Electromagnetic field generated by an off‐axis source in a cylindrically layered medium with an arbitrary number of horizontal discontinuities

Abstract

We investigate the propagation of electromagnetic waves in a cylindrically layered medium with an arbitrary number of horizontal discontinuities. The dielectric constant, conductivity, and magnetic permeability of the medium are functions of ρ and z only (i.e., independent of the azimuthal angle ϕ), but the field generated by an off‐axis source in this medium is in general a function of ρ, ϕ, and z. This two and a half‐dimensional (2.5-D) problem is often encountered in electromagnetic well logging, as well as in other areas such as optical fiber communications and integrated optics. We show that a coupling exists between the transverse electric (TE) and transverse magnetic (TM) components of the field even in the absence of the horizontal discontinuities, which makes it difficult to solve for the field. We apply an efficient numerical mode‐matching (NMM) algorithm to tackle this 2.5-D problem. This algorithm uses the local reflection and transmission operators developed in the recent work on the diffraction of nonaxisymmetric waves in a cylindrically layered medium with a single horizontal discontinuity. For several special geometries, we compare the numerical results from this NMM algorithm with analytical solutions as well as the earlier numerical results for axisymmetric cases, and found excellent agreement between them. As an application to the geophysical subsurface sensing, we solve several practical problems, and find that a large eccentricity effect can occur in realistic electromagnetic well logging. Moreover, this large eccentricity effect is strongly coupled with thin‐bed effect. Conventional log interpretation methods cannot adequately account for these effects. With the NMM algorithm developed here, all these different effects can be accounted for simultaneously and accurately.