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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]

Abstract Geological structures influence the formation and evolution of sedimentary rocks. The Minas do Camaquã fault zone is a primary structure of the Camaquã Basin, controlling the uplift of the ore-bearing units of the Santa Bárbara Group. To the south of the Camaquã River, the fault zone deforms alluvial and eolian sequences attributed either to the Santa Bárbara or Guaritas groups. In this study, a facies and petrographic composition and diagenetic analysis are presented to understand the evolution of the fault zone. Facies analysis was accomplished using high-resolution orthophoto mosaics and field surveys. Seven sedimentary facies were defined, grouped into three facies associations. Facies associations correspond to a succession of climate-influenced depositional environments. The transition from humid to dry conditions occurs from a fluvial (facies association 1) to eolian environments (facies association 2). These deposits are overlaid at the top by a high energy environment deposits characterized by amalgamated gravelly and sandy bodies, corresponding to an alluvial environment (facies association 3). Despite a small compositional variation, sandstones present a continental block provenance which may be related to mixed anorogenic or orogenic provenance. Diagenetic features are similar in the three facies associations, suggesting the same burial history for the sedimentary deposits separated by the fault zone. The Minas do Camaquã fault zone in the study area is an intraformational structure, as analyzed sequences are attributed to the Guaritas Group, implying a relatively high degree of deformation late after its deposition. Highlights • Fault zone separates steeply inclined from horizontal sequences. • Three facies associations were interpreted from field and remote sensing data. • Sandstones detrital composition indicates continental block and mixed provenance. • Fault zone does not limit diagenetic variations suggesting a single burial history. • Units separated by the fault zone correspond to the Guaritas Group. [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]