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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]