Louis Moresi

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 upwelling 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 tp 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 tb: 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.

NUMERICAL INVESTIGATION OF 2D CONVECTION WITH EXTREMELY LARGE VISCOSITY VARIATIONS

Previous experimental studies of convection in fluids with temperature‐dependent viscosity reached viscosity contrasts of the order of 105. Although this value seems large, it still might not be large enough for understanding convection in the interiors of Earth and other planets whose viscosity is a much stronger function of temperature. The reason is that, according to theory, above 104–105 viscosity contrasts, convection must undergo a major transition—to stagnant lid convection. This is an asymptotic regime in which a stagnant lid is formed on the top of the layer and convection is driven by the intrinsic, rheological, temperature scale, rather than by the entire temperature drop in the layer. A finite element multigrid scheme appropriate for large viscosity variations is employed and convection with up to 1014 viscosity contrasts has been systematically investigated in a 2D square cell with free‐slip boundaries. We reached the asymptotic regime in the limit of large viscosity contrasts and obtained s...

Evolution and diversity of subduction zones controlled by slab width.

Subducting slabs provide the main driving force for plate motion and flow in the Earth’s mantle, and geodynamic, seismic and geochemical studies offer insight into slab dynamics and subduction-induced flow. Most previous geodynamic studies treat subduction zones as either infinite in trench-parallel extent (that is, two-dimensional) or finite in width but fixed in space. Subduction zones and their associated slabs are, however, limited in lateral extent (250–7,400 km) and their three-dimensional geometry evolves over time. Here we show that slab width controls two first-order features of plate tectonics—the curvature of subduction zones and their tendency to retreat backwards with time. Using three-dimensional numerical simulations of free subduction, we show that trench migration rate is inversely related to slab width and depends on proximity to a lateral slab edge. These results are consistent with retreat velocities observed globally, with maximum velocities (6–16 cm yr-1) only observed close to slab edges (<1,200 km), whereas far from edges (>2,000 km) retreat velocities are always slow (<2.0 cm yr-1). Models with narrow slabs (≤1,500 km) retreat fast and develop a curved geometry, concave towards the mantle wedge side. Models with slabs intermediate in width (∼2,000–3,000 km) are sublinear and retreat more slowly. Models with wide slabs (≥4,000 km) are nearly stationary in the centre and develop a convex geometry, whereas trench retreat increases towards concave-shaped edges. Additionally, we identify periods (5–10 Myr) of slow trench advance at the centre of wide slabs. Such wide-slab behaviour may explain mountain building in the central Andes, as being a consequence of its tectonic setting, far from slab edges.

Scaling of time-dependent stagnant lid convection: Application to small-scale convection on Earth and other terrestrial planets

Small-scale convection associated with instabilities at the bottom of the lithospheric plates on the Earth and other terrestrial planets occurs in the stagnant lid regime of temperature-dependent viscosity convection. Systematic numerical simulations of time-dependent, internally heated stagnant lid convection suggest simple scaling relationships for a variety of convective parameters and in a broad range of power law viscosities. Application of these scaling relationships to the Earths oceanic lithosphere shows that for either diffusion or dislocation viscosity of olivine, convective instabilities occur in the lower part of the lithosphere between 85 and 100 km depth (the rheological sublayer). “Wet” olivine satisfies constraints on the heat flux and mantle temperature better than “dry” olivine, supporting the view that the upper mantle of the Earth is wet. This is also consistent with the fact that the rheological sublayer is located below the Gutenberg discontinuity which was proposed to represent a sharp change in water content. The viscosity of asthenosphere is (3–6)×1018 Pa s, consistent with previous estimates. The velocities of cold plumes are relatively high reaching several meters per year in the dislocation creep regime. A low value of the heat flux in old continental cratons suggests that continental lithosphere might be convectively stable unless it is perturbed by processes associated with plate tectonics and hot plumes. The absence of plate tectonics on other terrestrial planets and the low heat transport efficiency of stagnant lid convection can lead to widespread melting during the thermal evolution of the terrestrial planets. If the terrestrial planets are dry, small-scale convection cannot occur at subsolidus temperatures.

