Ponding, plume material

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 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). 

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

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.

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... 

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. 

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.

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 ... 

Sleep, N. H. 1994. Lithospheric thinning by midplate mantle plumes and the thermal history of hot plume material ponded at lithospheric depths. Journal of Geophysical Research, 99, 9327-9343. 

As a flrst guess, a starting plume may be represented by a volume Q of material ponding beneath a flat base of the lithosphere. Initially the material has radius Ro and central height Hq, that is, dimensionally... 

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