Refraction effect in geothermal heat flow due to a 3D prismoid, situated in the substratum of two-layer Earth

Abstract

We present mathematical modelling of the stationary geothermal field for the two-layered Earth which includes a three-dimensional perturbing body below the first layer (in the substratum). The body is in the form of 3D prismoid with sloping side faces, while its upper and lower face are rectangles at the planes z = z1, z2. The theoretical formulae are based on the generalized theory of the double-layer potential and boundary integral equation (BIE). Special attention is paid to the quadrilateral prismoids bounded by planar skew faces. The numerical calculations were performed for the 3D prismoids (blocks) with thermal conductivity different to the ambient substratum, while the upper face of the prismoid may be in contact with the upper layer. Numerous graphs are shown for the disturbance of the heat flow on the surface of the Earth or inside the first layer.

Keywords

• geothermics, heat flow refraction, double-layer potential, boundary integral equations, boundary element methods, solid-angle-of-view calculations