Mantle Convection

1] We present a new statistical method to construct a model for the chemical composition of Earth's primitive mantle along with its variance. Earth's primitive mantle is located on the melting trend exhibited by the global compilation of mantle peridotites, using cosmochemical constraints on the relative abundances of refractory lithophile elements (RLE). This so-called pyrolite approach involves the least amount of assumptions, thereby being probably most satisfactory compared to other approaches. Its previous implementations, however, suffer from questionable statistical treatment of noisy geochemical data, leaving the uncertainty of model composition poorly quantified. In order to properly take into account how scatters in peridotite data affect this geochemical inference, we combine the following statistical techniques: (1) modeling a nonlinear melting trend in the multidimensional compositional space through the principal component analysis, (2) determining the primitive mantle composition on the melting trend by simultaneously imposing all of cosmochemical constraints with least squares, and (3) mapping scatters in original data into the variance of the final model through the bootstrap resampling technique. Whereas our model is similar to previous models in terms of Mg, Si, and Fe abundances, the RLE contents are at $2.16 ± 0.37 times the CI chondrite concentration, which is lower than most of previous estimates. The new model is depleted by >20% in a number of incompatible elements including heat-producing elements, U, Th, and K, and this depleted nature is further amplified (up to 60%) in terms of predicted composition for the present-day mantle.

We investigate shear band orientations for a simple plastic formulation in the context of incompressible viscous flow. This type of material modelling has been introduced in literature to enable the numerical simulation of the deformation and failure of the lithosphere coupled with the mantle convection. In the present article, we develop a linear stability analysis to determine the admissible shear band orientations at the onset of bifurcation. We find that the so-called Roscoe angle and Coulomb angle are both admissible solutions. We present numerical simulations under plane strain conditions using the hybrid particle-in-cell finite element code Underworld.

Geosciences, along with many other disciplines in science and engineering, faces an exponential increase in the amount of data generated from observation, experiment and large-scale, high-resolution 3-D numerical simulations. In this communication we describe the fundamentals of visualization necessary to meet these challenges. We present several alternative methodologies such as 2D/3D feature extraction, segmentation methods, and flow topology, to help better understand the physical structure of the data. We use AMIRA from TGS to demonstrate our concepts. Examples are drawn from fields in computational fluid dynamics, 3-D mantle convection and seismic tomography. Finally, we present our perspective on the future of visualization.

The mantle plume hypothesis is now widely known to explain hotspot volcanoes, but direct evidence for actual plumes is weak, and seismic images are available for only a few hotspots. In this work, we present whole-mantle tomographic images under 60 major hotspots on Earth. The lateral resolution of the tomographic images is about 300 km under the continental hotspots and 400-600 under the oceanic hotspots. Twelve plume-like, continuous low-velocity (low-V) anomalies in both the upper and lower mantle are visible under Hawaii,

This study explores a chemo-thermo-dynamic subduction zone model that solves for slab dehydration during subduction. We investigate how changes in the incoming plate's hydration and thermal structure may effect the efficiency of sub-arc water release from sediments, crust, and serpentinized mantle. We find that serpentinized lithospheric mantle may not only be an important fluid source to trigger arc melting but is also an efficient 'transport-lithology' to recycle chemically bound water into the deeper mantle. In fact, an old slab may remain sufficiently cold during subduction to retain up to 40% of its initial 'mantle' water at 8 GPa ( f 240-km depth) after serpentine transforms to higher pressure hydrous phase A.

We present a model to assess the viability of the creation of volcanic eruptions of up to flood-basalt size from a giant impactor striking a relatively thin lithosphere. A 300-km-radius crater in 75-km-thick lithosphere can create 106 km3 of magma from instantaneous in situ decompression of mantle material with a potential temperature of 1300 °C. For a range of lithospheric

The timing and duration of surface uplift associated with large igneous provinces provide important constraints on mantle convection processes. Here we review geological indicators of surface uplift associated with five continent-based magmatic provinces: Emeishan Traps (260 million years ago: Ma), Siberian Traps (251 Ma), Deccan Traps (65 Ma), North Atlantic (Phase 1, 61 Ma and Phase 2, 55 Ma), and Yellowstone (16 Ma to recent). All five magmatic provinces were associated with surface uplift. Surface uplift can be measured directly from sedimentary indicators of sea-level in the North Atlantic and from geomorpholocial indicators of relative uplift and tilting in Yellowstone. In the other provinces, surface uplift is inferred from the record of erosion. In the Deccan, North Atlantic and Emeishan provinces, transient uplift that results from variations in thermal structure of the lithosphere and underlying mantle can be distinguished from permanent uplift that results from the extraction and emplacement of magma. Transient surface uplift is more useful in constraining mantle convection since models of melt generation and emplacement are not required for its interpretation. Observations of the spatial and temporal relationships between surface uplift, rifting and magmatism are also important in constraining models of LIP formation. Onset of surface uplift preceded magmatism in all five of the provinces. Biostratigraphic constraints on timing of uplift and erosion are best for the North Atlantic and Emeishan Provinces, where the time interval between significant uplift and first magmatism is less than 1 million years and 2.5 million years respectively. Rifting post-dates the earliest magmatism in the case of the North Atlantic Phase 1 and possibly in the case of Siberia. The relative age of onset of offshore rifting is not well constrained for the Deccan and the importance of rifting in controlling magmatism is disputed in the Emeishan and Yellowstone Provinces. In these examples, rifting is not a requirement for onset of LIP magmatism but melting rates are significantly increased when rifting occurs.

