USING THE AUTOCORRELATION FUNCTION FOR THREE-DIMENSIONAL KINEMATIC ANALYSIS: A CAUTIONARY TALE

The autocorrelation function (ACF) of Heilbronner (1992) is an image analysis tool that uses the Fast Fourier Transform (FFT) to describe the shape of translucent regions of an image. The ACF can be used to produce a fabric ellipse derived from the amount of light passing through the entire thin section when displaced against itself in all x- and y- coordinated directions.

We collected fabric data from 30 deformed quartzites from the Eriboll Sandstone, NW Scotland. Our data suggests that the ACF has the ability to measure fabric intensity and orientation in three-dimensions. By analyzing three mutually perpendicular thin sections, we were able to combine our sectional data into fabric ellipsoids. The error associated with determining a best-fit ellipsoid was remarkably small. In fact, ca. 70% of the samples had fitting errors which were less than those associated with the more traditional strain analysis of the deformed quartz grains. This suggests that the ACF is measuring an existing penetrative fabric in the rock, though the interpretation of these fabric ellipsoids is far from straight forward.

When comparing the ACF-determined fabric ellipsoids with the more traditional grain shape/strain analysis, we found considerable differences in both the ellipsoid shapes and orientations. We anticipated that the fabric ellipsoid would have a more flattened shape because of the effect of phylosilicates on the rock fabric. However, only ca. 40% of the fabric ellipsoids have more highly flattened ellipsoids than their associated strain ellipsoid. The mean difference in the Lode's ratios for corresponding samples was ca. 0.2. We did not anticipate a significant difference in the orientation of the ellipsoid's principle axes; however, the corresponding axes differed by an average of nearly 27 degrees.

While collecting ACF data is considerably more rapid than measuring the dimensions of individual grains, it unfortunately cannot replace the more traditional methods of strain analysis, even for relatively pure quartzites like the Eriboll Sandstone.