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.

Terrestrial heat flow above the Andean Subduction Zone in Bolivia and Peru

“…The values of heat flow established in this investigation have been determined in three ways. At sites with wellestablished temperature-depth profiles that either are sufficiently far below the local topography to avoid horizontal components of heat flow or are overlain by moderate topography which does not induce significant horizontal components, the heat flow has been calculated by the mean interval heat flow method and/or the Bullard method [Bullard, 1939] At sites where topography imparts a significant signature at the depths of the temperature measurements, heat flow is determined by a numerical method [Henry and Pollack, 1985] that simultaneously treats both topographic and subsurface structural effects on the temperature field and yields the single best fitting value of regional heat flow consistent with a distributed suite of temperature observations. The method, while applicable to the common situation of temperature observations in isolated vertical boreholes, is particularly suited to determining heat flow from an ensemble of observations in We also applied this methodology to nine Andean sites reported by Uyeda and colleagues [Uyeda and Watanabe, 1982] for which topographic information was available.…”

Accounting for palaeoclimate and topography: A rigorous approach to correction of the British geothermal dataset

“…172-175) but this simply reported their preferred heat flow values, with no indication of whether a topographic correction had been made, let alone how it has been determined. Subsequent works on UK geothermics, such as Rollin (1995), and Busby et al (2011) have indeed omitted discussion of this topic, notwithstanding the thorough analyses that have been made for non-UK datasets (e.g., Blackwell et al, 1980;Henry and Pollack, 1985).…”

“…Blackwell et al, 1980;Henry and Pollack, 1985), the present study shall focus on the use of analytic corrections. Since many UK geothermal boreholes are located in valleys, the adopted analytic correction shall be that for a Lees Valley (cf.…”

Terrestrial heat flow in the Sirt Basin, Libya, and the pattern of heat flow across northern Africa

“…Heat production was calculated using the relationship from Birch [1954], and the results are given in Table 2. Suleiman [1985] did not report an uncertainty for these measurements, but uncertainties in heat production measurements using gamma ray spectrometry reported by other investigators are typically _ •20% [e.g., Nyblade et al, 1990; Ballard et al, 1987 To investigate the effect of heat refraction on heat flow from horsts and grabens, two-dimensional thermal models were constructed using a finite difference modeling technique that solves the heat conduction equation [Henry and Pollack, 1985]. In the models, a background heat flow of 72 mW m -2 was used along with a thermal conductivity contrast of 1 W m -1 K 'l between basement and sediments (Figure 4).…”