Julian P. Lowman

Continental collisions in wide aspect ratio and high Rayleigh number two‐dimensional mantle convection models

Distinct rigidly moving oceanic and continental plates of finite thickness are incorporated into a two-dimensional numerical model of mantle convection. We investigate upper mantle convection in models having aspect ratios as great as 24 and compare our findings with the results of earlier studies which were limited to aspect ratio 4 models. In addition, we implement models of whole mantle flow by specifying high Rayleigh number convection and thinner nondimensional plates. We are thus able to compare the results of continental collision models which include similarly sized continents in the cases of upper and whole mantle convection. For each case considered we model a pair of identical continents being carried toward a site of plate convergence by underlying counterrotating mantle convection cells. Upon collision, the continents form a motionless, rigid, model supercontinent, while oceanic plate material continues to recycle through the mantle. Following the continental collision, our models of upper mantle convection exhibit a reorganization of the convective planform below the model supercontinent into a smaller wavelength mode which is unable to generate the net stress needed to break apart the continent; alternating compressive and tensile deviatoric stress associated with the small scale flow results in a low integrated stress. In contrast the large scale of whole mantle convection enables flow reversals to produce shear stresses acting in a common direction over extensive areas of the base of a continent, the integrated effect of which is capable of causing continental rifting. The conventional view of the role of thermal blanketing in continental rifting does not apply in the whole mantle convection scenario.

Episodic tectonic plate reorganizations driven by mantle convection

Abstract Periods of relatively uniform plate motion were interrupted several times throughout the Cenozoic and Mesozoic by rapid plate reorganization events [R. Hey, Geol. Soc. Am. Bull. 88 (1977) 1404–1420; P.A. Rona, E.S. Richardson, Earth Planet. Sci. Lett. 40 (1978) 1–11; D.C. Engebretson, A. Cox, R.G. Gordon, Geol. Soc. Am. Spec. Pap. 206 (1985); R.G. Gordon, D.M. Jurdy, J. Geophys. Res. 91 (1986) 12389–12406; D.A. Clague, G.B. Dalrymple, US Geol. Surv. Prof. Pap. 1350 (1987) 5–54; J.M. Stock, P. Molnar, Nature 325 (1987) 495–499; C. Lithgow-Bertelloni, M.A. Richards, Geophys. Res. Lett. 22 (1995) 1317–1320; M.A. Richards, C. Lithgow-Bertelloni, Earth Planet. Sci. Lett. 137 (1996) 19–27; C. Lithgow-Bertelloni, M.A. Richards, Rev. Geophys. 36 (1998) 27–78]. It has been proposed that changes in plate boundary forces are responsible for these events [M.A. Richards, C. Lithgow-Bertelloni, Earth Planet. Sci. Lett. 137 (1996) 19–27; C. Lithgow-Bertelloni, M.A. Richards, Rev. Geophys. 36 (1998) 27–78]. We present an alternative hypothesis: convection-driven plate motions are intrinsically unstable due to a buoyant instability that develops as a result of the influence of plates on an internally heated mantle. This instability, which has not been described before, is responsible for episodic reorganizations of plate motion. Numerical mantle convection experiments demonstrate that high-Rayleigh number convection with internal heating and surface plates is sufficient to induce plate reorganization events, changes in plate boundary forces, or plate geometry, are not required.

Mantle convection models of continental collision and breakup incorporating finite thickness plates

Abstract A two-dimensional numerical model has been developed to study mantle convection during continental collision and breakup. The model incorporates rigidly moving continental and oceanic plates with distinct thermal and mechanical properties, and finite thickness. We systematically investigate the influences of continental width, diffusivity, thickness and internal heating on continental collision and breakup. In addition, we consider the influence of different degrees of internal heating in the mantle. For each case considered we model a pair of identical continents being carried towards a site of plate convergence by underlying counter-rotating mantle convection cells. The continents collide at the mid-plane of the model to form a motionless, rigid, conducting supercontinent whereas oceanic plate material continues to recycle through the mantle. We find that changes in the mechanical boundary conditions at the upper surface are important factors in initiating flow reversals below the supercontinent. More generally, our findings, based on 144 models, are that the following factors favour the initiation of flow reversals below the supercontinent: wider continents, lower thermal diffusivity of continental plates, thicker plates and continental crustal heating. Furthermore, lower percentages of internal heating in the mantle are necessary to sustain and promote the subcontinental flow reversals in our models.

