Estimates of the Magnitude of Topographical Effects on Surface Heat Flow from Finite Element Modelling

Abstract

Surface heat flow calculations are employed by geothermal exploration companies to estimate the geothermal gradient down to depths of 3 km to 6 km. Surface heat flow is typically calculated from coincident thermal conductivity data or estimates, and temperatures obtained by drilling a slim-line hole down to depths of 300 m to 1000 m. At such shallow depths the effect of a variable surface topography needs to be considered when performing temperature extrapolations to greater depth. This is because, for a given crustal volume with an undulating surface, heat will tend to flow towards topographic lows and away from topographic highs as it migrates from the base to the ground surface. A linear approximation method was developed by Lees (1910) to correct for topography under idealised geometric mountain ranges. This study presents results from a series of finite element method (FEM) models that predict the magnitude of variation of surface heat flow at the surface of a homogenous two-dimensional slice of crust with a uniformly curved surface. The results from this simple geometry are then compared to irregular topographic surfaces derived from real world examples. The main advantage of using the FEM method, described in this study, - rather than the method described by Lees (1910) - is that any regular or irregular surface topography may be used.