An analytical study of a two‐layer transient thermal conduction problem as applied to soil temperature surveys

Abstract

The soil temperature survey is an inexpensive exploration method in groundwater and geothermal resource investigations. In its simplest form, temperatures measured in shallow holes are analyzed to deduce variations in material properties. Typical interpretation schemes are based on simple, one‐layer solutions to the Fourier conduction equation using the annual solar cycle as a surface heat source. We present a solution to the more complicated two‐layer problem that can be computed using inexpensive personal computers and spreadsheet software. The most demanding mathematical requirement is the ability to manipulate a [Formula: see text] matrix. Testing the solution over a range of thermal diffusivity values expected in common soils and rocks reveals that the solution is very sensitive to variations in the thermal diffusivity of the surface layer and to the depth of the interface with the lower layer. When the boundary to the lower layer is less than about 10 m deep, a soil temperature survey is expected to be sensitive to the diffusivity variations in the lower layer. Because variations in shallow thermal properties often can be significant, this two‐layer method should be useful in areas with distinct shallow layering, (e.g., where there is a shallow water table or a thin soil layer).