Extrapolating the Fractal Characteristics of an Image Using Scale-Invariant Multiple-Point Statistics

The resolution of measurement devices can be insufficient for certain purposes. We propose to stochastically simulate spatial features at scales smaller than the measurement resolution. This is accomplished using multiple-point geostatistical simulation (direct sampling in the present case) to interpolate values at the target scale. These structures are inferred using hypothesis of scale invariance and stationarity on the spatial patterns found at the coarse scale. The proposed multiple-point super-resolution mapping method is able to deal with “both continuous and categorical variables,” and can be extended to multivariate problems. The advantages and limitations of the approach are illustrated with examples from satellite imaging.     

Influence of time, temperature, confining pressure and fluid content on the experimental compaction of spherical grains

Theoretical models of compaction processes, such as for example intergranular pressure-solution (IPS), focus on deformation occurring at the contacts between spherical grains that constitute an aggregate. In order to investigate the applicability of such models, and to quantify the deformation of particles within an aggregate, isostatic experiments were performed in cold-sealed vessels on glass sphere aggregates at 200 MPa confining pressure and 350 °C with varying amounts of fluid. Several runs were performed in order to investigate the effects of time, fluid content, pressure and temperature, by varying one of these parameters and holding the others fixed. In order to compare the aggregates with natural materials, similar experiments were also performed using quartz sand instead of glass spheres. Experiments with quartz show evidence of IPS, but the strain could not be quantified. Experiments with glass spheres show evidence of several types of deformation processes: both brittle (fracturing) and ductile (plastic flow and fluid-enhanced deformation, such as IPS). In experiments with a large amount of water (≥ 5 vol.%), dissolution and recrystallization of the glass spheres also occurred, coupled with crystallization of new material filling the initial porosity. Experiments performed with a fluid content of less than 1 vol.% indicate creep behavior that is typical of glass deformation, following an exponential law. These experiments can also be made to fit a power law for creep, with a stress exponent of n = 10.5 ± 2.2 in both dry and wet experiments. However, the pre-factor of the power law creep increases 5 times with the addition of water, showing the strong effect of water on the deformation rate. These simple and low-cost experiments provide new insights on the rheology of soda-lime glass, which is used in analogue experiments, and of glass-bearing rocks under mid-crustal P–T conditions. They also highlight the strong enhancement of plasticity of natural rocks in presence of fluid or of a glassy phase.     

Hydraulic testing of low-permeability formations: A case study in the granite of Cadalso de los Vidrios, Spain

In recent years, the study of low-permeability geological formations has undergone considerable development. This is mainly due to the use of natural geological barriers to confine waste disposals, preventing leaking water from bringing contaminants into contact with the biosphere and the groundwater resources.In that context, the Spanish Geological Survey (IGME, Spanish acronym), supported by the National Radioactive Waste Management Agency (ENRESA, Spanish acronym) and with the technical advice of the Swedish Nuclear Fuel and Waste Management Company (SKB) designed and built a Mobile Hydrogeological Unit (UMH, Spanish acronym) for low-permeability formations characterization, which has been operational since 1997 and has been used for different purposes. Among other possibilities, the UMH allows conducting: constant transient-state flow-rate injection tests, constant-head transient-state injection tests, pseudo-stationary state injection tests, pressure fall-off tests, slug tests and pulse tests.The main objectives of this article are to describe the hydraulic characterization methodology used by IGME to carry out hydraulic tests in low permeability environment, to compare different testing methods and to summarize the results that have been obtained when characterizing the leucogranites of Cadalso de los Vidrios in Spain.The study area presents an increasing interest for granite production inside the Community of Madrid. The petrological and structural characteristics of the granite rocks and the core-samples extracted from a 200 m deep borehole investigation are described. The packer tests are conducted with the Mobile Hydrogeological Unit.The tests are interpreted with the help of analytical solutions. The main software used is Hytool, an open source matlab toolbox that provides a library of analytical solutions and a set of routines to facilitate hydraulic tests interpretation.The results allow the elaboration of a comparative analysis of the applied hydraulic tests and to define the hydraulic conductivity optimum application interval most suited for each of the used methods.Hydraulic conductivity values obtained varies from 3.20·10^− 7 m/s, for the upper weathered layer, to 2.80·10^− 12 m/s, for the test section from 97.36 to 116.15 m depth.Finally, the hydraulic conductivity values obtained in this area are compared with other case studies of granite formations around the world.     

Reconstruction of Incomplete Data Sets or Images Using Direct Sampling

With increasingly sophisticated acquisition methods, the amount of data available for mapping physical parameters in the geosciences is becoming enormous. If the density of measurements is sufficient, significant non-parametric spatial statistics can be derived from the data. In this context, we propose to use and adapt the Direct Sampling multiple-points simulation method (DS) for the reconstruction of partially informed images. The advantage of the proposed method is that it can accommodate any data disposition and that it can indifferently deal with continuous and categorical variables. The spatial patterns found in the data are mimicked without model inference. Therefore, very few assumptions are required to define the spatial structure of the reconstructed fields, and very limited parameterization is needed to make the proposed approach extremely simple from a user perspective. The different examples shown in this paper give appealing results for the reconstruction of complex 3D geometries from relatively small data sets.     

