Theoretical Investigation of the Electromagnetic Wave Propagation Tool

Abstract

A theoretical investigation of the electromagnetic wave propagation tool (EPT)® is presented. An asymptotic analysis, using contour integration, was utilized to derive approximations for the waves at the receivers of the EPT tool. The waves at the receivers are decomposed into a guided wave and a lateral wave. When the mudcake layer is thin, the lateral wave nearly satisfies the guidance condition of the mudcake layer, and its algebraic decay is diminished from the negative of the three-halves power with distance (thick mudcake) to the negative one-half power with distance. In this case, the guided wave and the lateral wave both propagate with a wave number close to the wave number of the invaded zone. Indeed, plots of the directional dependence of the transmitted wave in the invaded zone demonstrate that more power is directed along the planar boundary in the invaded zone when the mudcake layer is thin. Plots of the total magnetic field and the magnetic field from the guided wave at the receiver locations are presented as a function of mudcake thickness. These plots show the dominance of the guided wave for increasing mudcake thickness. Travel times are also computed, using both asymptotic approximations and a plane-wave assumption. These results are then compared with the results of Freedman and Vogiatzis. Excellent agreement with the plane wave assumption is found for a thin mudcake layer. This analysis validates the schemes used by Schlumberger for interpreting the EPT tool log.