Informed Local Smoothing in 3D Implicit Geological Modeling

Geological models are commonly used to represent geological structures in 3D space. A wide range of methods exists to create these models, with much scientific work focusing recently on implicit representation methods, which perform an interpolation of a three-dimensional field where the relevant boundaries are then isosurfaces in this field. However, this method has well-known problems with inhomogeneous data distributions: if regions with densely sampled data points exist, modeling artifacts are common. We present here an approach to overcome this deficiency through a combination of an implicit interpolation algorithm with a local smoothing approach. The approach is based on the concepts of nugget effect and filtered kriging known from conventional geostatistics. It reduces the impact of regularly occurring modeling artifacts that result from data uncertainty and data configuration and additionally aims to improve model robustness for scale-dependent fit-for-purpose modeling. Local smoothing can either be manually adjusted, inferred from quantified uncertainties associated with input data or derived automatically from data configuration. The application for different datasets with varying configuration and noise is presented for a low complexity geologic model. The results show that the approach enables a reduction of artifacts, but may require a careful choice of parameter settings for very inhomogeneous data sets.