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FIGURE 5.13 Azimuthal rotation apparent resistivity data plotted on a polar coordinate graph.
resistivity depth model from which synthetically generated apparent resistivity data are in good agreement with actual field measurements. An important issue needing special emphasis with respect to both forward and inverse computer modeling is that within the limits of measurement error for pa, there are often several resistivity depth models, differing from one another to a certain extent, that are able to provide a good fit between the measured apparent resistivity data and synthetically generated apparent resistivity data. Consequently, the resistivity depth model obtained through these computer analysis procedures may not always be "unique," and it is worth keeping in mind the possibility that other models exist that can adequately account for the observed apparent resistivity data.
The apparent resistivity measurements from an azimuthal rotation survey carried out at a particular location are plotted on a polar coordinate graph (Figure 5.13). Each plotted pa measurement shown in Figure 5.13 is associated with an angle and a radial length. Given a specific pa measurement, the orientation of the electrode array, clockwise from true north, is specified by the angle. As an example, a pa value plotted with an angle of 45° represents a measurement obtained with a northeastsouthwestoriented electrode array. Figure 5.13 is representative of an azimuthal rotation survey where pa measurements were made as the electrode array was pivoted about a stationary point in increments of 15° through a complete sweep of 360°. The radial length from the center of the graph to a data point represents the magnitude of the pa measurement.
For any location where an azimuthal rotation survey is conducted, a circular pattern for the pa measurements plotted on a polar graph implies that resistivity is the same in all directions (resistivity is isotropic). If the plotted pa measurements instead have the pattern of an ellipse, then resistivity varies with direction (resistivity is anisotropic). The principle (longest) axis of the ellipse indicates the electrode array orientation for which the maximum pa value or values, paMax, were acquired during the azimuthal rotation survey. The orientation of this principle axis often corresponds with the trend of aligned features in the subsurface. The fact that paMax is found along an orientation coinciding with linear subsurface trends is somewhat counterintuitive but is explained by the "anisotropy paradox" (Keller and Frischknecht, 1966; Parasnis, 1986). Taylor and Fleming (1988) determined azimuthal rotation resistivity surveys to be useful for characterizing fracture systems in glacial till. For vertical fractures with an average length greater than the length of the electrode array, the overall fracture system trend was found to coincide with the principle axis of the polar graph pa ellipse (the orientation corresponding to paMax). The magnitude of paMax proved to be a good indicator of fracture density. The presence of two major fracture systems results in the polar graph of pa having two superimposed ellipses and, therefore, two principle axes (Taylor and Fleming, 1988).
Two of the more detailed and comprehensive data analysis products from resistivity surveying include horizontal (areal) apparent resistivity (or apparent electrical conductivity) maps and resistivity (or electrical conductivity) depth sections. Measurements from a constant separation traversing survey are commonly collected along a set of equally spaced transects covering a study area. With a complete data set (all pa or aa, ECa values for all transects), interpolation and contouring procedures can be applied to produce a map showing horizontal changes in pa or aa, ECa.
Figure 5.14 shows two horizontal ECa maps of the same agricultural test plot located in Columbus, Ohio. Measurement transects were spaced 3.1 m apart. The data used to produce Figure 5.14a

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