Heat flow density values and paleoclimate determined from stochastic inversion of four temperature-depth profiles from the Superior Province of the Canadian Shield

Abstract

Abstract It has long been recognized that terrestrial heat flow density observations from boreholes may be biased due to non-steady surface temperature conditions. This calls for paleoclimatic corrections which have conventionally been obtained by solving a forward problem based on the equation of heat conduction and models of the surface temperature history and the thermal properties structure. While computationally convenient, the forward method fails 1. (1) to provide a stringent quantitative representation of all available data with confidence limits 2. (2) to extract all available information in an optimum manner 3. (3) to provide confidence limits on the parameters of interest. A stochastic inverse method which overcomes these shortcomings is described. The method treats the surface temperature history, the thermal conductivity structure and the background heat flow as unknowns which have been constrained a priori with soft bounds. The bounds ensure numerical stability and prevent unrealistic solutions when the a-priori hypothesis is safe. The technique is applied to geothermal data from four 600-m deep boreholes in the Superior Province of the Canadian Shield. The examples show how it is possible to constrain simultaneously the recent surface temperature history and the steady-state background heat flow from shallow geothermal data, and furthermore show how uncertainty about the average ground temperature during the Wisconsin Glaciation may be taken into account.