Studies Of Mantle Convection Research Articles

Dynamics of the African Plate 75 Ma: From Plate Kinematic Reconstructions to Intraplate Paleo‐Stresses

AbstractPlate reconstruction studies show that the Neotethys Ocean was closing due to the convergence of Africa and Eurasia toward the end of the Cretaceous. The period around 75 Ma reflects the onset of continental collision between the two plates as convergence continued to be taken up mostly by subduction of the Neotethys slab beneath Eurasia. The Owen transform plate boundary in the northeast accommodated the fast northward motion of the Indian plate relative to the African plate. The rest of the plate was surrounded by mid‐ocean ridges. Africa was experiencing continent‐wide rifting related to northeast‐southwest extension. We aim to quantify the forces and paleostresses that may have driven this continental extension. We use the latest plate kinematic reconstructions in a grid search to estimate horizontal gravitational stresses (HGSs), plate boundary forces, and the plate's interaction with the asthenosphere. The contribution of dynamic topography to HGSs is based on recent mantle convection studies. We model intraplate stresses and compare them with the strain observations. The fit to observations favors models where dynamic topography amplitudes are smaller than 300 m. The results also indicate that the net pull transmitted from slab to the surface African plate was low. To put this into context, we notice that available tectonic reconstructions show fragmented subduction zones and various colliding micro‐continents along the northern margin of the African plate around this time. We therefore interpret a low net pull as resulting from either a small average slab length or from the micro‐continents' resistance to subduction.

Benchmarking multiphysics software for mantle convection

Numerical simulations are a highly valuable tool for improving our understanding of mantle dynamics. COMSOL Multiphysics® is a commercial software suite designed to numerically model experiments featuring multiple branches of physics. This modeling approach applies to mantle convection, which can be viewed as a combination of fluid dynamics and thermodynamics. COMSOL® is of interest to the geoscience community due to its ease of use compared to other available codes, and it has been used in previous mantle convection studies. However, COMSOL® has not been extensively benchmarked for mantle convection. In this study, we confirm the accuracy of COMSOL® against several established benchmarks pertaining to a variety mantle convection features and geometries. Overall, we find reasonable agreement between the results from COMSOL® and reported benchmark data. This study may also serve the geoscience community as a guide for using COMSOL® to model mantle convection.

Possible tectonic patterns along the eastern margin of Gondwanaland from numerical studies of mantle convection

Two end-member scenarios have been proposed for the tectonic situation along the eastern margins of Gondwanaland before Zealandia was formed ca. 100 million years ago (Ma), namely: (1) A subduction zone located far from the eastern margin of Zealandia, wherein Zealandia may have separated from Gondwanaland by plume push of an active hotspot plume.; (2) A subduction zone located along the eastern margin of Gondwanaland, wherein Zealandia possibly separated from Gondwanaland via trench/subduction retreat. Assuming that the thermal structure of the deep mantle and source of hotspot plumes remained relatively stationary over the last hundred million years, major hotspot plumes with a large buoyancy flux did not exist under Zealandia; the eastern margins of Gondwanaland were far from two large low-shear-velocity provinces under the Africa–Atlantic and South Pacific regions. Herein, through numerical studies of three-dimensional global mantle convection, we examined the mantle convection and surface tectonic patterns at ~100 Ma. The present model considered the real configuration of Gondwanaland at the model surface to observe long-term variations of mantle convection and the resulting surface tectonic conditions. The results demonstrate that the extensive subduction zones developed preferentially along the eastern margin of Gondwanaland when the temperature anomaly of the lower mantle was primarily dominated by high-temperature regions under present-day Africa–Atlantic and South Pacific regions. The results of this study support one of the proposed hypotheses, where the breakup at the eastern margins of Gondwanaland at ~100 Ma occurred via trench/subduction retreat.

