Spherical Mantle Convection Models Research Articles

Basal Mantle Flow Over LLSVPs Explains Differences in Pacific and Indo‐Atlantic Hotspot Motions

AbstractSurface hotspot motions are approximately a factor of two faster in the Pacific than the Indo‐Atlantic, and the Indo‐Atlantic large low shear velocity province (LLSVP) appears to be significantly taller than the Pacific LLSVP. Hypothesizing that surface hotspot motions are correlated with the motion of plume sources on the upper surface of chemically distinct, intrinsically dense LLSVPs, we use 3D spherical mantle convection models to compute the velocity of plume sources and compare with observed surface hotspot motions. No contrast in the mean speed of Pacific and Indo‐Atlantic hotspots is predicted if the LLSVPs are treated as purely thermal anomalies and plume sources move laterally across the core‐mantle boundary. However, when LLSVP topography is included in the model, the predicted hotspot speeds are, on average, faster in the Pacific than the Indo‐Atlantic, even when modest topography is assigned to both LLSVPs (e.g., 100–300 km). The difference in mean hotspot speed increases to a factor of two for larger and laterally variable LLSVP topography estimated from seismic tomographic model S40RTS (up to 1,100–1,500 km for the Indo‐Atlantic region vs. 700–1,400 km for the Pacific region) and our results also broadly reproduce the convergence of Pacific hotspots toward the center of the Pacific LLSVP. These largescale features of global hotspot motions are only reproduced when ambient mantle material flows over large, relatively stable topographical features, suggesting that LLSVPs are chemically distinct and intrinsically dense relative to ambient mantle material.

Robust global mantle flow trajectories and their validation via dynamic topography histories

SUMMARYThe ability to construct time-trajectories of mantle flow is crucial to move from studies of instantaneous to time-dependent earth models and to exploit geological constraints for mantle convection modelling. However mantle convection is chaotic and subject to the butterfly effect: the trajectories of two identical mantle convection models initialized with slightly different temperature fields diverge exponentially in time until they become uncorrelated. Because one may use seismic inferences about the mantle state as a starting or terminal condition to project mantle flow forward or backward in time, and because the seismic inference is invariably subject to uncertainties, this seemingly would rule out any construction of robust mantle flow trajectories. Here we build upon earlier work which showed that assimilation of the horizontal component of the surface velocity field from a known reference model allows one to overcome the butterfly effect and to construct robust mantle flow trajectories, regardless of the choice of the initial state perturbation. To this end, we use high resolution 3-D spherical mantle convection models in four end-member configurations: an isoviscous purely internally heated model, an isoviscous purely bottom heated model, a model with a radial increase in viscosity along with pure internal heating as well as a model that combines the effects of radial viscosity increase, internal and bottom heating. In order to capture the impact of seismic filtering, we perturb the initial temperature fields of these end-member models through either radial or horizontal smoothing of the temperature field or the application of the tomographic filter of seismic model S20RTS. We assess the quality of the constructed model trajectories via a number of statistical measures as well as comparisons of their dynamic topography histories. The latter is an essential step since mantle flow cannot be directly observed but has to be inferred via its surface manifestations. Importantly, linking mantle flow to surface observations yields patterns representable on a latitude–longitude grid similar to meteorological observables such as precipitation. This invites the application of meteorological quality metrics, such as the power ratio and Taylor diagram, to assess the quality of mantle flow trajectories. We introduce these metrics for the first time in the context of mantle convection and demonstrate their viability based on the compact manner in which they summarize model performance.

