Geostatistical simulation of rock physical and geochemical properties with spatial filtering and its application to predictive geological mapping

Highlights

• Geological modeling often consists of a single interpretation of the subsurface.

• Interpreted geological categories may be correlated with quantitative covariates.

• Simulating and classifying these covariates provide multiple geological models.

• Filtering undesired spatial components (nugget effect) improves the classification.

• Concepts are applied for predictive geological modeling in an iron deposit.

Abstract

Constructing an interpretive geological model of the subsurface based on site-specific geological, geophysical and geochemical sampling information is a primary step in the prospection, exploration and modeling of ore deposits, in order to understand geological heterogeneity and to predict the rock properties in the subsurface, which is critical for all the following stages of the mining process. To improve the accuracy of such geological models, a geostatistical approach based on the conditional simulation of quantitative variables followed with their classification into geological categories is proposed. The novelty is the use of coregionalization analysis that allows decomposing the quantitative information into uncorrelated components associated with different spatial scales and filtering the undesired components from the simulation outcomes, in particular, the nugget effect that represents small-scale variability and measurement errors.

The methodology is illustrated with the predictive geological mapping in an iron ore deposit hosted by banded iron formations, based on a set of physical and geochemical variables such as metal grades available from geochemical assays and rock types available from geological core logging. First, the quantitative variables are simulated conditionally to exploration drill hole data, then classified into rock types. The simulation in which the nugget effect has been removed provides more regular boundaries between rock type domains and improves the predictability of the rock type, with an 90.1% cross-validation accuracy score against a 79.9% for the simulation that reproduces the spatial variability without any filtering. Despite its small amplitude, the small-scale variability in the quantitative variables considerably deteriorates the rock type classification.

Introduction

Understanding geological heterogeneity and predicting the rock properties in the subsurface is a challenging issue in all stages of the exploration of ore deposits, from the identification of prospective areas and/or geochemical anomalies to the modeling of the mineral resources and ore reserves (Delavar et al., 2012; Talebi et al., 2015, Talebi et al., 2016; Afzal et al., 2012, Afzal et al., 2016; Hajsadeghi et al., 2016; Daneshvar Saein, 2017; Wang et al., 2019). Such tasks rely on site-specific knowledge combined with geological and geochemical sampling information from geophysical surveys, core sample logs and assays, which allow the construction of an interpretive geological model, i.e., a 3D representation of the extent of rock type, alteration and/or mineralization domains in the subsurface (Duke and Hanna, 2001; Sinclair and Blackwell, 2002; Knödel et al., 2007; Marjoribanks, 2010; Charifo et al., 2013; Rossi and Deutsch, 2014; Chanderman et al., 2017; Séguret and Emery, 2019; Hajsadeghi et al., 2020; Jin et al., 2020; Mirzaei et al., 2020).

Most studies on constructing interpretive geological models focus on integrating different sources of information for building more accurate models, graphical analyses using related developed software packages to provide a better image of the subsurface and available data or using data inversion methods (Guillen et al., 2008; Lelièvre, 2009). Also, some studies present machine learning or geostatistical clustering algorithms for constructing interpretive geological models (Fouedjio et al., 2018). However, in general, a single representation of the subsurface is constructed and no measure of its accuracy is available. In this context, it is of interest to design quantitative methods that allow assessing the accuracy of a geological model and the uncertainty in the categories assigned to each node or block of this model.

In a recent work, Adeli et al. (2018) propose a geostatistical approach aimed at validating an interpretive geological model and at finding the areas of an ore deposit with a high probability of being misinterpreted. The approach relies on calculating, for each block of the geological model, a measure of the consistency between its interpreted category and the quantitative information brought by the sampling of rock physical and geochemical covariates. It includes the geostatistical modeling and joint simulation of these covariates, followed by a decision-tree classification algorithm to convert the simulated covariates into a geological category, for each target block and each realization. Comparing the prior (ignoring the sampling data) and posterior (conditioned to the sampling data) probabilities of categories for each target block allows identifying the blocks that are most likely to be incorrectly interpreted in light of the information from the quantitative covariates.

The present work builds upon the approach by Adeli et al. (2018) and proposes a methodology to improve the accuracy of the constructed geological model. The methodology relies on the existence of spatial cross-correlations between the geological categories used to define the interpretive geological model and quantitative covariates known through sampling (e.g., drill hole assays). The key idea is to simulate a smoothed version of the covariates, through the filtering of the nugget effect or of the spatial components with a small range of correlation that can be associated with measurement errors or noise, and to use the smoothed simulated values for defining the geological categories. It is believed that the spatial components associated with large-scale structures can better explain geological categories than the measured (noisy) variables.

The outline of the paper is as follows. Section 2 presents the theoretical background of the proposal, with emphasis on coregionalization analysis, the decomposition of coregionalized variables into components acting at different spatial scales and the conditional simulation of specific spatial components. The methodology is illustrated on an iron deposit in Section 3. Discussions are drawn in Section 4 and conclusions in Section 5.