To appraise the look-around and look-ahead technologies used in geosteering, an extension to the sensitivity function is presented by considering jointly with the resolution. The development is of critical importance to the data interpretation of LWD azimuthal electromagnetic tools introduced in the recent years. The extended sensitivity distribution describes the geologic boundary detectability.
The spatial distribution of low-frequency electro-magnetic fields in conductive medium is dominated by two factors, namely the exponential decay as function of skin-depth and the geometric spreading which is inversely proportional to the distance cubed. The electromagnetic fields fade away rapidly and consequently so is the associated sensitivity function. The smaller field strength or poorer sensitivity far away from the tool also dictates that the resolution farther away from the tool is much worse than that near the tool. To improve the detectability of geologic target, based on the physics observed, this paper extends the spatial sensitivity function by taking the tool resolution into consideration. The space is divided into cells with the cell-size conforming approximately to the natural resolution, for example, geometric progression. The new sensitivity function is the traditional one multiplied with the cell size to better describe the look-around and look-ahead capabilities, where the emphasis is on the detection of the bed-boundaries as far ahead or around as possible.
It is observed that the iso-sensitivity envelope encompassing 50% of cumulative contribution from the tools is within the distance of about one source-receiver coil-separation, L, or less. This is consistent with the depth of investigation for wireline induction logging tools defined through the integrated geometric factor at the same percentage. The observed iso-sensitivity envelope for 90% of cumulative contribution is about 2 to 3 L's away from the tool, while the iso-sensitivity surface for 99% is observed to be from a volume of about 4L to 5L or slightly more around the tool. For various coil-configurations, it finds that the X-X (likewise Y-Y) coil-combination is more sensitive to look-ahead boundary-detection when the geologic boundary is perpendicular to the sensor. The look-around investigation with sensor parallel to the beddings may benefit relatively more from, for example, the 45-degree tilted-coil configuration.