| Abstract: | Basic Laterolog devices employ a measure-current focusing technique to provide well logs of formation resistivity that feature sharp vertical definition combined with a depth of investigation much improved over those of normals of comparable spacings. To develop the concept of measure-current focusing, a disk-electrode arrangement analogous to a guard-ring capacitor is considered first, leading finally to consideration of a real sonde in a cylindrical borehole. In the latter, auxiliary currents are adjusted to maintain substantially at zero the vertical potential gradients above and below the central measure-current electrode; this has the effect of focusing the measure-current beam. However, prediction of sonde responses on the basis of current patterns can in some cases be misleading. Indeed, for a given Laterolog array, one may use a (reciprocalmode) current pattern radically different from the one defined by the basic (direct-mode) measure-current focusing scheme and still obtain the same resistivity measurement. This feature is illustrated for Laterolog 3 by use of transfer impedances, and demonstrated for certain more general cases using the reciprocity theorem. Comparisons of Laterolog responses across typical thin beds, both non-invaded and invaded, with those of normal devices of a comparable range of spacings illustrate the improved vertical resolution obtained with Laterolog devices. The examples also show the different magnitudes of the auxiliary currents (thenceforth designated “bucking”- or “focusing” currents) used in the direct and reciprocal modes and illustrate how these currents must continuously vary in order to maintain the focused condition as the sonde moves through the bed. Finally, briefly considering possible applications of Laterolog-type arrays in surface prospecting, it is shown that a one-dimensional array laid out on the surface does not provide the same degree of measure-current focusing as is obtained in a borehole. Some improvement is obtained with a combination of two crossed linear arrays. Much more is obtained using a circular array. |
