Non-uniqueness of inverse transmissivity field calibration and predictive transport modeling

Recent work with stochastic inverse modeling techniques has led to the development of efficient algorithms for the construction of transmissivity (T) fields conditioned to measurements of T and head. Small numbers of calibration targets and correlation between model parameters in these inverse solutions can lead to a relatively large region in parameter space that will produce a near optimal calibration of the T field to measured heads. Most applications of these inverse techniques have not considered the effects of non-unique calibration on subsequent predictions made with the T fields. Use of these T fields in predictive contaminant transport modeling must take into account the non-uniqueness of the T field calibration. A recently developed ‘predictive estimation’ technique is presented and employed to create T fields that are conditioned to observed heads and measured T values while maximizing the conservatism of the associated predicted advective travel time. Predictive estimation employs confidence and prediction intervals calculated simultaneously on the flow and transport models, respectively. In an example problem, the distribution of advective transport results created with the predictive estimation technique is compared to the distribution of results created under traditional T field optimization where model non-uniqueness is not considered. The predictive estimation technique produces results with significantly shorter travel times relative to traditional techniques while maintaining near optimal calibration. Additionally, predictive estimation produces more accurate estimates of the fastest travel times.     

Geostatistics applied to best-fit interpolation of orientation data

Automatic methods used in geosciences to interpolate between orientation data have often limited applicability and strength, in particular where large ranges of orientations occur. In this paper, we show that geostatistical methods yield rather strong and powerful results when applied to directional data. The procedure involves the calculation of variograms, followed by a kriging interpolation of the data. In order to free from the circular property of directional data, the treatment of initial angular data sets is performed using scalar values provided by the direction cosines of double-angle values. The strength and application of the method are demonstrated by the analysis of theoretical and natural data sets. Natural examples are focused on the calculation and the analysis of cleavage trajectory maps.     

Geostatistical study of the feldspar content and quality of a granite deposit

In order to characterise the saleable feldspar in a granite deposit, a methodology was developed in accordance with the exploitation process. This consisted of mechanically extracting the surface layer of the batholith and separating the feldspar from the quartz using the granulometric separation method, given that the size of the grains of the feldspar is greater than that of quartz.

Following washing, grinding and magnetic separation of the feldspar in order to eliminate the ferromagnesium minerals, the saleable feldspar was characterised in terms of the factors that determine its market value, namely, its content in Al₂O₃, SiO₂, Na₂O and K₂O.

Following the opening of prospecting pits in the granite massif, samples were analysed in the laboratory using three different granulometric cuts and by reproducing the treatment process. The values for the quality variables of saleable feldspar were obtained, and the results were interpolated to the entire deposit using the kriging method.

In order to summarise the information from the above-mentioned variables, a quality index was constructed using multivariate statistics and by employing market criteria, and subsequently, the values of the index were interpolated to the entire deposit using bidimensional kriging.

The map of saleable quality feldspar from the deposit permits both affirmation of the treatment process yield for each granulometric cut and the planning of extraction from the deposit to obtain a homogeneous quality in the saleable feldspar.     

Mapping groundwater quality in the Netherlands

Maps of 25 groundwater quality variables were obtained by estimating 4 km × 4 km block median concentrations. Estimates were presented as approximate 95% confidence intervals related to four concentration levels mostly obtained from critical levels for human consumption. These maps were based on measurements from 425 monitoring sites of national and provincial groundwater quality monitoring networks. The estimation procedure was based on a stratification by soil type and land use. Within each soil-land use category, measurements were interpolated. Spatial dependence between measurements and regional differences in mean level were taken into account. Stratification turned out to be essential: no or partial stratification (using either soil type or land use) results in essentially different maps. The effect of monitoring network density was studied by leaving out the 173 monitoring sites of the provincial monitoring networks. Important changes in resulting maps were assigned to loss of information on short-distance variation, as well as loss of location-specific information. For 12 variables, maps of changes in groundwater quality were made by spatial interpolation of short-term predictions calculated for each well screen from time series of yearly measurements over 5–7 years, using a simple regression model for variation over time and taking location-specific time-prediction uncertainties into account.

From a policy point of view, the resulting maps can be used either for quantifying diffuse groundwater contamination and location-specific background concentrations (in order to assist local contamination assessment) or for input and validation of policy supporting regional or national groundwater quality models. The maps can be considered as a translation of point information obtained from the monitoring networks into information on spatial units, the size of which is used in regional groundwater models. The maps enable location-specific network optimization. In general, the maps give little reason for reducing the monitoring network density (wide confidence intervals).     

