Heat flow in the presence of topography: Numerical analysis of data ensembles

Abstract

We present a method of estimating subsurface temperatures and true regional heat flow in the presence of perturbing topography, variable surface temperature, and subsurface thermal conductivity contrasts. The method involves solution of the steady‐state three‐dimensional heat conduction equation by finite‐difference numerical techniques. The topography is represented by an irregular upper boundary and the variable surface temperature as a boundary condition along the irregular upper surface. Internal structural configurations and conductivity contrasts are easily accommodated. The principal variable input into the system is the deep basal (unperturbed) heat flow. The best value of heat flow is obtained by minimizing, in a least‐squares sense, the differences between observed and calculated temperatures. Temperature observations commonly are distributed irregularly in the near‐surface (perturbed) environment, in multiple vertical or inclined boreholes, tunnels, and/or mine galleries. The method is particularly suited to simultaneous analysis of an ensemble of distributed observations, in contrast to methods that focus on the perturbation to the temperature gradient in the vicinity of a single borehole. We used the method to reduce data obtained at fifteen newly established heat flow sites in the Bolivian and Peruvian Andes. We illustrate with three examples—a two‐dimensional model from the Bolivar Mine, Bolivia; (2) a three‐dimensional model using variable conductivity from the Cerro Verde Mine, Peru; and (3) a three‐dimensional model at the Colquiri Mine, Bolivia where temperature measurements were few and the distance between the individual boreholes was fairly large.