The far field of a borehole radar and its reflection at a planar interface

The far held of an electric Hertzian dipole located in a borehole is expressed as the product of a transmission coefficient and the far field of a dipole in a homogeneous region. The derivation uses the method of steepest descent, and gives physical insight into the wave phenomena that are important for borehole radar. The received field inside the borehole due to a planar interface located in the vicinity of the borehole is calculated using geometrical optics and the principle of reciprocity. The resulting expression is validated by numerically comparing it with a finite-difference time-domain solution. In an idealized situation, the reflection from the oil-mater boundary in a horizontal well can be detected with a borehole radar.