Quantifying the uncertainty of volume fraction estimation in bimrocks - A backward analysis approach

The uncertainty of estimates for a one-dimensional volume fraction is often evaluated by statistical analysis of a large number of scan-line measurements in a domain. According to the stereology hypothesis, the uncertainty of a one-dimensional volume fraction may be treated as the uncertainty of a volume fraction (Vf). The latter is the focus of the present study. This existing approach to estimating the uncertainty of volume fraction is referred to as “forward analysis.” However, different domains can yield the same Vf values when they are obtained using the forward analysis with scan-line measurements. This paper presents a “backward analysis” in which a large number of block-in-matrix rocks (bimrocks) is generated from numerical simulations of scan-line measurements, and the Vf values of these bimrocks are evaluated. The uncertainty (i.e., coefficient of variation) in these Vf values is then assessed. A comparative study is conducted, which shows that the developed backward analysis and the existing forward analysis yield comparable results.