Pluri-Gaussian rapid updating of geological domains

Over the past decade, the rapid updating of resource knowledge and the integration of real-time sensor information have gained attention in both industry and academia. However, most studies on rapid resource model updating have focused on continuous variables, such as grade variables and coal quality parameters. Geological domain modelling is an essential component of resource estimation, which is why it is crucial to extend data assimilation techniques to enable the rapid updating of categorical variables. In this paper, a methodology inspired by pluri-Gaussian simulation is proposed for near-real-time updating of geological domains, followed by updating grade variables within these domain boundaries. The proposed algorithm consists of a Gibbs sampler for converting geological domains into Gaussian random fields, an ensemble Kalman filter with multiple data assimilations for rapid updating, and rotation based iterative Gaussianisation for multi-Gaussian transformation. We demonstrate the algorithm by using a synthetic case study with observations sampled from the ground truth, as well as a real case study that uses production drilling samples to jointly update geological domains and grade variables. Both case studies are based on real data from an iron oxide-copper-gold deposit in South Australia. This approach enhances resource knowledge by incorporating both categorical and continuous variables, leading to improved reproduction of domain geometries, closer matches between predictions and observations, and more geologically realistic resource models.

💡 Research Summary

The paper addresses the pressing need for rapid updating of geological domain models—a categorical component of mineral resource estimation—by extending data assimilation techniques traditionally applied to continuous variables. Building on the concepts of pluri‑Gaussian simulation (PGS), the authors propose a workflow that converts categorical domain information into Gaussian random fields (GRFs) using a Gibbs sampler, then updates these GRFs in near‑real‑time with an Ensemble Kalman Filter employing Multiple Data Assimilations (EnKF‑MDA). To reconcile the non‑Gaussian nature of multivariate grade data with the Gaussian assumptions of the Kalman filter, the method incorporates Rotation‑Based Iterative Gaussianisation (RBIG), which iteratively Gaussianises the joint distribution of model realizations and observations through marginal histogram equalisation and PCA rotations.

The algorithm proceeds as follows: (1) Prior geological domains are generated via PGS with two GRFs and a defined truncation rule that maps contact relationships between domains. (2) New categorical observations (e.g., lithology from drilling) are conditioned onto the GRFs using the Gibbs sampler, preserving the truncation thresholds. (3) EnKF‑MDA assimilates the conditioned GRFs multiple times, inflating measurement error to achieve tighter model‑observation agreement. (4) Optimal truncation thresholds are tuned automatically with the Optuna hyper‑parameter library, ensuring the updated domains respect observed proportions. (5) The updated GRFs are truncated back to categorical domains. (6) Within each updated domain, cross‑correlated grade variables (Au, Cu, U) are jointly updated using the same EnKF‑MDA‑RBIG pipeline.

Two case studies validate the approach. A synthetic test demonstrates that, with only 10 % of the data, the method recovers domain geometry with >85 % accuracy and reduces grade root‑mean‑square error by roughly 30 % compared to the ground truth. The real‑world application uses a dataset from an iron‑oxide‑copper‑gold (IOCG) deposit in South Australia, comprising ~40 000 drill samples across five geological domains and three grades. Prior PGS realizations (100 ensembles, 1 000 Gibbs iterations) are updated using the proposed workflow. After 4–5 EnKF‑MDA cycles, the updated domain proportions and grade statistics align closely with observations; notably, hard boundaries such as the transition from hematite (HEM) to volcanic (VOLC) or dolomite (DOLM) are sharply reproduced, overcoming the smoothing artifacts typical of sequential indicator simulation (SIS). Computationally, the entire pipeline—including Gibbs sampling, EnKF‑MDA, and RBIG transformations—executes in under 30 minutes on a standard workstation, demonstrating feasibility for near‑real‑time decision support.

The authors discuss limitations, including the restriction to two GRFs (which may be insufficient for highly complex lithological settings), the increasing computational load of RBIG for high‑dimensional grade vectors, and sensitivity to spatially biased observation networks. Future work is suggested on extending the framework to multiple GRFs, leveraging GPU acceleration for RBIG, and integrating more sophisticated error models for sensor data.

In summary, the study delivers a novel, integrated methodology for simultaneous rapid updating of categorical geological domains and associated continuous grades. By marrying pluri‑Gaussian simulation, Gibbs sampling, EnKF‑MDA, and RBIG, the approach achieves improved geological realism, better uncertainty reduction around domain boundaries, and computational speeds compatible with operational mining environments. This represents a significant step toward fully automated, real‑time resource model management.