Coincident loop transient induction wireline logging is examined as the borehole analog of the well-known land and airborne time-domain electromagnetic (EM) method. The concept of whole-space late-time apparent resistivity is modified from the half-space version commonly used in land and airborne geophysics and applied to the coincident loop voltages produced from various formation, borehole, and invasion models. Given typical tool diameters, off-time measurements with such an instrument must be made on the order of nanoseconds to microseconds — much more rapidly than for surface methods. Departure curves of the apparent resistivity for thin beds, calculated using an algorithm developed to model the transient response of a loop in a multilayered earth, indicate that the depth of investigation scales with the bed thickness. Modeled resistivity logs are comparable in accuracy and resolution with standard frequency-domain focused induction logs. However, if measurement times are longer than a few microseconds, the thicknesses of conductors can be overestimated, whereas resistors are underestimated. Thin-bed resolution characteristics are explained by visualizing snapshots of the EM fields in the formation, where a conductor traps the electric field while two current maxima are produced in the shoulder beds surrounding a resistor. Radial profiling is studied using a concentric cylinder earth model. Results found that true formation resistivity can be determined in the presence of either oil- or water-based mud, although in the latter case, measurements must be taken several orders of magnitude later in time. The ability to determine true formation resistivity is governed by the degree that the EM field heals after being distorted by borehole fluid and invasion, a process visualized and particularly evident in the case of conductive water-based mud.

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