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The ferricrete units (Fe oxide cemented colluvial-alluvial sediment) of the Yilgarn Craton in Western Australia formed during the humid tropical and sub-tropical climates of the Cenozoic. Ferricretes are generally developed on long-lived paleodrainage systems and are products of the ferruginisation of detritus provided by the continuous erosion of upslopes. These iron-rich accumulations can become Au-enriched, as is the case in several locations previously discovered in the Yilgarn Craton; many of these host economic secondary gold deposits (e.g., Moolart Well, Mt Gibson, and Bulchina), typically occurring downslope of low saprolite hills and near paleovalleys (i.e., inset-valleys). Inset-valleys are a common paleotopographic feature buried under Quaternary alluvial and colluvial sedimentary cover. Maps of these ancient channel networks can be used as a proxy for targeting ferricrete gold deposits. These inset-valley systems generally form dendritic and noisy patterns in high-resolution aeromagnetic data due to the presence of maghemite-rich nodules and detrital magnetic pisoliths on their flanks. The main aim of this study was to use high-resolution aeromagnetic data to target ferricrete units related to inset-valleys systems across the Yilgarn Craton. A spatial predictive model was used to learn and predict the geological units of interest from pre-processed aeromagnetic data. The predicted inset-valleys systems were able to confine the exploration space and define a new exploration frontier for ferricrete gold deposits.

The particularities of geosystems and geoscience data must be understood before any development or implementation of statistical learning algorithms. Without such knowledge, the predictions and inferences may not be accurate and physically consistent. Accuracy, transparency and interpretability, credibility, and physical realism are minimum criteria for statistical learning algorithms when applied to the geosciences. This study briefly reviews several characteristics of geoscience data and challenges for novel statistical learning algorithms. A novel spatial spectral clustering approach is introduced to illustrate how statistical learners can be adapted for modelling geoscience data. The spatial awareness and physical realism of the spectral clustering are improved by utilising a dissimilarity matrix based on nonparametric higher-order spatial statistics. The proposed model-free technique can identify meaningful spatial clusters (i.e. meaningful geographical subregions) from multivariate spatial data at different scales without the need to define a model of co-dependence. Several mixed (e.g. continuous and categorical) variables can be used as inputs to the proposed clustering technique. The proposed technique is illustrated using synthetic and real mining datasets. The results of the case studies confirm the usefulness of the proposed method for modelling spatial data.

Prediction of true classes of surficial and deep earth materials using multivariate spatial data is a common challenge for geoscience modelers. Most geological processes leave a footprint that can be explored by geochemical data analysis. These footprints are normally complex statistical and spatial patterns buried deep in the high-dimensional compositional space. This paper proposes a spatial predictive model for classification of surficial and deep earth materials derived from the geochemical composition of surface regolith. The model is based on a combination of geostatistical simulation and machine learning approaches. A random forest predictive model is trained, and features are ranked based on their contribution to the predictive model. To generate potential and uncertainty maps, compositional data are simulated at unsampled locations via a chain of transformations (isometric log-ratio transformation followed by the flow anamorphosis) and geostatistical simulation. The simulated results are subsequently back-transformed to the original compositional space. The trained predictive model is used to estimate the probability of classes for simulated compositions. The proposed approach is illustrated through two case studies. In the first case study, the major crustal blocks of the Australian continent are predicted from the surface regolith geochemistry of the National Geochemical Survey of Australia project. The aim of the second case study is to discover the superficial deposits (peat) from the regional-scale soil geochemical data of the Tellus Project. The accuracy of the results in these two case studies confirms the usefulness of the proposed method for geological class prediction and geological process discovery.

Spatial uncertainty modelling and prediction of a set of regionalized dependent variables from various sample spaces (e.g. continuous and categorical) is a common challenge for geoscience modellers and many geoscience applications such as evaluation of mineral resources, characterization of oil reservoirs or hydrology of groundwater. To consider the complex statistical and spatial relationships, categorical data such as rock types, soil types, alteration units, and continental crustal blocks should be modelled jointly with other continuous attributes (e.g. porosity, permeability, seismic velocity, mineral and geochemical compositions or pollutant concentration). These multivariate geospatial data normally have complex statistical and spatial relationships which should be honoured in the predicted models. Continuous variables in the form of percentages, proportions, frequencies, and concentrations are compositional which means they are non-negative values representing some parts of a whole. Such data carry just relative information and the constant sum constraint forces at least one covariance to be negative and induces spurious statistical and spatial correlations. As a result, classical (geo)statistical techniques should not be implemented on the original compositional data. Several geostatistical techniques have been developed recently for the spatial modelling of compositional data. However, few of these consider the joint statistical and/or spatial relationships of regionalized compositional data with the other dependent categorical information. This PhD thesis explores and introduces approaches to spatial modelling of regionalized compositional and categorical data. The first proposed approach is in the multiple-point geostatistics framework, where the direct sampling algorithm is developed for joint simulation of compositional and categorical data. The second proposed method is based on two-point geostatistics and is useful for the situation where a large and

Talebi, H., Peeters, L. J. M., Otto, A., & Tolosana-Delgado, R. (2021). A truly spatial random forests algorithm for geoscience data analysis and modelling. Mathematical Geosciences. Advance online publication. https://doi.org/10.1007/s11004-021-09946-w

Talebi, H., Peeters, L. J. M., Mueller, U., Tolosana-Delgado, R., & van den Boogaart, K. G. (2020). Towards geostatistical learning for the geosciences: A case study in improving the spatial awareness of spectral clustering. Mathematical Geosciences, 52(8), 1035-1048. https://doi.org/10.1007/s11004-020-09867-0

Talebi, H., Lo, J., & Mueller, U. (2017). A Hybrid Model for Joint Simulation of High-Dimensional Continuous and Categorical Variables. In Geostatistics Valencia 2016 (pp. 415-430). Springer, Cham. Available here

Talebi, H., Mueller, U., Tolosana-Delgado, R., Grunsky, E. C., McKinley, J. M., & de Caritat, P. (2019). Surficial and deep earth material prediction from geochemical compositions. Natural Resources Research, 28(3), 869-891. Available here

Talebi, H., Mueller, U., & Tolosana-Delgado, R. (2019). Joint simulation of compositional and categorical data via direct sampling technique–Application to improve mineral resource confidence. Computers & Geosciences, 122, 87-102. Available here.

Talebi, H., Mueller, U., Tolosana-Delgado, R., & van den Boogaart, K. G. (2019). Geostatistical simulation of geochemical compositions in the presence of multiple geological units: Application to mineral resource evaluation. Mathematical Geosciences, 51(2), 129-153. Available here

Talebi, H., Sabeti, E.H., Azadi, M., & Emery, X. (2016). Risk quantification with combined use of lithological and grade simulations: Application to a porphyry copper deposit. In Ore Geology Reviews. 75. 42-51. Available here.

Talebi, H., Mueller, U., Peeters, L. J. M., Otto, A., de Caritat, P., Tolosana-Delgado, R., & van den Boogaart, K. G. (2022). Stochastic modelling of mineral exploration targets. Mathematical Geosciences. Advance online publication. https://doi.org/10.1007/s11004-021-09989-z

Talebi, H., Mueller, U., Peeters, L. J. M., Otto, A., de Caritat, P., Tolosana-Delgado, R., & van den Boogaart, K. G. (2022). Stochastic modelling of mineral exploration targets. Mathematical Geosciences. Advance online publication. https://doi.org/10.1007/s11004-021-09989-z