Shijie Zhong

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.

Thermochemical structures beneath Africa and the Pacific Ocean

Large low-velocity seismic anomalies have been detected in the Earths lower mantle beneath Africa and the Pacific Ocean that are not easily explained by temperature variations alone. The African anomaly has been interpreted to be a northwest–southeast-trending structure with a sharp-edged linear, ridge-like morphology. The Pacific anomaly, on the other hand, appears to be more rounded in shape. Mantle models with heterogeneous composition have related these structures to dense thermochemical piles or superplumes. It has not been shown, however, that such models can lead to thermochemical structures that satisfy the geometrical constraints, as inferred from seismological observations. Here we present numerical models of thermochemical convection in a three-dimensional spherical geometry using plate velocities inferred for the past 119 million years. We show that Earths subduction history can lead to thermochemical structures similar in shape to the observed large, lower-mantle velocity anomalies. We find that subduction history tends to focus dense material into a ridge-like pile beneath Africa and a relatively more-rounded pile under the Pacific Ocean, consistent with seismic observations.

Mantle Convection with Plates and Mobile, Faulted Plate Margins

A finite-element formulation of faults has been incorporated into time-dependent models of mantle convection with realistic rheology, continents, and phase changes. Realistic tectonic plates naturally form with self-consistent coupling between plate and mantle dynamics. After the initiation of subduction, trenches rapidly roll back with subducted slabs temporarily laid out along the base of the transition zone. After the slabs have penetrated into the lower mantle, the velocity of trench migration decreases markedly. The inhibition of slab penetration into the lower mantle by the 670-kilometer phase change is greatly reduced in these models as compared to models without tectonic plates.

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.

Degree-1 mantle convection and the crustal dichotomy on Mars

The surface of Mars consists of an old, heavily cratered and elevated southern hemisphere and younger, resurfaced and depressed northern hemisphere, a feature often termed the crustal dichotomy. The global crustal structure [Zuber et al., 2000] revealed by topography and gravity data from the Mars Global Surveyor spacecraft, and the possible late formation of the boundary zone between the hemispheres [McGill and Dimitriou, 1990], have been proposed to indicate an endogenic origin for the dichotomy. However, degree-1 mantle convection that is required for any endogenic process to be viable cannot be produced with conventional mantle convection models [Schubert et al., 1990]. We have studied the role of radially stratified viscosity on mantle deformation by using Rayleigh^Taylor instability analyses in a spherical shell geometry. Our analyses reveal that when mantle viscosity is stratified with a weak asthenosphere, deformation at long wavelengths is more efficient than that at short wavelengths. The weaker the asthenosphere, the longer the wavelength at which the deformation is the most efficient. A thicker asthenosphere also favors the deformation at long wavelengths. Both the Rayleigh^Taylor instability analyses and numerical modeling of mantle convection show that degree-1 convection can be produced within the Martian mantle provided that the mantle had a weak asthenosphere (V500 km thick and V10 2 times weaker than the underlying mantle) early in planetary history. The degree-1 convection causes preferential heating of one hemisphere that may explain the primary features associated with the dichotomy in crustal structure. fl 2001 Elsevier Science B.V. All rights reserved.

Controls on trench topography from dynamic models of subducted slabs

A finite element method with constrained elements and Lagrange multipliers is used to study tectonic faults in a viscous medium. A fault, representing the interface between overriding and subducting plates, has been incorporated into a viscous flow model of a subduction zone in which both thermal buoyancy and the buoyancy associated with the phase change from olivine to spinel are included. The fault causes stress to concentrate in its vicinity, giving rise to a weak plate margin and a mobile plate if a power law rheology is used. Surface dynamic topography with either a Newtonian or a power law rheology and with typical subduction zone parameters is characterized by a narrow and deep trench and a broadly depressed back arc basin. This suggests that oceanic trenches and back arc basins over subduction zones are dynamically compensated by viscous flow. Our models show that trench depth increases with fault dip angle, slab dip angle, slab length, and age of oceanic lithosphere just prior to subduction. The influence of fault dip angle and age of lithosphere on trench depth is greater than the influence of slab dip angle and slab length. These relationships of trench depth versus subduction zone parameters explain well the statistics of observed trench depths. For those subduction zones with oceanic lithosphere on both sides of the trench, observed trench depths have been corrected for fault and slab dip angles, based on the relationships from the dynamic models. After correction to a common set of parameters, trench depth correlates linearly with age of lithosphere prior to subduction with a slope which is close to what models having high viscosities within the transition zone and lower mantle predict. Comparison between the trench depths, corrected for fault and slab dip angles, and model trench depths suggests that the resisting tangential stress on faults in subduction zones may range from 15 MPa to 30 MPa, depending on model details.