Constraints on Mantle Viscosity From Intermediate‐Wavelength Geoid Anomalies in Mantle Convection Models With Plate Motion History

AbstractThe Earth's long‐ and intermediate‐wavelength geoid anomalies are surface expressions of mantle convection and are sensitive to mantle viscosity. While previous studies of the geoid provide important constraints on the mantle radial viscosity variations, the mantle buoyancy in these studies, as derived from either seismic tomography or slab density models, may suffer significant uncertainties. In this study, we formulate 3‐D spherical mantle convection models with plate motion history since the Cretaceous that generate dynamically self‐consistent mantle thermal and buoyancy structures, and for the first time, use the dynamically generated slab structures and the observed geoid to place important constraints on the mantle viscosity. We found that non‐uniform weak plate margins and strong plate interiors are critical in reproducing the observed geoid and surface plate motion, especially the net lithosphere rotation (i.e., degree‐1 toroidal plate motion). In the best‐fit model, which leads to correlation of 0.61 between the modeled and observed geoid at degrees 4–12, the lower mantle viscosity is ∼1.3–2.5 × 1022 Pa⋅s and is ∼30 and ∼600–1,000 times higher than that in the transition zone and asthenosphere, respectively. Slab structures and the geoid are also strongly affected by slab strength, and the observations prefer moderately strong slabs that are ∼10–100 times stronger than the ambient mantle. Finally, a thin weak layer below the 670‐km phase change on a regional scale only in subduction zones produces stagnant slabs in the mantle transition zone as effectively as a weak layer on a global scale.

Controls on the present-day dynamic topography predicted from mantle flow models since 410 Ma

SUMMARYMantle convection induces dynamic topography, the lithosphere's surface deflections driven by the vertical stresses from sublithospheric mantle convection. Dynamic topography has important influences on a range of geophysical and geological observations. Here, we studied controls on the Earth's dynamic topography through 3-D spherical models of mantle convection, which use reconstructed past 410 Myr global plate motion history as time-dependent surface mechanical boundary condition. The numerical model assumes the extended-Boussinesq approximation and includes strongly depth- and temperature-dependent viscosity and phase changes in the mantle. Our results show that removing the chemical layer above the core–mantle boundary (CMB) and including depth-dependent thermal expansivity have both a limited influence on the predicted present-day dynamic topography. Considering phase transitions in our models increases the predicted amplitude of dynamic topography, which is mainly influenced by the 410 km exothermic phase transition. The predicted dynamic topography is very sensitive to shallow temperature-induced lateral viscosity variations (LVVs) and Rayleigh number. The preservation of LVVs significantly increases the negative dynamic topography at subduction zones. A decrease (or increase) of Rayleigh number increases (or decreases) the predicted present-day dynamic topography considerably. The dynamic topography predicted from the model considering LVVs and with a Rayleigh number of 6 × 108 is most compatible with residual topography models. This Rayleigh number is consistent with the convective vigor of the Earth as supported by generating more realistic lower mantle structure, slab sinking rate and surface and CMB heat fluxes. The evolution of the surface heat flux pattern is similar to the long-term eustatic sea level change. Before the formation of Pangea, large negative dynamic topography formed between the plate convergence region of Gondwana and Laurussia. The predicted dynamic topography similar to that of present-day has already emerged by about 262 Ma. Powers for degrees 1–3 dynamic topography at 337 and 104 Ma which correspond to times of higher plate velocities and higher surface heat fluxes are larger.

Geodynamically consistent inferences on the uniform sampling of Earth's paleomagnetic inclinations

Paleomagnetism is a key method to reconstruct the Earth's paleogeography and thus essential for understanding tectonic evolution, but it assumes that the Earth's magnetic field structure has always averaged to a geocentric axial dipole (GAD). The GAD hypothesis may be tested using the observed inclination frequency distribution, but only if continents sampled all of the Earth's latitudes uniformly, which is not known. Here, we provide new insight into the uniform sampling problem by employing a suite of 3D spherical mantle convection models that feature the self-consistent evolution of mantle convection, plate tectonics and continental drift over timescales of 2 Gyr or more. Our results suggest that continents unlikely sampled latitudes uniformly during the Phanerozoic, consistent with previous suggestions. This finding is robust for a variety of geodynamic evolutions with different mantle and lithosphere structures, at least in the absence of true polar wander. For longer sampling durations, uniform sampling typically becomes more feasible, but may only be achieved with confidence after time scales of minimum 1.3 Gyr. This time scale depends on the structure of the mantle and lithosphere and may be shortest when upper mantle viscosity is small such that reduced resistive drag at the cratonic base allows for faster continental drift. Weak plates (low plastic yield strength) promote more dispersed continent configurations, which tends to facilitate uniform sampling. If these conditions are not met, the uniform sampling time scale can easily exceed several billion years. Even the minimum estimate of 1.3 Gyr challenges the validity of using the Phanerozoic inclination frequency distribution to infer the past average magnetic field structure; the approach could however still be applicable using the Precambrian inclination record.

