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Forecasting the flow of groundwater requires a hydrostratigraphic model, which describes the architecture of the subsurface. State-of-the-art multiple-point statistical (MPS) tools are readily available for creating models depicting subsurface geology. We present a study of the impact of key parameters related to stochastic MPS simulation of a real-world hydrogeophysical dataset from Kasted, Denmark, using the snesim algorithm. The goal is to study how changes to the underlying datasets propagate into the hydrostratigraphic realizations when using MPS for stochastic modeling. This study focuses on the sensitivity of the MPS realizations to the geophysical soft data, borehole lithology logs, and the training image (TI). The modeling approach used in this paper utilizes a cognitive geological model as a TI to simulate ensemble hydrostratigraphic models. The target model contains three overall hydrostratigraphic categories, and the MPS realizations are compared visually as well as quantitatively using mathematical measures of similarity. The quantitative similarity analysis is carried out exhaustively, and realizations are compared with each other as well as with the cognitive geological model.The results underline the importance of geophysical data for constraining MPS simulations. Relying only on borehole data and the conceptual geology, or TI, results in a significant increase in realization uncertainty. The airborne transient electromagnetic SkyTEM data used in this study cover a large portion of the Kasted model area and are essential to the hydrostratigraphic architecture. On the other hand, the borehole lithology logs are sparser, and 410 boreholes were present in this study. The borehole lithology logs infer local changes in the immediate vicinity of the boreholes, thus, in areas with a high degree of geological heterogeneity, boreholes only provide limited large-scale structural information. Lithological information is, however, important for the interpretation of the geophysical responses. The importance of the TI was also studied. An example was presented where an alternative geological model from a neighboring area was used to simulate hydrostratigraphic models. It was shown that as long as the geological settings are similar in nature, the realizations, although different, still reflect the hydrostratigraphic architecture. If a TI containing a biased geological conceptualization is used, the resulting realizations will resemble the TI and contain less structure in particular areas, where the soft data show almost even probability to two or all three of the hydrostratigraphic units.

Most studies on the application of geostatistical simulations based on multiple-point statistics (MPS) to hydrogeological modelling focus on relatively fine-scale models and concentrate on the estimation of facies-level structural uncertainty. Much less attention is paid to the use of input data and optimal construction of training images. For instance, even though the training image should capture a set of spatial geological characteristics to guide the simulations, the majority of the research still relies on 2-D or quasi-3-D training images. In the present study, we demonstrate a novel strategy for 3-D MPS modelling characterized by (i) realistic 3-D training images and (ii) an effective workflow for incorporating a diverse group of geological and geophysical data sets. The study covers an area of 2810 km2 in the southern part of Denmark. MPS simulations are performed on a subset of the geological succession (the lower to middle Miocene sediments) which is characterized by relatively uniform structures and dominated by sand and clay. The simulated domain is large and each of the geostatistical realizations contains approximately 45 million voxels with size 100 m × 100 m × 5 m. Data used for the modelling include water well logs, high-resolution seismic data, and a previously published 3-D geological model. We apply a series of different strategies for the simulations based on data quality, and develop a novel method to effectively create observed spatial trends. The training image is constructed as a relatively small 3-D voxel model covering an area of 90 km2. We use an iterative training image development strategy and find that even slight modifications in the training image create significant changes in simulations. Thus, this study shows how to include both the geological environment and the type and quality of input information in order to achieve optimal results from MPS modelling. We present a practical workflow to build the training image and effectively handle different types of input information to perform large-scale geostatistical modelling.

We present an automatic method for parameterization of a 3-D model of the subsurface, integrating lithological information from boreholes with resistivity models through an inverse optimization, with the objective of further detailing of geological models, or as direct input into groundwater models. The parameter of interest is the clay fraction, expressed as the relative length of clay units in a depth interval. The clay fraction is obtained from lithological logs and the clay fraction from the resistivity is obtained by establishing a simple petrophysical relationship, a translator function, between resistivity and the clay fraction. Through inversion we use the lithological data and the resistivity data to determine the optimum spatially distributed translator function. Applying the translator function we get a 3-D clay fraction model, which holds information from the resistivity data set and the borehole data set in one variable. Finally, we use k-means clustering to generate a 3-D model of the subsurface structures. We apply the procedure to the Norsminde survey in Denmark, integrating approximately 700 boreholes and more than 100 000 resistivity models from an airborne survey in the parameterization of the 3-D model covering 156 km2. The final five-cluster 3-D model differentiates between clay materials and different high-resistivity materials from information held in the resistivity model and borehole observations, respectively.

