Abstract. Ground-penetrating radar (GPR) is widely used for determining mountain glacier thickness. However, this method provides thickness data only along the acquisition lines, and therefore interpolation has to be made between them. Depending on the interpolation strategy, calculated ice volumes can differ and can lack an accurate error estimation. Furthermore, glacial basal topography is often characterized by complex geomorphological features, which can be hard to reproduce using classical interpolation methods, especially when the field data are sparse or when the morphological features are too complex. This study investigates the applicability of multiple-point statistics (MPS) simulations to interpolate glacier bedrock topography using GPR measurements. In 2018, a dense GPR data set was acquired on the Tsanfleuron Glacier (Switzerland). These data were used as the source for a bedrock interpolation. The results obtained with the direct-sampling MPS method are compared against those obtained with kriging and sequential Gaussian simulations (SGSs) on both a synthetic data set – with known reference volume and bedrock topography – and the real data underlying the Tsanfleuron Glacier. Using the MPS modeled bedrock, the ice volume for the Scex Rouge and Tsanfleuron glaciers is estimated to be 113.9 ± 1.6 million cubic meters. The direct-sampling approach, unlike the SGS and kriging, allowed not only an accurate volume estimation but also the generation of a set of realistic bedrock simulations. The complex karstic geomorphological features are reproduced and can be used to significantly improve for example the precision of subglacial flow estimation.

Abstract. This study presents a novel workflow to model the internal heterogeneity of complex aquifers using the multiple-point statistics algorithm DeeSse. We illustrate the applicability of this workflow on the Roussillon's aquifer in the region of Perpignan (southern France). This work is part of a project aiming at assessing the groundwater dynamics of this Mediterranean aquifer in the context of a growing population, climate change, and increasing pressure on the freshwater resources. We focus here on the geological heterogeneity of the Continental Pliocene layer because it is expected to influence possible saltwater intrusion process and its corresponding uncertainty quantification. The main aim of the paper is therefore to describe the procedure that is used to model the aquifer heterogeneity with a relatively small number of direct geological observations and a well defined geological concept. When few direct observations are available, the traditional geostatistical approaches cannot be applied easily because variogram inference is difficult. On the opposite, multiple-point statistics simulations can rely on a conceptual geological model. Here, the conceptual model consists not only of a training image displaying the spatial organization of the main sedimentological elements in space, but also in a set of additional information such as general trends and paleo orientations of the sedimentological features. The direct sampling algorithm DeeSse can be used in this context to model the expected heterogeneity. The workflow involves creating 2D non-stationary training images (TI) coupled during simulation with auxiliary information and controlled by hard conditioning data obtained from interpreted electrofacies. To control the non-stationarity, a 3D trend map is obtained by solving numerically the diffusivity equation as a proxy to describe the spatial evolution of the sedimentary patterns, from the source of the sediments to the outlet of the system. A 3D continuous rotation map is estimated from paleo orientations of the fluvial system. Both trend and orientation maps are derived from geological insights gathered from outcrops and general knowledge of processes occurring in these types of sedimentary environments. Finally, the 3D model is obtained by stacking 2D simulations following the paleo-topography of the aquifer. The vertical facies transition between two 2D simulations is controlled by both the hard conditioning data set and by simulating conditional data points from one simulation to another. This process allows to bypass the creation of a 3D training image while preserving the vertical continuity of the sedimentary objects.

Abstract. This study introduces a novel workflow to model the heterogeneity of complex aquifers using the multiple-point statistics algorithm DeeSse. We illustrate the approach by modeling the Continental Pliocene layer of the Roussillon aquifer in the region of Perpignan (southern France). When few direct observations are available, statistical inference from field data is difficult if not impossible and traditional geostatistical approaches cannot be applied directly. By contrast, multiple-point statistics simulations can rely on one or several alternative conceptual geological models provided using training images (TIs). But since the spatial arrangement of geological structures is often non-stationary and complex, there is a need for methods that allow to describe and account for the non-stationarity in a simple but efficient manner. The main aim of this paper is therefore to propose a workflow, based on the direct sampling algorithm DeeSse, for these situations. The conceptual model is provided by the geologist as a 2D non-stationary training image in map view displaying the possible organization of the geological structures and their spatial evolution. To control the non-stationarity, a 3D trend map is obtained by solving numerically the diffusivity equation as a proxy to describe the spatial evolution of the sedimentary patterns, from the sources of the sediments to the outlet of the system. A 3D continuous rotation map is estimated from inferred paleo-orientations of the fluvial system. Both trend and orientation maps are derived from geological insights gathered from outcrops and general knowledge of processes occurring in these types of sedimentary environments. Finally, the 3D model is obtained by stacking 2D simulations following the paleo-topography of the aquifer. The vertical facies transition between successive 2D simulations is controlled partly by the borehole data used for conditioning and by a sampling strategy. This strategy accounts for vertical probability of transitions, which are derived from the borehole observations, and works by simulating a set of conditional data points from one layer to the next. This process allows us to bypass the creation of a 3D training image, which may be cumbersome, while honoring the observed vertical continuity.

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Abstract. Ground Penetrating Radar (GPR) is nowadays widely used for determining glacier thickness. However, this method provides thickness data only along the acquisition lines and therefore interpolation has to be made between them. Depending on the interpolation strategy, calculated ice volumes can differ and can lack an accurate error estimation. Furthermore, glacial basal topography is often characterized by complex geomorphological features, which can be hard to reproduce using classical interpolation methods, especially when the conditioning data are sparse or when the morphological features are too complex. This study investigates the applicability of multiple-point statistics (MPS) simulations to interpolate glacier bedrock topography using GPR measurements. In 2018, a dense GPR data set was acquired on the Tsanfleuron Glacier (Switzerland). The results obtained with the direct sampling MPS method are compared against those obtained with kriging and sequential Gaussian simulations (SGS) on both a synthetic data set – with known reference volume and bedrock topography – and the real data underlying the Tsanfleuron glacier. Using the MPS modelled bedrock, the ice volume for the Scex Rouge and Tsanfleuron Glacier is estimated to be 113.9 ± 1.6 Mio m3. The direct sampling approach, unlike the SGS and the kriging, allowed not only an accurate volume estimation but also the generation of a set of realistic bedrock simulations. The complex karstic geomorphological features are reproduced, and can be used to significantly improve for example the precision of under-glacial flow estimation.