David Bercovici

Whole-mantle convection and the transition-zone water filter

Because of their distinct chemical signatures, ocean-island and mid-ocean-ridge basalts are traditionally inferred to arise from separate, isolated reservoirs in the Earths mantle. Such mantle reservoir models, however, typically satisfy geochemical constraints, but not geophysical observations. Here we propose an alternative hypothesis that, rather than being divided into isolated reservoirs, the mantle is filtered at the 410-km-deep discontinuity. We propose that, as the ascending ambient mantle (forced up by the downward flux of subducting slabs) rises out of the high-water-solubility transition zone (between the 660 km and 410 km discontinuities) into the low-solubility upper mantle above 410 km, it undergoes dehydration-induced partial melting that filters out incompatible elements. The filtered, dry and depleted solid phase continues to rise to become the source material for mid-ocean-ridge basalts. The wet, enriched melt residue may be denser than the surrounding solid and accordingly trapped at the 410 km boundary until slab entrainment returns it to the deeper mantle. The filter could be suppressed for both mantle plumes (which therefore generate wetter and more enriched ocean-island basalts) as well as the hotter Archaean mantle (thereby allowing for early production of enriched continental crust). We propose that the transition-zone water-filter model can explain many geochemical observations while avoiding the major pitfalls of invoking isolated mantle reservoirs.

The generation of plate tectonics from mantle convection

Abstract In the last decade, significant progress has been made toward understanding how plate tectonics is generated from mantle dynamics. A primary goal of plate-generation studies has been the development of models that allow the top cold thermal boundary layer of mantle convection, i.e. the lithosphere, to develop broad and strong plate-like segments separated by narrow, weak and rapidly deforming boundaries; ideally, such models also permit significant strike-slip (toroidal) motion, passive ridges (i.e. pulled rather than pried apart), and self-consistent initiation of subduction. A major outcome of work so far is that nearly all aspects of plate generation require lithospheric rheologies and shear-localizing feedback mechanisms that are considerably more exotic than rheologies typically used in simple fluid-dynamical models of mantle flow. The search for plate-generating behavior has taken us through investigations of the effects of shear weakening (‘stick-slip’) and viscoplastic rheologies, of melting at ridges and low-viscosity asthenospheres, and of grain-size dependent rheologies and damage mechanics. Many such mechanisms, either by themselves or in combination, have led to self-consistent fluid-mechanical models of mantle flow that are remarkably plate-like, which is in itself a major accomplishment. However, many other important problems remain unsolved, such as subduction intiation and asymmetry, temporal evolution of plate geometry, rapid changes in plate motion, and the Archaean initiation of the plate-tectonic mode of convection. This paper presents a brief review of progress made in the plate-generation problem over the last decade, and discusses unresolved issues and future directions of research in this important area.

A two‐phase model for compaction and damage: 1. General Theory

A theoretical model for the dynamics of a simple two-phase mixture is presented. A classical averaging approach combined with symmetry arguments is used to derive the mass, momentum, and energy equations for the mixture. The theory accounts for surficial energy at the interface and employs a nonequilibrium equation to relate the rate of work done by surface tension to the rates of both pressure work and viscous deformational work. The resulting equations provide a basic model for compaction with and without surface tension. Moreover, use of the full nonequilibrium surface energy relation allows for isotropic damage, i.e., creation of surface energy through void generation and growth (e.g., microcracking), and thus a continuum description of weakening and shear localization. Applications to compaction, damage, and shear localization are investigated in two companion papers.

