Estimating rare-event failure probabilities related to managing subsurface systems is computationally challenging because geological uncertainty is high-dimensional and spatially structured. In many applications, reliable risk assessment requires thousands of forward simulations to quantify low-probability events with statistical confidence, which can become prohibitively expensive when each simulation involves complex numerical models. These challenges motivate the use of importance sampling, which can improve efficiency by concentrating simulations in the regions of the uncertainty space that contribute most to failure.,The key challenge addressed in this work is how to construct a generative model for the importance distribution when uncertainty is represented by spatial fields rather than low-dimensional vectors representing non-spatial uncertainties. To address this challenge, we present a methodology for importance sampling under spatial uncertainty that enables efficient estimation of rare-event probabilities related to managing the subsurface system. The approach combines dimensionality reduction of spatial variables with sensitivity-driven identification of the most influential components, which are then used to define a proposal distribution that concentrates sampling in failure-prone regions of the model space. Importance weights correct for the resulting sampling bias, yielding unbiased probability estimates while significantly reducing the number of simulations required.,The methodology is demonstrated using a real-case scenario of geological carbon storage in a depleted gas reservoir, where the goal is to estimate the probability of CO₂ leakage under uncertainty in reservoir geometry and porosity fields. Results show that the proposed importance sampling strategy achieves reliable probability estimates with approximately an order-of-magnitude reduction in computational cost compared to naïve Monte Carlo simulation.,Although illustrated for CO₂ leakage risk assessment, the proposed framework is general and can be applied to a wide range of subsurface decision problems involving spatial uncertainty and rare-event prediction.

The global energy transition requires increased production of critical minerals. However, selecting which target deposits to explore and subsequently to develop into active mines is a staged process: each exploration action generates new observations that reduce uncertainty and inform the next decision, whether to commit capital, delay, or abandon a target. Project viability is further constrained by socio-environmental factors that can also evolve as projects progress. Because decisions unfold incrementally, with each choice contingent on information from prior stages, this is inherently a sequential decision-making problem; we propose a Partially Observable Markov Decision Process (POMDP) framework to optimize mineral exploration and mine development strategies across multiple targets. Our model explicitly incorporates uncertainties in ore grade, tonnage, deposit depth, and commodity price, alongside a dynamic sustainability score that imposes escalating penalties when mining activities breach environmental and social license thresholds. By generating observations through exploration, the planner updates its belief state, weighing the value of new information against the options to proceed, delay, or abandon a target. We evaluate this belief-aware AI planner on synthetic multi-target scenarios, comparing its performance against a baseline AI planner that ignores early-stage sustainability metrics and a traditional multi-criteria decision-making (MCDM) agent that strictly maximizes Net Present Value. The results demonstrate that the proposed planner optimally balances profitability and risk, actively avoiding severe sustainability penalties even at the cost of abandoning high-grade or high-tonnage targets. Ultimately, this framework provides a strategic tool for aligning economic objectives with environmental stewardship and social acceptance.

The acquisition of geophysical data is becoming increasingly important in the context of critical mineral exploration. Geophysical data and inversion products are essential to map many components of the critical mineral system by detecting geophysical anomalies that can be interpreted by expert geologists. However, the inversion of airborne geophysical data acquired along flightlines into subsurface petrophysical properties remains an outstanding challenge. Many inversion techniques rely either on 1D deterministic inversion or on stochastic inversion on a local scale. The outcome of our work is the stochastic inversion along flightlines of 2D panels (flightline direction vs. depth), while at the same time producing plausible spatial variation in the petrophysical properties. Our method relies on a sequential application of Bayesian inversion, where we invert a sequence of 2D panels such that the variation in petrophysical properties avoids generation of artifacts across the panel boundaries. We show that our method can be used in a practical setting in the context of mineral exploration in the Cape Smith Belt of Canada.