Fig. 9

a 3-D synthetic vertically layered model used for the evaluation of the numerical algorithm validity. The spacings of grids are 2000 m laterally and 100 m vertically. b Numerically modeled 3-D temperature distribution based on the 3-D synthetic model. White inverted triangle and bordered cells denote the grid point from which a vertical temperature distribution was extracted and the areal extent of cells used for thermal property averaging at each depth. c Comparison of the vertical temperature profiles obtained from the 3-D finite difference numerical modeling result and calculation using 1-D analytical solutions Eq. 4a and 4b at the location marked by inverted white triangle in (a)