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A variational Gaussian process (VGP) model for implicit geological modeling is proposed, capable of modeling linear and non-linear trends. A new likelihood capable of honoring geological boundaries is introduced, and its performance is compared with the radial basis function (RBF) model. The model is tested on two case studies in mining, one of which relies only on photogrammetric data. The new approach generates more realistic surfaces on qualitative terms and provides an uncertainty measure. It is available as an open-source Python package. • A variational Gaussian process model for implicit geological modeling. • The model uses only discrete labels, not needing signed distances. • Anisotropy parameters can be learned semi-automatically. • Support for linear and non-linear trends. • A data-driven uncertainty measure is provided. [ABSTRACT FROM AUTHOR]

This work presents a Gaussian process model (a Bayesian derivation of kriging) for the interpolation of structural field data (dip and strike measurements). The structural data are treated as the directional derivatives of a latent potential field. The latent field's isosurfaces characterize the general structural trend in a region, and the predictive variance can be used as a measure of uncertainty. The model's parameters are optimized via maximum likelihood, avoiding the need for a variogram analysis. The model is tested using the orientation vectors of metamorphic foliation in meta-volcanic rocks of the Passo Feio Metamorphic Complex, in southern Brazil. An open-source implementation is available. • A potential field is modeled from orientation data alone with the Gaussian process. • Structural surfaces correspond to isovalues of the modeled field. • Covariance parameters are trained through maximum likelihood. • Open-source implementation available. [ABSTRACT FROM AUTHOR]

Implicit modeling has experienced a rise in popularity over the last decade due to its advantages in terms of speed and reproducibility in comparison with manual digitization of geological structures. The potential-field method consists in interpolating a scalar function that indicates to which side of a geological boundary a given point belongs to, based on cokriging of point data and structural orientations. This work proposes a vector potential-field solution from a machine learning perspective, recasting the problem as multi-class classification, which alleviates some of the original method's assumptions. The potentials related to each geological class are interpreted in a compositional data framework. Variogram modeling is avoided through the use of maximum likelihood to train the model, and an uncertainty measure is introduced. The methodology was applied to the modeling of a sample dataset provided with the software Move™. The calculations were implemented in the R language and 3D visualizations were prepared with the rgl package. [ABSTRACT FROM AUTHOR]