The representation of subsurface structures is an essential aspect of a wide variety of geoscientific investigations and applications, ranging from geofluid reservoir studies, over raw material investigations, to geosequestration, as well as many branches of geoscientific research and applications in geological surveys. A wide range of methods exist to generate geological models. However, the powerful methods are behind a paywall in expensive commercial packages. We present here a full open-source geomodeling method, based on an implicit potential-field interpolation approach. The interpolation algorithm is comparable to implementations in commercial packages and capable of constructing complex full 3-D geological models, including fault networks, fault–surface interactions, unconformities and dome structures. This algorithm is implemented in the programming language Python, making use of a highly efficient underlying library for efficient code generation (Theano) that enables a direct execution on GPUs. The functionality can be separated into the core aspects required to generate 3-D geological models and additional assets for advanced scientific investigations. These assets provide the full power behind our approach, as they enable the link to machine-learning and Bayesian inference frameworks and thus a path to stochastic geological modeling and inversions. In addition, we provide methods to analyze model topology and to compute gravity fields on the basis of the geological models and assigned density values. In summary, we provide a basis for open scientific research using geological models, with the aim to foster reproducible research in the field of geomodeling.

Three-dimensional structural geomodels are increasingly being used for a wide variety of scientific and societal purposes. Most advanced methods for generating these models are implicit approaches, but they suffer limitations in the types of interpolation constraints permitted, which can lead to poor modeling in structurally complex settings. A geometric deep learning approach, using graph neural networks, is presented in this paper as an alternative to classical implicit interpolation that is driven by a learning through training paradigm. The graph neural network approach consists of a developed architecture utilizing unstructured meshes as graphs on which coupled implicit and discrete geological unit modeling is performed, with the latter treated as a classification problem. The architecture generates three-dimensional structural models constrained by scattered point data, sampling geological units and interfaces as well as planar and linear orientations. The modeling capacity of the architecture for representing geological structures is demonstrated from its application on two diverse case studies. The benefits of the approach are (1) its ability to provide an expressive framework for incorporating interpolation constraints using loss functions and (2) its capacity to deal with both continuous and discrete properties simultaneously. Furthermore, a framework is established for future research for which additional geological constraints can be integrated into the modeling process.