Michael Gurnis

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.

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.

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.

Catastrophic initiation of subduction following forced convergence across fracture zones

Although the formation of subduction zones plays a central role in plate evolution, the processes and geological settings that lead to the initiation of subduction are poorly understood. Using a visco-elastoplastic model, we show that a fracture zone could be converted into a self-sustaining subduction zone after approximately 100 km of convergence. Modeled initiation is accompanied by rapid extension of the over-riding plate and explains the inferred catastrophic boninitic volcanism associated with Eocene initiation of the Izu-Bonin-Mariana (IBM) subduction zone. Using global plate reconstructions, we suggest that IBM nucleation was associated with a change in plate motion between 55 and 45 Ma. We estimate that the forces resisting IBM subduction initiation were substantially smaller than available driving forces.

Constraining mantle density structure using geological evidence of surface uplift rates: The case of the African Superplume

We explore the hypothesis that southern Africa is actively being uplifted by a large-scale, positively buoyant structure within the mid-lower mantle. Using a new formulation in which dynamic topography and uplift rate are jointly used, we place constraints on mantle density and viscosity. The solution of the momentum equation is coupled with the advection of the density field to solve for the surface uplift rate in both an axisymmetric and fully spherical geometry. We demonstrate how dynamic topography and its rate of change depend on density and lateral and radial variations in viscosity. In the full spherical models the geometry of mantle density is derived by scaling a tomographic shear velocity model. Using a variety of geologic observations, we estimate residual topography (i.e., the topography remaining after shallow sources of density are removed) and an average Cenozoic uplift rate to be 300–600 m and 5–30 m/Myr, respectively, for southern Africa. We are able to satisfy these constraints with a mantle model in which the mid-lower mantle beneath southern Africa is 0.2% less dense and has a viscosity of ∼ 10^22 Pa s. In addition, if the continental lithosphere is thick beneath southern Africa, as suspected from seismic inversions, and has a high effective viscosity, then we find that southern Africa can be further elevated owing to increased coupling between the deep mantle and surface. We show that recent estimates of mantle density, suggesting that the lowest parts of the African anomaly may be anomalously dense are compatible with geologic constraints. We conclude that uplift rate, when combined with estimates of present-day dynamic topography, provides a powerful tool to constrain the properties of the deep mantle.

Evolving force balance during incipient subduction

Nearly half of all active subduction zones initiated during the Cenozoic. All subduction zones associated with active back arc extension have initiated since the Eocene, hinting that back arc extension may be intimately associated with an interval (several tens of Myr) following subduction initiation. That such a large proportion of subduction zones are young indicates that subduction initiation is a continuous process in which the net resisting force associated with forming a new subduction zone can be overcome during the normal evolution of plates. Subduction initiation is known to have occurred in a variety of tectonic settings: old fracture zones, transform faults, and extinct spreading centers and through polarity reversal behind active subduction zones. Although occurring within different tectonic settings, four known subduction initiation events (Izu-Bonin-Mariana (IBM) along a fracture zone, Tonga-Kermadec along an extinct subduction boundary, New Hebrides within a back arc, and Puysegur-Fiordland along a spreading center) were typified by rapid uplift within the forearc followed by sudden subsidence. Other constraints corroborate the compressive nature of IBM and Tonga-Kermadec during initiation. Using an explicit finite element method within a two-dimensional domain, we explore the evolving force balance during initiation in which elastic flexure, viscous flow, plastic failure, and heat transport are all considered. In order to tie theory with observation, known tectonic settings of subduction initiation are used as initial and boundary conditions. We systematically explore incipient compression of a homogeneous plate, a former spreading center, and a fracture zone. The force balance is typified by a rapid growth in resisting force as the plate begins bending, reaching a maximum value dependent on plate thickness, but typically ranging from 2 to 3 × 1012 N/m for cases that become self-sustaining. This is followed by a drop in stress once a shear zone extends through the plate. The formation of a throughgoing fault is associated with rapid uplift on the hanging wall and subsidence on the footwall. Cumulative convergence, not the rate of convergence, is the dominant control on the force balance. Viscous tractions influence the force balance only if the viscosity of the asthenosphere is >1020 Pa s, and then only after plate failure. Following plate failure, buoyancy of the oceanic crust leads to a linear increase with crustal thickness in the work required to initiate subduction. The total work done is also influenced by the rate of lithospheric failure. A self-sustaining subduction zone does not form from a homogeneous plate. A ridge placed under compression localizes subduction initiation, but the resisting ridge push force is not nearly as large as the force required to bend the subducting plate. The large initial bending resistance can be entirely eliminated in ridge models, explaining the propensity for new subduction zones to form through polarity reversals. A fracture zone (FZ) placed in compression leads to subduction initiation with rapid extension of the overriding plate. A FZ must be underthrust by the older plate for ~100–150 km before a transition from forced to self-sustaining states is reached. In FZ models the change in force during transition is reflected by a shift from forearc uplift to subsidence. Subduction initiation is followed by trench retreat and back arc extension. Moderate resisting forces associated with modeled subduction initiation are consistent with the observed youth of Pacific subduction zones. The models provide an explanation for the compressive state of western Pacific margins before and during subduction initiation, including IBM and Tonga-Kermadec in the Eocene, and the association of active back arcs with young subduction zones. On the basis of our dynamic models and the relative poles of rotation between Pacific and Australia during the Eocene, we predict that the northern segment of the Tonga-Kermadec convergent margin would have initiated earlier with a progressive southern migration of the transition between forced and self-sustaining states.