Mantle convection flow reversals due to continental collisions

Rigidly moving continental and oceanic plates with distinct thermal and mechanical properties, and finite thickness, are included in a two-dimensional numerical model of mantle convection. Model plates typically span six vertical increments of a finite difference mesh. We model two identical continents being carried towards each other by a pair of underlying, counter-rotating, mantle convection cells. Upon meeting at the model mid-plane the model continents form a motionless, rigid, conducting, “supercontinent” along a portion of the upper boundary, while the model oceanic plates continue to move and recycle through the mantle. The resulting changes in the mechanical boundary conditions at the upper surface prove to be important factors in facilitating flow reversal below the supercontinent, leading to a subsequent dispersal of the individual continental blocks. We find the following factors to favour the development of sustained flow reversal below our model supercontinent: wider continents, lower thermal diffusivity of continental plates, thicker plates and lower proportions of internal radiogenic heating within the mantle.

Effects of mantle heat source distribution on supercontinent stability

A two-dimensional Cartesian geometry numerical model is used to study the influence of internal heating on the ability of mantle convection to rift and disperse an assembled supercontinent. Our wide aspect ratio models incorporate migrating plate boundaries and finite thickness rigid mobile oceanic and continental plates (∼12,000 km across). We examine models characterized by both whole mantle and upper mantle convection parameters. Specifying different degrees of internal heating in the mantle, we compare the patterns of convection that develop below stationary continental plates that form as a result of the aggregation of smaller mobile continents. Following continental collisions, we find that a reorganization of mantle flow may result in the development of deviatoric stresses at the base of the continental lithosphere, which are capable of initiating continental breakup. Our results suggest that continental basal stresses are largely controlled by the wavelength of the subcontinental convection pattern and that the inclusion of internal heating in the mantle generally increases this wavelength. For models with 80% internal heating (in which active upwellings are intrinsically absent), basal stresses arise primarily from subduction at the continental margins and result in a geologically reasonable duration for our model supercontinent assemblages (∼200 Myr). For models with 40% or less internal heating, continental breakup is controlled by mantle upwellings and our supercontinents remain intact much longer (∼600–700 Myr).

Thermal evolution of the mantle following continental aggregation in 3D convection models

The claim that supercontinents insulate the mantle is largely based on recognition that seismically slow mantle below the Atlantic-African geoid high coincides with the former location of Pangea. We investigate the viability of continental insulation by varying both plate geometries and mantle properties in six three-dimensional (3D) mantle convection models. The efficiency of continental insulation is quantified by calculating the rate of change of the average temperature in the subcontinental mantle. Our findings generally agree with two-dimensional (2D) modeling results. However, we conclude that 2D convection models may exaggerate subcontinental heating, particularly in largely bottom heated cases, and that subcontinental heating results from an absence of subduction in the subcontinental mantle rather than the insulation of active upwellings. Correspondingly, we find that when large degrees of internal heating are present in the mantle, hotter-than-average regions evolve below large oceanic plates.

