Precision and accuracy of modal analysis methods for clastic deposits and rocks: A statistical and numerical modeling approach

Abstract

Quantifying the proportions of certain components in rocks and deposits (modal analysis or componentry) is important in earth sciences. Relevant methods for cross-sections (two- dimensional exposures) of clastic rocks include point counts or line counts. The accuracy of these methods has been supposed to be good in the literature but not necessarily verified empirically. Natural materials are inappropriate for assessing accuracy because the true proportions of each component are unknown. The precision of modal analysis methods has traditionally been evaluated from statistical models (primarily the normal approximation to the binomial distribution) but again rarely verified in practice because it is also extremely difficult to obtain different slices through the same material at outcrop scale. Here we create a set of numerical models of red and blue spheres with different proportions and sizes and cut 60 slices through the models, on which we perform point counts and line counts. We show that both of these methods are indeed able to retrieve the correct volumetric proportions of components, on average, when enough fragments are counted or intersected. As already known, precision is controlled by component abundance and the number of points counted or clasts intersected. However, we show that other important factors include differences between slices, which are relevant for our unequal-size models, and the proportion of voids, matrix, and/or cement in the rock. We present empirical precision charts for clast counts and line counts based on our models and make recommendations for future field studies.