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Spatial distribution of cadmium and lead in the sediments of the western Anzali wetlands on the coast of the Caspian Sea (Iran)

Spatial distribution patterns of total cadmium (Cd) and lead (Pb), their bioavailable fractions and total organic matter in sediment from Anzali wetlands are provided. Total sediment Pb was higher than Cd (34.95 versus 0.024 μg/g dry weight). The geoaccumulation index indicated that the sediment was “uncontaminated”, but some stations were categorized as “unpolluted” to “moderately polluted”. Less than 0.01 of Pb existed in exchangeable and carbonate fractions. The sum of exchangeable and carbonate-bound fractions of Cd was 42%, suggesting that Cd poses high risk to the aquatic ecosystems. Total Cd and Pb exhibited positive relationships with total organic matter. Considering spatial distribution maps of total and bioavailable fractions of metals suggested that high concentrations of metals does not necessarily indicate high bioavailable fraction. The methodologies we used in this study can be in more effective management of aquatic ecosystems, as well as ecological risk assessment of metals, and remediation programs.     

Delineation of geological facies from poorly differentiated data

The ability to delineate geologic facies and to estimate their properties from sparse data is essential for modeling physical and biochemical processes occurring in the subsurface. If such data are poorly differentiated, this challenging task is complicated further by the absence of a clear distinction between different hydrofacies at locations where data are   available. We consider three alternative approaches for analysis of poorly differentiated data: a k$k$-means clustering algorithm, an expectation–maximization algorithm, and a minimum-variance algorithm. Two distinct synthetically generated geological settings are used to analyze the ability of these algorithms to assign accurately the membership of such data in a given geologic facies. On average, the minimum-variance algorithm provides a more robust performance than its two counterparts, and when combined with a nearest neighbor algorithm, it also yields the most accurate reconstruction of the boundaries between the facies.     

A non-parametric automatic blending methodology to estimate rainfall fields from rain gauge and radar data

Quantitative estimation of rainfall fields has been a crucial objective from early studies of the hydrological applications of weather radar. Previous studies have suggested that flow estimations are improved when radar and rain gauge data are combined to estimate input rainfall fields. This paper reports new research carried out in this field. Classical approaches for the selection and fitting of a theoretical correlogram (or semivariogram) model (needed to apply geostatistical estimators) are avoided in this study. Instead, a non-parametric technique based on FFT is used to obtain two-dimensional positive-definite correlograms directly from radar observations, dealing with both the natural anisotropy and the temporal variation of the spatial structure of the rainfall in the estimated fields. Because these correlation maps can be automatically obtained at each time step of a given rainfall event, this technique might easily be used in operational (real-time) applications. This paper describes the development of the non-parametric estimator exploiting the advantages of FFT for the automatic computation of correlograms and provides examples of its application on a case study using six rainfall events. This methodology is applied to three different alternatives to incorporate the radar information (as a secondary variable), and a comparison of performances is provided. In particular, their ability to reproduce in estimated rainfall fields (i) the rain gauge observations (in a cross-validation analysis) and (ii) the spatial patterns of radar fields are analyzed. Results seem to indicate that the methodology of kriging with external drift [KED], in combination with the technique of automatically computing 2-D spatial correlograms, provides merged rainfall fields with good agreement with rain gauges and with the most accurate approach to the spatial tendencies observed in the radar rainfall fields, when compared with other alternatives analyzed.     

The use of secondary information in geostatistical target area identification

The identification and characterization of target areas at former bombing ranges is the first step in investigating these sites for residual unexploded ordnance. Traditionally, magnetometer surveys along transects are used in identifying areas with high densities of magnetic anomalies, which are likely former target areas. Combining magnetometer survey data with other data sources may reduce the level of survey data required for site characterization, increasing characterization efficiency. Here, several techniques for incorporating secondary information into kriging estimates of magnetic anomaly density are investigated for a former bombing range located near Pueblo, Colorado. In particular, kriging with external drift, collocated ordinary cokriging, and simple kriging with local means (SKLM) are used to incorporate information from a secondary variable. The secondary variable consists of a grid of crater density values derived from a topographic light detection and ranging (LIDAR) analysis. The craters, which are clearly identifiable in the LIDAR data, were generated through munitions use at the site and are therefore related to the target locations. The results from this study indicate that the inclusion of the secondary information in the kriging estimates does benefit target area characterization and provides a means of elucidating target area details from only limited magnetometer transect data. For the Pueblo site, the use of SKLM with the crater density as a secondary variable and only limited magnetometer transect data, provided results comparable to those obtained from using much larger magnetometer transect data sets.     