The source location of mantle plumes from 3D spherical models of mantle convection

Mantle plumes are thought to originate from thermal boundary layers such as Earth's core-mantle boundary (CMB), and may cause intraplate volcanism such as large igneous provinces (LIPs) on the Earth's surface. Previous studies showed that the original eruption sites of deep-sourced LIPs for the last 200 Myrs occur mostly above the margins of the seismically-observed large low shear velocity provinces (LLSVPs) in the lowermost mantle. However, the mechanism that leads to the distribution of the LIPs is not clear. The location of the LIPs is largely determined by the source location of mantle plumes, but the question is under what conditions mantle plumes form outside, at the edges, or above the middle of LLSVPs. Here, we perform 3D geodynamic calculations and theoretical analyses to study the plume source location in the lowermost mantle. We find that a factor of five decrease of thermal expansivity and a factor of two increase of thermal diffusivity from the surface to the CMB, which are consistent with mineral physics studies, significantly reduce the number of mantle plumes forming far outside of thermochemical piles (i.e., LLSVPs). An increase of mantle viscosity in the lowermost mantle also reduces number of plumes far outside of piles. In addition, we find that strong plumes preferentially form at/near the edges of piles and are generally hotter than that forming on top of piles, which may explain the observations that most LIPs occur above LLSVP margins. However, some plumes originated at pile edges can later appear above the middle of piles due to lateral movement of the plumes and piles and morphologic changes of the piles. ∼65–70% strong plumes are found within 10 degrees from pile edges in our models. Although plate motion exerts significant controls over the large-scale mantle convection in the lower mantle, mantle plume formation at the CMB remains largely controlled by thermal boundary layer instability which makes it difficult to predict geographic locations of most mantle plumes. However, all our models show consistently strong plumes originating from the lowermost mantle beneath Iceland, supporting a deep mantle plume origin of the Iceland volcanism.

Constraints on mantle viscosity structure from continental drift histories in spherical mantle convection models

Earth's continents drift in response to the force balance between mantle flow and plate tectonics and actively change the plate-mantle coupling. Thus, the patterns of continental drift provide relevant information on the coupled evolution of surface tectonics, mantle structure and dynamics. Here, we investigate rheological controls on such evolutions and use surface tectonic patterns to derive inferences on mantle viscosity structure on Earth. We employ global spherical models of mantle convection featuring self-consistently generated plate tectonics, which are used to compute time-evolving continental configurations for different mantle and lithosphere structures. Our results highlight the importance of the wavelength of mantle flow for continental configuration evolution. Too strong short-wavelength components complicate the aggregation of large continental clusters, while too stable very long wavelength flow tends to enforce compact supercontinent clustering without reasonable dispersal frequencies. Earth-like continental drift with episodic collisions and dispersals thus requires a viscosity structure that supports long-wavelength flow, but also allows for shorter-wavelength contributions. Such a criterion alone is a rather permissive constraint on internal structure, but it can be improved by considering continental-oceanic plate speed ratios and the toroidal-poloidal partitioning of plate motions. The best approximation of Earth's recent tectonic evolution is then achieved with an intermediate lithospheric yield stress and a viscosity structure in which oceanic plates are ∼ 103 × more viscous than the characteristic upper mantle, which itself is ∼ 100–200 × less viscous than the lowermost mantle. Such a structure causes continents to move on average ∼ (2.2 ± 1.0) × slower than oceanic plates, consistent with estimates from present-day and from plate reconstructions. This does not require a low viscosity asthenosphere globally extending below continental roots. However, this plate speed ratio may undergo strong fluctuations on timescales of several 100Myr that may be linked to periods of enhanced continental collisions and are not yet captured by current tectonic reconstructions.

