Less is more: Weakly supervised interpolation using geological neural fields

Structural geological modelling methods currently depend on subjective stratigraphic interpretations, typically from geological maps and borehole logs. Implicit interpolation approaches can represent these interpreted geological units as scalar field values, to objectively derive a numerical representation of subsurface geometry, however sensitivity to the underlying geological interpretations (and biases or errors) remain. 

In this contribution we present a neural-network based interpolation approach that removes the need for subjective value constraints. This network, or neural field, learns the relationship between input coordinates and scalar values, a flexible approach that has been recently demonstrated in the context of geological modelling. However, unlike previous approaches, we are able to constrain our model directly with objectively measured quantities (e.g., from geochemical assays, downhole petrophysical logs and/or hyperspectral core scan results). This is achieved by coupling the spatial neural field with a property neural field that learns to reconstruct measured quantities given a predicted scalar field value. Simultaneous training of these two neural fields encourages the spatial field to find a solution (subsurface geometry) that is most informative for predicting the measured properties. Constraints on the gradient (i.e. bedding orientation) and scalar value (i.e. stratigraphic unit) can also be included to further guide the neural fields, but are not required.

We demonstrate this weakly-supervised modelling approach on several synthetic datasets, and show how it could be applied to construct “self-updating” models that are iteratively updated as new geophysical, geochemical or hyperspectral data become available. These preliminary results indicate that unlabelled geological data can be used as powerful objective constraints for future geological modelling workflows, to ultimately derive accurate and unbiased representations of the subsurface.