A low viscosity wedge in subduction zones

Geochemical, petrologic and seismological observations indicate that there may be high concentrations of water in the region above a subducting slab (the mantle wedge), which could decrease the viscosity of the mantle locally by several orders of magnitude. Using numerical models we demonstrate that a low viscosity wedge has a dramatic influence on the force balance in a subduction zone and leads to an observable signal in the topography, gravity and geoid. A regional dynamic model of the Tonga–Kermadec subduction zone shows that the viscosity of the wedge is at least a factor of 10 smaller than surrounding mantle lithosphere and asthenosphere, consistent with estimates from seismic dissipation and deformation experiments.

Next-generation plate-tectonic reconstructions using GPlates

Plate tectonics is the kinematic theory that describes the large-scale motions and events of the outermost shell of the solid Earth in terms of the relative motions and interactions of large, rigid, interlocking fragments of lithosphere called tectonic plates. Plates form and disappear incrementally over time as a result of tectonic processes. There are currently about a dozen major plates on the surface of the Earth, and many minor ones. The present-day configuration of tectonic plates is illustrated in Figure 7.1. As the interlocking plates move relative to each other, they interact at plate boundaries, where adjacent plates collide, diverge, or slide past each other. The interactions of plates result in a variety of observable surface phenomena, including the occurrence of earthquakes and the formation of large-scale surface features such as mountains, sedimentary basins, volcanoes, island arcs, and deep ocean trenches. In tum, the appearance of these phenomena and surface features indicates the location of plate boundaries. For a detailed review of the theory of plate tectonics, consult Wessel and Muller (2007).

The Dynamics of Plate Tectonics and Mantle Flow: From Local to Global Scales

Improving Earth Models The geophysical processes responsible for shaping the planets surface and interior need largescale simulations, but to achieve high resolution at these scales is costly and tends to focus on gradual processes such as plate tectonics. By using large parallel supercomputers, Stadler et al. (p. 1033; see the Perspective by Becker; see the cover) have improved on a commonly used method—adaptive mesh refinement—to increase the resolution of global geodynamic models to the scale of a single kilometer and been able to reveal unexpected insights into localized processes, such as subduction zone mechanics, thermal anomalies in the lower mantle, and the speed of movement of oceanic plates. Computational advances enable the modeling of global geophysical processes to the scale of a kilometer. Plate tectonics is regulated by driving and resisting forces concentrated at plate boundaries, but observationally constrained high-resolution models of global mantle flow remain a computational challenge. We capitalized on advances in adaptive mesh refinement algorithms on parallel computers to simulate global mantle flow by incorporating plate motions, with individual plate margins resolved down to a scale of 1 kilometer. Back-arc extension and slab rollback are emergent consequences of slab descent in the upper mantle. Cold thermal anomalies within the lower mantle couple into oceanic plates through narrow high-viscosity slabs, altering the velocity of oceanic plates. Viscous dissipation within the bending lithosphere at trenches amounts to ~5 to 20% of the total dissipation through the entire lithosphere and mantle.

Rapid Continental Subsidence Following the Initiation and Evolution of Subduction

Dynamic topography resulting from initiation of slab subduction at an ocean-continent margin causes the continental lithosphere to subside rapidly. As subduction continues and the slab shallows, a basin depocenter and forebulge migrate in toward the continental interior. Finally, closure of the ocean basin leads to regional uplift. These active margin processes have commonly been ascribed to supracrustal loading, but numerical modeling shows that dynamic subsidence rates can exceed 100 meters per million years and are similar to rates of sediment accumulation along convergent North American plate margins over the Phanerozoic.