Interactive Estimation of the Fractal Properties of Carbonate Rocks

Abstract: Scale invariance of intrinsic patterns is an important concept in geology that can be observed in numerous geological objects and phenomena. These geological objects and phenomena are described as containing statistically selfsimilar patterns often modeled with fractal geometry. Fractal geometry has been used extensively to characterize pore space and fracture distribution of both carbonate and clastic rocks as well as the transport properties of porous media and fluid flow in reservoirs. The fractal properties are usually estimated from thin-section photomicrograph images or scanning electron microscope images. For complex rock such as carbonate rocks, automatic feature detection methods are often inaccurate. In addition, the rocks may be have been subjected to facies selective diagenesis which preferentially affect some of the rock fabric, thus increasing the difficulty in automatic detection of certain features. We present an interactive program, GeoBoxCount, for analyzing thin-section images and calculating the fractal dimension interactively. The program relies on the geologists insight in interpreting the features of interest; this significantly improves the accuracy of feature selection. The program provides two options for calculating the fractal dimension: the Hausdorff and the Minkowsi-Bouligand box-counting methods.