A Lagrangian integration point finite element method for large deformation modeling of viscoelastic geomaterials

We review the methods available for large deformation simulations of geomaterials before presenting a Lagrangian integration point finite element method designed specifically to tackle this problem. In our Ellipsis code, the problem domain is represented by an Eulerian mesh and an embedded set of Lagrangian integration points or particles. Unknown variables are computed at the mesh nodes and the Lagrangian particles carry history variables during the deformation process. This method is ideally suited to model fluid-like behavior of continuum solids which are frequently encountered in geological contexts. We present benchmark examples taken from the geomechanics area.

Constraints on the lateral strength of slabs from three-dimensional dynamic flow models

If the viscosity of subducted lithosphere is described purely by temperature and pressure, it should remain considerably more viscous than the surrounding material as it descends through the upper mantle. Many dynamic models of the long wavelength geoid associated with slabs require an increase in viscosity from the upper to the lower mantle but assume the perturbation to the lateral viscosity structure arising from the slabs themselves can be ignored. Previous studies indicate that strong and localized viscosity variations should have a dramatic influence on the geoid. We present 3D finite element models of the regional geoid of the Western Pacific subduction zones. Slab buoyancies and viscosities are defined using the distribution of seismicity. The geoid is very sensitive to the lateral strength of the slab. Very viscous slabs penetrating a low viscosity mantle generate significant (10–50 m) long wavelength geoid lows: opposite to the geoid high which is observed over slabs. To obtain a geoid high comparable to that observed, the lower mantle viscosity must be 60–200 times greater than the upper mantle viscosity and the slab must be in contact with the lower mantle. These strict requirements suggest that slabs have been weakened and cannot act as stress guides from the deep mantle to the surface.

Stagnant lid convection on Venus

The effect of strongly temperature-dependent viscosity on convection in the interior of Venus is studied systematically with the help of finite element numerical models. For viscosity contrasts satisfying experimental constraints on the rheology of rocks, Venus is likely to be in the regime of stagnant lid convection. This regime is characterized by the formation of a slowly creeping, very viscous lid on top of the mantle-Venusian lithosphere and is in agreement with the tectonic style observed on Venus. Stagnant lid convection explains large geoid to topography ratios on Venus by the thermal thinning of a thick lithosphere. The thickness of the lithosphere can be as large as 400-550 km for Beta Regio and 200-400 km on average. Geoid and topography data and experimental data on the rheology of rocks provide constraints on the viscosity of the mantle, 10 20 -10 21 Pa s ; the convective stresses in the interior, 0.2-0.5 MPa ; the stresses in the lid, 100-200 MPa ; the velocity in the interior, 0.5-3 cm yr -1 ; and the heat flux beneath the lithosphere, 8-16 mW m -2 . Parameterized convection calculations of thermal history of Venus are difficult to reconcile with a thick present-day lithosphere. However, a sufficiently thick lithosphere can be formed if a convective regime with mobile plates was replaced by stagnant lid convection around 0.5 b.y. ago. One of the possible explanations for the cessation of Venusian plate tectonics is that during the evolution of Venus, stresses in the lid dropped below the yield strength of the lithosphere. This model predicts a drastic drop in the heat flux, thickening of the lithosphere, and suppression of melting and is consistent with the hypothesis of cessation of resurfacing on Venus around 0.5 b.y. ago.

