The terrain effect on terrestrial heat flow

Abstract

A new approach to the topographic correction for terrestrial heat flow measurements is presented. The approach features calculation of a Fourier series fit to the surface temperature‐surface elevation data where the surface temperatures are based on a model that includes surface temperature variations due to microclimate variations. The mathematics of the terrain correction problem are similar to the upward (away from source) continuation problem in gravity and magnetics so several solutions, in addition to the Fourier series approach, are available in the literature that allow an accurate calculation of the correction provided the surface boundary condition is properly specified. However, the usual boundary condition applied, a linear relation between ground surface temperature and elevation, is shown to be inadequate for drill holes in the depth range 30–200 m no matter how low the topographic relief. Thus a model of ground surface temperature is developed that includes the effects of elevation, slope orientation, and slope angle. Because of the effects of microclimate, the classical models that have isothermal surfaces that generally parallel the topographic surface are significantly in error in many cases, and the patterns of isotherms near the topographic surface are more complicated than was previously recognized. This complexity causes gradient variations with depth in 30‐ to 200‐m holes that have not been previously recognized as being related to topographic effects. Because the temperature effects of slope orientation and inclination do not scale with respect to the magnitude of the relief, significant terrain corrections may be required even in areas of relatively low relief. The application of the technique is illustrated by application to a line dipole hill and a group of drill holes near Wilbur, Washington. In addition, several examples of two‐dimensional terrain effects and one example of three‐dimensional terrain effects are illustrated for topographic sections in the northwestern United States. In the United States, most ‘anomalous’ gradients in the upper 100–200 m of drill holes in impermeable rocks can be explained by a combination of topographic and microclimatic effects, without resorting to temporal climatic changes or unknown types of water effects. The depth of the holes necessary for reliable heat flow measurements in such settings is a signal to noise problem where the noise is the effect at depth of the microclimatically related surface temperature variations, coupled with the topographic effect, and the signal is a temperature increase at any depth due to the background geothermal gradient. Typically, the noise has decreased to a few degrees centigrade per kilometer within the depth range 100–200 m. Thus the general conclusion has been that these depths of holes are required for reliable heat flow values. In fact, when linear temperature‐depth data are observed in shallower holes or when appropriate corrections are made, reliable measure ments in impermeable rocks may be consistently made in holes no deeper than 100 m.