Crustal temperature and heat production: Implications of the linear heat-flow relation

The surprising linear relation between surface heat flow and heat production in plutons is easily explained in terms of an exponential decrease of heat production with depth in the crust. If the linear relation is assumed to be true in a mathematical sense, it can be shown that this is the only possible explanation, provided that three other assumptions that seem geologically reasonable are made. The decrement D of the exponential function is determined empirically from surface observations since theory requires that it be equal to the slope parameter of the linear relation. Recently published heat-flow results indicate that D varies little from one province to another, and this suggests a model in which D is a general geochemical property of the crust beneath plutons. The outer layer of variable heat production, suggested by the linear relation, is identified with a zone of partial melting in which the heat-producing elements were redistributed exponentially during the plutonic process. The analysis suggests that this zone typically includes a substantial portion of the crust, and that the upward concentration of crustal heat production and heat flow from much of the continental mantle are both somewhat greater than has generally been supposed. The model leads to simple estimates of crustal temperatures beneath plutons.