Attila Galsa

Quantitative investigation of physical properties of mantle plumes in three-dimensional numerical models

Numerical calculations have been carried out to investigate the physical properties of mantle plumes in highly viscous thermal convection depending on the Rayleigh number (Ra). The Boussinesq approximation was applied in a three-dimensional Cartesian domain filled with isoviscous, purely bottom-heated fluid with infinite Prandtl number. In order to monitor the dynamical behavior of plumes an automatic plume detecting routine was developed based on the temperature between the plume and its surroundings. It was established that as the convection becomes more vigorous with increasing Rayleigh number the average cross-sectional area of an individual plume decreases (∼Ra−2∕3), the vertical velocity in plumes increases (∼Ra2∕3), while the average temperature in plumes is independent of Ra. It means that the volume and the heat transport in an individual plume is independent of the Rayleigh number. The number of plumes forming in the box increases (∼Ra1∕3) which is in accordance with the scale analysis using the...

THE NUMBER OF HOTSPOTS IN MANTLE CONVECTION: EFFECT OF DEPTH-DEPENDENT VISCOSITY AND INTERNAL HEATING IN TWO-DIMENSIONAL MODELS

Two-dimensional numerical models of mantle convection have been calculated for a range of high Rayleigh numbers, depth-dependent viscosity and basal plus internal heating. Large aspect ratio boxes have been used in the calculations in order to estimate the expected areal density of upwellings in infinite fluid layers. The results are analyzed with regard to the number of the Earth’s hotspots which are assumed to be surface imprints of cylindrical upwellings in the mantle. For a pure whole-mantle situation, 6–7 upwellings can be expected. If the upper mantle convects separately above the 660 km discontinuity (allowing a second convective layer below 660 km depth), the theoretically estimated number of upper-mantle plumes can be as high as 250. Given the number of real hotspots (42 to 117 according to different compilations), it is suggested that the flow regime of the mantle is intermediate between the pure whole-mantle or pure two-layer circulation.

New Methods for Modeling Laterolog Resistivity Corrections

The paper presents methods for laterolog response modeling. In Coulomb’s charges method, Laplace’s equation is solved for the electric field distribution in rock medium with internal boundaries between different resistivity layers. There, the boundary problem is reduced to Fred-holm integral equation of the second kind. The second method uses a finite element array to model apparent resistivity from laterolog. The task is treated as DC problem and the Laplace equation is solved numerically. The presented methods were applied to borehole data covering a typical stratigraphie section of the Fore-Sudetic Monocline in southwestern Poland. Apparent resistivity was calculated using the Coulomb’s charges method and alternatively modeled using a finite element method which gave similar results. Then, a series of linear corrections for borehole, shoulder bed, and filtration effects for apparent resistivity obtained by the Coulomb’s charges method demonstrated the feasibility of calculating true resistivity of virgin and invaded zones. The proposed methods provide a flexible solution in modeling which can be adapted to other logs.

Effect of temperature-dependent viscosity on mantle convection

Two-dimensional numerical calculations in cylindrical shell geometry have been carried out to investigate the effect of the temperature-dependent viscosity on the pattern and the characteristic parameters of the thermal convection occurring in the Earth’s mantle. Systematic model runs established that the viscosity decreasing with the temperature is reduced around the hot core-mantle boundary (CMB) which facilitates ‘the heat transport’ from ‘the core to the mantle’. On the other hand, the viscosity increases near the cold surface which hinders the heat outcome and results in higher mantle temperature and lower surface velocity. A power law relation was revealed between the strength of the temperature-dependence and the observed parameters, such as the velocity, surface mobility, heat flow, average temperature and viscosity. Two additional ‘mantle-like’ models were built up with extra strong temperature-dependent viscosity to imitate the flow in the Earth’s mantle. In model 1, in which the viscosity decreases seven orders of magnitude with the temperature increase, a highly viscous stagnant lid evolves along the cold surface which does not participate in the convection. The existence of the stagnant surface lid reduces the surface heat flow and generates a low viscosity asthenosphere beneath the lid with vigorous small-scale convection. In model 2, in which the viscosity decreases only six orders of magnitude with the temperature and the pressure-dependent viscosity is stronger, does not form a surface stagnant lid, highly viscous ‘slabs’ submerge to the CMB and effectively influence the hot upwelling plumes. Based on our numerical results it is necessary to implicate the yield stress into the simulations in order to obtain a highly viscous, ‘rigid’ surface lid, the lithosphere which can be broken up and subduct down to the mantle.