Deussen, Philipp; Galvanin, Federico; (2023) A joint model-based design of experiments approach for the identification of Gaussian Process models in geological exploration. Presented at: Sargent CPSE Model-Based Design of Experiments Symposium, London, UK.

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Abstract

When searching for potential mining sites, accurately modelling mineral concentrations or rock qualities in the subsurface is a crucial task. However, drilling in these locations is an expensive process, so reliable interpolation and efficient sampling techniques are required (Rossi & Deutsch, 2014). Gaussian Processes (GPs), also known as Kriging models, were first developed in the mining industry in the 1950s and continue to be widely used in resource modelling (Sahimi, 2011). As the true nature of the subsurface is unknown, assumptions must be made about the kernel function, which describes correlation structures between probable distributions of spatial phenomena, and its parameters must be estimated. This is typically accomplished through expert judgement and exploratory data analysis of preliminary samples. Model predictions are updated iteratively as more drilling data becomes available, with a focus on balancing expected exploitation (high grade intercepts) and exploration (minimising the Kriging variance) (Jafrasteh & Suarez, 2020). However, problems can arise if the chosen kernel is incorrect or if high uncertainty affects parameters. This poster showcases a joint model-based design approach (Galvanin et al., 2016) aiming to optimise three objectives: 1) reducing parametric uncertainty; 2) increasing the exploration of the design space to avoid local optima; 3) maximising the distinguishability of candidate model predictions to identify the most suitable kernel function with the minimum number of samples. Two different kernels in an Ordinary Kriging GP were used as candidate models and in-silico data was generated using one kernel. Starting from some initial samples, the optimal design strategy iteratively determined sampling locations to maximise the distinguishability between model predictions with a constraint ensuring that each iteration reduces prediction variance. The correct model could be distinguished and the data approximated well with a limited number of drilling experiments while satisfactorily estimating kernel parameters.

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