Paleoclimate change and heat flow density inferred from temperature data in the Superior Province of the Canadian sheild

Abstract

Four boreholes, located near Cochrane, Hearst, Minchin Lake, and Otoskwin River in the Superior Province of the Canadian Shield, were logged in 1969/1970, and again in the summer of 1985. We have used the obtained temperature-depth ( T- z) data and the thermal property measurements to estimate the ground surface temperature (GST) histories and the heat flow densities at these sites, using a least squares inverse method. The method employs the theory of heat conduction in a laterally homogeneous Earth and the concept of incorporating a priori information to stabilize and uniquely determine the solution. We formulate the least squares optimization problem in the functional spaces and solve it with a quasi-Newton iterative gradient method. The functional space formulation allows the gradient operator to be obtained by solving only forward problems and the quasi-Newton method, which has a second order convergence, allows the a posteriori covariance operator to be readily computed. Except for the Cochrane hole, where systematic errors appear to exist in the temperature measurements, the two T- z logs for each hole, whether inverted individually or simultaneously, yield highly consistent, though not identical, results. All of the estimated GST histories, except that for Otoskwin River, exhibit a broad low centered around 1800 A.D. (the Little Ice Age), preceeded by a warm period in the Mid-Holocene (the Little Climatic Optimum) and followed by a warming trend in the last 100 years. However, the GST histories differ significantly from hole to hole in terms of the amplitude and the timing of their temporal variations. This suggests that the T- z data may have been significantly perturbed by local topography, lateral heterogeneities in the subsurface thermal properties, groundwater circulation, etc., which are not taken into account in the theory of one-dimensional heat conduction.