The modeling of crustal thermal regimes is basically the inference of subsurface distributions of heat flow density and temperature by continuing downward the near-surface measurements of heat flow density, temperature, thermal conductivity, and heat production. To account for the uncertainties in the near-surface data and in the subsurface distributions of thermal conductivity and heat prdouction, and to provide explicit estimates for the uncertainties in the resulting models, we have employed a Bayesian inverse formulation that incorporates the a priori information on model parameters in the form of a joint gaussian probability density function and that gives the inverse solution in the form of the most probable estimates and the a posteriori covariance matrix for the model parameters. To illustrate the method, we apply it to the modeling of thermal regimes along East European geotraverses EEGT 5 and EEGT 1, using both a linear 5-point finite difference and a quadrilateral isoparametric finite element discretization. Two features are emphasized. First, we introduce an a priori autocovariance function for the heat flow density at model base to help stabilize the solution. Second, we demonstrate the improvement in solution accuracy and resolution when a priori temperature information is available and incorporate in the inversion.

For the geotraverses studied, the finite difference and finite element formulations yields essentially identical results, although there is a substantial difference in the extent of their parameterization. In general, the surface and basal heat flow densities are similar in shape, implying a relatively uniform total crustal heat production across the geotrverses. Both the heat flow densities and the crustal temperatures exhibit strong lateral variations that appear to correlate with the tectonic age: the heat flow densities and tempeatures are low in the Precambrian East European Platform, relatively higher in the Variscan units, high in the Alps, and very high in the Pannonian Basin. The results support the presence of lateral variations of up to 40 mW m-2 in the Moho heat flow density, provided that one accepts as resonable an a priori standard deviastion of 25% for the surface heat flow density and an uncertainity of a factor of two for the heat production. Finally, the a posteriori and the observed surface heat flow densities match well but exceptions occur in localized regions, suggesting the presence of perturbing effects that cannot be accounted for in a steady state, purely conductive model. ¿American Geophysical Union 1990