MORPHOMETRIC ANALYSIS OF CAVES USING FRACTAL INDICES

One of the objectives of morphometric studies of caves is to differentiate their genetic categories and to use that information to study the evolution of karst systems. Cave type and morphology are determined by hydrogeologic and geologic factors, so by inverse analogy, cave type and morphology could be used to determine the hydrologic and geologic conditions under which caves developed. Euclidian metrics have traditionally been used to quantify and compare cave morphologies even though caves have irregular and complex shapes. Caves have been shown to possess characteristics that identify them as fractals within certain ranges of scales, so the use of Euclidean-based metrics alone to define and characterize them may actually be a limitation in morphometric analyses. Other factors that limit full morphometric analyses of caves include focus on two-dimensional cave data as these are typically what are available, and exploration bias as cave exploration and documentation are limited to spaces that are humanly passable, epitomizing the subjective nature of anthropomorphic-based measurements. This research uses three-dimensional cave data to explore the fractal nature of cave morphology via pattern recognition techniques that can be used to calculate fractal indices. Fractal dimension that quantifies the complexity of a pattern, and lacunarity that determines pattern texture are used as complimentary indices as some seemingly dissimilar patterns can have the same fractal dimension. Fractal indices are calculated using standard box counting and sliding box counting methods and the results are statistically analyzed to differentiate cave types.

The use of fractal geometry in cave morphometric analysis may provide a viable means of describing cave dimensions and morphology, and by virtue of is predictive potential, may serve as a means of overcoming exploration bias. Should these quantitative morphological distinctions in cave patterns prove to be robust, the implications are that cave morphometry as defined by fractal indices could be used as an identifier for types of geological and hydrological controls on the development of caves and cavernous permeability. However, any interpretation based on fractal indices must be made within the constraints of the natural system that holds the fractal object.