ESTIMATING UNCERTAINTY IN NORMALIZED FRY PLOTS USING A BOOTSTRAP APPROACH

Abstract

The normalized Fry method is a powerful and commonly used tool for measuring fabric in aggregates of packed grains. The significance of these parameters is often unclear because the associated uncertainty is unknown. Basic statistical hypotheses, such as deciding if a sample has a fabric, or if the fabrics of two samples are significantly different, requires knowledge of associated uncertainty.For this study a bootstrap version of the normalized Fry method was developed. This program randomly selects normalized center-to-center distances, with replacement, from the population of all possible center-to-center distances. For each sample 100 bootstrap normalized Fry plots were constructed using different combinations of center-to-center distances. The variation of fabric parameters for these 100 analyses is used to estimate the uncertainty associated with the sample.Results of bootstrap analyses of sandstones, oolitic limestones and synthetic data sets, show considerable variation in fabric parameter uncertainty, apparently related to both lithology and the degree of fabric development. Fabrics with axial ratios less than 2.0 appear only to be significant to one decimal place. The variation of fabric uncertainty makes it important to determine the uncertainty associated with individual samples. The deformation model for a field example developed based on conventional normalized Fry plots needed to be more complicated than deformation models that allowed for variation of fabric parameters.