Detecting subtle hydrochemical anomalies with multivariate statistics: an example from ‘homogeneous’ groundwaters in the Great Artesian Basin,Australia

The major ion composition of Great Artesian Basin groundwater in the lower Namoi River valley is relatively homogeneous in chemical composition. Traditional graphical techniques have been combined with multivariate statistical methods to determine whether subtle differences in the chemical composition of these waters can be delineated. Hierarchical cluster analysis and principal components analysis were successful in delineating minor variations within the groundwaters of the study area that were not visually identified in the graphical techniques applied. Hydrochemical interpretation allowed geochemical processes to be identified in each statistically defined water type and illustrated how these groundwaters differ from one another. Three main geochemical processes were identified in the groundwaters: ion exchange, precipitation, and mixing between waters from different sources. Both statistical methods delineated an anomalous sample suspected of being influenced by magmatic CO₂ input. The use of statistical methods to complement traditional graphical techniques for waters appearing homogeneous is emphasized for all investigations of this type. Copyright © 2006 John Wiley & Sons, Ltd.     

Mixture models and atypical values

The resolution of a mixture of two or more populations into its component distributions may be markedly influenced by one or a few atypical values. The maximum likelihood solution effectively assigns (part of) each observation to one or another of the components via the posterior probabilities, even though the observation may be widely discrepant from all components. This paper presents a modification of the mixture problem, in which the typicality of each observation is considered, as well as the posterior probabilities, with the contribution of atypical observations being downweighted. The extension to the multivariate case is discussed.     

Use of multivariate statistical methods in data-base maintenance

Multivariate statistical methods may be used to enhance large data bases by predicting missing information and verifying unchecked data vectors. In addition, new techniques may be used for exploratory purposes to investigate the interrelationships between variables. The techniques are being applied successfully in coal mining.     

REVIEWS OF GEOGRAPHIC SOFTWARE

Geographic Software Reviewed in this article: LIFE TABLES and the LESLIE MATRIX. CONDUIT MENTMAP2 . Lawrence W. Carstensen Jr . PC-MATLAB , Version 1.0. The Math Works, Inc. QUICKMAP , version 1.0. Sammamish Data Systems, Inc. SYSTAT: THE SYSTEM FOR STATISTICS , Version 2.1, Systat Inc. USA DISPLAY . Instant Tecall     

Application of a neural network model in establishing a stage–discharge relationship for a tidal river

This paper presents the applicability of neural network (NN) modelling for forecasting and filtering problems. The multilayer feedforward (MLFF) network was first constructed to forecast the tidal‐level variations at the mouth of the River Chao Phraya in Thailand. Unlike the well‐known conventional harmonic analysis, the NN model uses a set of previous data for learning and then forecasting directly the time‐series of tidal levels. It was found that lead time of 1 to 24 hourly tidal levels can be predicted successfully using only a short‐time hourly learning data. The MLFF network was further used to establish a stage–discharge relationship for the tidal river. The results show a considerably better performance of the NN model over the conventional models. In addition, the stage–discharge relationship obtained by the NN model can indicate reasonably well the important behaviour of the tidal influences. Copyright © 2003 John Wiley & Sons, Ltd.     

On minimum spanning trees and the intergradation of clusters

Cluster analysis groups samples, but does not generally show gradations between clusters. To illustrate these relationships, principal-coordinate analysis and multidimensional scaling can be employed, but these methods may not be appropriate due to structural distortion. A minimum spanning tree (MST) computes a point-to-point path through the original matrix, and clusters are mapped on the MST diagram. The MST linkages, therefore, provide a natural continuum between the clusters, without distortion. Forty-six Silurian Tonoloway Limestone samples were analyzed for 16 sedimentary features indicative of subaerial exposure. Cluster analysis identified nine clusters which were reduced to five final, ordered groups by MST.     

Reconstruction of Three-Dimensional Pacific Temperature with Argo and Satellite Observations

Combining Argo temperature and salinity profiles with satellite-derived sea surface temperature (SST), weekly three-dimensional temperature fields of the Pacific Ocean were reconstructed for the period January 2000 to December 2010. The data reconstruction methodology we used has three salient features: the first is a combined application of the Optimal Interpolation (OI) and the Multivariate Data Interpolating Empirical Orthogonal Function (MDINEOF) methods, the second is an emphasis on the multivariate nature of the vertical thermohaline structure, and the third is the inclusion of a continuous satellite-derived SST dataset to compensate for the discontinuities and the lack of surface observations in Argo data. Comparisons with other observations and data products indicate that our gridded temperature product is able to capture the main features of temperature distribution as well as its variability from intraseasonal to interannual time scales, thus providing a useful new dataset for ocean and climate studies.

