MULTI-SCALE FRACTAL ANALYSIS OF FRACTURES WITHIN A GRANITOID OUTCROP NEAR PISECO LAKE, ADIRONDACKS, USING HIGH-RESOLUTION SEM AND GIGAPAN IMAGERY

The appeal of fractal geometry and fractal analysis lies in the ability to recognize self-similarity of natural phenomena, which can validate the practice of extending laboratory observations to larger scales. Fractal analysis quantifies, with a single number, qualities such as irregularity or clustering tendency. The fractal dimension (D) characterizes the spatial distributions intermediate between extremes described by Euclidean dimensions. In the case of fracture traces (as lines) along an outcrop face, D quantifies the tendency of such lines to fill a plane. Fractal analysis of fractures is most commonly performed on fracture spacing using either 1D (scan line), or 2D (box-counting) methods. Additionally, such fracture spacing studies are limited by the resolution of imagery. Multi-scale studies attempt to stitch together and identify similar D values at regional, outcrop, and even thin-section scales, but few studies account for perspective errors, as they focus specifically on outcrops with little surface roughness (flat plane). In this research, we evaluate fracture spacing self-similarity at multiple scales using scanning electron microscope (SEM) imagery of thin sections, hand sample analyses, and GigaPan high-resolution, outcrop-scale panoramic imagery. A chloritized granitoid outcrop near the Piseco Lake anticline in the central Adirondack region, New York, served as a field test site for the multi-scale fractal analysis. This highly fractured outcrop also has high surface roughness, which is accounted for by collecting GigaPan panoramic imagery, which was taken at specific orientations parallel to at least one major fracture orientation. Using both 1D and 2D methods (scan-line and box-counting) we assess the self-similarity of fracture spacing from different orientations and explore fractal dimensionality in a 3D environment. The latter is done by comparing D values of fracture data derived from GigaPan imagery taken at different orientations for all scales of study. This study helps prove the efficacy of multi-scale fractal analysis for the interpretation of geologic outcrops from hand-sample or thin-section analyses.