A. Mark Jellinek

The influence of a chemical boundary layer on the fixity, spacing and lifetime of mantle plumes

Seismological observations provide evidence that the lowermost mantle contains superposed thermal and compositional boundary layers that are laterally heterogeneous. Whereas the thermal boundary layer forms as a consequence of the heat flux from the Earths outer core, the origin of an (intrinsically dense) chemical boundary layer remains uncertain. Observed zones of ‘ultra-low’ seismic velocity suggest that this dense layer may contain metals or partial melt, and thus it is reasonable to expect the dense layer to have a relatively low viscosity. Also, it is thought that instabilities in the thermal boundary layer could lead to the intermittent formation and rise of mantle plumes. Flow into ascending plumes can deform the dense layer, leading, in turn, to its gradual entrainment. Here we use analogue experiments to show that the presence of a dense layer at the bottom of the mantle induces lateral variations in temperature and viscosity that, in turn, determine the location and dynamics of mantle plumes. A dense layer causes mantle plumes to become spatially fixed, and the entrainment of low-viscosity fluid enables plumes to persist within the Earth for hundreds of millions of years.

An early lunar core dynamo driven by thermochemical mantle convection.

Although the Moon currently has no internally generated magnetic field, palaeomagnetic data, combined with radiometric ages of Apollo samples, provide evidence for such a magnetic field from ∼3.9 to 3.6 billion years (Gyr) ago, possibly owing to an ancient lunar dynamo. But the presence of a lunar dynamo during this time period is difficult to explain, because thermal evolution models for the Moon yield insufficient core heat flux to power a dynamo after ∼4.2 Gyr ago. Here we show that a transient increase in core heat flux after an overturn of an initially stratified lunar mantle might explain the existence and timing of an early lunar dynamo. Using a three-dimensional spherical convection model, we show that a dense layer, enriched in radioactive elements (a ‘thermal blanket’), at the base of the lunar mantle can initially prevent core cooling, thereby inhibiting core convection and magnetic field generation. Subsequent radioactive heating progressively increases the buoyancy of the thermal blanket, ultimately causing it to rise back into the mantle. The removal of the thermal blanket, proposed to explain the eruption of thorium- and titanium-rich lunar mare basalts, plausibly results in a core heat flux sufficient to power a short-lived lunar dynamo.

Mixing and compositional stratification produced by natural convection: 1. Experiments and their application to Earth's core and mantle

An extensive series of laboratory experiments is used to quantify the circumstances under which fluids can be mixed by natural convection at high flux Rayleigh number. A compositionally buoyant fluid was injected at a fixed rate into an overlying layer of ambient fluid from a planar, horizontally uniform source. The nature of the resulting compositional convection was found to depend on two key dimensionless parameters: a Reynolds number Re and the ratio U of the ambient fluid viscosity to the input fluid viscosity. Increasing the Reynolds number corresponded to increasing the vigor of the convection, while the viscosity ratio was found to determine the spacing between plumes and whether buoyant fluid rose as sheets (U 1). From measurements of the final density profile in the fluid after the experiments we quantified the extent to which buoyant liquid was mixed in terms of a thermodynamic mixing efficiency E. The mixing efficiency was found to be high (E > 0.9) when either the Reynolds number was large (Re > 100) or the viscosity ratio was small (U 200. The amount of mixing was related to whether ascending plumes generated a large-scale circulation in the ambient fluid. When our results are applied to the differentiation of the Earths core, we suggest that the convection resulting from the release of buoyant residual liquid into the liquid outer core due to crystallization at the boundary between the inner and the outer core will probably lead to nearly complete mixing. In the dynamically very different context of the mantle, mantle plumes are predicted to ascend through the mantle and pond beneath the lithosphere, whereas convection driven by the subduction of oceanic lithosphere is expected to produce moderate to extensive mixing of the mantle. When the competing plate and plume modes of mantle convection are considered together, we find that owing to a larger driving buoyancy flux, the plate-scale flow will destroy any stratification at the top of the mantle produced by mantle plumes. Applying our results to the “stagnant lid” style of thermal convection predicted to occur in the mantles of the Moon, Mercury, Mars, Venus, and pre-Archean Earth, we expect the respective flows to produce minor thermal stratification at the respective core-mantle boundaries. In part 2 of this study [Jellinek and Kerr, this issue] we apply our results to the differentiation of magma chambers and komatiite lava flows.

Plume capture by divergent plate motions: implications for the distribution of hotspots, geochemistry of mid-ocean ridge basalts, and estimates of the heat flux at the core–mantle boundary

Abstract The coexistence of stationary mantle plumes with plate-scale flow is problematic in geodynamics. We present results from laboratory experiments aimed at understanding the effects of an imposed large-scale circulation on thermal convection at high Rayleigh number (106≤Ra≤109) in a fluid with a temperature-dependent viscosity. In a large tank, a layer of corn syrup is heated from below while being stirred by large-scale flow due to the opposing motions of a pair of conveyor belts immersed in the syrup at the top of the tank. Three regimes are observed, depending on the ratio V of the imposed horizontal flow velocity to the rise velocity of plumes ascending from the hot boundary, and on the ratio λ of the viscosity of the interior fluid to the viscosity of the hottest fluid in contact with the bottom boundary. When V≪1 and λ≥1, large-scale circulation has a negligible effect on convection and the heat flux is due to the formation and rise of randomly spaced plumes. When V>10 and λ>100, plume formation is suppressed entirely, and the heat flux is carried by a sheet-like upwelling located in the center of the tank. At intermediate V, and depending on λ, established plume conduits are advected along the bottom boundary and ascending plumes are focused towards the central upwelling. Heat transfer across the layer occurs through a combination of ascending plumes and large-scale flow. Scaling analyses show that the bottom boundary layer thickness and, in turn, the basal heat flux q depend on the Peclet number, Pe, and λ. When λ>10, q∝Pe1/2 and when λ→1, q∝(Peλ)1/3, consistent with classical scalings. When applied to the Earth, our results suggest that plate-driven mantle flow focuses ascending plumes towards upwellings in the central Pacific and Africa as well as into mid-ocean ridges. Furthermore, plumes may be captured by strong upwelling flow beneath fast-spreading ridges. This behavior may explain why hotspots are more abundant near slow-spreading ridges than fast-spreading ridges and may also explain some observed variations of mid-ocean ridge basalt (MORB) geochemistry with spreading rate. Moreover, our results suggest that a potentially significant fraction of the core heat flux is due to plumes that are drawn into upwelling flows beneath ridges and not observed as hotspots.

Mixing and compositional stratification produced by natural convection: 2. Applications to the differentiation of basaltic and silicic magma chambers and komatiite lava flows

The petrogenesis of igneous rocks can be controlled significantly by the mixing of dissimilar magmas. Within the contexts of basaltic and silicic magma chambers and komatiite lava flows we identify circumstances in which the extent to which contrasting magmas are mixed by natural convection potentially controls their differentiation. To evaluate the amount of mixing in each context, we apply the experimental results from part 1 [Jellinek et al., this issue] of this study, in which we quantified the conditions under which fluids could be mixed by convection at large Rayleigh numbers (> 1011). When our laboratory results are applied to basaltic magma chambers, we find that convection driven by compositionally buoyant magma released during floor crystallization or floor dissolution will produce partial to nearly complete mixing of the ascending fluid in chambers that are tens of meters to kilometers high, respectively. We also conclude that substantial floor melting (with extensive mixing) is expected only for basaltic chambers emplaced in the deep crust. During the turbulent flow of Archean komatiites, underlying sediments melted by forced convective heat transfer are predicted to have been mixed nearly completely into the overriding lavas. During the replenishment of silicic magma chambers by basaltic magmas we predict that the convection of buoyant silicic magma overrun by a spreading injection of denser basalt will cause little mixing. However, after emplacement, heat transfer from a basalt layer will gradually melt and mobilize its felsic floor, producing a small flux of buoyant felsic liquid that will be mixed extensively.

