Scott D. King

Edge-driven convection

We consider a series of simple calculations with a step-function change in thickness of the lithosphere and imposed, far-field boundary conditions to illustrate the influence of the lithosphere on mantle flow. We consider the effect of aspect ratio and far-field boundary conditions on the small-scale flow driven by a discontinuity in the thickness of the lithosphere. In an isothermal mantle, with no other outside influences, the basic small-scale flow aligns with the lithosphere such that there is a downwelling at the lithospheric discontinuity (edge-driven flow); however, the pattern of the small-scale flow is strongly dependent on the large-scale thermal structure of a much broader area of the upper mantle. Long-wavelength temperature anomalies in the upper mantle can overwhelm edge-driven flow on a short timescale; however, convective motions work to homogenize these anomalies on the order of 100 million years while cratonic roots can remain stable for longer time periods. A systematic study of the effect of the boundary conditions and aspect ratio of the domain shows that small-scale, and large-scale flows are driven by the lithosphere. Edge-driven flow produces velocities on the order of 20 mm/yr. This is comparable to calculations by others and we can expect an increase in this rate as the mantle viscosity is decreased.

An alternative mechanism of flood basalt formation

All large continental igneous provinces and most high-temperature magmas (picrites, komatiites) are found on the margins of cratonic lithosphere. The standard plume model of flood basalt formation offers no explanation for this observation. We propose that thick lithosphere (usually Archean) adjacent to thinner lithosphere may control the locations of flood basalt provinces. The boundary between thick and thin lithosphere focuses both the strain in the lithosphere and the upwelling convection. In addition, the non-uniform boundary condition actually induces a small-scale form of convection that is not present in simple convection and plume models. Whereas plumes are a form of convective instability rising from the base of a convecting system heated from below, the form of convection we are discussing is triggered from above. Unlike other lithospheric mechanisms, the asymmetric lithosphere does not require convective thinning or heating of the plate in order to produce melting. This eliminates time delay between the arrival of the plume head and the onset of volcanism in the stretching model. We consider a series of calculations with a step-function change in thickness of the boundary layer and an externally imposed pull-apart. The flow in our models is shallow and sub-horizontal, and brings hot material from under the thicker (cratonic) boundary layer towards the pull-apart. A simple estimate of the amount of melt generated by this mechanism suggests that it is capable of producing a large igneous province, even for a dry mantle.

A comparison of methods for the modeling of thermochemical convection

We have compared several methods of studying thermochemical convection in a Boussinesq fluid at infinite Prandtl number. For the representation of chemical heterogeneity tracer, marker chain, and field methods are employed. In the case of an isothermal Rayleigh-Taylor instability, good agreement is found for the initial rise of the unstable lower layer; however, the timing and location of the later smaller-scale instabilities may differ between methods. For a simulation of entrainment by thermal convection of a dense layer at the bottom of the mantle we found good agreement for a few overturn times. After this, differences between the results can be large. We propose intrinsic differences between the methods and possibly chaotic mixing effects may be the cause of the lack of detailed agreement. The comparison shows that high resolution is necessary for a reasonable thermochemical study. This will pose severe restrictions on the applicability of these methods to three-dimensional situations.

Dawn Arrives at Ceres: Exploration of a Small Volatile-Rich World

On 6 March 2015, Dawn arrived at Ceres to find a dark, desiccated surface punctuated by small, bright areas. Parts of Ceres’ surface are heavily cratered, but the largest expected craters are absent. Ceres appears gravitationally relaxed at only the longest wavelengths, implying a mechanically strong lithosphere with a weaker deep interior. Ceres’ dry exterior displays hydroxylated silicates, including ammoniated clays of endogenous origin. The possibility of abundant volatiles at depth is supported by geomorphologic features such as flat crater floors with pits, lobate flows of materials, and a singular mountain that appears to be an extrusive cryovolcanic dome. On one occasion, Ceres temporarily interacted with the solar wind, producing a bow shock accelerating electrons to energies of tens of kilovolts.

Hotspots and edge-driven convection

Not every hotspot may be related to a deep-mantle plume, and there are a number of examples of intraplate volcanism that have never been suggested to be related to a mantle plume. The mechanism of origin for these intraplate volcanic events remains poorly understood; however, small-scale convection triggered at the edge of a continent or craton is one proposed mechanism. Drawing 600 and 1000 km circles around hotspots, a distance based on the scale-length of convective flow, and looking for circles that intersect cratonic roots discriminates between hotspots that are potentially generated by edge-driven convection and those that are not. The group of hotspots unfavorable for edge-driven convection agrees with other groups of proposed mantle plume hotspots.

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.

