Crustal thermal models along East European geotraverses: Inverse solutions

Abstract

The modeling of a two-dimensional, steady state, purely conductive crustal thermal regime is formulated as a stochastic inverse problem, using both a 5-point finite difference (FD) and a quadrilateral isoparametric finite element (FE) discretization. A priori information is incorporated in the form of a joint Gaussian probability density function (PDF) for the model parameters which consist of the discretized values of the heat flow densities (HFDs) at the surface ( q s ) and at the model base ( q b ), the heat production ( A), the thermal conductivity (λ), and the crustal temperature ( T). A simultaneous inversion then yields the most probable estimates and the error bounds for these parameters. The formulations are applied to the modeling of thermal regimes along East European geotraverses (EEGTs), using the structural models proposed by Čermák and Bodri (1986) as a basis for assigning a priori values. Appropriate a priori standard deviations (SDs) are assigned to constrain the model parameters to lie within some neighborhoods of the a priori values, and to ensure that q b is a smooth function along each geotraverse, a priori covariances are assigned between the discretized values. Finally, small a priori SDs are assigned to temperatures in those regions where the geotraverses intersect so as to ensure that the thermal models are consistent. The FD formulation has been applied to all five EEGTs, whereas the FE formulation apply only to the geotraverses EEGT 1 and EEGT 5. Where both formulations are used, essentially identical results are obtained. In general, the Moho HFD is low in the Precambrian East European Platform, relatively higher in the Variscan units, high in the Alps, and very high underneath the Pannonian Basin, with lateral variations of up to 40 mW m −2. The regional variations are statistically significant, if one accepts an a priori coefficient of variation of 25% for both q s and λ, and an a priori SD of 0.176 for log (A) which is equivalent to a factor of two for A.