Subduction controls the distribution and fragmentation of Earth’s tectonic plates.

The theory of plate tectonics describes how the surface of Earth is split into an organized jigsaw of seven large plates of similar sizes and a population of smaller plates whose areas follow a fractal distribution. The reconstruction of global tectonics during the past 200 million years suggests that this layout is probably a long-term feature of Earth, but the forces governing it are unknown. Previous studies, primarily based on the statistical properties of plate distributions, were unable to resolve how the size of the plates is determined by the properties of the lithosphere and the underlying mantle convection. Here we demonstrate that the plate layout of Earth is produced by a dynamic feedback between mantle convection and the strength of the lithosphere. Using three-dimensional spherical models of mantle convection that self-consistently produce the plate size–frequency distribution observed for Earth, we show that subduction geometry drives the tectonic fragmentation that generates plates. The spacing between the slabs controls the layout of large plates, and the stresses caused by the bending of trenches break plates into smaller fragments. Our results explain why the fast evolution in small back-arc plates reflects the marked changes in plate motions during times of major reorganizations. Our study opens the way to using convection simulations with plate-like behaviour to unravel how global tectonics and mantle convection are dynamically connected.

On retrodictions of global mantle flow with assimilated surface velocities

Modeling past states of Earth's mantle and relating them to geologic observations such as continental-scale uplift and subsidence is an effective method for testing mantle convection models. However, mantle convection is chaotic and two identical mantle models initialized with slightly different temperature fields diverge exponentially in time until they become uncorrelated, thus limiting retrodictions (i.e., reconstructions of past states of Earth's mantle obtained using present information) to the recent past. We show with 3-D spherical mantle convection models that retrodictions of mantle flow can be extended significantly if knowledge of the surface velocity field is available. Assimilating surface velocities produces in some cases negative Lyapunov times (i.e., e-folding times), implying that even a severely perturbed initial condition may evolve toward the reference state. A history of the surface velocity field for Earth can be obtained from past plate motion reconstructions for time periods of a mantle overturn, suggesting that mantle flow can be reconstructed over comparable times.

The long‐wavelength geoid from three‐dimensional spherical models of thermal and thermochemical mantle convection

AbstractThe Earth's long‐wavelength geoid anomalies have long been used to constrain the dynamics and viscosity structure of the mantle in an isochemical, whole mantle convection model. However, there is strong evidence that the seismically observed large low shear velocity provinces (LLSVPs) in the lower mantle underneath the Pacific and Africa are chemically distinct and likely denser than the ambient mantle. In this study, we have formulated dynamically self‐consistent 3‐D spherical mantle convection models to investigate how chemically distinct and dense piles above the core‐mantle boundary may influence the geoid. Our dynamic models with realistic mantle viscosity structure produce dominantly spherical harmonic degree‐2 convection, similar to that of the present‐day Earth. The models produce two broad geoid and topography highs over two major thermochemical piles in the lower mantle, consistent with the positive geoid anomalies over the Pacific and African LLSVPs. Our geoid analysis showed that the bottom layer with dense chemical piles contributes negatively to the total geoid, while the layer immediately above the chemical piles contributes positively to the geoid, canceling out the effect of the piles. Thus, the bottom part of the mantle, as a compensation layer, has zero net contribution to the total geoid, and the thickness of the compensation layer is ~1000 km or 2 to 3 times as thick as the chemical piles. Our results help constrain and interpret the large‐scale thermochemical structure of the mantle using surface observations of the geoid and topography, as well as seismic models of the mantle.

