Quantitative evaluation of grain shapes by utilizing Fourier and fractal analysis and implications for discriminating sedimentary environments

Abstract

Fourier and fractal analysis methods have allowed new advancements in determining the shape of sand grains. However, the full quantification of grain shapes has not as yet been accomplished, partly due to the difficulties in interpreting the results of Fourier analysis, and partly because fractal dimension changes are somewhat dependent on the measuring techniques used. This study focuses on the application of a method that integrates elliptic Fourier and principal component analysis methods (elliptic Fourier-PCA). This method reduces the number of extracted variables and enables a visual inspection of the results of Fourier analysis, an approach that facilitates the understanding of the sedimentological significances of the results obtained using this technique. The application of this El-liptic Fourier-PCA technique to sand grains collected from fluvial, beach, and glacial environments produced particle descriptors such as elongation index (EF) and multiple bump indices (EF, EF, and EF + EF). These descriptors indicate that glacial, beach, and fluvi-al sediments contain particles with shapes similar to circles, ellipses, and cylinders, respectively. A modified pixel dilation (mPD) method was used for fractal dimension analysis, primarily as a simple model experiment proved that the mPD method enabled better detection of the degree of surface smoothness than traditional boxcounting methods. Mean (FD) and coefficient of variation of fractal dimension (FDCv) values decrease from glacial to fluvial and beach particles, indicating that glacial particles retain rugged surfaces, whereas beach particles have smoother and more even surfaces due to increased abrasion. Of the grain shape indices used during this study, the FD and EF variables are key shape proxies that enable differentiation between sedimentary environments, with an FD-EF plot allowing the effective discrimination of particles derived from fluvial, beach, and glacial environments.