On formulations of compressible mantle convection

SUMMARY Mantle convection and long-term lithosphere dynamics in the Earth and other planets can be treated as the slow deformation of a highly viscous fluid, and as such can be described using the compressible Navier–Stokes equations. Since on Earth-sized planets the influence of compressibility is not a dominant effect, density deviations from a reference profile are at most on the order of a few percent and using the full governing equations poses numerical challenges, most modelling studies have simplified the governing equations. Common approximations assume a temporally constant, but depth-dependent reference profile for the density (the anelastic liquid approximation), or drop compressibility altogether and use a constant reference density (the Boussinesq approximation). In most previous studies of mantle convection and crustal dynamics, one can assume that the error introduced by these approximations was small compared to the errors that resulted from poorly constrained material behaviour and limited numerical accuracy. However, as model parametrizations have become more realistic, and model resolution has improved, this may no longer be the case and the error due to using simplified conservation equations might no longer be negligible: while such approximations may be reasonable for models of mantle plumes or slabs traversing the whole mantle, they may be unsatisfactory for layered materials experiencing phase transitions or materials undergoing significant heating or cooling. For example, at boundary layers or close to dynamically changing density gradients, the error arising from the use of the aforementioned compressibility approximations can be the dominant error source, and common approximations may fail to capture the physical behaviour of interest. In this paper, we discuss new formulations of the continuity equation that include dynamic density variations due to temperature, pressure and composition without using a reference profile for the density. We quantify the improvement in accuracy relative to existing formulations in a number of benchmark models and evaluate for which practical applications these effects are important. Finally, we consider numerical aspects of the new formulations. We implement and test these formulations in the freely available community software aspect, and use this code for our numerical experiments.

Towards global SEM mantle convection simulations on polyhedral-based grids

A novel approach to the construction of three-dimensional grids in spherical geometries is described. The grids are based on a range of underlying regular polyhedra. The faces of the polyhedra are arranged into a number of diamonds in the latitudinal and longitudinal directions to facilitate the creation of a structured mesh. Each polyhedron is completely characterized in terms of the arrangement of diamonds. The approach is shown to be very flexible in terms of the meshes that can be generated. It also aids comparisons between the grids used in many mantle convection studies. A spectral element discretization of Poisson’s equation is performed to demonstrate the efficacy of the grid generation technique. Rapidly convergent approximations are obtained that demonstrate that fewer degrees of freedom are required to obtain a desired level of accuracy compared with low-order finite element approximations. • Structured meshes for problems defined in 3D spherical domains are generated. • The approach is based on the projection of a regular polyhedron onto a sphere. • Spectral element approximations of Poisson’s equation are generated. • Excellent error reduction is obtained on all of the polyhedral grids generated.

Influences on the positioning of mantle plumes following supercontinent formation

AbstractSeveral mantle convection studies analyzing the effects of supercontinent formation and dispersal show that the genesis of subcontinental plumes results from the formation of subduction zones at the edges of the supercontinent rather than from the effect of continental thermal insulation or thermochemical piles. However, the influence of subduction zone location on the position of subcontinental plumes has received little attention. This study analyzes 2‐D and 3‐D numerical models of supercontinent formation (in an isochemical mantle) to assess the role of subduction and mantle viscosity contrast in the generation of subcontinental mantle plumes. We find that once a critical supercontinent width is reached, plumes do not form under the center of a supercontinent. In studies featuring a low viscosity lower mantle, the surface positions of the initial plumes (arriving within 90 Myr of supercontinent assembly) become locked beneath the continent at a distance 2000–3000 km from the continental margin. However, the broad downwellings in simulations that feature a high‐viscosity lower mantle trigger plumes at a greater distance from the continental margin subduction. For all mantle viscosity profiles, subcontinental plumes show dependence on the location of supercontinent margin subduction. As theories differ on the role of core‐mantle boundary chemical piles in plume formation, it is significant that our isochemical models show that the formation of subduction zones at the margins of a supercontinent has a profound effect on subcontinental mantle dynamics. Our results may help to explain what determined the eruption sites of past (and future) large igneous provinces.

Three-dimensional visualization of numerically simulated, present-day global mantle flow

The behavior of mantle convection plays a primary role in the earth’s dynamic evolution. Numerical simulation of mantle convection is one of the most powerful tools to resolve the thermal and mechanical evolution in the earth’s mantle. The developments in numerical techniques and increases in computational power over the last 10–15 years have facilitated great progress in simulation studies of mantle convection. In addition, with increases in computational resolution, one can expect greater focus on the use of three-dimensional (3D) visualization of mantle convection in gaining a deeper understanding of mantle dynamics. This paper presents simulations of the present-day, instantaneous global mantle flow based on geophysical observations such as seismic tomography models and 3D visualizations of present-day mantle convection. Numerical results are summarized in terms of two aspects of geodynamics: (1) the mixing properties and topological structure of the mantle interior, and (2) the presence of strong mantle upwelling beneath the South Pacific enhanced by the low-viscosity D″ layer.

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.

