“Theory of a coil-type resistivity sensor for MWD application,” The Log Analyst, vol. 32, pp. 603-611, No.5, 1991.
Many MWD (measurement-while-drilling) tools carry coil-type resistivity sensors consisting of transmitting and receiving coils located in shallow grooves on the drill collar. A theoretical analysis of this type of resistivity sensor, neglecting the effect of the groove, is carried out using rigorous electromagnetic theory. The raw data recorded by the tool are amplitude ratio and phase difference, which are converted to apparent resistivity logs using a homogeneous medium as the reference. Consequently the amplitude-based resistivity, Ra, and the phase-based resistivity, Rp, are generally separated in inhomogeneous media. If the depth of investigation is defined as 50% of the "integrated pseudogeometrical factor" (IPGF), then Ra and Rp logs will have two different investigation depths. The apparent dual-investigation depths are due to the conversion algorithm and the IPGF definition. In fact, the Ra and Rp logs survey the same formation volume. Furthermore, even though Ra has greater depth of investigation than Rp based on the IPGF definition, Ra is not necessarily always closer to the resistivity of the uninvaded formation than is Rp. The best way to interpret the MWD resistivity logs in the invaded zone is to use all information available, make an initial interpretation, and then verify it by using computer simulation. The formula needed for such simulation is presented in this paper.