Geothermal heat flux anomaly due to a 3D prismoid situated in the second layer of a three-layered Earth

Abstract

We present mathematical modelling of the stationary geothermal field for the
three-layered earth which includes a three-dimensional perturbing body below the first
layer (over the halfspace substratum). The unperturbed temperature field corresponds to
the uniform vertical heat flux. The perturbing 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), the thermal conductivity of which was greater than that in the
ambient second layer, while the upper face of the prismoid may be in contact with the
upper layer and the lower face may touch the bottom halfspace. Numerous graphs are
shown for the disturbance of the temperature and heat flow distribution on the surface of
the Earth or inside all three layers.