Old continental geotherms: constraints on heat production and thickness of continental plates

Abstract

Summary. Absolute and mutual constraints on radioactive heat productivity, plate thickness and steady state continental geotherms are demonstrated for a model in which heat productivity comprises a near-surface, exponentially decreasing component and a component independent of depth. For a given surface heat flux there are separate upper limits on each component and a limiting trade-off curve between them. Below these limits there are linear trade-offs imposed if either the plate thickness or the temperature at a given depth are known, and, in principle, tighter bounds are imposed on each component. Preliminary application of the model shows that a kimberlite pyroxene geotherm requires a plate at least 200km thick and that lower plate (upper continental mantle) heat productivities may be (but are not required to be) as great as about 0.1 yW m3, which is about ten times the heat productivity of chrondrites. The estimation of continental geotherms depends strongly on assumptions about the vertical distribution of radioactive heat sources in the continental plates and on whether or not a steady state is assumed to have been achieved. The thickness of the plate is also directly involved, since the base of the plate can be defined as the depth at which a characteristic temperature is reached. It is the purpose of this paper to demonstrate, using a simple but plausible model, the relationships between temperature, heat production and plate thickness, including some absolute limits on heat production. The relationships can be used to evaluate the implications of various independent estimates of these quantities, and some examples are discussed here. An obvious limit on heat production is that in the steady state no more heat can be generated in the plate than emerges at the surface. A constraint with less obvious implications is that the geotherm must reach the mantle temperature at a reasonable depth. These constraints will be demonstrated here using a simple model of heat source distribution which is nevertheless plausible enough to give quantitatively useful results. Attention will be confined here to steady state models. Although the possibility of indefinitely continued cooling and thickening of the continental plates has been discussed (Pollack & Chapman 1977), a severe problem with this hypothesis is that the associated thermal subsidence should be accompanied by lOkm or more of crustal thickening, a