The geological record of consolidation and uplift of crustal protolith identifies three major groupings of Archaean cratonic nuclei . These comprise 'Ur' (∼3.0 Ga cratons of Southern Africa, Western Australia), 'Arctica' (∼2.5 Ga cratons of Greenland, Fennoscandia, Laurentia and Siberia) and 'Atlantica' (∼2.0 Ga cratons of Western Africa and South America). In this paper the ∼2.9-2.0 Ga record from these cratons is used to develop a palaeogeographic model based on (i) the proximities recognised from geological evidence and (ii) the correlation of ∼2.7-2.2 Ga palaeomagnetic poles between Ur and Arctica . The solution shows that Archaean continental crust had aggregated into a crescent-shaped supercontinent, 'Protopangaea', by mid-Archaean times. The outer wings comprised core elements of Ur and Arctica which appear to have retained internal quasi-integrity with respect to each other until the end of the Proterozoic eon. Crust in between was still consolidating in early Palaeoproterozoic times and would ultimately include the Atlantica cratonic grouping. Geological tracers, including straight belts and mineral provinces, form lineaments parallel to the arcuate shape of the protocontinent and, as presently defined, the reconstruction indicates that a minimum of 35-56% of the present continental crust had been extracted from the mantle by these times. Derivation of the reconstruction is facilitated because the bulk of the ∼2.7-2.2 Ga poles imply very low rates of apparent polar wander (APW, <10 mm/year) during this ∼5 Ga interval. These low APW rates correlate with the later granite-greenstone tectonics and are presumed to reflect dominant small scale convection. In contrast rapid APW after ∼2.2 Ga records a transition to typical Proterozoic tectonics with large scale mobility reflected in the accretion of mobile belts to the core Ur-Atlantica-Arctica assemblage. The reason why continental crust accretes into supercontinents of symmetrical crescent-shaped form is also addressed. By analogy with Phanerozoic Pangaea and the present-day geoid it is interpreted to have resulted from large-scale, presumably whole mantle, convection systems driving the continental crust towards regions of minimum gravitational potential.

Flament, N., Gurnis, M. and Müller, R. D.

The topography of Earth is primarily controlled by lateral differences in the density structure of the crust and lithosphere. In addition to this isostatic topography, flow in the mantle induces deformation of its surface leading to dynamic topography. This transient deformation evolves over tens of millions of years, occurs at long wavelength, and is relatively small (<2 km) in amplitude. Here, we review the observational constraints and modeling approaches used to understand the amplitude, spatial pattern, and time dependence of dynamic topography. The best constraint on the present-day dynamic topography induced by sublithospheric mantle flow is likely the residual bathymetry calculated by removing the isostatic effect of oceanic lithospheric structure from observed bathymetry. Increasing knowledge of the thermal and chemical structure of the lithosphere is important to better constrain present-day mantle flow and dynamic topography. Nevertheless, at long wavelengths (>5000 km), we show that there is good agreement between published residual topography fields, including the one described here, and present-day dynamic topography predicted from mantle flow models, including a new one. Residual and predicted fields show peak-to-peak amplitudes of roughly ±2 km and a dominant degree two pattern with high values for the Pacific Ocean, southern Africa, and the North Atlantic and low values for South America, western North America, and Eurasia. The flooding of continental interiors has long been known to require both larger amplitudes and to be temporally phase-shifted compared with inferred eustatic changes. Such long-wavelength inferred vertical motions have been attributed to dynamic topography. An important consequence of dynamic topography is that long-term global sea-level change cannot be estimated at a single passive margin. As a case study, we compare the results of three published models and of our model to the subsidence history of well COST-B2 offshore New Jersey. The <400 ± 45 m amount of anomalous subsidence of this well since 85 Ma is best explained by models that predict dynamic subsidence of the New Jersey margin during that period. Explicitly including the lithosphere in future global mantle flow models should not only facilitate such comparisons between model results and data, but also further constrain the nature of the coupling between the mantle and the lithosphere.

In 1859 Antonio Snider proposed that rapid, horizontal divergence of crustal plates occurred during Noah's Flood. Modern plate tectonics theory is now conflated with assumptions of uniformity of rate and ideas of continental "drift." Catastrophic plate tectonics theories, such as Snider proposed more than a century ago, appear capable of explaining a wide variety of data-including biblical and geologic data which the slow tectonics theories are incapable of explaining. We would like to propose a catastrophic plate tectonics theory as a framework for Earth history.

At the transition from the Permian to the Triassic, Eurasia was the site of voluminous flood-basalt extrusion and rifting. Major flood-basalt provinces occur in the Tunguska, Taymyr, Kuznetsk, Verkhoyansk–Vilyuy and Pechora areas, as well as in the South Chinese Emeishen area. ...

The apparent stability of Archean cratons and cratonic keels for billions of years is a difficult observation for geodynamic modeling to explain. While it may be straight-forward to assert that chemical buoyancy and high viscosity are needed to stabilize cratons, there are many questions regarding craton formation, variability (both in space and time), and evolution that remain unanswered. In numerical studies, strong and buoyant cratonic keels survive relatively undeformed for several mantle overturn times (the equivalent of several hundred million years); extending this to several billion years remains a challenge. The strength required to stabilize keels in some of these numerical experiments exceeds reasonable estimates of the laboratory measurements of strength of mantle materials (including both the effects of temperature and melt-depletion). In addition, the most common explanation of keel formation, vertical stacking of subducted plate, requires the keel material to be deformable at the time of formation and soon afterward the keel material becomes strong enough to resist shearing. The extent to which cratonic keels interact with and influence the pattern of mantle convection, by nucleating small-scale edge-driven convection or by coupling plate motions to deeper mantle flow, remains an open question. D Archean cratons are relatively flat, stable regions of the crust that have remained undeformed since the Precambrian, forming the ancient cores of the continents . Most primary diamond deposits occur in Archean cratons and there are no recognized primary diamond deposits intruding rocks younger than 1.6 Gyr [1]. The graphite-diamond phase transition occurs at 120-150 km depths and low (b1000 8C) temperatures . Thus, the occurrence of diamonds provides an important constraint on the thermal state of the lower lithosphere. As illustrates, only relatively-low surface-heatflow geotherms pass through the diamond stability field in the 120-150 km depth range. Seismic velocities under Archean cratons are significantly faster than normal subcontinental mantle (e.g., ) and this suggests 0012-821X/$ -see front matter D

