ABSTRACT

The problem exists in which the harmonic(s) have the greatest potential for a clear, unambiguous solution upon subsequent shape analysis. In addition, shape data must be acquired economically, allowing analysis of hundreds of particles per sample and tens or hundreds of samples in any particular investigation. Amplitude spectra of a finite Fourier series in closed form are used as shape descriptors of each particle. The mixing proportions and end member compositions have proven to be of value with respect to a variety of sedimentological investigations using shape and size frequency data. The lower harmonics are a measure of gross shape while the higher harmonics measure increasingly fine-scaled surface features. The width of the intervals can be unequal and depends only on the shape of the distribution of the entire pooled data set. The lower the relative entropy of a data set, the more contrast exists between samples contained in that set.