INTRODUCTION

Azimuthal resistivity measurements are made to determine the orientation of steeply dipping joints and fractures that may be important for sitting water wells or setting up groundwater models. Before describing the field work and data analysis let’s revisit the "geoelectric section".

SEVERAL KINDS OF RESISTIVITY

For a unit stack of layers we defined transverse resistance and horizontal conductance. Now we define "average transverse resistivity" as transverse resistance divided by the thickness of the stack (current flow normal to layering). We also define "average lateral resistivity" as thickness of stack divided by horizontal conductance (current flow parallel to layering).

The "coefficient of anisotropy" (lambda) is the square root of transverse resistivity divided by lateral resistivity. This dimensionless ratio is always equal to or larger than one. We also define "mean bulk resistivity" as the square root of lateral resistivity times transverse resistivity. This equals the coefficient of anisotropy times the lateral resistivity.

MODEL, FIELD PROCEDURE AND ANALYSIS

For our field experiment we use a Wenner array with fixed a-spacing and fixed central point location. We measure apparent resistivity for different azimuths of the array. A ten degree interval of orientation might be suitable. If there are vertical joints closely spaced with respect to the a-spacing, a polar plot of apparent resistivity values will show an ellipse (model assumes one resistivity for the solid rock and another for the fill in joints of finite width). The long axis equals the mean bulk resistivity and is aligned parallel to the strike of the joints. The short axis of the ellipse is normal to the strike of the joints and the apparent resistivity equals the lateral resistivity. Using the formulae given above we can find the coefficient of anisotropy and the transverse resistivity.

MULTIPLE JOINT SETS

I have read that the "effect of multiple fracture sets is additive" (Taylor and Fleming, 1988) but have not seen a derivation to substantiate this claim.

CALCULATION OF FRACTURE POROSITY

For a simple model of rock cut by parallel joints we can readily calculate fracture porosity from the lateral and transverse sensitivities and a knowledge of the resistivity of the pore fluid (I. e. of the material filling the joints).

REFERENCES AND CASE HISTORIES

Al Hagrey, 1994, Geophysics, v. 59, pp. 881-.

Carpenter et al., 1991, Geophysics, v. 56, pp. 1896-.

Skjernaa and Jorgensen, 1994, Applied Hydrology, v. 2, pp. 19-.

Taylor and Fleming, 1988, GroundWater, v. 26, pp. 464-.