Non-arc basalts of Archean and Proterozoic age have model primary magmas that exhibit mantle potential temperatures T P that increase from 1350°C at the present to a maximum of ∼ 1500-1600°C at 2.5-3.0 Ga. The overall trend of these temperatures converges smoothly to that of the present-day MORB source, supporting the interpretation that the non-arc basalts formed by the melting of hot ambient mantle, not mantle plumes, and that they can constrain the thermal history of the Earth. These petrological results are very similar to those predicted by thermal models characterized by a low Urey ratio and more sluggish mantle convection in the past. We infer that the mantle was warming in deep Archean-Hadean time because internal heating exceeded surface heat loss, and it has been cooling from 2.5 to 3.0 Ga to the present. Non-arc Precambrian basalts are likely to be similar to those that formed oceanic crust and erupted on continents. It is estimated that ∼ 25-35 km of oceanic crust formed in the ancient Earth by about 30% melting of hot ambient mantle. In contrast, komatiite parental magmas reveal T P that are higher than those of non-arc basalts, consistent with the hot plume model. However, the associated excess magmatism was minor and oceanic plateaus, if they existed, would have had subtle bathymetric variations, unlike those of Phanerozoic oceanic plateaus. Primary magmas of Precambrian ambient mantle had 18-24% MgO, and they left behind residues of harzburgite that are now found as xenoliths of cratonic mantle. We infer that primary basaltic partial melts having 10-13% MgO are a feature of Phanerozoic magmatism, not of the early Earth, which may be why modern-day analogs of oceanic crust have not been reported in Archean greenstone belts.

Since its formation, the Earth is slowly cooling. The heat produced by the core and the radioactive decay in the mantle is evacuated toward the surface by convection. The evolving convective structures thereby created control a diversity of surface phenomena such as vertical motion of continents or sea level variation. The study presented here attempts to determine which convective structures can be predicted, to what extent and over what timescale.

Because of the chaotic nature of convection in the Earth's mantle, uncertainties in initial conditions grow exponentially with time and limit forecasting and hindcasting abilities. Following the twin experiments method initially developed by {\it Lorenz} [1965] in weather forecast, we estimate for the first time the Lyapunov time and the limit of predictability of Earth's mantle convection. Our numerical solutions for 3D spherical convection in the fully chaotic regime, with diverse rheologies, suggest that a 5\% error on initial conditions limits the prediction of Earth's mantle convection to 95 million years.

The quality of the forecast of convective structures also depends on our ability to describe the mantle properties in a realistic way. In 3D numerical convection experiments, pseudo plastic rheology can generate self-consistent plate tectonics compatible at first order with Earth surface behavior [{\it Tackley}, 2008]. We assessed the role of the temperature dependence of viscosity and the pseudo plasticity on reconstructing slab evolution, studying a variety of mantle thermal states obtained by imposing 200 million years of surface velocities extracted form tectonic reconstructions [{\it Seton et al.}, 2012; {\it Shephard et al.}, 2013]. The morphology and position of the reconstructed slabs largely vary when the viscosity contrast increases and when pseudo plasticity is introduced. The errors introduced by the choices in the rheological description of the mantle are even larger than the errors created by the uncertainties in initial conditions and surface velocities.
 
  This work shows the significant role of initial conditions and rheology on the quality of predicted convective structures, and identifies pseudo plasticity and large viscosity contrast as key ingredients to produce coherent and flat slabs, notable features of Earth's mantle convection.

The ophiolitic peridotites in the Wadi Arais area, south Eastern Desert of Egypt, represent a part of Neoproterozoic ophiolites of the Arabian-Nubian Shield (ANS). We found relics of fresh dunites enveloped by serpentinites that show abundances of bastite after orthopyr-oxene, reflecting harzburgite protoliths. The bulk-rock chemistry confirmed the harzburgites as the main protoliths. The primary mantle minerals such as orthopyroxene, olivine and chromian spinel in Arais serpentinites are still preserved. The orthopyroxene has high Mg# [0Mg/ (Mg + Fe 2+)], ~0.923 on average. It shows intra-grain chemical homogeneity and contains, on average, 2.28 wt.% A1 2 O 3 , 0.88 wt.% Cr 2 O 3 and 0.53 wt.% CaO, similar to primary orthopyroxenes in modern forearc peridotites. The olivine in harzburgites has lower Fo (93−94.5) than that in dunites (Fo 94.3 −Fo 95.9). The Arais olivine is similar in NiO (0.47 wt.% on average) and MnO (0.08 wt.% on average) contents to the mantle olivine in primary peridotites. This olivine is high in Fo content, similar to Mg-rich olivines in ANS ophiolitic harzburgites, because of its residual origin. The chromian spinel, found in harzburgites, shows wide ranges of Cr#s [0Cr/(Cr + Al)], 0.46−0.81 and Mg#s, 0.34−0.67. The chromian spinel in dunites shows an intra-grain chemical homogeneity with high Cr#s (0.82−0.86). The chromian spinels in Arais peridotites are low in TiO 2 , 0.05 wt.% and Y Fe [0 Fe 3+ /(Cr + Al + Fe 3+)], ~0.06 on average. They are similar in chemistry to spinels in forearc peridotites. Their compositions associated with olivine's Fo suggest that the harzbur-gites are refractory residues after high-degree partial melting (mainly ~25−30 % partial melting) and dunites are more depleted, similar to highly refractory perido-tites recovered from forearcs. This is in accordance with the partial melting (>20 % melt) obtained by the whole-rock Al 2 O 3 composition. The Arais peridotites have been possibly formed in a sub-arc setting (mantle wedge), where high degrees of partial melting were available during subduction and closing of the Mozambique Ocean, and emplaced in a forearc basin. Their equilibrium temperature based on olivine−spinel thermometry ranges from 650 to 780 °C, and their oxygen fugacity is high (Δlog ƒO 2 02.3 to 2.8), which is characteristic of mantle-wedge peridotites. The Arais peridotites are affected by secondary processes forming microinclusions inside the dunitic olivine, abundances of car-bonates and talc flakes in serpentinites. These microinclusions have been formed by reaction between trapped fluids and host olivine in a closed system. Lizardite and chrysotile, based on Raman analyses, are the main serpentine minerals with lesser antigorite, indicating that serpentines were possibly formed under retrograde metamorphism during exhumation and near the surface at low T (<400 °C).

