Contents I. Introduction
Directional well-logging resistivity tools are routinely used in hydrocarbon exploration to determine, for example, horizontal and vertical resistivities in anisotropic Earth formations and relative dip angle during deviated drilling [1]–[5]. For logging-while-drilling (LWD) tools, tilted-coil antennas provide directional data for real-time geosteering. Resistivity tools typically consist of multiple tilted-coil antennas wrapped around a cylindrical metallic mandrel. A transmitter coil excites eddy currents in the surrouding Earth formation [6]. This current is proportional to the formation conductivity and produces a secondary electric field and induced voltage in the receivers. Various techniques have been proposed to model this problem. These include brute-force numerical methods such as finite-differences (FD) [7]–[10] and finite elements (FE) [11]–[13], and pseudoanalytical approaches [4], [5], [14]–[19]. The former can handle arbitrarily complex Earth formations but suffer from high computational costs. The latter are less flexible but less computationally costly. Many pseudoanalytical approaches approximate coil antennas as magnetic dipoles, which ignores mandrel effects and finite-size antenna effects. Pseudoanalytical approaches that do include these two effects [4], [5] have attracted much interest in recent years as they provide better accuracy.
