Quantify uncertainty in scanline estimates of volumetric fraction of anisotropic birmocks

An analytical solution on the uncertainty in the estimates of volumetric fraction of different compositions in a Bimrock is presented in this paper. The derivation was developed based upon the concept of representative volumes. To tackle the anisotropic orientation of blocks, this study developed the concept of a parallelogram representative volume element that contains an ellipse. Our results demonstrate that the uncertainties in the estimates depend upon the aspect ratio, orientation, and diameter of blocks and the level of volumetric fraction. We further simplified the analytical expression in terms of intercept length. Our results were verified through numerical simulation albeit preliminary.