Abstract
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.
Highlights
The consideration of 2D manifolds in 3D space relates to the underlying geological concept that abrupt events in geological history are today often present in the form of significant changes in rock properties, which are observed as distinct boundaries
We suggest to use the well-known concept of Kernel density estimation (KDE) to infer local smoothing values
We will show the application of informed local smoothing in geomodeling using a synthetic modeling example with varying data configuration
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. A representation of structures and boundaries in the subsurface forms the basis for scientific and economic endeavors (see [1] for a recent overview). The consideration of 2D manifolds in 3D space relates to the underlying geological concept that abrupt events in geological history are today often present in the form of significant changes in rock properties, which are observed as distinct boundaries. Tectonic events often result in localized deformation zones which, in the case of brittle deformation, leads to the development of faults and fault networks, which can often be approximated by 2D manifolds for many purposes
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