Unsupervised classification of multivariate geostatistical data: Two algorithms

International audienceWith the increasing development of remote sensing platforms and the evolution of sampling facilities in mining and oil industry, spatial datasets are becoming increasingly large, inform a growing number of variables and cover wider and wider areas. Therefore, it is often necessary to split the domain of study to account for radically different behaviors of the natural phenomenon over the domain and to simplify the subsequent modeling step. The definition of these areas can be seen as a problem of unsupervised classification, or clustering, where we try to divide the domain into homogeneous domains with respect to the values taken by the variables in hand. The application of classical clustering methods, designed for independent observations, does not ensure the spatial coherence of the resulting classes. Image segmentation methods, based on e.g. Markov random fields, are not adapted to irregularly sampled data. Other existing approaches, based on mixtures of Gaussian random functions estimated via the expectation-maximization algorithm, are limited to reasonable sample sizes and a small number of variables. In this work, we propose two algorithms based on adaptations of classical algorithms to multivariate geostatistical data. Both algorithms are model free and can handle large volumes of multivariate, irregularly spaced data. The first one proceeds by agglomerative hierarchical clustering. The spatial coherence is ensured by a proximity condition imposed for two clusters to merge. This proximity condition relies on a graph organizing the data in the coordinates space. The hierarchical algorithm can then be seen as a graph-partitioning algorithm. Following this interpretation, a spatial version of the spectral clustering algorithm is also proposed. The performances of both algorithms are assessed on toy examples and a mining dataset

Domaining by clustering multivariate geostatistical data

International audienceDomaining is very often a complex and time-consuming process in mining assessment. Apart from the further delineation of envelopes, a significant number of parameters (lithology, alteration, grades?) are to be combined in order to characterize domains or sub domains. This rapidly leads to a huge combinatory. Hopefully the number of domains should be limited, while ensuring their connectivity as well as the stationarity of the variables within each domain. In order to achieve this goal, different methods for the spatial clustering of multivariate data are explored and compared. A particular emphasis is placed on the ways to modify existing procedures of clustering in non spatial settings to enforce the spatial connectivity of the resulting clusters. K-means, spectral methods and EM-based algorithms are reviewed. The methods are illustrated on mining data

Choice of a methodological approach for the estimation of recoverable resources with uranium deposits in central Jordan

International audienceChoosing a resource estimation approach for uranium deposits central Jordan needs to consider various issues; the particular geological context of these deposits, the varying degree of reliability of input data and the level of selectivity that can be reasonably envisaged at a production stage. These issues make this resource estimation challenging from a geostatistical perspective. Here, we provide details of the approach used during resource estimation for the surficial part of uranium deposits in central Jordan; as a more standard approach has been applied to the deeper parts of these deposits. The workflow is as follows: (i) Interpolation of the geometry of the mineralised formation. Kriging with external drift is applied to model hangingwall and footwall surfaces. (ii) Estimation of global resources by 2D estimation of layer thicknesses and uranium accumulation using channel samples within delineated areas. (iii) Accounting for vertical selectivity and development of grade tonnage curves using uniform conditioning (UC) followed by localised post-processing (called LUC) delivering, a 3D block model at the selective mining unit support scale. A description of the UC/LUC approach and the adaptations made in order to account for the variable thickness is presented in this paper. This approach involves performing UC on each panel in turn with a thickness varying from panel to panel. This leads to a specific change of support coefficients for each panel. The illustrations of this approach are taken from one specific zone within the Central Jordan deposits. © 2015 Institute of Materials, Minerals and Mining and The AusIMM

Modeling the geometry of a mineral deposit domain with a Potential Field

International audienceThe potential field method, successfully applied in geological modeling, has been developed in the very different context of mineral deposit modeling, where in comparison to geological mapping we have many drill holes but usually few structural data. After a reminder of the fundamentals of the method, new advances related to the incorporation of soft data and to the assessment of the uncertainty are presented. The principle of the method is to derive the geometry of the domain under study from a 3D interpolation of a scalar field, known as the potential field, by cokriging from information on contacts with drill holes and on structural data linked with the gradient of the potential field. Still the information brought by the drill holes is much more abundant than just the transitions from outside to inside the domain (or the reverse). Soft information is efficiently added to the hard contact data by means of additional control points processed with the Gibbs sampler algorithm. Finally the potential field approach provides side products such as the cokriging variance, and the gradient of the estimated potential field, which can be turned into an uncertainty on the location of the domain boundary or used to map the probability that a specific location lies within the domain. The proposed potential field method is put into practice in a case study of a gold rich porphyry deposit, La Colosa. On the exploration drillholes, hardness measurements related to lithology and alteration have been collected by Equotip equipment. After simple pre-processing of this data, one domain has been modeled and probability map has been calculated

Etude de la planification d'une exploitation miniere par simulation sur modele de gisements

Action concertee: Valorisation des ressources du sous-solSIGLEAvailable from Centre de Documentation Scientifique et Technique, CNRS, 26 rue Boyer, 75971 Paris Cedex 20 (France) / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc