Tine B. Larsen

Dynamical consequences of depth-dependent thermal expansivity and viscosity on mantle circulations and thermal structure

The effects of both depth-dependent thermal expansivity and depth-dependent viscosity on mantle convection have been examined with two-dimensional finite-element simulations in aspect-ratio ten boxes. Surface Rayleigh numbers between 107 and 6 × 107 have been considered. The effects of depth-dependent properties, acting singly or in concert, are to produce large-scale circulations with a few major upwellings. The interior of the mantle is cooled by the many cold instabilities, which are slowed down and eventually swept about by the large-scale circulation. The interior temperature of the mantle can be influenced by the trade-off between depth-dependent properties and internal heating. For chondritic abundance of internal-heating and depth-dependent thermal expansivity, the viscosity increase across the mantle can be no greater than a factor of around ten in order to keep the lower mantle adiabatic. The thermal contrasts between the cold blobs and the surrounding mantle are strongly reduced by depth-dependent properties, whereas the lateral differences between the hot upwelling and the ambient lower mantle can be significant, over several hundred degrees. Depth-dependent properties also encourage the formation of a stronger mean-flow in the upper mantle, which may be important for promoting long-term polar motions.

Depth to Moho in Greenland: receiver-function analysis suggests two Proterozoic blocks in Greenland

Abstract The GLATIS project (Greenland Lithosphere Analysed Teleseismically on the Ice Sheet) with collaborators has operated a total of 16 temporary broadband seismographs for periods from 3 months to 2 years distributed over much of Greenland from late 1999 to the present. The very first results are presented in this paper, where receiver-function analysis has been used to map the depth to Moho in a large region where crustal thicknesses were previously completely unknown. The results suggest that the Proterozoic part of central Greenland consists of two distinct blocks with different depths to Moho. North of the Archean core in southern Greenland is a zone of very thick Proterozoic crust with an average depth to Moho close to 48 km. Further to the north the Proterozoic crust thins to 37–42 km. We suggest that the boundary between thick and thin crust forms the boundary between the geologically defined Nagssugtoqidian and Rinkian mobile belts, which thus can be viewed as two blocks, based on the large difference in depth to Moho (over 6 km). Depth to Moho on the Archean crust is around 40 km. Four of the stations are placed in the interior of Greenland on the ice sheet, where we find the data quality excellent, but receiver-function analyses are complicated by strong converted phases generated at the base of the ice sheet, which in some places is more than 3 km thick.

Ultrafast mantle plumes and implications for flood basalt volcanism in the Northern Atlantic Region

Abstract Recent geochemical and geochronological data on Paleocene flood basalts from West Greenland, SE Greenland and the British Isles show that volcanic activity at these widely separated locations commenced nearly simultaneously around 61–62 Ma ago, and that the duration of this initial phase of flood basalt magmatism was of the order of a few million years or less. A small, fast moving upper mantle plume which rapidly spreads out horizontally, on encountering the base of the lithosphere, appears to be a viable mechanism to explain these observations. However, in order to reconcile the idea of an ultrafast plume with the observed plate velocities, a physical mechanism is needed for inducing a separation of timescales between the plume speed and the surrounding mantle circulation. Thermal convection with a non-Newtonian temperature- and depth-dependent rheology provides such a mechanism wherein extremely fast plumes ascending at velocities between one to tens of meters per year can be produced in an otherwise slowly convecting mantle moving at cm/yr. This transport mechanism is capable of bringing up very hot matter from the transition zone to the lithosphere. The fast upward velocities lead to the production of high viscous heating rates surrounding the plume upon impinging the lithosphere. It is thus possible to explain the near simultaneous onset of magmatism in West Greenland, SE Greenland and the British Isles in the early Tertiary by a fast moving mantle plume spreading out horizontally with a velocity of around 0.5 m/yr. For resolving numerically the thermal-mechanical state of these strongly time-dependent mantle flows, extremely high spatial resolution, on the kilometer scale, is required. Finally we suggest the possibility that the source of the fast upper-mantle plume under Iceland may be rooted in the lower mantle. This is consistent with the recent findings by seismic tomography of a deep mantle plume under Iceland.

ULTRAFAST UPWELLING BURSTING THROUGH THE UPPER MANTLE

A high-resolution calculation of strongly time-dependent thermal convection in the upper mantle with non-Newtonian, temperature-dependent rheology shows that, for an effective Rayleigh number of around 106, extremely fast upwellings, at times exceeding 10 m/yr, can be generated a few hundred kilometers below the lithosphere. There is a clear separation of timescales between this fast jet and the more slowly convecting mantle. Within this fast vertical shear layer is embedded a thermal boundary layer with a width of the order of 50 km. The development of the fast non-Newtonian upwelling is characterized by the growth of the plume head to a large enough size, before the plume takes off rapidly at a depth of around 350 km. Upon impinging the base of the lithosphere, this fast plume thins the lithosphere and the flow then becomes a horizontally moving hot sheet, extending out for around 1000 km. This scenario is found to repeat itself at the same location about 10 Myr after the first plume impingement.