Materials circulation in Earth's mantle will be modified if partial melting occurs in the transition zone. Melting in the transition zone is plausible if a significant amount of incompatible components is present in Earth's mantle. We review the experimental data on melting and melt density and conclude that melting is likely under a broad range of conditions, although conditions for dense melt are more limited. Current geochemical models of Earth suggest the presence of relatively dense incompatible components such as K 2 O and we conclude that a dense melt is likely formed when the fraction of water is small. Models have been developed to understand the structure of a melt layer and the circulation of melt and volatiles. The model suggests a relatively thin melt-rich layer that can be entrained by downwelling current to maintain "steady-state" structure. If deep mantle melting occurs with a small melt fraction, highly incompatible elements including hydrogen, helium and argon are sequestered without much effect on more compatible elements. This provides a natural explanation for many paradoxes including (i) the apparent discrepancy between whole mantle convection suggested from geophysical observations and the presence of long-lived large reservoirs suggested by geochemical observations, (ii) the helium/heat flow paradox and (iii) the argon paradox. Geophysical observations are reviewed including electrical conductivity and anomalies in seismic wave velocities to test the model and some future directions to refine the model are discussed.

Although more and more robust evidence for whole mantle convection comes from seismic tomography and geoid modeling, the rare gases and other isotopic or trace element signatures of ridge and hotspot basalts indicate the presence of various isolated geochemical reservoirs in the mantle. We discuss this discrepancy between fluid dynamic views of mantle convection and chemical observations. We compare the

Two fundamentally different orogenic systems have existed on Earth throughout the Phanerozoic. Circum-Pacific accretionary orogens are the external orogenic system formed around the Pacific rim, where oceanic lithosphere semicontinuously subducts beneath continental lithosphere. In contrast, the internal orogenic system is found in Europe and Asia as the collage of collisional mountain belts, formed during the collision between continental crustal fragments. External orogenic systems form at the boundary of large underlying mantle convection cells, whereas internal orogens form within one supercell. Here we present a compilation of hafnium isotope data from zircon minerals collected from orogens worldwide. We find that the range of hafnium isotope signatures for the external orogenic system narrows and trends towards more radiogenic compositions since 550 Myr ago. By contrast, the range of signatures from the internal orogenic system broadens since 550 Myr ago. We suggest that for the external system, the lower crust and lithospheric mantle beneath the overriding continent is removed during subduction and replaced by newly formed crust, which generates the radiogenic hafnium signature when remelted. For the internal orogenic system, the lower crust and lithospheric mantle is instead eventually replaced by more continental lithosphere from a collided continental fragment. Our suggested model provides a simple basis for unravelling the global geodynamic evolution of the ancient Earth.

Benchmark comparisons are an essential tool to verify the accuracy and validity of computational approaches to mantle convection. Six 2D Cartesian compressible convection codes are compared for steady-state constant and temperature-dependent viscosity cases as well as time-dependent constant viscosity cases. In general we find good agreement between all codes when comparing average flow characteristics such as Nusselt number and root-mean-square velocity. At Rayleigh numbers near 10 6 and dissipation numbers between 0 and 2, the results differ by approximately 1%. Differences in discretization and use of finite volumes vs. finite elements dominate the differences. There is a small systematic difference between the use of the anelastic liquid approximation compared to that of the truncated anelastic liquid approximation. In determining the onset of time-dependence, there was less agreement between the codes with a spread in the Rayleigh number where the first bifurcation occurs ranging from 7.79 × 10 5 to 1.05 × 10 6 .

In order to better understand continental growth history, we have determined the U-Pb age of about 1500 detrital zircons from river sands in three major rivers in North America and South America, and have estimated the rate of continental growth in order to discuss the linkage between continental growth and the thermal evolution of the mantle. The method for estimating continental growth from the age population of a significant number of detrital zircons in river sands has three advantages; (1) the almost even collection of zircons from sedimentary rocks and granitic basements in the hinterlands of the major rivers, (2) determination of the age of juvenile crust due to the high closure temperature of the U-Pb systematics of zircons, and the removal of the influence of recycling of crustal materials within the continental crust, and (3) direct determination of the age of continental formation.

The origin of anomalous tectonic subsidence (ATS) of large intracontinental basins long after their most recent phase of extension and last thermal perturbation is the subject of a long standing debate. We show that deep-Earth processes may contribute to the subsidence of these tectonically stable basins by analysing the Tertiary mantle convection-driven topography history of a global set of more than 220 intracontinental basins, integrated into a plate kinematic framework. Most basins are affected by increasing negative dynamic topography over the last 70 Myr, due to the motion of many continents away from large mantle upwellings and towards downwellings previously located along the perimeter of the supercontinent Pangaea. During continental dispersal, increasing negative dynamic topography causes dynamic subsidence of the basins, creating additional accommodation space. We utilise a parameter from a global crustal analysis of intraplate basins, termed "anomalous tectonic subsidence", to quantify sediment accumulation not related to crustal stretching. We propose that dynamic subsidence due to plate motions relative to the underlying mantle, as well as variations in the large-scale convection patterns can significantly contribute to the creation (and destruction) of accommodation space in intraplate basins.

