Electric dipole scattering from a finitely conducting cylinder

Abstract

The time-harmonic electromagnetic fields for an arbitrarily oriented electric dipole over a cylindrical structure are derived in substantial detail. The problem is formulated by the classical method of separation of variables with an angular mode Fourier–Bessel series. Using boundary conditions on tangential components of E and H, we obtain integral representations for the electromagnetic fields in each of the homogeneous regions. The analysis is simplified by using the axial components of the electric and magnetic fields as potentials. The electromagnetic response of resistive or conductive structures is very important in fields such as hydrogeology, mineral exploration, archeology, civil engineering, geotechnics and hydrocarbon exploration. In many of these applications, numerical modeling is performed to aid in the acquisition and interpretation of data. Validation of these numerical routines involves comparison between numerical results obtained from simplified models and their analytical solutions. For validation by two-dimensional analytical solutions, the electrical response of a cylinder in a homogeneous medium is probably the best choice (if not the only one), however, most computational routines assume that the cylindrical structure is perfectly conductive or resistive, which can be a problem in the computation of some numerical solutions. Thus, we have developed here a procedure to obtain the semianalytic solution for the electromagnetic response of a finite conducting cylinder in the vicinity of an electric dipole, so that it can be reliably used as a form of validation for 2D electromagnetic numerical modeling programs. As part of the code verification, we analyze the modeled fields based on the behavior of the electric currents that form in the regions near the cylindrical heterogeneity, as well as a secondary field validation where we compare the results of a more general frequency-domain EM numerical method.