Influence of convergent plate boundaries on upper mantle flow and implications for seismic anisotropy

Shear-wave splitting observations in the region of the upper mantle enveloping subduction zones have been interpreted as showing extensive regions of trench-parallel flow, despite the difficulty of reconciling such behavior with a sound model based on the forces that drive mantle motion. To gain insight into the observations, we systematically investigate flow patterns around the cold downwelling sheets associated with consumed plate material in a three-dimensional numerical mantle convection model. First, we compare results from calculations employing prescribed plate geometries and kinematic plate velocities where the convergent plate boundary morphology is varied while keeping the plate velocity and convective parameters fixed. Subsequently, we examine the flow around sheet-like downwellings in a number of convection calculations featuring dynamically evolving plate velocities. All of the calculations include thick viscous plates and a stratified mantle viscosity. In all of the models examined, we find that at mid-upper mantle depths, flow directions no longer align with plate motion and the influence of buoyancy-driven downwellings clearly dominates flow solutions. In the first models analyzed, a pair of plates are included in the calculations, and the large-scale flow is generally roll-like. In the final model we investigate the interaction of four plates and a plate geometry characterized by triple junctions. We examine a sequence from this calculation that features a triple junction of convergent boundaries. In this model, large-scale flow characterized by convection rolls is superseded by a complex flow solution where flow in the mid-upper mantle neither aligns uniformly with the plate motion nor necessarily follows the forcing associated with local buoyancy sources. In this setting, upper mantle flow in the vicinity of the sheet-like downwellings featured in the solution moves orthogonal, obliquely, and even parallel to different sections of the convergent plate boundaries. In the latter case our calculations of the deformation of a fixed volume parcel of upper mantle material suggest that an olivine lattice-preferred orientation should develop that would result in a fast polarizing direction for seismic shear waves parallel to the slab. Our findings have implications for the interpretation of flow in the upper mantle based on seismic anisotropy.

Stagnant lid convection in bottom‐heated thin 3‐D spherical shells: Influence of curvature and implications for dwarf planets and icy moons

Because the viscosity of ice is strongly temperature dependent, convection in the ice layers of icy moons and dwarf planets likely operates in the stagnant lid regime, in which a rigid lid forms at the top of the fluid and reduces the heat transfer. A detailed modeling of the thermal history and radial structure of icy moons and dwarf planets thus requires an accurate description of stagnant lid convection. We performed numerical experiments of stagnant lid convection in 3-D spherical geometries for various ice shell curvatures f (measured as the ratio between the inner and outer radii), effective Rayleigh number Ram, and viscosity contrast Δ�� . From our results, we derived scaling laws for the average temperature of the well-mixed interior, �� m, and the heat flux transported through the shell. The nondimensional temperature difference across the bottom thermal boundary layer is well described by (1 − �� m )= 1.23 �� f 1.5 ,

Influences on the positioning of mantle plumes following supercontinent formation

Several 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.

The impact of Rayleigh number on assessing the significance of supercontinent insulation

Several processes unfold during the supercontinent cycle, more than one of which might result in an elevation in subcontinental mantle temperatures, thus multiple interpretations of the concept of continental insulation exist. Although a consensus seems to have formed that subcontinental mantle upwellings appear below large continents extensively ringed by subduction zones, there are differing views on what role continental insulation plays in the production of elevated mantle temperatures. Here we investigate how the heating mode of the mantle can change the influence of the “thermal blanket” effect. We present 2‒D and 3‒D Cartesian geometry mantle convection simulations with thermally and mechanically distinct oceanic and continental plates. The evolution of mantle thermal structure is examined after continental accretion at subduction zones (e.g., the formation of Pangea) for a variety of different mantle‒heating modes. Our results show that in low‒Rayleigh number models the impact of the role of continental insulation on subcontinental temperatures increases, when compared to models with higher convective vigor. Broad, hot upper mantle features generated in low‒Rayleigh number models (due, in part, to the thermal blanket effect) are absent at higher Rayleigh numbers. We find that subcontinental heating in a high‒Rayleigh number flow occurs almost entirely as a consequence of the influence of subduction initiation at the continental margin, rather than the influence of continental insulation. In our models featuring Earth‒like convective vigor, we find that it is difficult to obtain subcontinental temperatures in significant excess of suboceanic temperatures over timescales relevant to supercontinent aggregation.