Mathematical Modeling of Geothermal Fields in Black Sea

Abstract

Mathematical modeling of geothermal fields in Black Sea is of great significance when creating integrated geophysical models of the region and their geological interpreting. Temperature calculation requires the solution of the heat conductivity equation with corresponding boundary conditions. This means extrapolating the measured on the sea bottom heat flow in accordance with assumptions concerning the deep structure of the main geological provinces, the depth distribution of the heat sources, and the thermal conductivity coefficient. Up to now in Black Sea are measured over 750 value of heat flow, which we used in our models. In this paper a 3D mathematical solution of the heat conductivity equation in an inhomogeneous media was used to calculate temperature distribution in earth’s crust and upper mantle in Black Sea. The boundary conditions are: 1) Fixed temperature conditions at the sea bottom. 2) Symmetry of the temperature fields at the vertical boundaries; 3) Knowledge of the temperature or heat flow at the base of the area investigated, which generally not available. The solution of the above problem requires the solution of the inverse problem. For this purpose we used Tikhonov’s regularization method. To define the block crustal structure and the corresponding distribution of heat sources, the results of deep seismic sounding and new seismological tomography were employed. The proper calculation of the temperature field was performed by the program package Solid Works (COSMOS) 2011. The results of temperature modeling are summarized in schemes, which show the calculated temperatures related to 10, 30, 50, and 70 km. The agreement of calculated temperatures at the points of intersection of the investigated profiles is generally good. The corrected bottom sea heat flow due to the effect of sedimentation range from 50 to 70 mW/m2. The regional variation of the Moho temperature is from 380 to 720oC. The Moho heat flow may range from 15-25 to 30-40 mW/m2. The crustal contribution to the bottom sea heat flow due to radiogenic heat sources amounts to 10-25 mW/m2 The results clearly confirm the possible existence of the astenosphere under the Black Sea basin. Temperature modeling permits assessing the thickness of the thermal lithosphere. An attempt for a new geological interpretation was performed.