WEBINAR: Measuring and modelling rock microstructures: a compositional perspective (29-02-2024)

19/02/2024

Measuring and modelling rock microstructures:  a compositional perspective  

Raimon Tolosana Delgado

 

 

Abstract: A current hard nut to crack in mathematical petrology is the characterisation of rock microstructure, i.e. a description of the spatial arrangement of mineral crystals, their size and orientations and the association between minerals. This is important in several applcations, such as the quantification of the migration behavior of radionuclides via reactive flow transport through crystalline rocks encasing a nuclear waste repository, the prediction of the product microstructure once we mill an ore (hence its economic value), or the generation of realistic virtual samples for online petrology exercises.

The first difficulty is in the conceptualisation of a parametrisation for the microstructure population. One way to describe it, not the only one, uses three components: a mean compositonal vector (showing the average relative abundance of each mineral phase), a symmetric matrix valued association parameter (showing the tendency ot each pair of minerals to be in contact) and a description of the crystal size distribution of each mineral. For the compositionally trained eye it is evident that each of these parameters belong to a restricted space, hence the relevance of compositional data analysis and related methods for this problem. Of course, these parameters represent a high dimensional set, which indicate a need of large volumes of data to fit them.

Currently, the only way to acquire such data is through automated mineralogy systems. Rock samples (of a few square cm) are polished, the resulting surface is scanned, all crystals are segmented and each is attributed a mineral class. Standard image analysis tools provide as well shape and size paraneters, contact lengths between crystals and so on. Millions of crystals are typically measured in one single sample. A single sample needs hundreds of MB to a few GB of storage in a database file. Statistical models, e.g. to interpolate rock microstructure between samples, establish regression models of the influence of microstructure onto a response variable, or an ANOVA with microstructural response to evaluate if two microstructures are significantly different, are mostly open problems, presently only solved for some of the parameters mentioned above. Also, the stereologic degradation occurring by estimating 3D properties from a random 2D cut is a known problem with solutions yet to be found.

In this talk we will go through the problems of this kind of restricted data, how tools and models from computer geometry, compositional data anaylsis, stochastic geometry, data science and statistics needed to be combined to start tackling these problems, and which of them remain open.

 

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Please note that the webinar will be recorded. Feel free to forward this message to your colleagues who may be interested in attending.

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