Theoretical relations exist in the literature for calculating the responses of electrode-type resistivity logging tools when they are centered in the wellbore and the formations are thick and homogeneous (Fok, 1933; Stefanesco et al, 1929-32). These analyses are usually restricted to devices using dc or low-frequency surveying currents, and they generally make use of the approximation of point electrodes. An analysis has also been made comparing the responses of such tools in anisotropic and isotropic formations (Kunz and Moran, 1958).In this paper, relations are derived for calculating the responses of electrode-type logging tools when the sonde is not centered in the wellbore. Although similar relations could be applied to tilted sondes, the discussion in this paper is mainly restricted to the simple eccentered case in which the axis of the sonde is parallel to the axis of the hole.As will be shown, eccentering has a comparatively small effect on the responses of a normal device. On the other hand, certain types of focused-log devices, in which a large proportion of the focusing current flows parallel to the hole, may exhibit an appreciable eccentering effect; this is particularly true when the contrast between formation resistivity and hole-fluid resistivity is large. Spherically-Focused-Log (SFL) resistivity devices (Schuster et al, 1971) have this type of current distribution, and, depending on electrode spacings, they may be appreciably influenced by eccentering. The applications shown in this paper will largely be done from SFL computations and measurements.The theoretical relations have been used in the development of a spherically focused tool less affected by eccentering.Tool responses predicted on the basis of the theoretical relations were found to be consistent with the results of test-tank measurements made for one of the devices studied. Some field experiments have been made with centered and eccentered spherically focused tools, and more are to be done.

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