On the Image Model of a Buried Horizontal Wire

TLDR: In this article, it was shown that the modified image (or reflection coefficient) method in EFIE-based solutions (e.g., the Pocklington equation) leads to a large error (larger than 20%) in the low-frequency range for the computation of the current distribution in conductors longer than 10m.

Abstract: It is common practice in the engineering analysis process to use an approximate image method for the computation of the current in buried horizontal conductors (in the literature, this is often referred to as the “modified image” or “reflection coefficient” method). According to this approach, the earth/air interface is replaced by a positive mirror image of the charge and current in the conductor, and its field is multiplied by a suitable reflection coefficient. Different opinions on the validity of this approximation have been expressed in published debates, but more systematic analysis of the error introduced by this approach is not available in the literature. To establish the amount of error, we compare the computation results of the image model with the rigorous Sommerfeld integral method for a wide range of parameters. Contrary to widespread opinion, our results suggest that the modified image (or reflection coefficient) method in EFIE-based solutions (e.g., the Pocklington equation) leads to a large error (larger than 20%) in the low-frequency range for the computation of the current distribution in conductors longer than 10 m. In such a case, MPIE-based methods are preferred for use to achieve a smaller error (approximately 5%). Guidelines for the application of image models related to the conductor, earth and excitation parameters, upper frequency limit, and modeling method are presented.