Using fractal analysis to quantitatively characterize the shapes of volcanic particles

[1] The shapes of volcanic particles reflect numerous eruptive parameters (e. g., magma viscosity, volatile content, and degree of interaction with water) and are useful for understanding fragmentation and transport processes associated with volcanic eruptions. However, quantitative analysis of volcanic particle shapes has proven difficult because of their morphological complexity and variability. Here a newly developed procedure for shape analysis based on fractal geometry is described and tested. Although volcanic particle shapes are not truly fractal, their complexity can be effectively characterized in terms of fractal values (pseudofractal dimensions) reflecting morphological invariance over discrete ranges of scale. Using fractal data produced by dilation of a particle's two-dimensional boundary, a spectrum of fractal dimensions is calculated for each particle by taking the first derivative of the dilation data. Compared with fractal methods that express shape in terms of only one or two fractal dimensions, typically derived from the slope of data on a Richardson plot, this technique results in better discrimination between samples. In addition, use of multiple fractal values allows incorporation of multivariate statistical analysis, further strengthening the differentiating power of the technique. This fractal spectrum technique yields promising results for samples of sideromelane shards from Iceland and is likely to be effective at characterizing other kinds of volcanic particle shapes.