Implementation and application of adaptive mesh refinement for thermochemical mantle convection studies

Numerical modeling of mantle convection is challenging. Owing to the multiscale nature of mantle dynamics, high resolution is often required in localized regions, with coarser resolution being sufficient elsewhere. When investigating thermochemical mantle convection, high resolution is required to resolve sharp and often discontinuous boundaries between distinct chemical components. In this paper, we present a 2‐D finite element code with adaptive mesh refinement techniques for simulating compressible thermochemical mantle convection. By comparing model predictions with a range of analytical and previously published benchmark solutions, we demonstrate the accuracy of our code. By refining and coarsening the mesh according to certain criteria and dynamically adjusting the number of particles in each element, our code can simulate such problems efficiently, dramatically reducing the computational requirements (in terms of memory and CPU time) when compared to a fixed, uniform mesh simulation. The resolving capabilities of the technique are further highlighted by examining plume‐induced entrainment in a thermochemical mantle convection simulation.

South Pacific mantle plumes imaged by seismic observation on islands and seafloor

The South Pacific region is characterized by a broadly elevated seafloor known as the South Pacific superswell. This region has a concentration of midplate volcanoes that experienced massive eruptions in the mid‐Cretaceous period (90–120 Ma). These characteristics suggest the presence of a large‐scale mantle plume beneath the South Pacific, called the South Pacific superplume. The geometry, origin depth, temperature, and composition of the superplume remain controversial, however, mainly due to the lack of seismological data that documents the mantle structure beneath the South Pacific. Seismic stations are sparse in the area due to its remote ocean environment. To obtain a better seismic image of the superplume, we deployed temporary broadband seismographs on oceanic islands and the seafloor in the South Pacific, which made possible the highest spatial resolution that has ever been achieved for the mantle structure beneath the region. The seismic image obtained from this new seismic data indicates that large‐scale low‐velocity anomalies (on the order of 1000 km in diameter), indicative of the superplume, are located from the bottom of the mantle to a depth of 1000 km, and small‐scale low‐velocity anomalies (on the order of 100 km in diameter) are present above it. A comparison of the seismic image with recent mantle convection studies based upon laboratory and numerical experiments suggests that the superplume may be a hot and chemically distinct mantle dome, and that the small‐scale anomalies may be narrow plumes generated from the top of the dome. This model may explain various characteristics of hot spots in the South Pacific, such as the seafloor swell, short‐lived hot spot chains, and the periodicity of massive eruptions.

Modeling mantle convection in the spherical annulus

Most methods for modeling mantle convection in a two-dimensional (2D) circular annular domain suffer from innate shortcomings in their ability to capture several characteristics of the spherical shell geometry of planetary mantles. While methods such as rescaling the inner and outer radius to reduce anomalous effects in a 2D polar cylindrical coordinate system have been introduced and widely implemented, such fixes may have other drawbacks that adversely affect the outcome of some kinds of mantle convection studies. Here we propose a new approach that we term the “spherical annulus,” which is a 2D slice that bisects the spherical shell and is quantitatively formulated at the equator of a spherical polar coordinate system after neglecting terms in the governing equations related to variations in latitude. Spherical scaling is retained in this approximation since the Jacobian function remains proportional to the square of the radius. We present example calculations to show that the behavior of convection in the spherical annulus compares favorably against calculations performed in other 2D annular domains when measured relative to those in a fully three-dimensional (3D) spherical shell.

Mantle convection: A review

The solid-state convection in the Earth mantle is characterized by plate tectonics, which shapes the tectonic activities of the Earth, and superplumes as broad hot regions chemically distinct from the surrounding regions in deep lower mantle. Recent numerical studies of mantle convection suggest that the rigidly moving plates occur on the Earth because the rupture strength of plate margins is sufficiently low, while that of plate interiors is high enough to inhibit spontaneous formation of new plate boundaries by the weight of the plates themselves. This implies that the activity of plate tectonics has fluctuated much in the Earth history. Recent numerical studies also suggest that the superplumes develop owing to the chemical differentiation of the mantle by ridge magmatism. Superplumes have probably induced frequent and vigorous hot spot volcanism in the early Earth. It is now within reach to construct an integrated model for tectonic and structural evolution of the mantle in the Earth and other terrestrial planets.

