Optimised multivariate Gaussians for probabilistic subsurface characterisation

Subsurface characterisation relies heavily on geological information such as borehole data, which are often sparse and uncertain. Traditionally borehole interpretation is often qualitative and without formal incorporation of uncertainties. In this paper, we propose a methodology based on multivariate Gaussian probability distributions to generate probabilistic 3D geologic models using borehole data including the associated uncertainties. We focus on uncertainties related to geologists' interpretation of where interfaces between geologic layers occur. This is done using multivariate Gaussian distributions with parameters optimised based on fitted probability distributions from borehole data and expert input. More specifically, at each borehole location, the geological layers are fitted with 3D Gaussian distributions that reflect the uncertain geologic knowledge. The proposed method is quite versatile allowing one to include different uncertainties in the formulation of the optimisation process. The model and the algorithms were implemented in MatLab and applied to the case of the Masdar City Subsurface in Abu Dhabi, United Arab Emirates for the identification of Sabkha, a high salinity geologic layer characteristic of the region, which is prone to dissolution and large settlements. The results are in the form of the probabilistic profiles and maps that reflect the probability of occurrence of the different geologies.