Modeling and Fitting of Three-Dimensional Mineral Microstructures by Multinary Random Fields

Modeling a mineral microstructure accurately in three dimensions allows to render realistic mineralogical patterns which can be used for threedimensional processing simulations and calculation of three-dimensional mineral quantities.
The present study introduces a flexible approach to model the microstructure of mineral material composed of a large number of facies. The common plurigaussian method, a valuable approach in geostatistics, can account for correlations within each facies and in principle be extended to correlations between the facies.
Assuming stationarity and isotropy, founded on a new description of this model, formulas for first- and second-order characteristics,
such as volume fraction, correlation function and cross-correlation function can be given by a multivariate normal distribution. In this particular situation, based on first- and second-order statistics, a fitting procedure can be developed which requires only numerical inversion of several one-dimensional monotone functions.
The paper describes the whole workflow; from getting the covariance structure fast from two-dimensional particle pixel images, by using Fourier transform, over model fitting to sampling and efficiently representing the resulting threedimensional microstructure by tessellations.
The applicability is demonstrated for the three-dimensional case by modeling the microstructure from a Mineral Liberation Analyzer (MLA) image data set of an andesitic basalt breccia.