Uncertainty analysis and inversion of geothermal conductive models using random simulation methods

Abstract

<div lang="en" class="abs"><p class="abs_header">Abstract</p><p>Knowledge of the thermal conditions in the lithosphere is based on theoretical models of heat transfer constrained by geological and geophysical data. The present dissertation focuses on the uncertainties of calculated temperature and heat flow density results and on how they depend on the uncertainties of thermal properties of rocks, as well as on the relevant boundary conditions. Due to the high number of involved variables of typical models, the random simulation technique was chosen as the applied tool in the analysis. Further, the random simulation technique was applied in inverse Monte Carlo solutions of geothermal models. In addition to modelling technique development, new measurements on thermal conductivity and diffusivity of middle and lower crustal rocks in elevated pressure and temperature were carried out.</p><p>In the uncertainty analysis it was found that a temperature uncertainty of 50 K at the Moho level, which is at a 50 km’s depth in the layered model, is produced by an uncertainty of only 0.5 W m⁻¹ K⁻¹ in thermal conductivity values or 0.2 orders of magnitude uncertainty in heat production rate (mW m⁻³). Similar uncertainties are obtained in Moho temperature, given that the lower boundary condition varies by ± 115 K in temperature (nominal value 1373 K) or ± 1.7 mW m⁻² in mantle heat-flow density (nominal value 13.2 mW m⁻²). Temperature and pressure dependencies of thermal conductivity are minor in comparison to the previous effects.</p><p>The inversion results indicated that the Monte Carlo technique is a powerful tool in geothermal modelling. When only surface heat-flow density data are used as a fitting object, temperatures at the depth of 200 km can be inverted with an uncertainty of 120–170 K. When petrological temperature-depth (pressure) data on kimberlite-hosted mantle xenoliths were used also as a fitting object, the uncertainty was reduced to 60–130 K. The inversion does not remove the ambiguity of the models completely, but it reduces significantly the uncertainty of the temperature results.</p></div>