Investigation of Stratigraphic Uncertainty for Three-Dimensional Geological Modelling

Regarding the variability of subsurface geo-data, investigating uncertainty in geological strata has generally been ignored. However, because geological strata reveal the regularities of geo-data distribution, assessing stratigraphic uncertainty with a universal method in three-dimensional (3D) geological modelling is beginning to attract attention. As an advanced stochastic simulation method, the random field method has been used widely to estimate geo-data in one and two dimensions, but this method is always challenging because of the difficulty in interpreting the scale of fluctuation (SoFs), which are the key parameters regarding the outcome performance. Furthermore, the determination of SoFs proposed in previous research is no longer applicable because there is no numerical meaning for spatially discretized stratum points. To address this problem, the present study investigates the adaptability of the random field method in stratigraphic uncertainty 3D geological modelling with a series of possible inputs, such as smoothing coefficient and distance and depth factors. The horizontal SoFs are obtained based on the borehole coordinates, while the vertical SoF is defined according to the stratum thickness distribution. Each voxel in the space is assigned a probability distribution obtained from the Gaussian autocorrelation function, where the concept of information entropy can be used for uncertainty quantification. The proposed method is applied in a hypothetical case and an actual field case, which are illustrated by solid-voxel-based 3D models. The outcomes regarding different inputs are presented, and the uncertainty of the underground strata is well-quantified.

Keywords: Stratigraphic uncertainty, 3D geological modelling, random field, scale of fluctuation, information entropy