Uncertainties in 3-D stochastic geological modeling of fictive grain size distributions in detrital systems

Geological 3-D models are very useful tools to predict subsurface properties. However, they are always subject to uncertainties, starting from the primary data. To ensure the reliability of the model outputs and, thus, to support the decision-making process, the incorporation and quantification of uncertainties have to be integrated into the geo-modeling strategies. Among all modeling approaches, the novel D_i models method was conceived as a stochastic approach to make predictions of the 3-D lithological composition of detrital systems, based on estimating the fictive grain size distribution of the sediment mixture by using soil observations from drilled materials. Within the present study, we aim to adapt the geo-modeling framework of this method in order to incorporate uncertainties linked to systematic imprecisions in the soil observations used as input data. Following this, uncertainty quantification measures are proposed, based on entropy and joint entropy for the main outcomes of the method, i.e., the partial percentile lithological models, and for the whole sediment mixture. Both the ability of the uncertainty quantification measures and the uncertainty propagation derived from the extension of the method are investigated in the model outcomes in a simulation experiment with real data conducted in a small-scale domain located in Munich (Germany). The results show that this adaptation of the D_i models method overcomes potential bias caused by ignoring imprecise input data, thus providing a more realistic assessment of uncertainty. The uncertainty measures provide very useful insight for quantifying local uncertainties, comparing between average uncertainties and for better understanding how the implementation parameters of the geo-modeling process influence the property estimation and the underlying uncertainties. The main findings of the present study have great potential for providing robust uncertainty information about model outputs, which ultimately strengthens the decision-making process for practical applications based on the implementation of the D_i models method.