Statistical cyclicity of the supercontinent cycle

Supercontinents like Pangea impose a first-order control on Earth's evolution as they modulate global heat loss, sea level, climate, and biodiversity. In a traditional view, supercontinents form and break up in a regular, perhaps periodic, manner in a cycle lasting several 100 Myr as reflected in the assembly times of Earth's major continental aggregations: Columbia, Rodinia, and Pangea. However, modern views of the supercontinent cycle propose a more irregular evolution on the basis of an improved understanding of the Precambrian geologic record. Here we use fully dynamic spherical mantle convection models featuring plate-like behavior and continental drift to investigate supercontinent formation and breakup. We further dismiss the concept of regularity but suggest a statistical cyclicity in which the supercontinent cycle may have a characteristic period imposed by mantle and lithosphere properties, but this is hidden in immense fluctuations between different cycles that arise from the chaotic nature of mantle flow.

Focussing of stress by continents in 3D spherical mantle convection with self-consistent plate tectonics

[1] 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.

Heat fluxes at the Earth's surface and core–mantle boundary since Pangea formation and their implications for the geomagnetic superchrons

The Earth's surface and core–mantle boundary (CMB) heat fluxes are controlled by mantle convection and have important influences on Earth's thermal evolution and geodynamo processes in the core. However, the long-term variations of the surface and CMB heat fluxes remain poorly understood, particularly in response to the supercontinent Pangea — likely the most significant global tectonic event in the last 500 Ma. In this study, we reconstruct temporal evolution of the surface and CMB heat fluxes since the Paleozoic by formulating three-dimensional spherical models of mantle convection with plate motion history for the last 450 Ma that includes the assembly and break-up of supercontinent Pangea. Our models reproduce well present-day observations of the surface heat flux and seafloor age distribution. Our models show that the present-day CMB heat flux is low below the central Pacific and Africa but high elsewhere due to subducted slabs, particularly when chemically dense piles are present above the CMB. We show that while the surface heat flux may not change significantly in response to Pangea assembly, it increases by ~ 16% from 200 to 120 Ma ago as a result of Pangea breakup and then decreases for the last 120 Ma to approximately the pre-200 Ma value. As consequences of the assembly and breakup of Pangea, equatorial CMB heat flux reaches minimum at ~ 270 Ma and again at ~ 100 Ma ago, while global CMB heat flux is a maximum at ~ 100 Ma ago. These extrema in CMB heat fluxes coincide with the Kiaman (316–262 Ma) and Cretaceous (118–83 Ma) Superchrons, respectively, and may be responsible for the Superchrons.

Temperature beneath continents as a function of continental cover and convective wavelength

Geodynamic modeling studies have demonstrated that mantle global warming can occur in response to continental aggregation, possibly leading to large‐scale melting and associated continental breakup. Such feedback calls for a recipe describing how continents help to regulate the thermal evolution of the mantle. Here we use spherical mantle convection models with continents to quantify variations in subcontinental temperature as a function of continent size and distribution and convective wavelength. Through comparison to a simple analytical boundary layer model, we show that larger continents beget warming of the underlying mantle, with heating sometimes compounded by the formation of broader convection cells associated with the biggest continents. Our results hold well for purely internally heated and partially core heated models with Rayleigh numbers of 105 to 107 containing continents with sizes ranging from that of Antarctica to Pangea. Results from a time‐dependent model with three mobile continents of various sizes suggests that the tendency for temperatures to rise with continent size persists on average over timescales of billions of years.