1] Plate tectonics constitutes our primary framework for understanding how the Earth works over geological timescales. High-resolution mapping of relative plate motions based on marine geophysical data has followed the discovery of geomagnetic reversals, mid-ocean ridges, transform faults, and seafloor spreading, cementing the plate tectonic paradigm. However, so-called ''absolute plate motions,'' describing how the fragments of the outer shell of the Earth have moved relative to a reference system such as the Earth's mantle, are still poorly understood. Accurate absolute plate motion models are essential surface boundary conditions for mantle convection models as well as for understanding past ocean circulation and climate as continent-ocean distributions change with time. A fundamental problem with deciphering absolute plate motions is that the Earth's rotation axis and the averaged magnetic dipole axis are not necessarily fixed to the mantle reference system. Absolute plate motion models based on volcanic hot spot tracks are largely confined to the last 130 Ma and ideally would require knowledge about the motions within the convecting mantle. In contrast, models based on paleomagnetic data reflect plate motion relative to the magnetic dipole axis for most of Earth's history but cannot provide paleolongitudes because of the axial symmetry of the Earth's magnetic dipole field. We analyze four different reference frames (paleomagnetic, African fixed hot spot, African moving hot spot, and global moving hot spot), discuss their uncertainties, and develop a unifying approach for connecting a hot spot track system and a paleomagnetic absolute plate reference system into a ''hybrid'' model for the time period from the assembly of Pangea ($320 Ma) to the present. For the last 100 Ma we use a moving hot spot reference frame that takes mantle convection into account, and we connect this to a pre -100 Ma global paleomagnetic frame adjusted 5°in longitude to smooth the reference frame transition. Using plate driving force arguments and the mapping of reconstructed large igneous provinces to core-mantle boundary topography, we argue that continental paleolongitudes can be constrained with reasonable confidence. Citation: Torsvik, T. H., R. D. Müller, R. Van der Voo, B. Steinberger, and C. Gaina (2008), Global plate motion frames: Toward a unified model, Rev. Geophys., 46, RG3004,

We present an overview of the relation between mantle dynamics and plate tectonics, adopting the perspective that the plates are the surface manifestation, i.e., the top thermal boundary layer, of mantle convection. We review how simple convection pertains to plate formation, regarding the aspect ratio of convection cells; the forces that drive convection; and how internal heating and temperature-dependent viscosity affect convection. We examine how well basic convection explains plate tectonics, arguing that basic plate forces, slab pull and ridge push, are convective forces; that sea-floor structure is characteristic of thermal boundary layers; that slab-like downwellings are common in simple convective flow; and that slab and plume fluxes agree with models of internally heated convection. Temperature-dependent viscosity, or an internal resistive boundary (e.g., a viscosity jump and/or phase transition at 660km depth) can also lead to large, plate sized convection cells. Finally, we survey the aspects of plate tectonics that are poorly explained by simple convection theory, and the progress being made in accounting for them. We examine non-convective plate forces; dynamic topography; the deviations of seafloor structure from that of a thermal boundary layer; and abrupt platemotion changes. Plate-like strength distributions and plate boundary formation are addressed by considering complex lithospheric rheological mechanisms. We examine the formation of convergent, divergent and strike-slip margins, which are all uniquely enigmatic. Strike-slip shear, which is highly significant in plate motions but extremely weak or entirely absent in simple viscous convection, is given ample discussion. Many of the problems of plate boundary formation remain unanswered, and thus a great deal of work remains in understanding the relation between plate tectonics and mantle convection. ¥ , thermal expansivity ¦ , dynamic viscosity § , thermal diffusivity¨, the layer's thickness © , and the gravitational field strength (acting normal to the layer and downward). These properties reflect how much the system facilitates convection (e.g., larger ¥ , , and ¦ allow more buoyancy) or impedes convection (e.g., larger § and¨imply that the fluid more readily resists motion or diffuses thermal anomalies away). The combination of these properties in the ratio " ! gives a temperature that ¡ ¤ ¢ must exceed in order to cause convection. The Rayleigh number is the . Black represents cold fluid, light gray is hot fluid. The temperature field shows symmetric convection cells, upwellings, downwellings and thermal boundary layers thickening in the direction of motion (at the top and bottom of the layer, in between the upwellings and downwellings). dimensionless ratio of these temperatures © ¥ ¦ ¡ ¤ ¢ © § and therefore indicates how well the heating represented by ¡ ¤ ¢ will drive convection in this system. Stability analysis predicts that the onset of convection, triggered by the least stable mode, will occur when

Over the past 15 yr, numerical models of convection in Earth's mantle have made a leap forward: they can now produce self-consistent plate-like behaviour at the surface together with deep mantle circulation. These digital tools provide a new window into the intimate connections between plate tectonics and mantle dynamics, and can therefore be used for tectonic predictions, in principle. This contribution explores this assumption. First, initial conditions at 30, 20, 10 and 0 Ma are generated by driving a convective flow with imposed plate velocities at the surface. We then compute instantaneous mantle flows in response to the guessed temperature fields without imposing any boundary conditions. Plate boundaries self-consistently emerge at correct locations with respect to reconstructions, except for small plates close to subduction zones. As already observed for other types of instantaneous flow calculations, the structure of the top boundary layer and upper-mantle slab is the dominant character that leads to accurate predictions of surface velocities. Perturbations of the rheological parameters have little impact on the resulting surface velocities. We then compute fully dynamic model evolution from 30 and 10 to 0 Ma, without imposing plate boundaries or plate velocities. Contrary to instantaneous calculations, errors in kinematic predictions are substantial, although the plate layout and kinematics in several areas remain consistent with the expectations for the Earth. For these calculations, varying the rheological parameters makes a difference for plate boundary evolution. Also, identified errors in initial conditions contribute to first-order kinematic errors. This experiment shows that the tectonic predictions of dynamic models over 10 My are highly sensitive to uncertainties of rheological parameters and initial temperature field in comparison to instantaneous flow calculations. Indeed, the initial conditions and the rheological parameters can be good enough for an accurate prediction of instantaneous flow, but not for a prediction after 10 My of evolution. Therefore, inverse methods (sequential or data assimilation methods) using short-term fully dynamic evolution that predict surface kinematics are promising tools for a better understanding of the state of the Earth's mantle.

