Abstract. Uncertainties are common in geological models and have a considerable impact on model interpretations and subsequent decision-making. This is of particular significance for high-risk, high-reward sectors. Recent advances allows us to view geological modeling as a statistical problem that we can address with probabilistic methods. Using stochastic simulations and Bayesian inference, uncertainties can be quantified and reduced by incorporating additional geological information. In this work, we propose custom loss functions as a decision-making tool that builds upon such probabilistic approaches. As an example, we devise a case in which the decision problem is one of estimating the uncertain economic value of a potential fluid reservoir. For subsequent true value estimation, we design a case-specific loss function to reflect not only the decision-making environment, but also the preferences of differently risk-inclined decision makers. Based on this function, optimizing for expected loss returns an actor's best estimate to base decision-making on, given a probability distribution for the uncertain parameter of interest. We apply the customized loss function in the context of a case study featuring a synthetic 3-D structural geological model. A set of probability distributions for the maximum trap volume as the parameter of interest is generated via stochastic simulations. These represent different information scenarios to test the loss function approach for decision-making. Our results show that the optimizing estimators shift according to the characteristics of the underlying distribution. While overall variation leads to separation, risk-averse and risk-friendly decisions converge in the decision space and decrease in expected loss given narrower distributions. We thus consider the degree of decision convergence to be a measure for the state of knowledge and its inherent uncertainty at the moment of decision-making. This decisive uncertainty does not change in alignment with model uncertainty but depends on alterations of critical parameters and respective interdependencies, in particular relating to seal reliability. Additionally, actors are affected differently by adding new information to the model, depending on their risk affinity. It is therefore important to identify the model parameters that are most influential for the final decision in order to optimize the decision-making process.

Abstract. Uncertainties are common in geological models and have a considerable impact on model interpretations and subsequent decision making. This is of particular significance for high-risk, high-reward sectors, such as hydrocarbon exploration and production. Recent advances allows us to view geological modeling as a statistical problem that we can address with probabilistic methods. Using stochastic simulations and Bayesian inference, uncertainties can be quantified and reduced by incorporating additional geological information. In this work, we propose custom loss functions as a decision-making tool that builds upon such probabilistic approaches. As an example, we devise a case in which the decision problem is one of estimating the uncertain volume of a structural hydrocarbon trap. We construct a synthetic 3-D model to represent a potential hydrocarbon system and develop algorithms for automatic trap volume calculation. Various volume probability distributions for different information scenarios are attained via Monte Carlo error propagation and Markov chain Monte Carlo sampling. For subsequent true value estimation, we design a case-specific loss function to reflect not only the decision-making environment, but also the preferences of differently risk-affine actors. Based on this function, optimizing for expected loss returns an actor's best estimate to base decision making on. Our results show that the optimizing estimators shift according to the characteristics of the underlying value distribution. While overall spread leads to separation, risk-averse and risk-friendly decisions converge in the decision space and decrease in expected loss given narrower distributions. We thus consider the degree of decision convergence to be a measure for the state of knowledge and its inherent uncertainty at the moment of decision making. This decisive uncertainty does not change in alignment with model uncertainty but depends on alterations of critical parameters and respective interdependencies, in particular relating to seal reliability. Additionally, actors are affected differently by one set of information, depending on their risk affinity. It is therefore important to identify the model parameters which are most influential for the final decision in order to optimize the decision-making process.

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This is an interesting paper, I think that the use of loss functions in this setting is a useful development and one with considerable potential, and I think that the paper is to be welcomed because of this. • We thank the reviewer for this motivating content on the topic itself. C1