Estimation of transit trip production using Factorial Kriging with External Drift: an aggregated data case study

Studies in transportation planning routinely use data in which location attributes are an important source of information. Thus, using spatial attributes in urban travel forecasting models seems reasonable. The main objective of this paper is to estimate transit trip production using Factorial Kriging with External Drift (FKED) through an aggregated data case study of Traffic Analysis Zones in São Paulo city, Brazil. The method consists of a sequential application of Principal Components Analysis (PCA) and Kriging with External Drift (KED). The traditional Linear Regression (LR) model was adopted with the aim of validating the proposed method. The results show that PCA summarizes and combines 23 socioeconomic variables using 4 components. The first component is introduced in KED, as secondary information, to estimate transit trip production by public transport in geographic coordinates where there is no prior knowledge of the values. Cross-validation for the FKED model presented high values of the correlation coefficient between estimated and observed values. Moreover, low error values were observed. The accuracy of the LR model was similar to FKED. However, the proposed method is able to map the transit trip production in several geographical coordinates of non-sampled values.     

Kernel Principal Component Analysis for Efficient,Differentiable Parameterization of Multipoint Geostatistics

This paper describes a novel approach for creating an efficient, general, and differentiable parameterization of large-scale non-Gaussian, non-stationary random fields (represented by multipoint geostatistics) that is capable of reproducing complex geological structures such as channels. Such parameterizations are appropriate for use with gradient-based algorithms applied to, for example, history-matching or uncertainty propagation. It is known that the standard Karhunen–Loeve (K–L) expansion, also called linear principal component analysis or PCA, can be used as a differentiable parameterization of input random fields defining the geological model. The standard K–L model is, however, limited in two respects. It requires an eigen-decomposition of the covariance matrix of the random field, which is prohibitively expensive for large models. In addition, it preserves only the two-point statistics of a random field, which is insufficient for reproducing complex structures. In this work, kernel PCA is applied to address the limitations associated with the standard K–L expansion. Although widely used in machine learning applications, it does not appear to have found any application for geological model parameterization. With kernel PCA, an eigen-decomposition of a small matrix called the kernel matrix is performed instead of the full covariance matrix. The method is much more efficient than the standard K–L procedure. Through use of higher order polynomial kernels, which implicitly define a high-dimensionality feature space, kernel PCA further enables the preservation of high-order statistics of the random field, instead of just two-point statistics as in the K–L method. The kernel PCA eigen-decomposition proceeds using a set of realizations created by geostatistical simulation (honoring two-point or multipoint statistics) rather than the analytical covariance function. We demonstrate that kernel PCA is capable of generating differentiable parameterizations that reproduce the essential features of complex geological structures represented by multipoint geostatistics. The kernel PCA representation is then applied to history match a water flooding problem. This example demonstrates that kernel PCA can be used with gradient-based history matching to provide models that match production history while maintaining multipoint geostatistics consistent with the underlying training image.     

Explorative data analysis of heavy metal contaminated soil using multidimensional spatial regression

To obtain data on heavy metal contaminated soil requires laborious and time-consuming data sampling and analysis. Not only has the contamination to be measured, but also additional data characterizing the soil and the boundary conditions of the site, such as pH, land use, and soil fertility. For an integrative approach, combining the analysis of spatial distribution, and of factors influencing the contamination, and its treatment, the Mollifier interpolation was used, which is a non-parametric kernel density regression. The Mollifier was capable of including additional independent variables (beyond the spatial dimensions x and y) in the spatial interpolation and hence explored the combined influence of spatial and other variables, such as land use, on the heavy metal distribution. The Mollifier could also represent the interdependence between different heavy metal concentrations and additional site characteristics. Although the uncertainty measure supplied by the Mollifier at first seems somewhat unusual, it is a valuable feature and supplements the geostatistical uncertainty assessment.     

A three-dimensional high-resolution reservoir model of the Eocene Shahejie Formation in Bohai Bay Basin,integrating stratigraphic forward modeling and geostatistics

Reservoir characterization based on geostatistics method requires well constraints (e.g. seismic data with high quality) to predict inter-well reservoir quality that is conformed to geological laws. Nevertheless, the resolution of seismic data in multiple basins or reservoirs is not high enough to recognize the distribution of different types of sand bodies. In this paper, we propose a new method to improve the precision of reservoir characterization: reservoir modeling with the constrains of sedimentary process model and sedimentary microfacies. We employed stratigraphic forward modeling, a process-based method, to constrain the reservoir modeling in one oil-bearing interval of the third member of Eocene Shahejie Formation in J-Oilfield of Liaoxi Sag, Bohai Bay Basin.We divide reservoir modeling into two orders using different types of constrains. In the first order, we use the simulated shale model from stratigraphic forward model that is corrected by wells data as a 3D trend volume to constrain the reservoir sand-shale modeling. In the second order, different types of sedimentary microfacies in the sandy part of the model are further recognized and simulated within the constrains of sedimentary microfacies maps. Consequently, the porosity, permeability and oil saturation are modeled under the control of precise sedimentary microfacies model. The high-resolution reservoir model shows that the porosity, permeability and oil saturation of distributary channel is generally above 20%, 10md and 50%, respectively, which are much higher than that of other types of sedimentary microfacies. It can be concluded that comparing to other types of sedimentary facies, distributary channel has better physical properties and more oil accumulation in the fan-delta front and therefore is the most favorable zones for petroleum development in the research area.