We have developed open-source finite-element software for 2-D and 3-D dynamic and quasi-static modeling of crustal deformation. This software, PyLith (current release is 1.5), combines the quasi-static viscoelastic modeling functionality of PyLith 0.8 and its predecessors (LithoMop and Tecton) and the wave propagation modeling functionality of EqSim. The target applications require resolution at spatial scales ranging from tens of meters to hundreds of kilometers and temporal scales for dynamic modeling ranging from milliseconds to minutes or temporal scales for quasi-static modeling ranging from minutes to thousands of years. PyLith development is part of the NSF funded Computational Infrastructure for Geodynamics (CIG) and the software runs on a wide variety of platforms (laptops, workstations, and Beowulf clusters). Binaries (Linux, Darwin, and Windows systems) and source code are available from geodynamics.org. PyLith uses a suite of general, parallel, graph data structures call...

We re-evaluate the possibility that Earth's rotation contributes to plate tectonics on the basis of the following observations: 1) plates move along a westerly polarized flow that forms an angle relative to the equator close to the revolution plane of the Moon; 2) plate boundaries are asymmetric, being their geographic polarity the first order controlling parameter; unlike recent analysis, the slab dip is confirmed to be steeper along W-directed subduction zones; 3) the global seismicity depends on latitude and correlates with the decadal oscillations of the excess length of day (LOD); 4) the Earth's deceleration supplies energy to plate tectonics comparable to the computed budget dissipated by the deformation processes; 5) the Gutenberg-Richter law supports that the whole lithosphere is a self-organized system in critical state, i.e., a force is acting contemporaneously on all the plates and distributes the energy over the whole lithospheric shell, a condition that can be satisfied by a force acting at the astronomical scale. Assuming an ultra-low viscosity layer in the upper asthenosphere, the horizontal component of the tidal oscillation and torque would be able to slowly shift the lithosphere relative to the mantle.

Two-dimensional convection models with moving continents show that continents profoundly affect the pattern of mantle convection. If the continents are wider than the wavelength of the convection cells (~3000 km, the thickness of the mantle), they cause neighboring deep mantle thermal upwellings to coalesce into a single focused upwelling. This focused upwelling zone will have a potential temperature anomaly of about 200°C, much higher than the 100°C temperature anomaly of upwelling zones generated beneath typical oceanic lithosphere. Extensive high-temperature melts (including flood basalts and late potassic granites) will be produced, and the excess temperature anomaly will induce continental uplift (as revealed in sea level changes) and the eventual breakup of the supercontinent. The mantle thermal anomaly will persist for several hundred million years after such a breakup. In contrast, small continental blocks (<1000 km diameter) do not induce focused mantle upwelling zones. Instead, small continental blocks are dragged to mantle downwelling zones, where they spend most of their time, and will migrate laterally with the downwelling. As a result of sitting over relatively cold mantle (downwellings), small continental blocks are favored to keep their cratonic roots. This may explain the long-term survival of small cratonic blocks (e.g., the Yilgarn and Pilbara cratons of western Australia, and the West African craton). The optimum size for long-term stability of a continental block is <3000 km. These results show that continents profoundly affect the pattern of mantle convection. These effects are illustrated in terms of the timing and history of supercontinent breakup, the production of high-temperature melts, and sea level changes. Such two-dimensional calculations can be further refined and tested by three-dimensional numerical simulations of mantle convection with moving continental and oceanic plates.

A convection problem with temperature-dependent viscosity in an infinite layer is presented. As described, this problem has important applications in mantle convection. The existence of a stationary bifurcation is proved together with a condition to obtain the critical parameters at which the bifurcation takes place. For a general dependence of viscosity with temperature a numerical strategy for the calculation of the critical bifurcation curves and the most unstable modes has been developed. For a exponential dependence of viscosity on temperature the numerical calculations have been done. Comparisons with the classical Rayleigh-Bénard problem with constant viscosity indicate that the critical threshold decreases as the exponential rate parameter increases.

A remarkable diversity of geophysical techniques is being used to probe the transition zone between the outer core and the lower mande. This inaccessible region, 2900 km below the Earth's surface, is now recognized to profoundly influence the style of mantle convection, thermal and chemical plume formation, secular variation, and possibly reversals of the magnetic field, core-mantle exchanges of angular momentum, long-wavelength gravitational variations, and chemical evolution of the Earth. Establishing the thermal and chemical structure of the lowermost mande and outermost core is critical to our understanding of the dynamic processes near this transition zone, and progress is now accelerating as a result of an interdisciplinary approach. Recent contributions from seismology, mineral physics, geomagnetism, and geodynamics are synthesized in this article, and a model with a combined thermal and chemical boundary layer at the core-mantle boundary is proposed. The recent formation of the IUGG and AGU committees for SEDI (Studies of the Earth's Deep Interior) is facilitating communication in this and related interdisciplinary efforts to understand how the interior of the planet works.

Geological and geophysical constraints to reconstruct the evolution of the Central Mediterranean subduction zone are presented. Geological observations such as upper plate stratigraphy, HP-LT metamorphic assemblages, foredeep/trench stratigraphy, arc volcanism and the back-arc extension process are used to define the infant stage of the subduction zone and its latest, back-arc phase. Based on this data set, the time dependence of the amount of subducted material in comparison with the tomographic images of the upper mantle along two cross-sections from the northern Apennines and from Calabria to the Gulf of Lyon can be derived. Further, the reconstruction is used to unravel the main evolutionary trends of the subduction process. Results of this analysis indicate that (1) subduction in the Central Mediterranean is as old as 80 Myr, (2) the slab descended slowly into the mantle during the first 20-30 Myr (subduction speeds were probably less than 1 cm year x1 ), (3) subduction accelerated afterwards, producing arc volcanism and back-arc extension and (4) the slab reached the 660 km transition zone after 60-70 Myr. This time-dependent scenario, where a slow initiation is followed by a roughly exponential increase in the subduction speed, can be modelled by equating the viscous dissipation per unit length due to the bending of oceanic lithosphere to the rate of change of potential energy by slab pull. Finally, the third stage is controlled by the interaction between the slab and the 660 km transition zone. In the southern region, this results in an important re-shaping of the slab and intermittent pulses of back-arc extension. In the northern region, the decrease in the trench retreat can be explained by the entrance of light continental material at the trench.

