The central-loop time-domain electromagnetic (TEM) method has been widely used in hydrogeological prospecting. Because this type of TEM configuration is relatively insensitive to lateral resistivity contrasts, the mathematical derivation of an apparent resistivity formula, valid for later recording times, is greatly simplified. However, no simple formula exists for an in-loop off-center TEM sounding. In this type of acquisition, the field response is recorded at several points surrounding the central location. In-loop TEM surveys are frequently employed to obtain high spatial resolution within engineering geophysical exploration. Although the apparent resistivity formula of a fixed-loop TEM system is also applicable for the non-central receiver points used in an in-loop TEM system, the apparent resistivity values need to be extracted using an iterative method that requires complicated integrations. Presently, no fast method exists that can give access to the apparent resistivity values in a direct manner. The main objective of this paper is to present a possible solution to this computational problem. A new solution is presented that takes as a starting point a circular transmitter loop where an analytical solution exists for non-central receiver points. This analytical solution is further approximated through the combined use of least-mean square (LSQR) determined polynomial coefficients and an equivalent circular loop to represent the rectangular loop. The new apparent resistivity formula, valid for in-loop TEM, has been tested on field data. A successful case study from central China is presented where an increased sensitivity to locate water-filled zones has been obtained.

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