Geophysical data integration,stochastic simulation and significance analysis of groundwater responses using ANOVA in the Chicot Aquifer system,Louisiana, USA

Data integration is challenging where there are different levels of support between primary and secondary data that need to be correlated in various ways. A geostatistical method is described, which integrates the hydraulic conductivity (K) measurements and electrical resistivity data to better estimate the K distribution in the Upper Chicot Aquifer of southwestern Louisiana, USA. The K measurements were obtained from pumping tests and represent the primary (hard) data. Borehole electrical resistivity data from electrical logs were regarded as the secondary (soft) data, and were used to infer K values through Archie’s law and the Kozeny-Carman equation. A pseudo cross-semivariogram was developed to cope with the resistivity data non-collocation. Uncertainties in the auto-semivariograms and pseudo cross-semivariogram were quantified. The groundwater flow model responses by the regionalized and coregionalized models of K were compared using analysis of variance (ANOVA). The results indicate that non-collocated secondary data may improve estimates of K and affect groundwater flow responses of practical interest, including specific capacity and drawdown.

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Résumé  L’intégration de données entre en jeu lorsque plusieurs niveaux intermédiaires d’assistance sont nécessaires pour corréler données primaires et secondaires de diverses manières. Le présent article décrit une méthode géostatistique qui intègre les mesures de conductivité hydraulique (K) et les données de résistivité électrique, afin d’estimer plus efficacement la distribution de K dans l’Aquifère Supérieur de Chicot, au sud-ouest de la Louisiane (Etats-Unis). Les mesures de K sont issues des pompages d’essai et représentent les données primaires (“dures”). Les données des diagraphies de résistivité électrique ont été considérées comme des données secondaires (“molles”), à partir desquelles les valeurs de K ont été déduites, par la loi d’Archie et l’équation de Kozeny-Carman. Un pseudo semi-variogramme croisé a été développé afin de pallier à l’absence de colocalisation des données de résistivité. Les incertitudes sur les semi-variogrammes automatiques et sur les pseudo semi-variogrammes croisés ont été quantifiées. Les réponses du modèle d’écoulement des eaux souterraines aux modèles régionalisés et co-régionalisés de K ont été comparés, par les analyses de variance (ANOVA). Les résultats montrent que les données secondaires non-colocalisées peuvent améliorer les estimations de K, et affecter efficacement les réponses des écoulements souterrains, y compris les débits spécifiques et les rabattements.

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Resumen  La integración de datos es un gran desafío cuando existen diferentes niveles de apoyo entre datos primarios y secundarios que es necesario correlacionar de varias maneras. Se describe un método geoestadístico el cual integra mediciones de conductividad hidráulica (K) y datos de resistividad eléctrica para tener una mejor estimación de la distribución de K en el Acuífero Chicot Superior del suroeste de Luisiana, Estados Unidos de América. Las mediciones de K se obtuvieron de pruebas de bombeo y representan los datos primarios (duros). Los datos de sondeos de resistividad eléctrica se consideraron como datos secundarios (suaves) y se usaron para inferir valores de K a través de la ley de Archie y la ecuación de Carman-Kozeny. Se desarrolló un pseudo semivariograma cruzado para enfrentar la falta de colocación de datos de resistividad. Se cuantificaron las incertidumbres en los auto-semivariogramas y en los semivariogramas cruzados. Las respuestas del modelo de flujo de agua subterránea por los modelos coregionalizados y regionalizados de K se compararon usando el análisis de varianza (ANOVA). Los resultados indican que los datos secundarios no colocados pueden mejorar los estimados de K y afectar las respuestas de flujo de agua subterránea de interés práctico, incluyendo capacidad específica y descenso.