Mantle Shear-Wave Velocity Structure Beneath the Hawaiian Hot Spot

Earths Plume Plumbing Volcanic hot spots, such as the one that continues to build the Hawaiian Islands, are thought to form by one of two mechanisms: Either mantle plumes bring hot, buoyant material to the surface from deep within the Earths interior, or extensive processing of the upper mantle by plate tectonics causes localized volcanism in stressed or heterogeneous crust. Wolfe et al. (p. 1388; see the cover; see the news story by Kerr) used an extensive array of ocean-bottom and land-based seismometers to reveal the structure of the mantle beneath Hawaii. These high-resolution images reveal a high-temperature plume originating from the lower mantle. Extensive seismological data support a mantle plume origin for the Hawaiian volcanic hot spot. Defining the mantle structure that lies beneath hot spots is important for revealing their depth of origin. Three-dimensional images of shear-wave velocity beneath the Hawaiian Islands, obtained from a network of sea-floor and land seismometers, show an upper-mantle low-velocity anomaly that is elongated in the direction of the island chain and surrounded by a parabola-shaped high-velocity anomaly. Low velocities continue downward to the mantle transition zone between 410 and 660 kilometers depth, a result that is in agreement with prior observations of transition-zone thinning. The inclusion of SKS observations extends the resolution downward to a depth of 1500 kilometers and reveals a several-hundred-kilometer-wide region of low velocities beneath and southeast of Hawaii. These images suggest that the Hawaiian hot spot is the result of an upwelling high-temperature plume from the lower mantle.

Generation of plate tectonics from lithosphere–mantle flow and void–volatile self-lubrication

Abstract The formation of plate tectonics from mantle convection necessarily requires nonlinear rheological behavior. Recent studies suggest that self-lubricating rheological mechanisms are most capable of generating plate-like motion out of fluid flows. The basic paradigm of self-lubrication is nominally derived from the feedback between viscous heating and temperature-dependent viscosity. Here, we propose a new idealized self-lubrication mechanism based on void (e.g., pore and/or microcrack) generation and volatile (e.g., water) ingestion. We test this void–volatile self-lubrication mechanism in a source–sink flow model; this leads to a basic nonlinear system which permits the excitation of strike–slip (toroidal) motion (a necessary ingredient of plate-like motion) out of purely divergent (i.e., poloidal or characteristically convective) flow. With relatively inviscid void-filling volatiles, the void–volatile mechanism yields a state of highly plate-like motion (i.e., with uniformly strong “plate” interiors, weak margins, and extremely focussed strike–slip shear zones). Moreover, the void–volatile model obeys a chemical diffusion time scale that is typically much longer than the thermal convection time scale; the model thus complies with the observation that plate boundaries are long lived and survive even while inactive. The void–volatile model of self-lubrication therefore predicts self-focussing shear zones, plate generation, and plate-boundary longevity through what has long been suspected to be a key ingredient for the existence of plate tectonics, i.e., water.

Plate tectonics, damage and inheritance

The initiation of plate tectonics on Earth is a critical event in our planet’s history. The time lag between the first proto-subduction (about 4 billion years ago) and global tectonics (approximately 3 billion years ago) suggests that plates and plate boundaries became widespread over a period of 1 billion years. The reason for this time lag is unknown but fundamental to understanding the origin of plate tectonics. Here we suggest that when sufficient lithospheric damage (which promotes shear localization and long-lived weak zones) combines with transient mantle flow and migrating proto-subduction, it leads to the accumulation of weak plate boundaries and eventually to fully formed tectonic plates driven by subduction alone. We simulate this process using a grain evolution and damage mechanism with a composite rheology (which is compatible with field and laboratory observations of polycrystalline rocks), coupled to an idealized model of pressure-driven lithospheric flow in which a low-pressure zone is equivalent to the suction of convective downwellings. In the simplest case, for Earth-like conditions, a few successive rotations of the driving pressure field yield relic damaged weak zones that are inherited by the lithospheric flow to form a nearly perfect plate, with passive spreading and strike-slip margins that persist and localize further, even though flow is driven only by subduction. But for hotter surface conditions, such as those on Venus, accumulation and inheritance of damage is negligible; hence only subduction zones survive and plate tectonics does not spread, which corresponds to observations. After plates have developed, continued changes in driving forces, combined with inherited damage and weak zones, promote increased tectonic complexity, such as oblique subduction, strike-slip boundaries that are subparallel to plate motion, and spalling of minor plates.

Double flood basalts and plume head separation at the 660-kilometer discontinuity.

Several of the worlds flood basalt provinces display two distinct times of major eruptions separated by between 20 million and 90 million years. These double flood basalts may occur because a starting mantle plume head can separate from its trailing conduit upon passing the interface between the upper mantle and the lower mantle. This detached plume head eventually triggers the first flood basalt event. The remaining conduit forms a new plume head, which causes the second eruptive event. The second plume head is predicted to arrive at the lithosphere at least 10 million years after the first plume head, in general agreement with observations regarding double flood basalts.

