Spherical Mantle Convection Models Research Articles

Influence of past and present-day plate motions on spherical models of mantle convection: implications for mantle plumes and hotspots

SUMMARY We explore the influence of tectonic plate motions, given by the no-net-rotation (NNR)NUVEL-1 model, on a 3-D spherical model of mantle convection in which plates can be coupled to the underlying mantle flow in a dynamically consistent manner. We first derived a reference convection model in which only the NUVEL-1 geometry of the tectonic plates is prescribed. The plate rotations are then predicted on the basis of the buoyancy forces in the mantle, ensuring a dynamical balance of torques acting on the plates. This dynamically consistent reference convection model, which is based on a simple two-layer viscosity profile, yields the main features of plate tectonics: linear subduction zones, passive diverging zones and four mantle plumes. We next developed a time-dependent convection model, which is initiated with the average radial temperature field extracted from the reference convection model, and in which we imposed the NNR-NUVEL-1 plate velocities. This convection simulation yields six focused upwelling plumes, whose location and number is very similar to the primary terrestrial hotspots which have been recently identified (Courtillot et al. 2003). In all convection models incorporating the NNR-NUVEL-1 plate motions, we find that the surface heat flow and mantle potential temperature stay essentially constant, demonstrating the compatibility between the observed NNR-NUVEL-1 velocities and the internal buoyancy forces in the mantle. To determine the robustness of these results we carried out complementary convection simulations incorporating the past 120 Ma history of tectonic plate evolution. These simulations yielded shifting ‘hotlines’ at the core‐mantle boundary, but the locations of the overlying hotspot plumes remained relatively stable. The configuration of the hotlines in the convection experiments with and without evolving surface plate geometries are very similar to each other, showing that convection models with present-day plate configurations are sufficient for capturing the essential characteristics of the present-day thermal structure in the mantle. In a final experiment, the prescribed NNR-NUVEL-1 plate velocity constraint is released, allowing the plates to rotate freely in response to the underlying mantle flow. We find that the initial evolution of this model is characterized by a strong stability of the mantle thermal structures, in particular the upwelling plumes. An important and novel feature of the convection model with free plate motions is the predicted opening of the African plate along the East African Rift boundary, which occurs in response to the large-scale mantle flow and does not appear to require the presence of upwelling plumes directly beneath the rift.

Heterogeneity and time dependence in 3D spherical mantle convection models with continental drift

Feedback between continents and large-scale mantle flow through thermal blanketing has long been surmised as a mechanism for continental drift and Wilson cycles. Paleomagnetism provides evidence for extensive continental displacements (∼ 10,000 km) on time scales of 100–200 million years, comparable to an intrinsic overturn in whole mantle convection. Here we model continental motions in vigorous 3D spherical convection models, focusing on the effects of continent size, mantle heating mode, and a strong increase in lower mantle viscosity. Continents covering 30%, 10%, and 3% of Earth's surface (representative of the former supercontinent Pangea, present-day Asia, and Antarctica, respectively) are introduced into simple end member mantle convection models characterized by pure core or internal heating, and uniform or layered mantle viscosity. Supercontinents promote temperature anomalies on the largest scales (spherical harmonic degrees 1 and 2), primarily through the organization of the long-wavelength convective planform inherent in models with a high-viscosity lower mantle. Bottom heating can promote long-wavelength heterogeneity by clustering plumes beneath the continent. However, in isoviscous models small-scale structure persists away from the continent regardless of the heating mode. Supercontinents respond to long-wavelength heterogeneity by following great circle paths with variations in velocity on time scales of 1 billion years. Smaller continents are unable to promote long-wavelength structure, and the resulting motions are governed by bursts in velocity on time scales of the order of 100 million years. Continental velocities are roughly a factor of ∼ 3 smaller than those in oceanic regions, an observation that may help explain the observed difference in the speed of predominantly continental or oceanic plates.

Spherical shell models of mantle convection with tectonic plates

Abstract A simple three-dimensional spherical model of mantle convection, where plates are taken into account in the top boundary condition, allows to investigate the plate tectonics–mantle convection coupling in a self-consistent way. Avoiding the strong difficulties inherent in the numerical treatment of rheology, the plate condition appears efficient in reproducing the Earth-like features as subduction, mid-oceanic ridges and hotspots. Whereas the free-slip condition leads to a classical polygonal cell pattern with cylindrical hot plumes surrounded by downwellings, the plate condition favors the development of strong linear downwellings associated to passive diverging zones along plate boundaries. These cold currents, very similar to subductions, act the main role in mantle convection: they drive the whole circulation. In that context, hot plumes remain almost independent, except if on the long term, cold material spreading at the core surface induces a slight migration, below a few mm/yr, of their surface impingement. The main result is that plate tectonics appear to be more than a simple mode of organization of the surface movements, it is the essence of the Earth mantle dynamics.

