Fourier Shape Analysis, FSA: Freeware for Quantitative Study of Particle Morphology

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Shape analysis is of paramount importance in sedimentology. Particle morphology is a very useful texture parameter that provides information about particle history and is used to characterize and classify sedimentary material. Particle shape description has been both an important and a controversial subject. The most convincing description of shape defines particle shape by three hierarchical parameters: form, roundness, and surface texture (Barrett, 1980). Many different methods have been proposed to measure these parameters. Among them, Fourier shape analysis is particularly notable. Fourier analysis separates the three parameters into frequency ranges. The low frequency range is related to form, the middle frequency range to roundness and the high frequency to surface texture. However, determining where the boundaries lie between the different morphological classes is not an easy task and has been an unsolvable problem since the FSA method was first proposed. The same is true for the signal-to-noise limit. To date, this information has been obtained empirically and with great uncertainty. One of the most important contributions of this work has been to quantitatively constrain the harmonic ranges corresponding to the morphological ranges proposed by Barrett, and to determine the best possible approximation for the upper limit of the signal and the onset of noise. To estimate these ranges, we propose here two original methodologies based on analysis of the cumulative amplitude spectrum (CAS), and on simulating the effect of artificial noise acting on a well-known geometric figure. The CAS of 3664 volcaniclastic particles and of 106 artificially silhouette charts have been quadrisected into form, roundness, roughness and noise using an optimization process. The analysis indicates overall that the limits are well constrained into a narrow range of harmonics with a small variance. The results obtained are reliable and allow the range of harmonics that contains a useful signal to be extended up to harmonic 256. The method has been successfully applied to the standard figures of Krumbein (1941a) and of Powers (1953), efficiently separating the different classes of roundness. As an example, the methodology has been applied to a real-life case where there was doubt about the pristine nature of the materials from some outcrops related to the block-and-ash flow deposit of the July 17, 1999 eruption of the Colima volcano. The results obtained applying the method show promising results, indicating the potential of FSA information to solve this ambiguity. The powerful, user-friendly FSA software that we distribute freely (open code) can be very useful for characterizing volcano-sedimentary and sedimentary deposits. To date, there is no other software for FSA studies. Moreover, FSA can be useful in other fields of science and engineering where quantitative particle shape analysis is needed.