3-D stochastic geological modelling of the sediment texture in detrital systems: prediction of fictive grain size distributions and uncertainty quantification

The growing use of multiple practical applications in the subsurface, especially in the more densely populated urban areas, demands both the development of new methods and the adaptation of existing approaches for predicting the geological heterogeneity. To this should be added the related uncertainty, since the reliability of the prediction is critical for practical decision purposes. Many of the urban areas are built in detrital depositional environments characterized by the sediment texture of the clastic mixture, which refers to the grain sizes of the particles.

The novel D_i models method was conceived to accurately forecast the three-dimensional lithological composition of detrital systems by means of predicting the fictive grain size distribution of the clastic mixture through a geostatistical framework. The input data used are the direct soil observations from drilled materials described in the field according to the standards for soil description. These data are subject to systematic imprecisions in the lithological descriptions linked to the inherent generalizations of the standards used and to the subjectivity of on-site personnel.

In this context, the incorporation into the geostatistical framework of the above-cited uncertainties linked to systematic imprecisions in the input data is addressed. This process focuses on integrating the uncertainties detected in the semi-quantitative and qualitative descriptions of soil observations from drilled materials by capturing the lower and upper limits of the fictive GSD of the clastic sediments inferred from the soil descriptions. In terms of the underlying random variables, this implies the introduction of lithological noise with two equiprobable sets of input data in the simulation. Subsequently, the concepts of entropy and joint entropy are applied for uncertainty quantification of the main outputs of the D_i models method, i.e., the partial percentile lithological models and the Most Uniform Lithological Model. A simulation experiment consisting of seven model setups was conducted to test the ability of the uncertainty measures with various underlying random function models and to evaluate the impacts of incorporating uncertainties from imprecise input data. The results show that the incorporation of the uncertainties in the input data into the geostatistical framework of the D_i models method overcomes potential bias caused by ignoring the inaccuracies in the input data, thus providing a more realistic assessment of uncertainty. Moreover, the uncertainty measures provide very useful scalar measures for quantifying uncertainties in the grain size distributions, comparing between average uncertainties and for better understanding how the implementation parameters of the geo-modelling process influence the property forecast and the underlying uncertainties. The proposed uncertainty measures can be used to support practical decisions made based on the implementation of the D_i models method.