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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]