GeoINR 1.0: an implicit neural network approach to three-dimensional geological modelling

Implicit neural representation (INR) networks are emerging as a powerful framework for learning three-dimensional shape representations of complex objects. These networks can be used effectively to model three-dimensional geological structures from scattered point data, sampling geological interfaces, units, and structural orientations. The flexibility and scalability of these networks provide a potential framework for integrating many forms of geological data and knowledge that classical implicit methods cannot easily incorporate. We present an implicit three-dimensional geological modelling approach using an efficient INR network architecture, called GeoINR, consisting of multilayer perceptrons (MLPs). The approach expands on the modelling capabilities of existing methods using these networks by (1) including unconformities into the modelling; (2) introducing constraints on stratigraphic relations and global smoothness, as well as associated loss functions; and (3) improving training dynamics through the geometrical initialization of learnable network variables. These three enhancements enable the modelling of more complex geology, improved data fitting characteristics, and reduction of modelling artifacts in these settings, as compared to an existing INR approach to structural geological modelling. Two diverse case studies also are presented, including a sedimentary basin modelled using well data and a deformed metamorphic setting modelled using outcrop data. Modelling results demonstrate the method's capacity to fit noisy datasets, use outcrop data, represent unconformities, and efficiently model large geographic areas with relatively large datasets, confirming the benefits of the GeoINR approach.