Seismic tremors and magma wagging during explosive volcanism

Volcanic tremor is a ubiquitous feature of explosive eruptions. This oscillation persists for minutes to weeks and is characterized by a remarkably narrow band of frequencies from about 0.5 Hz to 7 Hz (refs 1–4). Before major eruptions, tremor can occur in concert with increased gas flux and related ground deformation. Volcanic tremor is thus of particular value for eruption forecasting. Most models for volcanic tremor rely on specific properties of the geometry, structure and constitution of volcanic conduits as well as the gas content of the erupting magma. Because neither the initial structure nor the evolution of the magma-conduit system will be the same from one volcano to the next, it is surprising that tremor characteristics are so consistent among different volcanoes. Indeed, this universality of tremor properties remains a major enigma. Here we employ the contemporary view that silicic magma rises in the conduit as a columnar plug surrounded by a highly vesicular annulus of sheared bubbles. We demonstrate that, for most geologically relevant conditions, the magma column will oscillate or ‘wag’ against the restoring ‘gas-spring’ force of the annulus at observed tremor frequencies. In contrast to previous models, the magma-wagging oscillation is relatively insensitive to the conduit structure and geometry, which explains the narrow band of tremor frequencies observed around the world. Moreover, the model predicts that as an eruption proceeds there will be an upward drift in both the maximum frequency and the total signal frequency bandwidth, the nature of which depends on the explosivity of the eruption, as is often observed.

Viscous coupling at the lithosphere-asthenosphere boundary

Tectonic plate motions reflect dynamical contributions from subduction processes (i.e., classical “slab-pull” forces) and lateral pressure gradients within the asthenosphere (“asthenosphere-drive” forces), which are distinct from gravity forces exerted by elevated mid-ocean ridges (i.e., classical “ridge-push” forces). Here we use scaling analysis to show that the extent to which asthenosphere-drive contributes to plate motions depends on the lateral dimension of plates and on the relative viscosities and thicknesses of the lithosphere and asthenosphere. Whereas slab-pull forces always govern the motions of plates with a lateral extent greater than the mantle depth, asthenosphere-drive forces can be relatively more important for smaller (shorter wavelength) plates, large relative asthenosphere viscosities or large asthenosphere thicknesses. Published plate velocities, tomographic images and age-binned mean shear wave velocity anomaly data allow us to estimate the relative contributions of slab-pull and asthenosphere-drive forces for the motions of the Atlantic and Pacific plates. Whereas the Pacific plate is driven largely by slab pull, the Atlantic plate is predicted to be strongly driven by basal forces related to viscous coupling to strong asthenospheric flow, consistent with recent observations related to the stress state of North America. In addition, compared to the East Pacific Rise (EPR), the relatively large lateral pressure gradient near the Mid-Atlantic Ridge (MAR) is expected to produce significantly steeper dynamic topography. Thus, the relative importance of this plate-driving force may partly explain why the flanking topography at the EPR is smoother than at the MAR. Our analysis also indicates that this plate-driving force was more significant, and heat loss less efficient, in Earths hotter past compared with its cooler present state. This type of trend is consistent with thermal history modeling results which require less efficient heat transfer in Earths past.

Magma dynamics, crystallization, and chemical differentiation of the 1959 Kilauea Iki lava lake, Hawaii, revisited

Abstract Using constraints from an extensive database of geological and geochemical observations along with results from fluid mechanical studies of convection in magma chambers, we identify the main physical processes at work during the solidification of the 1959 Kilauea Iki lava lakes. In turn, we investigate their quantitative influence on the crystallization and chemical differentiation of the magma, and on the development of the internal structure of the lava lake. In contrast to previous studies, vigorous stirring in the magma, driven predominately by the descent of dense crystal-laden thermal plumes from the roof solidification front and the ascent of buoyant compositional plumes due to the in situ growth of olivine crystals at the floor, is predicted to have been an inevitable consequence of very strong cooling at the roof and floor. The flow is expected to have caused extensive but imperfect mixing over most of the cooling history of the magma, producing minor compositional stratification at the roof and thermal stratification at the floor. The efficient stirring of the large roof cooling is expected to have resulted in significant internal nucleation of olivine crystals, which ultimately settled to the floor. Additional forcing due to either crystal sedimentation or the ascent of gas bubbles is not expected to have increased significantly the amount of mixing. In addition to convection in the magma, circulation driven by the convection of buoyant interstitial melt in highly permeable crystal-melt mushes forming the roof and the floor of the lava lake is envisaged to have produced a net upward flow of evolved magma from the floor during solidification. In the floor zone, mush convection may have caused the formation of axisymmetric chimneys through which evolved magma drained from deep within the floor into the overlying magma and potentially the roof. We hypothesize that the highly evolved, pipe-like ‘vertical olivine-rich bodies’ (VORBs) [Bull. Volcanol. 43 (1980) 675] observed in the floor zone, of the lake are fossil chimneys. In the roof zone, buoyant residual liquid both produced at the roof solidification front and gained from the floor as a result of incomplete convective mixing is envisaged to have percolated or ‘leaked‘ into the overlying highly-permeable cumulate, displacing less buoyant interstitial melt downward. The results from Rayleigh fractionation-type models formulated using boundary conditions based on a quantitative understanding of the convection in the magma indicate that most of the incompatible element variation over the height of the lake can be explained as a consequence of a combination of crystal settling and the extensive but imperfect convective mixing of buoyant residual liquid released from the floor solidification front. The remaining chemical variation is understood in terms of the additional influences of mush convection in the roof and floor on the vertical distribution of incompatible elements. Although cooling was concentrated at the roof of the lake, the floor zone is found to be thicker than the roof zone, implying that it grew more quickly. The large growth rate of the floor is explained as a consequence of a combination of the substantial sedimentation of olivine crystals and more rapid in situ crystallization due to both a higher liquidus temperature and enhanced cooling resulting from imperfect thermal and chemical mixing.