Keywords: seismic tomography mantle convection thermochemical buoyancy geoid and gravity dynamic topography superplumes Recent progress in seismic tomography provides the first complete 3-D images of the combined thermal and chemical anomalies that characterise the unique deep-mantle structure below the African continent. We present a tomography-based model of mantle convection that provides an excellent match to fundamental surface geodynamic constraints on internal density heterogeneity that includes both compositional and thermal contributions, where the latter are constrained by mineral physics. The application of this thermochemical convection model to the problem of African mantle dynamics yields a reconciliation of both surface gravity and topography anomalies to deep-seated mantle flow under the African plate, over a wider range of wavelengths than has been possible to date. On the basis of these results, we predict flow in the African asthenosphere characterised by a clear pattern of focussed upwellings below the major centres of late Cenozoic volcanism, including the Kenya domes, Hoggar massif, Cameroon volcanicline, Cape Verde and Canary Islands. The flow predictions also reveal a deep-seated, large-scale, active hot upwelling below the western margin of Africa under the Cape Verde Islands that extends down to the core-mantle boundary. The scale and dynamical intensity of this 'West African Superplume' is comparable to the 'South African Superplume' that has long been assumed to dominate the large-scale flow dynamics in the deep-mantle under Africa. We evaluate the plausibility of the predicted asthenospheric flow patterns through a comparison with seismic azimuthal anisotropy derived from independent analyses of African shear wave splitting data.

the regions south of Rockall trough and the Iceland-Faroes ridge), in s.d./(N/T I ) 1/2 , the standard error is ,1.5 cm s 21 . This translates to an uncertainty in transport per unit depth across the mouth of Rockall trough (two bins) and the Iceland-Faroes ridge (four bins) of ffiffiffiffiffiffiffiffiffiffi ½2; 4 p £ ð110 £ 10 3 mÞ £ ð0:015 m s 21 Þ < ½2; 3 £ 10 3 m 2 s 21 , where the numbers in brackets refer to the Rockall trough and the Iceland-Faroes ridge, respectively. This would be equivalent to 2.0-2.5 streamlines entering Rockall trough or crossing the Iceland-Faroes ridge, respectively.

We present an overview of the relation between mantle dynam- ics and plate tectonics, adopting the perspective that the plates are the surface manifestation, i.e., the top thermal boundary layer, of mantle convection. We review how simple convection pertains to plate formation, regarding the aspect ratio of convection cells; the forces that drive convection; and how internal heating and temperature-dependent

The understanding of mantle convection is one of the most puzzling problems of modern geophysics. Among the different approaches used by geophysicists to investigate mantle convection, seismic tomography is the only one able to visualize, at the same time, temperature, petrological anomalies, and flow directions from seismic velocity and anisotropy heter~ ogeneities. In order to enable a comparison with other geophysical observables, tomographic models are expanded into spherical harmonics. Most tomographic models agree that down to 300-400 km, deep structure is closely related to plate tectonics and continental distribution. Its corresponding spectral content regularly decreases with decreasing wavelength. At greater depths in the transition zone, degree 2 and (to a lesser extent) degree 6 distributions become predominant. A degree 2 pattern is also present in the lower mantle and is strongly correlated with the geoid but offset with respect to the degree 2 pattern of the transition zone. A simple flow pattern with two upgoing and two downgoing large-scale flows can be invoked to simply explain the predominance of degrees 2 and 6 for seismic velocity and degree 4 for radial anisotropy. Therefore below the apparent complexity of plate tectonics, it turns out that mantle convection is surprisingly simply organized in the transition zone. Between 400 and 1000 km, these large-scale flows are not independent from the circulation in the first 400 km but are connected to some of the most tectonically active zones (fast ridges and slabs). It is also suggested that the degree 6 which seems to be a marker of the hotspot distribution is not independent of the deep degree 2 but might be the consequence of this simple flow pattern. The good correlation between seismic tomography degree 6 and hotspot degree 6 favors an origin at depth of hotspots in the transition zone. Generally, the mantle cannot be divided into independent convecting cells but is characterized by imbricated convection, where different scales coexist and where exchange of matter is possible. Therefore seismic tomography is able to provide very strong constraints on possible models of mantle convection, but many features are still unexplained. Only very long spatial wavelengths are well resolved so far, and a complete understanding of mantle dynamics necessitates relating the different scales present in convective processes. 1. sus on the origin of plumes in a thermal boundary layer, but the depth of the origin of hotspots is still an open question. The rheology of the lithosphere and the existence of hotspots are two simple examples which illustrate the fact that mantle convection differs in many respects from "classical" convection (such as Benard convection) observed in usual viscous fluids. It involves a large range of scales, from the large scale of the Pacific Ocean to the small one of hotspots. Different approaches have been used to characterize and understand mantle convection. So far, none of them can provide a general and consistent explanation of simple features such as the shape and geometry of plates, the origin of hotspots, the number of layers in the mantle, etc. In that context the determination of three-dimensional models of seismic parameters of the mantle (also coined tomographic models) can be considered as a pragmatic or naturalist approach which consists of imaging the structure of convection in orpages 115-137 Paper number 94RG00099 116 ß Montagner: SEISMOLOGY AND MANTLE CONVECTION 32, 2 / REVIEWS OF GEOPHYSICS der to provide clues to the nature of driving mecha-

The Portable, Extensible Toolkit for Scientific computing (PETSc), which focuses on the scalable solution of problems based on partial differential equations, now incorporates new components that allow full composability of solvers for multiphysics and multilevel methods. Through strong encapsulation, we achieve arbitrary, dynamic composition of hierarchical methods for coupled problems and allow customization of all components in composite solvers. For example, we support block decompositions with nested multigrid as well as multigrid on the fully coupled system with block-decomposed smoothers. This paper provides an overview of PETSc's new multiphysics capabilities, which have been used in parallel applications including lithosphere dynamics, subduction and mantle convection, ice sheet dynamics, subsurface reactive flow, fusion, mesoscale materials modeling, and power networks.

