Plume material

Sleep, N. H., Ebinger, C. J. Kendall, J.-M. 2002. Deflection of mantle plume material by cratonic keels. In Fowler, C. M. R., Ebinger, C. J. Hawkesworth, C. j. (eds) The Early Earth Physical, Chemical and Biological Development. Geological Society, London, Special Publications, 199, 135-150. 

Deflection of mantle plume material by cratonic keels... 

Fouch et al. (1999) compared model simulations of asthenospheric flow and seismic observations, and found that a significant proportion of the shear-wave splitting can be explained by the deflection of asthenospheric flow around a cratonic root. In our study we are interested in the extra complication of anisotropy in flowing mantle plume material that hes beneath and around continental keels. 

We design our studies of plume-hthosphere interactions to (1) predict the distribution in space and time of hot, buoyant plume material beneath cratons of various shapes (2) determine the physical conditions favourable for the lateral distribution of plume material beneath cratonic keels, which may give rise to small-volume melts (e.g. kimberlites) (3) evaluate the longevity of cratonic keels beneath large and small cratons (4) predict the behaviour of viscous plume material at the edges of the plume in terms of thickness and temperature. As we show below, a significant thickness of plume material flows beneath a cratonic keel only where the plume rises beneath part of the craton, providing a viable mechanism for the emplacement of kimberlites. 

We summarize the results of several plume simulations for a small craton, using the approach of Sleep (1997). We then analyse the effect of plume material emplacement beneath cratonic keels and channels of different dimensions. This work presents new simulations of plume flow beneath the African continent that include deep keels beneath Archaean cratons, which were not considered in the simple models of Ebinger Sleep (1998). Flow velocities and strains predicted from our preferred model allow us to estimate the magnitude and direction of SKS splitting by plume flow around a cratonic keel. These patterns are then compared with SKS splitting patterns from normal mantle flow around a keel (e.g. Fouch et al. 1999). 

Fig. 1. Schematic diagram illustrating interactions between a mantle plume and a cratonic keel. Hot, buoyant plume material will pond in pre-existing thin zones, and be deflected by cratonic keels.

We obtain the final thickness of ponded plume material following Huppert (1982) for four geometrically ideal cases ponding of radially symmetric plume material beneath a very wide craton, ponding beneath a craton of limited area, 2D ponding where material flows outward along a channel of constant width, and 2D flow from a craton of limited width. The objective is to obtain the dimensional dependence of the thickness of plume material on physical parameters. 

The height of plume material at a distance R may increase or decrease with time depending on whether the volume of material carried per time across a radius 27rHF increases or decreases with distance that is, the change in 2-kRF across an... 

The case where the craton has a finite width, allowing the plume material to cascade off its sides, follows similarly. In this case, the plume material thickness remains zero at its edge h(Ro) = 0. Equation (4) becomes... 

To use the analytical (lubrication theory) results of Huppert (1982), we represent the plume material as an equivalent layer of constant viscosity rj and constant specific weight contrast Apg. We ignore viscous forces associated with downward flow of the normal mantle at the edges of the blob. The appropriateness of this assumption is discussed in the Appendix. The thickness of the material is h(R) where R is the radial distance from the centre of the blob. Outward flow of plume material is driven by the local slope at its base. The flux (in m s per circumferential length of the flow front) is analytically... 

The dimensional equation (4) instead uses the width of the edge of the plume material x at time t... 

The case for the edge of the plume material where /i = 0 stays constant follows similarly. The thickness of the centre of the plume is... 

Fig. 2. Graph of plume material thickness v. distance (normalized) from plume s centre for several lithospheric geometries. For linear flow (e.g. along a channel at the LAB below a pre-existing rift zone) and radial flow (e.g. plume arising beneath a flat-keeled craton) material from the plume head is relatively uniform in thickness, except at its edges where viscosity increases associated with cooling retard flow. The shape of the radial curve is similar for topography of limited (small craton) or infinite extent (large craton). Unlike the top two cases, the flow from the plume tail thins more rapidly with distance from the centre (continuous line).

Summarizing, coohng of plume material and consequent increase in viscosity near the edge of the plume has little effect on the rest of the flow. This result implies that plume material maintains a relatively constant thickness beneath a craton, except very near its steep edges. 

How far can plume material spread before it cools and becomes sluggish Initially, the plmne material is thick and spreads rapidly. Little cooling occurs away from the boundaries of the plume material and the centre of the ponded layer remains hot and fluid. Eventually, the plume material becomes thin enough that conduction becomes important. The time for a thickness of material to cool is... 

The effective heat flow transferred to the craton from the ponded plume material over geological time can be estimated. For example, if we assume a 40 km equivalent thickness of 200 K excess plume temperature ponds on average at a spot under the craton every 300 Ma and that the volume specific heat is 4 x 10 JK m, then the average additional heat flow is 3.4mW m . This is a modest part of typical mantle heat flows from cratonal regions (e.g. Jaupart et al. 1998). 

The steady-state solution for material fed by a plume tail is also obtained following Huppert (1982). For simplicity we centre the plume tail within a flat-bottomed region of radius Ro, which represents a small craton. The steady-state solution of (3) where the plume material thickness is zero at i = 2 o is... 

Our analytical models provide inferences on the behaviour of ponded plume material. 

Plume material does not pond beneath the cratonic keel unless the centre of the plume is located beneath the cratonic root. These relations hold for large and small cratons. Thus, in most cases the cratonic keel effectively deflects hot plume material to thinner fithosphere, providing a mechanism for the preservation of cratonic keels. 

Larger cratons will be more susceptible to rifting as a result of basal drag at the LAB. Variations in lithospheric thickness within a large craton may lead to ponding of plume material, generating extensional body forces within the cratonic interior. 

---