Effects of a perovskite‐post perovskite phase change near core‐mantle boundary in compressible mantle convection

Numerical simulations of compressible, isochemical mantle convection are used to investigate the effect of the perovskite to post‐perovskite phase transition at around 2700 km depth, which has recently been discovered by high‐pressure experiments and ab initio calculations, on the convective planform, temperature, and heat transport characteristics of the mantle. The usual phase transitions at 410 km (olivine‐spinel) and 660 km (spinel‐perovskite) are also included. The exothermic post‐perovskite phase change at 2700 km depth destabilizes the lower thermal boundary layer, increasing the heat flow, increasing interior mantle temperature, and increasing the number and time‐dependence of upwelling plumes. The resulting weak, highly time‐dependent upwellings also have a smaller horizontal spacing than the plumes that occur in the absence of the phase transition. While the influence of post‐perovskite phase change may be smaller than that of some other complexities, such as compositional stratification, it appears to have an important enough effect that it should not be ignored in dynamical studies of mantle convection.

The influence of thermochemical convection on the fixity of mantle plumes

A general feature of both isochemical and thermochemical studies of mantle convection is that horizontal plume velocities tend to be smaller than typical convective velocities, however, it is not clear which system leads to a greater fixity of mantle plumes. We perform two- and three-dimensional numerical calculations and compare both thermochemical and isochemical cases with similar convective vigor to determine whether presence of a dense component in the mantle can lead to smaller ratios of horizontal plume velocity to surface velocity. We investigate different viscosity and density contrasts between chemical components in the thermochemical calculations, and we perform isochemical calculations with both free-slip and no-slip bottom boundary conditions. We then compare both visually and quantitatively the results of the thermochemical and isochemical calculations to determine which leads to greater plume fixity. We find that horizontal plume velocities for thermochemical calculations are similar to those from isochemical calculations with no-slip bottom boundary conditions. In addition, we find that plumes tend to be more fixed for isochemical cases with free-slip bottom boundary conditions for two-dimensional calculations, however, in three dimensions, we find that plume fixity is similar to that observed in thermochemical calculations.

Pressure- and temperature-dependent thermal expansivity and the effect on mantle convection and surface observables

SUMMARY In most mantle convection studies with variable thermal expansivity only the pressure dependence is considered. Here we investigate the effect of temperature- and/or pressure-dependent thermal expansivity α on the distribution of buoyancy forces in mantle convection. Thermal expansivity is calculated for the dominant upper-mantle mineral, forsterite, and a map of its dependence on T and p is given. By studying simple 2-D steady-state constant-viscosity convection and comparing cases with constant α, α( p), α(T ) and α(p, T) we find that at mantle temperatures the pressure dependence of α is important. For the lithosphere the dependence of α on temperature dominates, since the temperature dependence of α is much stronger in the low-pressure regime. Also dynamic topography changes considerably (up to 15 per cent) if α is T- and p-dependent compared with a constant or only p-dependent case. Scaling laws for the Nusselt number and the rms velocity are obtained. They differ from the constant-α case by at most 12 per cent if an effective Rayleigh number based on the spatial average of α is used.

The influence of tectonic plates on mantle convection patterns, temperature and heat flow

SUMMARY The dynamic coupling between plate motion and mantle convection is investigated in a suite of Cartesian models by systematically varying aspect ratios and plate geometries. The aim of the study presented here is to determine to what extent plates affect mantle flow patterns, temperature and surface heat flux. To this end, we compare numerical convection models with free-slip boundary conditions to models that incorporate between one and six plates, where the geometries of the plates remain fixed while the plate velocities evolve dynamically with the flow. We also vary the widths of the plates and the computational domain in order to determine what constraint these parameters place on the mean temperature, heat flux and plate velocity of mantle convection models. We have investigated the influence of plates for three whole-mantle convection cases that differ in their heating modes (internally heated and basally heated) and rheologies (isoviscous and depth-dependent viscosity). We present a systematic investigation of over 30 models that exhibit increasingly complex behaviour in order to understand highly time-dependent systems using the insight gained from simpler models. In models with aspect ratios from 0.5 to 12 we find that for the same heating mode, variations in temperature can be as much as 40 per cent when comparing calculations with unit-width plates to models incorporating plates with widths equal to five times the model depth. Mean surface heat flux may decrease by 60 per cent over the same range of plate widths. We also find that internally heated mantle convection models incorporating plates exhibit novel behaviour that, we believe, has not been described previously in mantle convection studies. Specifically, in internally heated models, plate motion is characterized by episodic reversals in direction driven by changes in the mantle circulation from clockwise to counterclockwise and vice versa. These flow reversals occur in internally heated convection and are caused by a build-up of heat in the interiors of wide convection cells close to mantle downwellings. We find that flow reversals occur rapidly and are present in both single-plate and multiple-plate models that include internal heating. This behaviour offers a possible explanation for why the Pacific plate suddenly changed its direction some 43 Ma.

