Thermal convection has been modeled in a 3-D model box, in order to study the structure (diameter and temperature anomaly) of mantle plumes and their surface manifestation (topography, geoid anomaly, heat flow).
The variable parameters in the different models are the Rayleigh number (it varies between 5.106and 108), the depth-dependent viscosity and the rate of internal heating. In the simplest models the viscosity is assumed simply exponential increasing with depth by a factor of 10 and 100. Trying to model the real mantle viscosity distribution in some cases a narrow high and a low viscosity layer was added to model the lithosphere and the asthenosphere. In some models the possible bottom boundary layer of mantle convection, the D'' layer is also included. In some models internal heating was added with a non-dimensional value of H=10 corresponding to the concentration of radioactive elements in chondrite meteorites.The upper and the lower boundaries are supposed to be isothermal and stress-free. The sides of the box are reflecting boundaries. The size of the box was chosen to allow the evolution of only one plume in the corner of the box. Applying these conditions, the box represents one quarter of the whole convective cell. To calculate the anomalies, both upper and whole mantle scaling were used.
Summarizing and comparing the result with the observations, the following remarks can be drawn:
- The interior of the convective cell had a lower temperature in the case of high viscosity contrast. Therefore, the temperature anomaly of the plume became higher. In the topographic anomalies, there were no significant differences between the models of different viscosity contrast. The addition of the asthenosphere decreases the geoid and topographic anomalies. The lithosphere makes higher the temperature of the interior of the convective cell and reduces the surface heat flow anomaly leading towards better agreement with the observed values.The high viscosity layer at the CMB (D'' layer) has no effect on the surface manifestations, but changes the structure of the convection. The interior of the convective cell will be warmer.
- Basal heating dominates in every model, but the effect of internal heating on the studied features suggests that it cannot be neglected. It decreases the topographic, geoid and temperature anomalies.
- Seismic tomographic studies (Bijwaard and Spakman, 1999, Wolfe et al., 1997) suggest lower temperature anomalies of the upwellings than the calculated ones.
The most complex whole mantle model has the most similar value to the observations. The diameter of the plume also indicates rather a whole mantle convection, because the values at upper mantle convection are very low (<80 km).The calculated values of heat flow anomaly (50 - 600 mW/m2) are much higher than the observed values (10-20 mW/m2, Courtney and White, 1986). In general, the amplitudes of the calculated anomalies (geoid, topography) fit better to the observations, when upper mantle convection is supposed. Usually all modeled topographic heights are larger than the observations, except the lowest values. Geoid heights lie in the range of the real anomalies for almost every upper mantle model. The problematical part of these models is the horizontal extent of the anomalies, which is significantly smaller than the observations. The horizontal extent suggests whole mantle convection, but the amplitude of the topography in these models is significantly larger than the observed values. The geoid anomalies in these models are higher than the observed ones, except the models with asthenosphere and lithosphere.
References:
Bijwaard, H., and Spakman W., 1999. Tomographic evidence for a narrow whole mantle plume below Iceland. Earth Planet. Sci. Lett. 166: 121-126
Courtney, R. C. and White, R. S. 1986. Anomalous heat flow and geoid across the Cape Verde Rise: evidence for dynamic support from a thermal plume in the mantle. Geophys. J. R. Astron. Soc., 87: 815-867
Monnereau, M. and Cazenave, A. 1990. Depth and geoid anomalies over oceanic hotspot swells: a global survey. J. Geophys. Res., 95: 15: 429 - 15,438