Plume material thickness

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... 

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).

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... 

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 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. 

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

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). 

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. 

Our models include the movement of the lithosphere over a stationary hotspot, thereby allowing us to evaluate the effects of plume proximity on the distribution of plume material susceptible to melting. We have considered models with 150 km (Ebinger Sleep 1998) and 220 km thick cratonic keels, and varied the loca-... 

Fig. 5. Thermal evolution of the lithosphere along a cross-section of Africa through 34°E. Arrow shows the location of the plume relative to the northward-moving African plate since 45 Ma. It should be noted that lithosphere cools as y/t south of plume, as we have placed no restriction on maximum thickness of the continental lithosphere. The long-term effect of the plume heating can be crudely estimated, if we assume that a 40 km equivalent thickness of material that is 200 K hotter than normal mantle, and with specific heat 4 x 106 JK m", ponds beneath a craton every 300 Ma. The mantle heat flow is increased by 3.4 mWm, or 20-25% of typical mantle heat flow from cratonal areas (e.g. Jaupart et al. 1998). (b) Thickness of plume material ponded beneath lithosphere 45 Ma after plume onset.

Numerical and analytical models of the vertical and lateral flow of hot, buoyant plume material beneath variable thickness continental lithosphere show that steep gradients at the lithosphere-asthenosphere boundary (LAB) strongly influence the distribution of plume material, and, consequently, the location and volume of melt. Cratonic keels deflect the plume material, with only minor thinning and heating of the mantle lithosphere beneath the cratons. 

In this paper, we are mainly interested in the blob when it is about to pond that is, when it is thin and it has cooled somewhat so that its viscosity is higher than that of fresh plume material. These are the conditions for which lubrication theory applies. The blob is near this final state for much of its existence as the initial flow is fairly rapid. For somewhat cool plume material, which is a few tens of kilometres thick and has a spread over 1000 km, the criterion that II in (A9) is less than unity is likely to be satisfied and the scaling results in the text apply. 

As the viscosity of the normal mantle and that of plume material are unknown, we present scaling relationships for the spreading time of inviscid material. Truly inviscid material continues to spread forever. Here the plume material is fluid until conductive cooling increases its viscosity. Equating the cooling time in (12) to the spreading time from (A6) yields the ponding thickness for infinite radial flow ... 

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