Groundwater contaminant source identification based on QS-ILUES

When groundwater pollution occurs,to come up with an efficient remediation plan,it is particularly important to collect information of contaminant source(location and source strength)and hydraulic conductivity field of the site accurately and quickly.However,the information can not be obtained by direct observation,and can only be derived from limited measurement data.Data assimilation of observations such as head and concentration is often used to estimate parameters of contaminant source.As for hydraulic conductivity field,especially for complex non-Gaussian field,it can be directly estimated by geostatistics method based on limited hard data,while the accuracy is often not high.Better estimation of hydraulic conductivity can be achieved by solving inverse groundwater problem.Therefore,in this study,the multi-point geostatistics method Quick Sampling(QS)is proposed and introduced for the first time and combined with the iterative local updating ensemble smoother(ILUES)to develop a new data assimilation framework QS-ILUES.It helps to solve the contaminant source parameters and non-Gaussian hydraulic conductivity field simultaneously by assimilating hydraulic head and pollutant concentration data.While the pilot points are utilized to reduce the dimension of hydraulic conductivity field,the influence of pilot points’layout and the ensemble size of ILUES algorithm on the inverse simulation results are further explored.     

Spatial distribution of heavy metals in soils: a case study of Changxing,China

Six hundred and sixty-five soil samples were taken from Changxing County in Zhejiang Province, China, to characterize the spatial variability of Hg Cd, Pb, Cu, As and Cr. The geostatistics and geographic information system (GIS) techniques were applied, and the ordinary kriging and lognormal kriging were used to map the spatial patterns of the six heavy metals. Hg, Pb, Cu and As were fitted to the spherical model with a range of 85.75, 82.32, 86.10, and 23.17 km, respectively. Cr was fitted to the exponential model with a range of 6.27 km, and Cd was fitted to the linear model with a range of 37.66 km. Both Pb and Cu had strong spatial dependence due to the effects of natural factors including parent material, topography and soil type. Hg, Cd, Cr and As had, however, moderate spatial dependence, indicating an involvement of human factors. Meanwhile, based on the comparison between the original data and the guide values of the six metals, the disjunctive kriging technique was used to quantify their pollution risks. The results showed that only Cd and Hg exhibited pollution risks in the study area. The pollution source evaluated was closely corresponded with the real discharge of industrial production and the application of organomercury pesticides. The results of this study provide insight into risk assessment of environmental pollution and decision making for agricultural production and industrial adjustment of building materials.     

A Distance-based Prior Model Parameterization for Constraining Solutions of Spatial Inverse Problems

Spatial inverse problems in the Earth Sciences are often ill-posed, requiring the specification of a prior model to constrain the nature of the inverse solutions. Otherwise, inverted model realizations lack geological realism. In spatial modeling, such prior model determines the spatial variability of the inverse solution, for example as constrained by a variogram, a Boolean model, or a training image-based model. In many cases, particularly in subsurface modeling, one lacks the amount of data to fully determine the nature of the spatial variability. For example, many different training images could be proposed for a given study area. Such alternative training images or scenarios relate to the different possible geological concepts each exhibiting a distinctive geological architecture. Many inverse methods rely on priors that represent a single subjectively chosen geological concept (a single variogram within a multi-Gaussian model or a single training image). This paper proposes a novel and practical parameterization of the prior model allowing several discrete choices of geological architectures within the prior. This method does not attempt to parameterize the possibly complex architectures by a set of model parameters. Instead, a large set of prior model realizations is provided in advance, by means of Monte Carlo simulation, where the training image is randomized. The parameterization is achieved by defining a metric space which accommodates this large set of model realizations. This metric space is equipped with a “similarity distance” function or a distance function that measures the similarity of geometry between any two model realizations relevant to the problem at hand. Through examples, inverse solutions can be efficiently found in this metric space using a simple stochastic search method.     

