An assessment of the efficiency of a stereological correction for recovering the volumetric grade of particles from measures on polished sections

An application of the kernel-based inversion method for recovering the volumetric grade distribution of an assembly of particles from computer generated areal grade measures is presented. The application involves: 1. generation of a spatial mineral texture of a mineralized rock sample. 2. derivation of the (volumetric) liberation spectrum of the particulate resulting from the simulation of the sample fragmentation. 3. calculation of the inversion kernel based on measures of areal grade made on the intersection of random testing planes with the particles generated. 4. generation of areal measures on a virtual polished section. 5. solving the inversion problem for comparison of the recovered volumetric distribution with the original (simulated) liberation spectrum. The whole process allows to evaluate the efficiency of the inversion method achieved with an exact kernel and the suitability of the mathematical methods used for the inversion and their statistical significance; a plain (by number of occurrences) kernel and a weighted kernel (each occurrence counted with its area) are used. A hybrid recovering method is proposed that uses an estimator of second moments of the volumetric grade to provide a starting solution that is further improved with a weighted dampen least squares regularization procedure. The numerical procedure does not require the assumption of the hypothesis of random uniform isotropic fragmentation (RUIF) and can be applied to cases with mineral and gangue of different brittleness. The statistical reliability of the recovered volumetric distribution that depends upon the goodness of the distribution of the areal measures gathered on the polished section and the regularization used for inversion is also studied.