Distributional Data Assimilation for Reseource Model Updating

Some geometallurgical properties are expressed as distributional variables that are characterized by probability density functions. In order to describe these geometallurgical properties in space considering the whole distribution and not only the a few moments. There are methods for statistical interpolation and simulation of distributional data in space. However, not methods are available to sequential incorporation of information back into the spatial model.

The advantages of data assimilation algorithms for resource model updating in mining industry has been shown before for univariate and multivariate models. Based in the information collected during mining production about different features is becoming more popular due to sensor technology advances. The Ensemble Sequential Updating techniques provide a comprehensive solution for these challenges since, that allows to relate the potentially non-linear relation that exists between the resource and grade control model state variables and the observations. However, sensors might provide information about these observations in a distributional support.

This study aims to develop and implement a data assimilation algorithm for distributional variables in mining settings. There are different challenges to face in order to understand how the information that proceed from sensors informs about the geostatistical models and how to feed updated information back to the resource model. The state variables of such models are actually distributions which are infinite dimensional supported. We use the Bayes spaces framework that allows the characterization of distributional data. Within this framework we develop a new mathematical tool for data assimilation process reproducing the complete information content embedded in distributional data like particle size distribution.

The distributional data assimilation approach is tested in a virtual assets models created as a fully controllable environment with particle size distribution properties. After validation, a sensitivity analysis investigates the effects of different parameters and derived practical implementation aspects for an effective application within an operating mine.