A two-phase model for compaction and damage. 2. Applications to compaction, deformation, and the role of interfacial surface tension

New equations for the dynamics of a two-phase mixture are derived in a companion paper [Bercovici et al., this issue (a)]. These equations do not invoke a bulk viscosity as most previous papers have done, and use the existence of the pressure difference between the two phases, including the possibility of surface energy at the interface between the phases. In this paper we show how a two-phase mixture reacts to simple stress fields. As a basic example, we discuss the deformation of a porous material confined by an impermeable jacket and loaded by a porous piston and show that the fluid can never be totally extracted from the matrix. We demonstrate that an unconfined porous sample is stronger under shear deformation than under normal stress. We consider spherically symmetric compaction and show that some unphysical results obtained using a constant matrix bulk viscosity are naturally avoided in our approach. We discuss the problem of compaction of a two-phase liquid in the presence of surface tension. In a one-dimensional simulation the surface tension generates porosity instabilities that tend to localize the fluid into narrow sills and dikes that cannot reach the surface.

Three-dimensional thermal convection in a spherical shell

Independent pseudo-spectral and Galerkin numerical codes are used to investigate three-dimensional infinite Prandtl number thermal convection of a Boussinesq fluid in a spherical shell with constant gravity and an inner to outer radius ratio equal to 0.55. The shell is heated entirely from below and has isothermal, stress-free boundaries. Nonlinear solutions are validated by comparing results from the two codes for an axisymmetric solution at Rayleigh number Ra = 14250 and three fully three-dimensional solutions at Ra = 2000, 3500 and 7000 (the onset of convection occurs at Ra = 712). In addition, the solutions are compared with the predictions of a slightly nonlinear analytic theory. The axisymmetric solution is equatorially symmetric and has two convection cells with upwelling at the poles. Two dominant planforms of convection exist for the three-dimensional solutions: a cubic pattern with six upwelling cylindrical plumes, and a tetrahedral pattern with four upwelling plumes. The cubic and tetrahedral patterns persist for Ra at least up to 70000. Time dependence does not occur for these solutions for Ra [les ] 70000, although for Ra > 35000 the solutions have a slow asymptotic approach to steady state. The horizontal and vertical structure of the velocity and temperature fields, and the global and three-dimensional heat flow characteristics of the various solutions are investigated for the two patterns up to Ra = 70000. For both patterns at all Ra , the maximum velocity and temperature anomalies are greater in the upwelling regions than in the downwelling ones and heat flow through the upwelling regions is almost an order of magnitude greater than the mean heat flow. The preferred mode of upwelling is cylindrical plumes which change their basic shape with depth. Downwelling occurs in the form of connected two-dimensional sheets that break up into a network of broad plumes in the lower part of the spherical shell. Finally, the stability of the two patterns to reversal of flow direction is tested and it is found that reversed solutions exist only for the tetrahedral pattern at low Ra .

A two-phase model for compaction and damage. 3. Applications to shear localization and plate boundary formation

A new two-phase theory employing a nonequilibrium relation between interfacial surface energy, pressure, and viscous deformation [Bercovici et al., this issue] provides a model for damage (void generation and microcracking) and thus a continuum description of weakening, failure, and shear localization. Here we demonstrate applications of the theory to shear localization with simple shear flow calculations in which one phase (the matrix, representing, for example, silicate) is much stronger (more viscous) than the other phase (the fluid). This calculation is motivated as a simple model of plate boundary formation in a shear zone. Even without shear the two phases eventually separate due to gradients in surface tension. However, the influence of shear on phase separation is manifest in several ways. As shear velocity increases, the separation rate of the phases increases, demonstrating a basic feedback mechanism: Accumulation of the fluid phase causes focused weak zones on which shear concentrates, causing more damage and void generation and thus greater accumulation of fluid. Beyond a critical shear velocity, phase separation undergoes intense acceleration and focusing, leading to a “tear localization” in which the porosity becomes nearly singular in space and grows rapidly like a tear or crack. At an even higher value of shear velocity, phase separation is inhibited such that shear localization gives way to defocusing of weak zones suggestive of uniform microcracking and failure throughout the layer. Our two-phase damage theory thus predicts a wide variety of shear localization and failure behavior with a continuum model. Applications of the theory to various fields, such as granular dynamics, metallurgy, and tectonic plate boundary formation are numerous.