Quantitative discrimination of magma fragmentation and pyroclastic transport processes using the fractal spectrum technique

The morphology of volcanic particles can yield insight into magma fragmentation, transport processes, and style of eruption. However, the complexity and variability of volcanic particle shapes make quantitative characterization difficult. The technique applied in this study is based on fractal geometry, which has been successfully used to characterize a wide variety of particles and shapes. Here, fractal data is produced by dilation of the 2-D particle boundary to produce a full spectrum of fractal dimensions over a range of scales for each particle. Multiple fractal dimensions, which can be described as a fractal spectrum curve, are calculated by taking the first derivative of data points on a standard Richardson plot. Use of multiple fractal dimensions results in more effective discrimination than expressions of shape based on one or two fractal dimensions. Quantitative comparisons are carried out using multivariate statistical techniques such as cluster and principal components analysis. Applications to samples from well-documented eruptions (e.g. Mt. St. Helens 1980, Tambora 1815, Surtsey 1963–64) indicate that the fractal spectrum technique provides a useful means of characterizing volcanic particles and can be helpful for identifying the products of specific fragmentation processes (volatile exsolution, phreatomagmatic, quench granulation) and modes of volcanic transport/deposition (tephra fall, pyroclastic flow, blast/surge).