Geostatistical interpolation and simulation of geological properties considering regional deformation

Kriging is a widely used geostatistical tool to estimate the value of a spatially correlated property at a certain location based on sampled data in the surrounding domain. It creates a weighted average of this data based on the distances to the point that is to be predicted. Interpolated maps and simulated stationary fields play an important role in various geological fields like flow simulation and resource estimation.

Distances between locations in a specified domain thus play an important role in the kriging process and are traditionally measured as straight-line distances. In this work we develop an alternative distance metric to these Euclidian distances normally used in the geostatistical worklflow.

The metric is based on a scalar field that is calculated for 3-D geologic models that are interpolated based on a potential field method implemented in the open-source, implicit geologic modeling tool GemPy.

The measure follows the curvature of the deformation of stratigraphic units, which is relevant when modeling the distribution of a property that developed before deformation. As an undeformed state of the domain is represented by these distances, authorized variogram and covariance models are still valid with the introduced distance metric.

In addition, anisotropies can be modeled in relation to the deformation of a layer by manipulating the new distance metric. The kriging calculations and distance measurements are combined in a Sequential Gaussian Simulation to estimate an entire domain, while adequately modeling the underlying variance. We show first promising results of our work using the newly developed distance metric in different geological settings, including folded and faulted domains.