Mechanism for generating stagnant slabs in 3-D spherical mantle convection models at Earth-like conditions

Seismic tomography reveals the natural mode of convection in the Earth is whole mantle with subducted slabs clearly seen as continuous features into the lower mantle. However, simultaneously existing alongside these deep slabs are stagnant slabs which are, if only temporarily, trapped in the upper mantle. Previous numerical models of mantle convection have observed a range of behavior for slabs in the transition zone depending on viscosity stratification and mineral phase transitions, but typically only exhibit flat-lying slabs when mantle convection is layered or trench migration is imposed. We use 3-D spherical models of mantle convection which range up to Earth-like conditions in Rayleigh number to systematically investigate three effects on mantle dynamics: (1) the mineral phase transitions, (2) a strongly temperature-dependent viscosity with plastic yielding at shallow depth, and (3) a viscosity increase in the lower mantle. First a regime diagram is constructed for isoviscous models over a wide range of Rayleigh number and Clapeyron slope for which the convective mode is determined. It agrees very well with previous results from 2-D simulations by Christensen and Yuen (1985), suggesting present-day Earth is in the intermittent convection mode rather than layered or strictly whole mantle. Two calculations at Earth-like conditions (Ra and RaH=2í107 and 5í108, respectively) which include effects (2) and (3) are produced with and without the effect of the mineral phase transitions. The first calculation (without the phase transition) successfully produces plate-like behavior with a long wavelength structure and surface heat flow similar to Earth's value. While the observed convective flow pattern in the lower mantle is broader compared to isoviscous models, it basically shows the behavior of whole mantle convection, and does not exhibit any slab flattening at the viscosity increase at 660km depth. The second calculation which includes the phase transitions successfully exhibits the coexisting state of stagnant and penetrating slabs within the transition zone. These results indicate the importance of both a viscosity increase and mineral phase transitions for generating the structure of stagnant slabs observed by seismic tomography.

Giant impacts on early Mars and the cessation of the Martian dynamo

Although Mars currently has no global dynamo‐driven magnetic field, widespread crustal magnetization provides strong evidence that such a field existed in the past. The absence of magnetization in the younger large Noachian basins suggests that a dynamo operated early in Martian history but stopped in the mid‐Noachian. Within a 100 Ma period, 15 giant impacts occurred coincident with the disappearance of the global magnetic field. Here we investigate a possible causal link between the giant impacts during the early and mid‐Noachian and the cessation of the Martian dynamo at about the same time. Using three‐dimensional spherical mantle convection models, we find that impact heating associated with the largest basins (diameters >2500 km) can cause the global heat flow at the core‐mantle boundary to decrease significantly (10–40%). We suggest that such a reduction in core heat flow may have led to the cessation of the Martian dynamo.

Synthetic tomography of plume clusters and thermochemical piles

Seismic tomography elucidates broad, low shear-wave velocity structures in the lower mantle beneath Africa and the central Pacific with uncertain physical and compositional origins. One hypothesis suggests that these anomalies are caused by relatively hot and intrinsically dense material that has been swept into large thermochemical piles by mantle flow. An alternative hypothesis suggests that they are instead poorly imaged clusters of narrow thermal plumes. Geodynamical calculations predict fundamentally different characters of the temperature fields of plume clusters and thermochemical piles. However the heterogeneous resolution of tomographic models makes direct comparison between geodynamical temperature fields and tomographic shear-wave anomalies tenuous at best. Here, we compute synthetic tomographic images for 3D spherical mantle convection models and evaluate how well thermal plumes and thermochemical piles can be reconciled with actual seismic tomography images. Geodynamical temperature fields are converted to shear-wave velocity using experimental and theoretical mineral physics constraints. The resultant shear-wave velocity fields are subsequently convolved with the resolution operator from seismic model S20RTS to mimic the damping and distortion associated with heterogeneous seismic sampling of the mantle. We demonstrate that plume clusters are tomographically blurred into two broad, antipodal velocity anomalies in agreement with S20RTS and other global seismic models. Large, thermochemical piles are weakly distorted by the tomographic filter. The power spectrum of velocity heterogeneity peaks at spherical harmonic degree 3, unlike the degree-2 maximum in S20RTS, but decays rapidly similar to S20RTS and many other seismic models. Predicted tomography from thermochemical pile and plume cluster models correlate equally well with S20RTS given the uncertainties in the numerical modeling parameters. However, thermochemical piles match tomography better in visual comparison and in the overall character of the harmonic spectrum.