     

Spatial variability of soil properties in relation to land use and topography in a typical small watershed of the black soil region,northeastern China

Soil degradation resulted from unreasonable land use and erosion has been a serious problem in the black soil region of northeastern China. This paper seeks to understand the relationships between topsoil properties and topography and land use for land management targeting at improving soil quality in this region. A total of 292 soil samples and 81 volumetric rings were taken from a typical small watershed of the region in June 2005 for examining total carbon (TC), total nitrogen (TN), soil texture (classified into gravel, sand, silt, and clay), and bulk density (ρ _b), respectively. Spatial variability of these soil properties was evaluated with classical statistics and geostatistics methods. The results of classical statistics indicated that TC, TN, sand, silt, clay content, and ρ _b were moderate variables while gravel had great variability. Soil properties were mainly correlated to slope position, elevation and land types. Geostatistical analyses showed that the spatial autocorrelation for TC, TN, and silt was weak, strong for clay and moderate for and ρ _b sand, respectively. The spatial variations of soil properties are affected comprehensively by topographic factors, land use, erosion, and erosion control in this watershed. Past erosion, however, is the most important component to induce change of soil properties. In this small watershed, current soil and water conservation measures play an important role in controlling soil loss. But the restoration of soil properties was unsatisfactory. Comparing with untilled soil of this region, TC, TN, silt content are excessively low; whereas ρ _b, sand and clay content are excessively high; gravel appears at most sampling locations. It is necessary for improving soil properties to protect forest and grassland and change cultivation system of farmlands.     

Spatial analysis and hazard assessment of mercury in soil around the coal-fired power plant: a case study from the city of Baoji, China

Based on systematic sampling of soil around the coal-fired power plant (CFPP), the content of Hg was determined, using atomic fluorescence spectrometry. The result shows that the content of Hg in soil is different horizontally and vertically, ranges from 0.137 to 2.105 mg/kg (the average value is 0.606 mg/kg) and is more than the average content of Hg in Shaanxi, Chinese and world soil. In this study, spatial distribution and hazard assessment of mercury in soils around a CFPP were investigated using statistics, geostatistics and geographic information system (GIS) techniques. Ordinary kriging was carried out to map the spatial patterns of mercury and disjunctive kriging was used to quantify the probability of the Hg concentration higher than the threshold. The maps show that the spatial variability of the Hg concentration in soils was apparent. These results of this study could provide valuable information for risk assessment of environmental Hg pollution and decision support. An erratum to this article can be found at     

Spatial variability of soil organic matter and nutrients in paddy fields at various scales in southeast China

The present study examines the spatial dependency of soil organic matter and nutrients in paddy fields at three different scales using geostatistics and geographic information system techniques (GIS). The spatial variability of soil organic matter (SOM), total nitrogen (TN) and available phosphorus (AP) has been characterized using a total of 460, 131 and 64 samples that were, respectively, collected from the Hangzhou–Jiaxing–Huzhou (HJH) Plain (10 km), Pinghu county (1,000 m) and a test plot area (100 m) within the Pinghu county, Zhejiang province of the southeast China. Semivariograms showed that the SOM and TN had moderate spatial dependency on the large scale of HJH plain and moderate scale of Pinghu county with long spatial correlation distances. At the moderate scale of Pinghu county and the small scale of a test plot area, the AP data did not show any spatial correlation, but had moderate spatial dependency in HJH plain. Spherical and exponential variogram models were best fitted to all these soil properties. Maps of SOM and TN were generated through interpolation of measured values by ordinary kriging, and AP by lognormal kriging. This study suggests that precision management of SOM and TN is feasible at all scales, and precision management of AP is feasible at large scales.     

A Modeling Approach for the Study of Contamination in a Fractured Aquifer

The study of contaminants propagation in fractured and karstic aquifers shows uncertainties caused by the conditions of anisotropy of the medium and by the presence of cavities and residual products that could make fluid flow and solute transport unforeseeable. Therefore, in aquifers characterized by fissured and fractured solid matrix, in order to set up remediation strategies, it is necessary to represent the conditions of groundwater flow and contaminant propagation in such a way as to take into consideration the high heterogeneity connected to the presence of fractures and channels that act as preferential flow ways. The study carried out in a specified site, located in the city of Bari, heavily contaminated by petroliferous substances allows to build a model able to simulate subterranean draining conditions that prove to be as near as possible to the real ones. This simulation could be helpful for the prevision of the dynamic behavior of the aquifer during the period of the treatment in order to allow optimizations on the technical and economical point of view and in order to check the effective functionality of the system in the presence of anthropic constraints.     

The practice of fast conditional simulations through the LU decomposition of the covariance matrix

The LU-matrix approach to conditional simulations allows fast generation of large numbers of realizations for a given stochastic process. Simplicity, flexibility, and quality are its main advantages. Its implementation for cases where dense grids and/or large numbers of conditioning data cause computational problems is discussed. A case study is presented.