The volcanic history of Volcán Alcedo, Galápagos Archipelago: a case study of rhyolitic oceanic volcanism

Volcán Alcedo is one of the seven western Galápagos shields and is the only active Galápagos volcano known to have erupted rhyolite as well as basalt. The volcano stands 4 km above the sea floor and has a subaerial volume of 200 km3, nearly all of which is basalt. As Volcán Alcedo grew, it built an elongate domal shield, which was partly truncated during repeated caldera-collapse and partial-filling episodes. An outward-dipping sequence of basalt flows at least 250 m thick forms the steepest (to 33°) flanks of the volcano and is not tilted; thus a constructional origin for the steep upper flanks is favored. About 1 km3 of rhyolite erupted late in the volcanos history from at least three vents and in 2–5 episodes. The most explosive of these produced a tephra blanket that covers the eastern half of the volcano. Homogeneous rhyolitic pumice is overlain by dacite-rhyolite commingled pumice, with no stratigraphic break. The tephra is notable for its low density and coarse grain size. The calculated height of the eruption plume is 23–30 km, and the intensity is estimated to have been 1.2x108 kg/s. Rhyolitic lavas vented from the floor of the caldera and from fissures along the rim overlie the tephra of the plinian phase. The age of the rhyolitic eruptions is ≤120 ka, on the basis of K-Ar ages. Between ten and 20 basaltic lava flows are younger than the rhyolites. Recent faulting resulted in a moat around part of the caldera floor. Alcedo most resently erupted sometime between 1946 and 1960 from its southern flank. Alcedo maintains an active, transient hydrothermal system. Acoustic and seismic activity in 1991 is attributed to the disruption of the hydrothermal system by a regional-scale earthquake.

Scaling relationships for chemical lid convection with applications to cratonal lithosphere

We obtain scaling relationships for convection beneath a chemically distinct conducting lid and compare this situation with isochemical stagnant lid convection. In both cases, the vigor of convection depends upon the small temperature contrast across the actively convecting rheological boundary layer, that is, ΔTrheo, the temperature difference between the base of the lid and the underlying half-space. The laterally averaged convective heat flow beneath a chemical lid scales as q ∝ ΔTrheo4/3. Heat flow through a chemical lid approaches a stagnant lid value where the lid does not impact the rheological boundary layer. Such a condition is met when ΔTrheo/Tη ≈ 3.6, where Tη is the temperature change required to change viscosity by a factor of e. We apply our scaling relationships to the slow vertical tectonics of continental interiors: We find that whereas chemical lid convection governs the mantle heat flow to the base of cratons that are underlain by chemically buoyant lithosphere, classical stagnant lid convection governs heat flow into platforms. The laterally averaged heat flow supplied by isochemical stagnant lid convection to platforms has waned as the Earths mantle cooled. Consequently, the thickness of platform lithosphere, in thermal equilibrium with isochemical stagnant lid convection, has increased over time. Thermal contraction of the thickening platform lithosphere is expected to produce ∼300 m subsidence relative to cratons beneath air. This prediction explains why cratons tend to outcrop and platforms tend to be sediment covered.