Supercontinent formation from stochastic collision and mantle convection models

The large-scale tectonics in the last billion years (Ga) are predominated by the assembly and breakup of supercontinents Rodinia and Pangea. The mechanisms controlling the assembly of supercontinents are not clear. Here, we investigate the assembly of a supercontinent with 1) stochastic models of randomly-moving continental blocks and 2) 3-D spherical models of mantle convection with continental blocks. For the stochastic models, we determined the time required for all the blocks to assemble into a single supercontinent on a spherical surface. We found that the assembly time from our stochastic models is significantly longer than inferred for Pangea and Rodinia. However, our study also suggests that the assembly time from stochastic models is sensitive to the rules for randomly assigning continental motion in the models. In our dynamic models of mantle convection, continental blocks are modeled as deformable and compositionally distinct materials from the mantle. We found that mantle convective planform has significant effects on supercontinent assembly. For models with moderately strong lithosphere and the lower mantle relative to the upper mantle that lead to degree-1 mantle convection, continental blocks always assemble to a supercontinent in ∼ 250 million years (Ma) and this assembly time is consistent with inferred for Pangea and Rodinia. However, for models with intrinsically small-scale mantle flows, we found that even when continental blocks merge to form a supercontinent, the assembly times are too long and the convective structures outside of supercontinent regions are of too small wavelengths, compared with observed.

Controls on plume heat flux and plume excess temperature

Plume heat flux and plume excess temperature in the upper mantle inferred from surface observations may pose important constraints on the heat flux from the core and mantle internal heating rate. This study examined the relationship between plume heat flux Qp, core‐mantle boundary (CMB) heat flux Qcmb and plume excess temperature ΔTplume in thermal convection using both numerical modeling and theoretical analysis. 3‐D regional spherical models of mantle convection were computed with high resolution and for different Rayleigh number, internal heat generation rate, viscosity structures and dissipation number. An analytic model was developed for variations in Qp and ΔTplume with depth. The results can be summarized as following. (1) Mantle plumes immediately above the CMB carry nearly 80%–90% of the CMB heat flux. (2) Qp and ΔTplume decrease by approximately a factor of two for plumes to ascend from near the CMB to the upper mantle depth. (3) Our analytic model indicates that the decrease in Qp and ΔTplume is mainly controlled by the steeper adiabatic gradient of plumes compared with the ambient mantle and the reduction ratios for Qp and ΔTplume due to this effect depend upon the dissipation number and the distance over which plumes ascend. (4) The subadiabatic temperature also contributes to the reduction of Qp and ΔTplume, but its contribution is only 20% to 30%. Subadiabatic temperature from our models with >50% internal heating rate ranges from 35 K to 170 K for CMB temperature of 3400°C. (5) Our results confirms that ∼70% internal heating rate for the mantle or Qcmb of ∼11 TW is required to reproduce the plume‐related observations.

Topology of the postperovskite phase transition and mantle dynamics.

The postperovskite (ppv) phase transition occurs in the deep mantle close to the core-mantle boundary (CMB). For this reason, we must include in the dynamical considerations both the Clapeyron slope and the temperature intercept, T(int), which is the temperature of the phase transition at the CMB pressure. For a CMB temperature greater than T(int), there is a double crossing of the phase boundary by the geotherms associated with the descending flow. We have found a great sensitivity of the shape of the ppv surface due to the CMB from variations of various parameters such as the amount of internal heating, the Clapeyron slope, and the temperature intercept. Three-dimensional spherical models of mantle convection that can satisfy the seismological constraints depend on the Clapeyron slope. At moderate value, 8 MPa/K, the best fit is found with a core heat flow amounting for 40% of the total heat budget (approximately equal to 15 TW), whereas for 10 MPa/K the agreement is for a lower core heat flow (20%, approximately equal to 7.5 TW). In all cases, these solutions correspond to a temperature intercept 200 K lower than the CMB temperature. These models have holes of perovskite adjacent to ppv in regions of hot upwellings.