Subduction zones: observations and geodynamic models

Abstract This review of subduction and geodynamic models is organized around three central questions: (1) Why is subduction asymmetric? (2) Are subducted slabs strong or weak? (3) How do subducted slabs interact with phase transformations, changes in mantle rheology, and possibly chemical boundaries in the mantle? Based on laboratory measurements of the temperature dependence of olivine, one would conclude that the core of a subducting slab is at least 10,000 times more viscous than ambient mantle; however, there are a number of complementary but independent observations that suggest that slabs are much weaker than this. Slabs undergo significant deformation in the upper mantle and may thicken to twice their original width by the time they reach the base of the transition zone. The lack of a clear correlation between the observed dip angle of deep slabs and plate velocity, rate of trench migration, and slab age in modern subduction zones is consistent with hypothesis that subduction is a time-dependent phenomenon. Both tank and numerical convection experiments with plates conclude that subduction is not a steady phenomenon, but that slabs bend, thicken, stretch, and change dip through time. This is at odds with the assumptions used in steady-state slab thermal models, where slab deformation is not considered.

The effect of temperature dependent viscosity on the structure of new plumes in the mantle: Results of a finite element model in a spherical, axisymmetric shell

Abstract We have developed a finite element model of convection in a spherical, axisymmetric shell that we use to simulate upwelling thermal plumes in the mantle. The finite element method provides the flexibility to include realistic properties such as temperature-dependent viscosity, the focus of this paper. We used this model to investigate the effect of temperature-dependent viscosity on the structure of new plumes originating at the core-mantle boundary. Because the way in which mantle viscosity varies with temperature is not well constrained, we determined the plume structure using a variety of viscosity laws. We focus on 3 different viscosity laws: (1) constant viscosity; (2) weakly temperature-dependent viscosity, in which the viscosity increases by a factor of 10 between the hottest and the coldest material; and (3) strongly temperature-dependent viscosity, in which the viscosity varies by a factor of 1000. In a constant viscosity fluid, the plume exhibited a spout structure without a distinctive head. The plume head and tail consisted largely of material from the hot thermal boundary layer at the base of the spherical shell that represented the mantle. When the viscosity was strongly temperature-dependent, starting plumes developed a mushroom structure with a large, slow-moving head, followed by a narrow, faster moving tail. Material from the overlying shell was assimilated into the plume head during formation of the upwelling in models with strongly temperature-dependent viscosity, while the plume tail showed little entrainment. Constant viscosity models and models with weakly temperature-dependent viscosity showed almost no entrainment in the head or tail. The large plume head that formed in models with strongly temperature-dependent viscosity created and then shed “blobs” of material from the deep mantle that did not arrive at the surface near the plume but instead were deposited elsewhere in the upper mantle.

Subducted slabs and the geoid: 1. Numerical experiments with temperature-dependent viscosity

One of the most powerful constraints on mantle viscosity comes from the correlation of the long-wavelength (degree 4–9) geoid with that predicted by a density model for subducted slabs. The effect of lateral variations of viscosity should be most pronounced at subduction zones, due to the strong effect of temperature on viscosity. An idealized slab model with temperature-dependent viscosity is considered, with various lateral and vertical viscosity structures, using a two-dimensional finite element formulation. The viscosity parameterization affects the amplitude of the long-wavelength geoid anomaly but not the sign of the correlation between the geoid and density anomalies. Depth-dependent viscosity models with a high-viscosity lithospheric layer do not completely match the temperature-dependent (laterally varying) results, suggesting that the rheology of the slab does have an effect on the long-wavelength surface topography and geoid; however, this affect is minor, suggesting that the radial models of mantle viscosity inferred from surface observables are correct to first order. In contrast, the short-wavelength features are dramatically affected by the rheology of the region surrounding the downwelling. Further study of the shorter-wavelength geoid over subduction zones may provide better insight into subduction zone processes.

Why cold slabs stagnate in the transition zone

Oceanic lithosphere sinks, stagnates, and is deflected sub-horizontally beneath western Pacific island arcs, requiring buoyancy in the slab that is inconsistent with a thermal origin. The transformation of pyroxene to majoritic garnet occurs by extremely slow diffusion, and pyroxene is therefore unlikely to transform at equilibrium pressures and temperatures in the cold interior of slabs. We present high-resolution numerical simulations showing that when slow diffusion inhibits the dissolution of pyroxene into garnet, the slab becomes buoyant relative to the ambient mantle and stagnates, whereas when the phase transformations occur in equilibrium, there is no effect on the slab. We test the model by comparing slab temperature and geometry and find that sub-horizontal slabs are more likely colder than average, consistent with our numerical simulations.