Role of temperature‐dependent viscosity and surface plates in spherical shell models of mantle convection

Layered viscosity, temperature‐dependent viscosity, and surface plates have an important effect on the scale and morphology of structure in spherical models of mantle convection. We find that long‐wavelength structures can be produced either by a layered viscosity with a weak upper mantle or temperature‐dependent viscosity even in the absence of surface plates, corroborating earlier studies. However, combining the layered viscosity structure with a temperature‐dependent viscosity results in structure with significantly shorter wavelengths. Our models show that the scale of convection is mainly controlled by the surface plates, supporting the previous two‐dimensional studies. Our models with surface plates, layered and temperature‐dependent viscosity, and internal heating explain mantle structures inferred from seismic tomography. The models show that hot upwellings initiate at the core‐mantle boundary (CMB) with linear structures, and as they depart from CMB, the linear upwellings quickly change into quasi‐cylindrical plumes that dynamically interact with the ambient mantle and surface plates while ascending through the mantle. A linear up welling structure is generated again at shallow depths (<200 km) in the vicinity of diverging plate margins because of the surface plates. At shallow depths, cold downwelling sheets form at converging plate margins. The evolution of downwelling sheets depends on the mantle rheology. The temperature‐dependent viscosity strengthens the downwelling sheets so that the sheet structure can be maintained throughout the mantle. The tendency for linear upwelling and downwelling structures to break into plume‐like structures is stronger at higher Rayleigh numbers. Our models also show that downwellings to first‐order control surface plate motions and the locations and horizontal motion of upwellings. Upwellings tend to form at stagnation points predicted solely from the buoyancy forces of downwellings. Temperature‐dependent viscosity greatly enhances the ascending velocity of developed upwelling plumes, and this may reduce the influence of global mantle flow on the motion of plumes. Our results can explain the anticorrelation between hotspot distribution and fast seismic wave speed anomalies in the lower mantle and may also have significant implications to the observed stationarity of hotspots.

The origin of large scale structure in mantle convection: Effects of plate motions and viscosity stratification

Convection in Earth's mantle is dominated by long‐wavelength structure, as evidenced by the very “red” spectra of both seismic velocity heterogeneity in the deep mantle and the non‐hydrostatic gravity field, or geoid. Here we show that this large‐scale structure may be a consequence of two factors that influence the scale of mantle convection. First, the existence of surface plates, which tend to organize the flow. Second, a substantial increase in lower mantle viscosity for which there is considerable independent geophysical evidence. Combining these two factors in 3‐D spherical mantle convection models explains rather well the observed seismic spectrum of mantle heterogeneity.

Geometrical effects of curvature in axisymmetric spherical models of mantle convection

A two‐dimensional axisymmetric model of convection in a spherical shell has been developed in order to investigate the effects of curvature on model predictions of heat flow and temperature in the Earth's mantle. We restrict the solution domain to a belt centered midway between the poles of the axisymmetric coordinate system. This facilitates direct comparisons with models in cylindrical shells and plane layers, and avoids the physically unrealistic near‐pole effects associated with the axial symmetry at the poles. A boundary layer argument is suggested which accounts for the observed variations in heat flow and mean temperature from one level of curvature to another. In particular, plane layer results may be scaled to any desired degree of curvature. Similarities between previous model results in cylindrical shells and our results in spherical shells are noted, and it is shown that results in one geometry may be mapped into the other provided the ratio of the surface areas of the upper and lower boundaries is the same.

Three-Dimensional Spherical Models of Convection in the Earth's Mantle

Three-dimensional, spherical models of mantle convection in the earth reveal that upwelling cylindrical plumes and downwelling planar sheets are the primary features of mantle circulation. Thus, subduction zones and descending sheetlike slabs in the mantle are fundamental characteristics of thermal convection in a spherical shell and are not merely the consequences of the rigidity of the slabs, which are cooler than the surrounding mantle. Cylindrical mantle plumes that cause hotspots such as Hawaii are probably the only form of active upwelling and are therefore not just secondary convective currents separate from the large-scale mantle circulation. Active sheetlike upwellings that could be associated with mid-ocean ridges did not develop in the model simulations, a result that is in agreement with evidence suggesting that ridges are passive phenomena resulting from the tearing of surface plates by the pull of descending slabs.