Fast plumeheads: Temperature‐dependent versus non‐Newtonian rheology

In a series of two-dimensional Cartesian simulations with high resolution, on the order of 2 km, we have compared for the same effective Rayleigh number, around 106, the dynamics between Newtonian and non-Newtonian rheologies. A viscosity contrast due to temperature of 1200 has been employed throughout with surface dissipation numbers varying between 0.05 and 0.2. Peak velocities for non-Newtonian plumes are at least 50 times faster than the peak Newtonian velocities and reach magnitudes in excess of m/yr. Upon impinging the surface, plume head structures of the non-Newtonian rheology contain much greater complexity in the thermal-mechanical structure than for Newtonian plumes.

Fractal features in mixing of non-Newtonian and Newtonian mantle convection

Mixing processes in mantle convection depend on the rheology. We have investigated the dynamical differences for both non-Newtonian and Newtonian rheologies on convective mixing for similar values of the effective Rayleigh number. A high-resolution grid, consisting of up to 1500 = 3000 bi-cubic splines, was employed for integrating the advection partial differential equation, which governs the passive scalar field carried by the convecting velocity. We show that, for similar magnitudes of the averaged velocities and surface heat flux, the local patterns of mixing are quite different for the two rheologies. There is a greater richness in the scales of the spatial heterogeneities of the passive scalar field exhibited by the non-Newtonian flow. We have employed the box-counting technique for determining the temporal evolution of the fractal dimension, D, passive scalar field of the two rheologies. We have explained theoretically the development of different regimes in the plot of N, the number of boxes, covered by a range of colors in the passive scalar field, and S, the grid size used in the box-counting. Mixing takes place in several stages. There is a transition from a fractal type of mixing, characterized by islands and clusters to the complete homogenization stage. The manifestation of this transition depends on the scales of the observation, and the initial heterogeneity and on the rheology. Newtonian mixing is homogenized earlier for long-wavelength observational scales, while a very long time would transpire before this transition would take place for non-Newtonian rheology. These results show that mixing dynamics in the mantle have properties germane to fluid turbulence and self-similar scaling.

Dynamical consequences on fast subducting slabs from a self-regulating mechanism due to viscous heating in variable viscosity convection

The authors have studied 2-D time-dependent convection for a rheology which is both non-Newtonian and temperature-dependent. Strong effects associated with viscous heating are found in the downwelling sheets, which are heated on both sides with an intensity around O(10{sup 2}) times the chondritic value. The magnitude of viscous heating increases strongly with the subduction speed. The slab interior is weakened by viscous heating and slab breakoff then takes place. This process provides a self-regulating mechanism for governing the speed of intact slabs able to reach the deep mantle. Timescales associated with viscous heating are quite short, a few million years. Internal heating by radioactivity decreases the amount of shear heating. 13 refs., 5 figs.

Comparison of mixing properties in convection with the Particle‐Line Method

Spatial resolution in mixing processes is an acute problem. We propose a line method, akin to the contour dynamics technique, which is an extension of the particle method but with the particles redistributed on the line with time. We have used up to 10 5 particles per line and ten lines to investigate the dynamical and structural properties of mixing for both Newtonian and non-Newtonian temper- ature-dependent viscosity convection in 2D geometry. The spatial structures and the time history of the lines formed in Newtonian convection are dierent from those produced in non-Newtonian convection, which has the tendency for producing long-living horizontal structures. Ecient mixing in the upper mantle would be inhibited by non-Newtonian rheology.

Temperature‐dependent Newtonian and non‐Newtonian convection: Implications for lithospheric processes

Convection studies of temperature-dependent Newtonian and non-Newtonian rheology in aspect-ratio seven boxes have been carried out for volume averaged Rayleigh numbers between O(105) and O(107). Large lateral viscosity variations, O(104) are found for non-Newtonian cases with total temperature-dependent viscosity variations up to 250. Flow structures for both rheologies are distinguished by large-scale circulations with relatively stable descending limbs. Much larger hot thermal anomalies are found near the surface for non-Newtonian rheology. Lithospheric thinning is facilitated by non-Newtonian rheology because of stress-softening and the lubrication of the descending limbs by hot diapirs.

Generation of fast timescale phenomena in thermo-mechanical processes

Abstract We have studied thermo-mechanical mechanisms for producing fast timescale geological processes. A two-dimensional time-dependent convection model with the extended-Boussinesq approximation has been used in which both viscous and adiabatic heating are included. Both non-Newtonian and Newtonian temperature- and depth-dependent rheologies with a depth-dependent thermal expansivity have been considered. A fourth-order accurate scheme has been used with a vertical grid spacing as fine as 3 km being imposed in the upper portion of the mantle, and a horizontal grid spacing of around 10 km. Non-Newtonian rheology precipitates the development of very fast upwellings with large amounts of attendant viscous heating and high surface heat flow. Thermal instabilities with fast timescales occur near the surface during the plume impingement. The growth times of these instabilities are found to decrease significantly with the power-law index n and the convective vigor, and increase with larger surface dissipation number. For n = 3 the characteristic timescales are on the order of 1 Myr. Instabilities produced with Newtonian rheology occur over longer timescales. Non-Newtonian rheology also enhances the production of viscous heating to a magnitude which can be 10 4 times greater than that for chondritic heating. These results suggest that rapid geological events, less than 1 Myr, can be achieved with a non-Newtonian, temperature-dependent rheology by means of a positive thermo-mechanical feedback.