate cycle which seek to develop scenarios for atmospheric carbon dioxide variation over geologic time scales. Indeed, the testing of sealevel inversion, as performed here, may ultimately come from its degree of correspondence with past climate variation.-Author
The distribution of area of the ocean floor with age, t, is approximately described by dA/dt=C0(1-(t/tm)), where C0 is the rate of crustal generation and tm the maximum age. A linear differential area versus age relation can be explained by a balance between generation and consumption where consumption is uniformly distributed with age. The present distribution of consumption with age was estimated from the isochron map used to derive the area-age relation and a recently published set of angular velocity vectors describing present plate motions. The trenches appear to be distributed randomly with respect to age provinces in the oceans. Changes in the rate of plate generation and the distribution of consumption with age result in shifts in the area-age distribution. In turn, these shifts produce changes in the plate driving forces which act to restore the rate of plate generation and distribution of consumption to their initial states. This coupling between driving forces and the area-age distribution provides a feedback mechanism limiting the extent of any changes. A measure of the magnitude of shifts in the area-age distribution is given by global changes in sea level. The area-age relation can be combined with simple expressions for depth and heat flow versus age to obtain an empirical hypsometric distribution, parameterized in terms of age, and exact expressions for the heat loss from the ocean floor.-Author
A steady-state model of crust production and destruction for the past 180 m.y. was proposed by B. Parsons and advocated by D. Rowley. Such a model has serious implications for models of secular variations in, e.g., global sea level, global climate, and seawater chemistry. This paper presents an analysis of the steady-state model and then offers alternative extensions of that model that allow for non steady-state production of ocean crust with time. Results suggest that the observed linear decrease in area versus age of ocean floor does not force a steady-state view of seafloor spreading.
Specimens of naturally deformed peridotite were annealed and observed under the transmission electron microscope to study the kinetics of the recovery process in dry olivine. The lattice diffusion constant appropriate to climb, which we tentatively identify with 0−, was obtained at 1290° and 1450°C from the observed collapse of sessile dislocation loops. The data are represented by D = 3 × 104 exp [(—135 kcal/mole)/kT] cm2/sec. The climb of dislocations into subboundaries occurs by diffusion along dislocation cores with an activation energy of 140 ± 30 kcal/mole. The nature and distribution of dislocations in olivine grains from a Salt Lake crater lherzolite xenolith are incompatible with a Nabarro-Herring or subgrain creep model but consistent with a model based on dislocation climb.
Presented here are the first three-dimensional simulations of mantle convection to display self-consistently-generated plate tectonic-like behavior which is continuous in space and time. Plate behavior arises through a reasonable material description of silicate deformation, with a simple yield stress being sufficient to give first-order plate-like behavior. Toroidal:poloidal ratios are within geologically-observed limits. The sensitivity of the system to yield strength and the form of strength envelope is systematically investigated. Optimum plate character is obtained in a narrow range of yield strength, below which diffuse boundaries, and above which episodic behavior, and eventually a rigid lid, are observed. Models with mobile lids develop very long-wavelength horizontal structure- the longest wavelength possible in the domain. Two- dimensional models display much greater time-dependence than three- dimensional models.
We analyze tomographic models of the S-wave velocity in the mantle. The depth variation of laterally heterogeneous structure is parametrized in terms of the ``skewness,'' which yields information on mantle convection. Recent models show negative skewness in the lower half of the mantle. Assuming that the velocity anomaly is related to the temperature anomaly, this suggests that there is significant heat flow from the core.