Conditional simulation of intrinsic random functions of order k

Conditional simulation of intrinsic random functions of orderk is a stochastic method that generates realizations which mimic the spatial fluctuation of nonstationary phenomena, reproduce their generalized covariance and honor the available data at sampled locations. The technique proposed here requires the following steps: (i) on-line simulation of Wiener-Levy processes and of their integrations; (ii) use of the turning-bands method to generate realizations in Rⁿ; (iii) conditioning to available data; and (iv) verification of the reproduced generalized covariance using generalized variograms. The applicational aspects of the technique are demonstrated in two and three dimensions. Examples include the conditional simulation of geological variates of the Crystal Viking petroleum reservoir, Alberta, Canada.     

Mapping optimization based on sampling size in earth related and environmental phenomena

A critical sampling grid can be defined for an earth related natural variable distributed in space, according to established theoretical results and under certain mathematical conditions. Sampling above this critical limit does not substantially improve mapping results, while based on this limit the ideal process of reproducing the original phenomenon is theoretically defined. The aim of the present paper is, by using an innovative approach; to investigate the validity of commonly used interpolation algorithms, both stochastic and deterministic, below and above this critical sampling limit. When sampling is dense, application to a simulated spatial random field shows that the results are equally accurate with those derived with more sophisticated stochastic methods. On the other hand, when the sampling grid is sparse, deterministic methods produce less accurate results, therefore stochastic algorithms with minimum estimation error are a much better option. To further demonstrate these points, the interpolation algorithms were applied in three different sampling grid densities in a contaminated waste disposal site in Russia.     

Image fusion by spatially adaptive filtering using downscaling cokriging

The aim of this paper was to extend the method of downscaling cokriging for image fusion by making the method spatially adaptive in that the filter parameters (cokriging weights) can change across the image. The method can adapt itself to the usual statistical non-homogeneity (spatially variable mean, variance and correlation length) of a satellite sensor image that covers an area with different spatial patterns of geographical objects or different terrain types. The solution adopted was to estimate the models of covariances and cross-covariances (or semivariograms and cross-semivariograms) by the same procedure as described in Pardo-Iguzquiza et al. (2006) but with the method applied locally instead of globally. The correct implementation of this local estimation is the key for computational feasibility and prediction efficiency. Two parameters to be taken into account are the grid of locations on which a moving window is centred (local modelling is performed inside this window) and the size of this moving window. With respect to the latter parameter, there is a trade-off between a size small enough to make the procedure locally adaptive and large enough to produce reliable statistical estimates. The computational burden will impose limits to the distance between grid points on which the local moving window is centred. A case study with Landsat ETM+ images was used to show the implementation of the method and the result was evaluated using several statistics widely used for assessing the quality of a fused image, apart from its visual appearance.     

Spatial prediction model and its application to chemistry of atmospheric precipitation in Jordan

This study is concerned with the spatial variability of some wet atmospheric precipitation parameters such as; pH, conductivity (EC). The study also depicts the spatial variability of some ions (cations and anions) of atmospheric precipitation in Jordan such as, Ca²⁺, Mg²⁺, Na⁺ and K⁺, HCO₃⁻, Cl⁻, NO₃⁻ and SO₄²⁻. The basis of the work is to establish a relationship through the cumulative semivariogram technique between the distance ratios and the spatial dependence structure of the chemical composition of atmospheric precipitation. All semivariogram models are constructed in this study in order to understand the behavior of the spatial distribution. The spatial distributions of rainwater parameters show differences from station to station which is expressed in terms of angle, where the larger the angle the weaker the correlation. The semivariogram (SV) models are constructed to show the variation of the rainfall chemistry in Jordan. The SV models show weak correlation between mountain and leeside mountain stations, i.e. mountain and desert stations. On the other hand, good correlations are observed when transferring from south to north of the country. The larger is the found angle, the weaker is the correlation. For most of the SV model the correlation is found to be very weak between desert and mountainous locality. The Standard Regional Dependence Factor (SRDF) is used for prediction of the distribution of rain fall parameters. It shows the relative error between observed and predicted values of rainwater parameters. The overall regional relative error between the observed and estimated concentrations remains less than 15%.     

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.     

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.