Role of faults, nonlinear rheology, and viscosity structure in generating plates from instantaneous mantle flow models

Concentrated strain within plate margins and a significant toroidal component in global plate motion are among the most fundamental features of plate tectonics. A significant proportion of strain in plate margins is accommodated through motion on major tectonic faults. The decoupling influence of faulted plate margins primarily results from history-dependent lithospheric deformation rather than from instantaneous stress-weakening rheologies. For instantaneous mantle flow models, we argue that faults should be treated as preexisting mechanical structures. With models incorporating preexisting faults, a power law rheology with an exponent of 3, and slab pull and ridge push forces, we demonstrate that nonlinear interaction between weak faults and this power law rheology produces plate-like motion. Our models show that in order to produce plate-like motion, the frictional stress on faults needs to be small and the asthenosphere viscosity should be much weaker than that of lithosphere. While both plateness and the ratio of toroidal to poloidal velocities are reduced with increasing fault coupling, the viscosity contrast between the lithosphere and asthenosphere only influences plateness. This shows that both diagnostics, plateness and the ratio of toroidal to poloidal velocities, are necessary to characterize plate motion. The models demonstrate that weak transform faults can guide plate motion. This guiding property of transform faults and the decoupling of thrust faults result in oblique subduction where the strike of subducted slabs is oblique to transform faults. Subducted slabs beneath a dipping fault produce oceanic trench and fore bulge topography and principal stresses consistent with subduction zone observations.

Longevity and stability of cratonic lithosphere: Insights from numerical simulations of coupled mantle convection and continental tectonics

[1] The physical conditions required to provide for the tectonic stability of cratonic crust and for the relative longevity of deep cratonic lithosphere within a dynamic, convecting mantle are explored through a suite of numerical simulations. The simulations allow chemically distinct continents to reside within the upper thermal boundary layer of a thermally convecting mantle layer. A rheologic formulation, which models both brittle and ductile behavior, is incorporated to allow for plate-like behavior and the associated subduction of oceanic lithosphere. Several mechanisms that may stabilize cratons are considered. The two most often invoked mechanisms, chemical buoyancy and/or high viscosity of cratonic root material, are found to be relatively ineffective if cratons come into contact with subduction zones. High root viscosity can provide for stability and longevity but only within a thick root limit in which the thickness of chemically distinct, high-viscosity cratonic lithosphere exceeds the thickness of old oceanic lithosphere by at least a factor of 2. This end-member implies a very thick mechanical lithosphere for cratons. A high brittle yield stress for cratonic lithosphere as a whole, relative to oceanic lithosphere, is found to be an effective and robust means for providing stability and lithospheric longevity. This mode does not require exceedingly deep strength within cratons. A high yield stress for only the crustal or mantle component of the cratonic lithosphere is found to be less effective as detachment zones can then form at the crust-mantle interface which decreases the longevity potential of cratonic roots. The degree of yield stress variations between cratonic and oceanic lithosphere required for stability and longevity can be decreased if cratons are bordered by continental lithosphere that has a relatively low yield stress, i.e., mobile belts. Simulations that combine all the mechanisms can lead to crustal stability and deep root longevity for model cratons over several mantle overturn times, but the dominant stabilizing factor remains a relatively high brittle yield stress for cratonic lithosphere.

Some thoughts on the stability of cratonic lithosphere: Effects of buoyancy and viscosity

Continental cratons have not experienced major tectonic disruptions over a timescale of 109 years. The thickness of cratonic lithosphere also appears to have changed little over this timescale. These observations are often attributed to the presence of chemically buoyant and/or highly viscous subcratonic roots. Simple physical scaling relationships are developed to explore the buoyancy and/or viscosity conditions required to stabilize such roots against large-scale deformation and rapid remixing into the mantle. The scalings are tested using idealized numerical simulations with good general agreement. Applied to Earth, the scalings suggest that (1) buoyancy alone is unlikely to stabilize cratonic roots and (2) if root viscosity is to provide stability into the Archean, then roots must be 103 times as viscous as the mantle. Based on available experimental data, root dehydration cannot account for the required viscosity increase. Temperature-dependent viscosity can stabilize roots, but it does so at the expense of stagnating the entire mantle lithosphere, i.e., at the expense of sacrificing plate tectonics. This suggests that the plastic yielding properties of rocks at low temperatures will need to be more directly accounted for in future experiments exploring root stability.