Multiple-point geostatistical simulation (MPS) has recently become popular in stochastic hydrogeology, primarily because of its capability to derive multivariate distributions from a training image (TI). However, its application in three-dimensional (3-D) simulations has been constrained by the difficulty of constructing a 3-D TI. The object-based unconditional simulation program TiGenerator may be a useful tool in this regard; yet the applicability of such parametric training images has not been documented in detail. Another issue in MPS is the integration of multiple geophysical data. The proper way to retrieve and incorporate information from high-resolution geophysical data is still under discussion. In this study, MPS simulation was applied to different scenarios regarding the TI and soft conditioning. By comparing their output from simulations of groundwater flow and probabilistic capture zone, TI from both sources (directly converted from high-resolution geophysical data and generated by TiGenerator) yields comparable results, even for the probabilistic capture zones, which are highly sensitive to the geological architecture. This study also suggests that soft conditioning in MPS is a convenient and efficient way of integrating secondary data such as 3-D airborne electromagnetic data (SkyTEM), but over-conditioning has to be avoided.

Uncertainty of groundwater model predictions has in the past mostly been related to uncertainty in the hydraulic parameters, whereas uncertainty in the geological structure has not been considered to the same extent. Recent developments in theoretical methods for quantifying geological uncertainty have made it possible to consider this factor in groundwater modeling. In this study we have applied the multiple-point geostatistical method (MPS) integrated in the Stanford Geostatistical Modeling Software (SGeMS) for exploring the impact of geological uncertainty on groundwater flow patterns for a site in Denmark. Realizations from the geostatistical model were used as input to a groundwater model developed from Modular three-dimensional finite-difference ground-water model (MODFLOW) within the Groundwater Modeling System (GMS) modeling environment. The uncertainty analysis was carried out in three scenarios involving simulation of groundwater head distribution and travel time. The first scenario implied 100 stochastic geological models all assigning the same hydraulic parameters for the same geological units. In the second scenario the same 100 geological models were subjected to model optimization, where the hydraulic parameters for each of them were estimated by calibration against observations of hydraulic head and stream discharge. In the third scenario each geological model was run with 216 randomized sets of parameters. The analysis documented that the uncertainty on the conceptual geological model was as significant as the uncertainty related to the embedded hydraulic parameters.

Geophysical techniques are increasingly being used as tools for characterising the subsurface, and they are generally required to develop subsurface models that properly delineate the distribution of aquifers and aquitards, salt/freshwater interfaces, and geological structures that affect groundwater flow. In a study area covering 730 km2 across the border between Germany and Denmark, a combination of an airborne electromagnetic survey (performed with the SkyTEM system), a high-resolution seismic survey and borehole logging has been used in an integrated mapping of important geological, physical and chemical features of the subsurface. The spacing between flight lines is 200–250 m which gives a total of about 3200 line km. About 38 km of seismic lines have been collected. Faults bordering a graben structure, buried tunnel valleys, glaciotectonic thrust complexes, marine clay units, and sand aquifers are all examples of geological structures mapped by the geophysical data that control groundwater flow and to some extent hydrochemistry. Additionally, the data provide an excellent picture of the salinity distribution in the area and thus provide important information on the salt/freshwater boundary and the chemical status of groundwater. Although the westernmost part of the study area along the North Sea coast is saturated with saline water and the TEM data therefore are strongly influenced by the increased electrical conductivity there, buried valleys and other geological elements are still revealed. The mapped salinity distribution indicates preferential flow paths through and along specific geological structures within the area. The effects of a future sea level rise on the groundwater system and groundwater chemistry are discussed with special emphasis on the importance of knowing the existence, distribution and geometry of the mapped geological elements, and their control on the groundwater salinity distribution is assessed.