Dynamic feedback between a continentlike raft and thermal convection

Seismic observations of the mantle, which include long-wavelength structure, a k^(−1) dependence of heterogeneity on harmonic k, and a heterogeneous upper boundary layer, and supercontinent kinematics may be explained by the dynamic interaction between a continent like raft and thermal convection. We have formulated finite element models of convection with rafts simulating continental plates in a cylindrical geometry. The azimuthal interconnectivity of this geometry is vital to resolve the two-way dynamics between rafts and convection. Computations show that (1) raft motion is periodic, (2) long-wavelength thermal structure is significant within both thermal boundary layers and the fluid interior, and (3) the large-scale thermal structure with a wavelength longer than the width of raft is responsible for raft motion. These three results, which are observed for a range of Rayleigh numbers, internal heating rates, and raft sizes, are a direct consequence of the dynamic interaction between the raft and convection. The physical processes for a model with a Rayleigh number of 10^5 are representative: when the raft is stationary, due to the less efficient heat transfer through the raft and instabilities from the bottom boundary layer, heat accumulates beneath the raft and results in long-wavelength thermal anomalies. The long-wavelength thermal anomalies enhance raft motion. Accompanying the enhanced raft movement, the long-wavelength thermal anomalies diminish and the raft velocity decreases or the raft comes to rest. Since convection models without rafts generate less long-wavelength heterogeneity compared to the models with rafts, or continental plates, we suspect that continental plates may play a crucial role in mantle dynamics. Interestingly, raft motion with a period of about 10 transit times is usually significant; 10 transit times is about 600 m.y. if scaled to the Earth. This is close to the observed 300–500 m.y. period of supercontinent aggregation and dispersal.

Role of plates and temperature-dependent viscosity in phase change dynamics

The effects of plates and slabs on phase change dynamics have been investigated with convection models. Two complementary methods to simulate plates are used: material property and imposed surface velocity methods with temperature-dependent viscosity. For a wide range of model parameters, plates and slabs exert a significant control on phase change dynamics. As plate length (and hence plate age and convection cell aspect ratio) increases, both the propensity for slab penetration and the mass flux across an endothermic phase change increase. When cold downwellings are stiffened with a temperature-dependent rheology, slab penetration is enhanced, but total mass flux changes little. Plates organize large-scale flow and thermal structure and thereby affect phase change dynamics. As plates become larger, the resulting largerscale structures are influenced less by endothermic phase changes, thus reducing the degree of layering. A model showing completely layered convection for a plate of unit length becomes unlayered when the plate is 3 or 5 times longer. For a given Clapeyron slope, the proportion of time for slab penetration increases from zero for cases with small plates to more than 0.5 for cases with large plates. The degree of layering, plate velocity, and mass flux are controlled by large-scale structures, while slab penetration may be more related to small-scale features. Therefore, whether or not subducted slabs penetrate the phase change may not necessarily indicate that convection is entirely layered or entirely unlayered. The episodicity of convection induced by an endothermic phase change strongly depends on plate length, rheology, and Clapeyron slope. A large plate and a stiff slab both weaken the episodicity of convection. Only for a certain range of Clapeyron slopes can the phase change induce a strong episodic thermal convection.

Effects of plate and slab viscosities on the geoid

Abstract The effects of plate rheology (strong plate interiors and weak plate margins) and stiff subducted lithosphere (slabs) on the geoid and plate motions, considered jointly, are examined with three-dimensional spherical models of mantle flow. Buoyancy forces are based on the internal distribution of subducted lithosphere estimated from the last 160 Ma of subduction history. While the ratio of the lower mantle/upper mantle viscosity has a strong effect on the long-wavelength geoid, as has been shown before, we find that plate rheology is also significant and that its inclusion yields a better geoid model while simultaneously reproducing basic features of observed plate motion. Slab viscosity can strongly affect the geoid, depending on whether a slab is coupled to the surface. In particular, deep, high-viscosity slabs beneath the northern Pacific that are disconnected from the surface as a result of subduction history produce significant long-wavelength geoid highs that differ from the observation. This suggests that slabs in the lower mantle may be not as stiff as predicted from a simple thermally activated rheology, if the slab model is accurate.

Controls on sublithospheric small‐scale convection

[1] The Pacific upper mantle structures revealed from recent seismic studies prompt us to study the dynamics of sublithospheric small-scale convection (SSC) derived from thermal boundary layer instabilities of cooling lithosphere. As oceanic lithosphere cools and thickens, its sublayer may go unstable, thus producing SSC in the asthenosphere. By formulating two-dimensional (2-D) and three-dimensional (3-D) numerical models with realistic mantle rheology, we examine the controls on the onset time of SSC and its dynamic consequences. The onset of SSC is mainly controlled by two parameters: activation energy and asthenospheric viscosity, which can be recast as the FrankKamenetskii parameter q and a Rayleigh number Rai, respectively. Our models show that the onset time of SSC, tc, scales as Rai � 0.68 q 0.74 , independent of 2-D or 3-D geometry. Our scaling coefficient for q is significantly smaller than that from previous studies, but the weaker dependence on activation energy confirms the result of Korenaga and Jordan [2003]. We found that thermal structure associated with age offset across fracture zones has significant effects on the onset of SSC, and it causes the SSC to occur always first near the fracture zones. Asthenospheric thickness and plate motion may also have significant effects on the onset of SSC. When the thickness of asthenosphere is sufficiently small to be comparable with the wavelength of the SSC, the onset may be delayed significantly. Plate motion also tends to delay the onset of the SSC in our 2-D models. Although at the onset of SSC surface heat flux Q is consistent with the half-space cooling model prediction, Q may eventually deviate from the half-space cooling model prediction as thermal perturbations associated with SSC diffuse through the stable part of lithosphere or stagnant lid to the surface. We found that the time it takes for Q to deviate from the half-space cooling model after the onset of SSC, t, scales as Rai � 0.65 q 1.52 , while the thickness of the stagnant lid at the onset time, d, scales as Rai � 0.33 q 0.78 , which is consistent