The Di models method: geological 3-D modeling of detrital systems consisting of varying grain fractions to predict the relative lithological variability for a multipurpose usability

The coexistence of a wide variety of subsurface uses in urban areas requires increasingly demanding geological prediction capacities for characterizing the geological heterogeneities at a small-scale. In particular, detrital systems are characterized by the presence of highly varying sediment mixtures which control the non-constant spatial distribution of properties, therefore presenting a crucial aspect for understanding the small-scale spatial variability of physical properties. The proposed methodology uses the lithological descriptions from drilled boreholes and implements sequential indicator simulation to simulate the cumulative frequencies of each lithological class in the whole sediment mixture. The resulting distributions are expressed by a set of voxel models, referred to as Di models. This solution is able to predict the relative amounts of each grain fraction on a cell-by-cell basis and therefore also derive a virtual grain size distribution. Its implementation allows the modeler to flexibly choose both the grain fractions to be modeled and the precision in the relative quantification. The concept of information entropy is adapted as a measure of the disorder state of the clasts mixture, resulting in the concept of “Model Lithological Uniformity,” proposed as a measure of the degree of detrital homogeneity. Moreover, the “Most Uniform Lithological Model” is presented as a distribution of the most prevailing lithologies. This method was tested in the city of Munich (Germany) using a dataset of over 20,000 boreholes, providing a significant step forward in capturing the spatial heterogeneity of detrital systems and addressing model scenarios for applications requiring variable relative amounts of grain fractions.Bayerisches Staatsministerium für Umwelt und Verbraucherschutz http://dx.doi.org/10.13039/501100010219Technische Universität München (1025

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 Di 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 Di 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 Di models method

The Di models method: geological 3-D modeling of detrital systems consisting of varying grain fractions to predict the relative lithological variability for a multipurpose usability

<jats:title>Abstract</jats:title><jats:p>The coexistence of a wide variety of subsurface uses in urban areas requires increasingly demanding geological prediction capacities for characterizing the geological heterogeneities at a small-scale. In particular, detrital systems are characterized by the presence of highly varying sediment mixtures which control the non-constant spatial distribution of properties, therefore presenting a crucial aspect for understanding the small-scale spatial variability of physical properties. The proposed methodology uses the lithological descriptions from drilled boreholes and implements sequential indicator simulation to simulate the cumulative frequencies of each lithological class in the whole sediment mixture. The resulting distributions are expressed by a set of voxel models, referred to as <jats:italic>D</jats:italic><jats:sub><jats:italic>i</jats:italic></jats:sub> models. This solution is able to predict the relative amounts of each grain fraction on a cell-by-cell basis and therefore also derive a virtual grain size distribution. Its implementation allows the modeler to flexibly choose both the grain fractions to be modeled and the precision in the relative quantification. The concept of information entropy is adapted as a measure of the disorder state of the clasts mixture, resulting in the concept of “Model Lithological Uniformity,” proposed as a measure of the degree of detrital homogeneity. Moreover, the “Most Uniform Lithological Model” is presented as a distribution of the most prevailing lithologies. This method was tested in the city of Munich (Germany) using a dataset of over 20,000 boreholes, providing a significant step forward in capturing the spatial heterogeneity of detrital systems and addressing model scenarios for applications requiring variable relative amounts of grain fractions.</jats:p&gt