Structural geological models are widely used to represent relevant geological interfaces and property distributions in the subsurface. Considering the inherent uncertainty of these models, the non-uniqueness of geophysical inverse problems, and the growing availability of data, there is a need for methods that integrate different types of data consistently and consider the uncertainties quantitatively. Probabilistic inference provides a suitable tool for this purpose. Using a Bayesian framework, geological modeling can be considered as an integral part of the inversion and thereby naturally constrain geophysical inversion procedures. This integration prevents geologically unrealistic results and provides the opportunity to include geological and geophysical information in the inversion. This information can be from different sources and is added to the framework through likelihood functions. We applied this methodology to the structurally complex Kevitsa deposit in Finland. We started with an interpretation-based 3D geological model and defined the uncertainties in our geological model through probability density functions. Airborne magnetic data and geological interpretations of borehole data were used to define geophysical and geological likelihoods, respectively. The geophysical data were linked to the uncertain structural parameters through the rock properties. The result of the inverse problem was an ensemble of realized models. These structural models and their uncertainties are visualized using information entropy, which allows for quantitative analysis. Our results show that with our methodology, we can use well-defined likelihood functions to add meaningful information to our initial model without requiring a computationally-heavy full grid inversion, discrepancies between model and data are spotted more easily, and the complementary strength of different types of data can be integrated into one framework.

<p>Geological models, as 3-D representations of subsurface structures and property distributions, are used in many economic, scientific, and societal decision processes. These models are built on prior assumptions and imperfect information, and they often result from an integration of geological and geophysical data types with varying quality. These aspects result in uncertainties about the predicted subsurface structures and property distributions, which will affect the subsequent decision process.</p><p>We discuss approaches to evaluate uncertainties in geological models and to integrate geological and geophysical information in combined workflows. A first step is the consideration of uncertainties in prior model parameters on the basis of uncertainty propagation (forward uncertainty quantification). When applied to structural geological models with discrete classes, these methods result in a class probability for each point in space, often represented in tessellated grid cells. These results can then be visualized or forwarded to process simulations. Another option is to add risk functions for subsequent decision analyses. In recent work, these geological uncertainty fields have also been used as an input to subsequent geophysical inversions.</p><p>A logical extension to these existing approaches is the integration of geological forward operators into inverse frameworks, to enable a full flow of inference for a wider range of relevant parameters. We investigate here specifically the use of probabilistic machine learning tools in combination with geological and geophysical modeling. Challenges exist due to the hierarchical nature of the probabilistic models, but modern sampling strategies allow for efficient sampling in these complex settings. We showcase the application with examples combining geological modeling and geophysical potential field measurements in an integrated model for improved decision making.</p>

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