In contrast to modern-day plate tectonics, studying Precambrian geodynamics presents a unique challenge as currently there is no agreement upon paradigm concerning the global geodynamics and lithosphere tectonics for the early Earth. This review is focused on discussing results of recent modeling studies in the context of existing concepts and constraints for Precambrian geodynamics with an emphasis placed on three critical aspects: (1) subduction and plate tectonics, (2) collision and orogeny, and (3) craton formation and stability. The three key features of Precambrian Earth evolution are outlined based on combining available observations and numerical and analogue models. These are summarized below:

A comparison of the diamond productions from Panda (Ekati Mine) and Snap Lake with those from southern Africa shows significant differences: diamonds from the Slave typically are un-resorbed octahedrals or macles, often with opaque coats, and yellow colours are very rare. Diamonds from the Kaapvaal are dominated by resorbed, dodecahedral shapes, coats are absent and yellow colours are common. The first two features suggest exposure to oxidizing fluids/melts during mantle storage and/or transport to the Earth's surface, for the Kaapvaal diamond population.

Recent studies of olivine melts have confirmed rheological evidence that the seismic low velocity layer cannot be a region of partial mantle melt and is therefore not at ~1,200C yet this assumption was used for determining oceanic geothermal gradients that, in turn, were used to (1) estimate the radioactive content of oceanic mantle, (2) evaluate plate tectonic driving forces and (3) calculate thermal models of the oceanic lithosphere. The top of the asthenosphere is more likely to be at 500-900°C as is the top of the asthenosphere. If ~900C is adopted, then the oceanic geothermal gradients are corresponding less steep, the rate of mantle heat loss far loss, the concentration of radiogenic heat-producing elements in the mantle much less the oceanic lithosphere is colder and warms more slowly than currently modelled. Such considerations lead to a model of plate tectonics in which viscosity differences in the mantle derive from hydrous materials squeezed out of the liquid outer core as the inner core solidifies. These lower viscosity regions amalgamate and rise as diapirs having lower viscosities than the surrounding mantle but only marginally higher temperatures. Most phase changes in the upper mantle assist this convective flow, but the ~660km phase transition inhibits the vertical passage of mantle materials other than where they are fluidised. The descent of oceanic lithosphere remains dependent mostly on eclogite formation, with the downward passage through the ~660km transition occurring because of the presence of higher density phase (periclase and metallic iron). The lateral motion involves all of the upper mantle and parts of the lower mantle. The revised thermal model for subducting oceanic lithosphere enables intermediate and deep earthquakes to occur by brittle failure.

The lithospheric sinking along subduction zones is part of the mantle convection. Therefore, computing the volume of lithosphere recycled within the mantle by subducting slabs quantifies the equivalent amount of mantle that should be displaced, for the mass conservation criterion. The rate of subduction is constrained by the convergence rate between upper and lower plates and the motion of the subduction hinge H that may either converge or diverge relative to the upper plate. Here, starting from the analysis of the slab hinge kinemat-ics, we evaluate the subduction rate at 31 subduction zones worldwide, useful to compute volumes of sinking lithosphere into the mantle. Our results show that ~190 km 3 /yr and ~88 km 3 /yr of lithospheric slabs are currently subducting below H-divergent and H-convergent subduction zones, respectively. We also propose supporting numerical models providing asymmetric volumes of the subducted lithosphere, using the subduction rate instead of plate convergence, as boundary condition. Furthermore, H-divergent subduction zones appear to be coincident with subductions having "westward"-directed slabs, whereas H-convergent subduction zones are mostly compatible with those that have "eastward-to-northeastward"-directed slabs. On the basis of this geographical polarity, our lithospheric volume estimation gives ~214 km 3 /yr and ~88 km 3 /yr of subducting lithosphere, respectively. This entails that W-directed subduction zones contribute more than twice in lithos-pheric sinking into the mantle with respect to E-toNE directed ones. In accordance with the conservation of mass principle, this volumetric asymmetry in the mantle suggests a displacement of ~120 km 3 /yr of mantle material from west to east, providing a constraint for global asymmetric mantle convection. © 2019.

Global sea level and the pattern of marine inundation on the Australian continent are inconsistent. We quantify this inconsistency and show that it is partly due to a long wavelength, anomalous, downward tilting of the continent to the northeast by 300 m since the Eocene. This downward tilting occurred as Australia approached the subduction systems in South East Asia and is recorded by the progressive inundation of the northern margin of Australia. From the Oligocene to the Pliocene, the long wavelength trend of anomalous topography shows that the southern margin of Australia is characterized by relative subsidence. We quantify the anomalous topography of the Australian continent by computing the displacement needed to reconcile the interpreted pattern of marine incursion with a predicted topography in the presence of global sea level variations. On the southern margin, long wavelength subsidence was augmented by at least 250 m of shorter wavelength anomalous subsidence, consistent with the passage of the southern continental margin over a north-south elongated, 500 km wide, topographic anomaly approximately fixed with respect to the mantle. The present day reconstructed position of this depth anomaly is aligned with the Australian Antarctic Discordance and is consistent with the predicted passage of the Australian continent over a previously subducted slab. Both the long-wavelength continental tilting and smaller-scale paleo-topographic anomaly on the southern Australian margin may have been caused by subduction-generated dynamic topography. These new constraints on continental vertical motion are consistent with the hypothesis that mantle convection induced topography is of the same order of magnitude as global sea level change.

Numerical modelling of mantle convection, with lateral variations of viscosity, and both the 670 km depth endothermic and the 400 km exothermic phase changes, reveals that downwellings are weakened upon crossing the exothermic phase change. A high temperature/low viscosity section is developed within the downgoing current, owing to both the olivine to spinel phase transition and the slowing down of the flow due to the 670 km endothermic transition. This mechanism may cause the creation of a weak zone at 400 km that results in a preferential location for horizontal or vertical slab tearing as revealed by seismic gaps in many slabs.