Geothermal refraction problem for a 2-D body of polygonal cross-section buried in the two-layered earth

Abstract

We present the exact boundary integral formulae  for calculation of the geothermal  anomaly due  to  a two  dimensional body  whose  thermal conductivity  is λ_T   and  its cross-section is bounded by the closed general  polygonal  contour.  This  body  is buried  in the  superficial layer  of conductivity λ₁ . The  half-space  z > h with  the  thermal conductivity  λ₂  is considered as  a substratum of models.   The  boundary integral technique for the solution  of this  problem requires  the application of logarithmic potential  terms  in infinite  series.   Numerical calculations  based  on derived  formulae  revealed  that the  surface anomaly heat flow reflects  the “topography”  mainly  of the upper  boundary of the perturbing body.   The derived  algorithm and the developed  numerical program enable calculations for a number of interesting models:  intrusions, protrusions of the substratum etc.