Mantle Reservoirs and Mantle Convection: Lessons from the Hawaiian Plume

The Hawaiian plunae has long played a central role in conceptual, theoretical, geophysical and geochemical studies of mantle convection. Over the past 80 million years, the Hawaiian hotspot has been the site of the most voluminous intraplate basaltic volcanism on the Earth's surface, and still provides the strongest evidence to date for the presence of active upwelling in the upper mantle. There are several fundamental observations about Hawaiian volcanism which pertain to mantle convection on regional and global scales. Though geophysical studies are increasingly focused on looking for relative hotspot motions, the Hawaiian plume has remained essentially stationary (-t-100 km) over the past 80 Ma. Distinct structural lineaments ( 'Loa' and 'Kea' trends) along the youngest Hawaiian islands erupt compositionally distinct lavas, though there is a certain amount of overlap. Adjacent active Hawaiian volcanoes, separated by as little as 25 km, erupt compositionally distinct shield lavas, which places some limits on the lateral scale of source heterogeneity (Frey and Rhodes, 1993). Finally, there exist at least three (and possibly fouO compositionally distinct components in Hawaiian lavas, all of which are different in composition from the upper mantle source of MORB. Any model of mantle convection must be able to reproduce the thermal and chemical perturbations which are exemplified by the Hawaiian plume and its volcanic expression.

Measuring the pulse of a plume with the sedimentary record

Magmatic underplating associated with mantle plume activity is an important mechanism for driving regional surface uplift and denudation of large portions of the continents1,2. Such uplift occurs rapidly because substantial volumes of basaltic melt are added to the crust over geologically short periods of time (1–10 Myr)2, and can lead to large amounts of clastic sediment being shed into surrounding basins3. An intensively studied example of this process occurred in the North Sea basin during the Palaeogene period, where discrete pulses of deposition were triggered when sands were remobilized downslope from the shelf by turbidity currents and debris flows as a result of episodic changes of relative sea level3. Here we correlate the timing of these sediment pulses with the timing of surface uplift inferred to have been caused by episodic magmatic underplating on the continental shelf of northwestern Europe. This magmatism was related to activity of the Iceland plume, suggesting that individual pulses of sedimentation provide a potentially sensitive measure of plume activity, and so may be used to resolve time-dependent fluctuations in mantle plume activity predicted by theoretical studies of mantle convection.

A simple parameterized model of Earth's thermal history with the transition from layered to whole mantle convection

Recent studies of mantle convection suggest a possible scenario for Earth's history in which the convection has changed its style from layered to whole mantle because of the existence of an endothermic phase boundary. To understand the possible thermal consequence of this ‘transition’, we shall re-examine the thermal history of Earth with different types of convection mode (i.e., whole mantle convection, layered mantle convection and convection with a transition) using a simple parameterized scheme. For the whole mantle convection model we shall confirm the results presented by previous workers (i.e., a small β of <0.1 (the index of the power-law relation between the Nusselt and Rayleigh numbers) is required for a low Urey ratio (∼ 0.4) Earth. For the layered case the Urey ratio, β and the concentration of the radiogenic heat source in the lower mantle are restricted by the melting constraints. In order to avoid massive melting of the mantle at present and in the past, a depleted lower mantle is required, which confirms the results of the previous studies, although the amount of depletion is not so large as previous estimates. We shall also show that a low β (e.g., < 0.1) and low Urey ratio (∼ 0.4) Earth are not favourable for layered convection models, because they will predict massive melting of the mantle in the past and at the present. For the transition-type convection model, we find that early transition (e.g., older than 1 Ga B.P. is allowed for low β (< 0.1) with a low Urey ratio (∼ 0.4) or for high β (> 0.2) with a high Urey ratio (∼ 0.8). This is almost identical to the whole mantle case. The implication is that, because whole mantle convection is powerful enough, Earth may loose the memory of early layering that may have existed more than 1 Ga B.P. The change in flow velocity associated with the transition is expected to be a factor of five or more. The temperature of the upper mantle before the transition took place may be lower than the present mantle temperature.

Studies of Mantle Convection in Japan.

The geodynamic studies carried out in Japan during the period of 1982-1992 have been reviewed. The studies include (1) estimates of mantle viscosity from the data of post glacial rebound, (2) numerical studies on the effects of heterogeneous distribution of heat producing elements on mantle convection, (3) numerical studies on the effects of heterogeneous distribution of major elements on mantle convection, (4) numerical studies on the influences of temperature-dependence and anisotropy of viscosity on mantle convection, and (5) numerical studies on the effects of the phase-transitions in the transition layer on mantle convection.