Modeling a mineral microstructure accurately in three dimensions can render realistic mineralogical patterns which can be used for three-dimensional 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. The covariance structure is quickly obtained from two-dimensional particle pixel images using Fourier transform. Followed by model fitting and sampling, where the resulting three-dimensional microstructure is then efficiently represented by tessellations. The applicability is demonstrated for the three-dimensional case by modeling the microstructure from a Mineral Liberation Analyzer image data set of an andesitic basalt breccia.

在三个维度上对矿物微观结构进行准确建模可以呈现出逼真的矿物学模式，这些模式可用于三维处理模拟和三维矿物数量的计算。本研究引入了一种灵活的方法来模拟由大量相组成的矿物材料的微观结构。普通的普里高斯方法是地统计学中的一种有价值的方法，可以解释每个相内部的相关性，并且原则上可以扩展到相之间的相关性。假设平稳性和各向同性，以该模型的新描述为基础，可以通过多元正态分布给出体积分数，相关函数和互相关函数等一阶和二阶特征的公式。在这种情况下 基于一阶和二阶统计量，可以开发一种拟合过程，该过程仅需要对几个一维单调函数进行数值反演。本文描述了整个工作流程。使用傅立叶变换可以从二维粒子像素图像中快速获得协方差结构。然后进行模型拟合和采样，然后以方格图有效地表示三维三维结构。通过对安第斯玄武岩角砾岩的矿物解放分析仪图像数据集的微观结构建模，证明了其在三维情况下的适用性。使用傅里叶变换可以从二维粒子像素图像中快速获得协方差结构。然后进行模型拟合和采样，然后以方格图有效地表示三维三维结构。通过对来自安山玄武岩角砾岩的矿物解放分析仪图像数据集的微观结构建模，证明了其在三维情况下的适用性。使用傅立叶变换可以从二维粒子像素图像中快速获得协方差结构。然后进行模型拟合和采样，然后以方格图有效地表示三维三维结构。通过对来自安山玄武岩角砾岩的矿物解放分析仪图像数据集的微观结构建模，证明了其在三维情况下的适用性。