Random partitioning and adaptive filters for multiple-point stochastic simulation

Multiple-point geostatistical simulation is used to simulate the spatial structures of geological phenomena. In contrast to conventional two-point variogram based geostatistical methods, the multiple-point approach is capable of simulating complex spatial patterns, shapes, and structures normally observed in geological media. A commonly used pattern based multiple-point geostatistical simulation algorithms is called FILTERSIM. In the conventional FILTERSIM algorithm, the patterns identified in training images are transformed into filter score space using fixed filters that are neither dependent on the training images nor on the characteristics of the patterns extracted from them. In this paper, we introduce two new methods, one for geostatistical simulation and another for conditioning the results. At first, new filters are designed using principal component analysis in such a way to include most structural information specific to the governing training images resulting in the selection of closer patterns in the filter score space. We then propose to combine adaptive filters with an overlap strategy along a raster path and an efficient conditioning method to develop an algorithm for reservoir simulation with high accuracy and continuity. We also combine image quilting with this algorithm to improve connectivity a lot. The proposed method, which we call random partitioning with adaptive filters simulation method, can be used both for continuous and discrete variables. The results of the proposed method show a significant improvement in recovering the expected shapes and structural continuity in the final simulated realizations as compared to those of conventional FILTERSIM algorithm and the algorithm is more than ten times faster than FILTERSIM because of using raster path and using small overlap specially when we use image quilting.     

Environmental isotopes as indicators for ground water recharge to fractured granite

To assess the contribution of accumulated winter precipitation and glacial meltwater to the recharge of deep ground water flow systems in fracture crystalline rocks, measurements of environmental isotope ratios, hydrochemical composition, and in situ parameters of ground water were performed in a deep tunnel. The measurements demonstrate the significance of these ground water recharge components for deep ground water flow systems in fractured granites of a high alpine catchment in the Central Alps, Switzerland. Hydrochemical and in situ parameters, as well as delta(18)O in ground water samples collected in the tunnel, show only small temporal variations. The precipitation record of delta(18)O shows seasonal variations of approximately 14% and a decrease of 0.23% +/- 0.03% per 100 m elevation gain. delta(2)H and delta(18)O in precipitation are well correlated and plot close to the meteoric water line, as well as delta(2)H and delta(18)O in ground water samples, reflecting the meteoric origin of the latter. The depletion of 18O in ground water compared to 18O content in precipitation during the ground water recharge period indicates significant contributions from accumulated depleted winter precipitation to ground water recharge. The hydrochemical composition of the encountered ground water, Na-Ca-HCO3-SO4(-F), reflects an evolution of the ground water along the flowpath through the granite body. Observed tritium concentrations in ground water range from 2.6 to 16.6 TU, with the lowest values associated with a local negative temperature anomaly and anomalous depleted 18O in ground water. This demonstrates the effect of local ground water recharge from meltwater of submodern glacial ice. Such localized recharge from glaciated areas occurs along preferential flowpaths within the granite body that are mainly controlled by observed hydraulic active shear fractures and cataclastic faults.     

Modeling Fine‐Scale Geological Heterogeneity—Examples of Sand Lenses in Tills

Sand lenses at various spatial scales are recognized to add heterogeneity to glacial sediments. They have high hydraulic conductivities relative to the surrounding till matrix and may affect the advective transport of water and contaminants in clayey till settings. Sand lenses were investigated on till outcrops producing binary images of geological cross‐sections capturing the size, shape and distribution of individual features. Sand lenses occur as elongated, anisotropic geobodies that vary in size and extent. Besides, sand lenses show strong non‐stationary patterns on section images that hamper subsequent simulation. Transition probability (TP) and multiple‐point statistics (MPS) were employed to simulate sand lens heterogeneity. We used one cross‐section to parameterize the spatial correlation and a second, parallel section as a reference: it allowed testing the quality of the simulations as a function of the amount of conditioning data under realistic conditions. The performance of the simulations was evaluated on the faithful reproduction of the specific geological structure caused by sand lenses. Multiple‐point statistics offer a better reproduction of sand lens geometry. However, two‐dimensional training images acquired by outcrop mapping are of limited use to generate three‐dimensional realizations with MPS. One can use a technique that consists in splitting the 3D domain into a set of slices in various directions that are sequentially simulated and reassembled into a 3D block. The identification of flow paths through a network of elongated sand lenses and the impact on the equivalent permeability in tills are essential to perform solute transport modeling in the low‐permeability sediments.