RÉSUMÉ?[Traduit par la rédaction] En combinant les profils de température et de salinité Argo avec les températures de la surface de la mer dérivées des données satellitaires, nous avons reconstruit les champs tridimensionnels hebdomadaires de température de l'océan Pacifique pour la période de janvier 2000 à décembre 2010. La méthodologie de reconstruction des données que nous avons utilisée présente trois points saillants : le premier est une application combinée des méthodes de l'interpolation optimale et de la fonction orthogonale empirique d'interpolation de données multivariées (MDINEOF), le deuxième est une mise en évidence de la nature multivariée de la structure thermohaline verticale et le troisième est l'inclusion d'un ensemble continu de données de température de la surface de la mer dérivées des données satellitaires pour compenser les discontinuités et le manque d'observations de surface dans les données Argo. Les comparaisons avec d'autres observations et produits de données montrent que notre produit de températures à des points de grille est capable de discerner les caractéristiques principales de la distribution des températures de même que sa variabilité de l’échelle intrasaisonnière à l’échelle interannuelle, ce qui fournit un nouvel ensemble de données utile pour les études océaniques et climatiques.     

舟山近海日本囊对虾(Marsupenaeus japonicus)野生群体与露天养殖越冬群体间的形质差异

鉴于舟山沿海日本囊对虾秋苗养殖成活率显著低于春季和夏季人工养殖苗种之实际,深入开展适合于本地沿海养殖的日本囊对虾秋苗的优质亲体的选种研究显得十分必要。为此,作者采用聚类分析、主成分分析和判别分析等方法定量研究了舟山近海日本囊对虾野生群体和露天池塘越冬养成群体间的形质特征差异。结果表明:两者在本研究所涉18项形质评价指标中的相似性指数仅为11.11%,欧氏距离为4.243(P0.01);经主成分分析,提取到的5个特征值均大于1的主成分,累计贡献率达85.27%,其中第1主成分为以营养生理状况指数、额剑上缘锯齿数以及腹部肌肉发达程度为主导的体质强壮因子,第2主成分为以寻食视野与胸腔空间大小为主导的捕食运动功能因子,后3个主成分为以尾节肌肉发达程度为主导的避敌运动功能因子;采用逐步判别法,以判别贡献率较大的9项形质评价指标为自变量,所建Fisher分类函数方程组可清晰区分日本囊对虾野生群体和越冬养成群体,其中野生群体的判别准确率P1、P2分别为99.33%和96.13%,越冬养成群体的判别准确率P1、P2分别为96%和99.31%,两者综合判别准确率为97.67%。因此,日本囊对虾秋苗野生亲本形质特征的选择,应以秋苗越冬养成群体为参照。     

A New Fracability Evaluation Approach for Shale Reservoirs Based on Multivariate Analysis: A Case Study in Zhaotong Shale Gas Demonstration Zone in Sichuan,China

Fracability characterizes the effectiveness of hydraulic fracturing. The existing assessment methods cannot reflect the actual value of the effectiveness due to a lack of comprehensive consideration and neglect of the influences of engineering factors. This study aims to solve this problem by implementing geological static data and production dynamic data in multivariate analysis in Zhaotong shale gas demonstration zone. First, the reservoir quality index (RQI) was introduced to evaluate the exploration potential by integrating the geological parameters with gray relational analysis. Moreover, the differences in fracturing fluid types and proppant sizes were considered, and the operating parameters were normalized on the basis of the equivalence principle. Finally, the general reservoir fracability index (GRFI) was proposed based on a dimensioned processing of the various parameters. A case study was conducted to verify the accuracy and feasibility of this new approach. The results demonstrate that (1) the organic carbon and gas content are adjusted to contribute the most to the calculation of the RQI, while the effective porosity contributes the least; (2) the fracturing scale is the main operating parameter determining the fracability, which has the strongest correlation with the effectiveness of fracking; and (3) the GRFI has a positive correlation with shale gas production, and the lower limit of the GRFI of 2,000 corresponds to a daily production of 50,000 m3/d; this value is defined as the threshold value of a stripper well. The GRFI is consistent with the productivity trend of shale gas wells in the research block, which suggests that the new model is accurate and practical for well candidate selection.     

Multiple Discriminant Analysis of Marine Sediment Data

A multivariate statistical approach was used in the analysis of inter-relationships among marine benthic infaunal structure, physical and chemical characteristics of sediment samples and toxicity data derived from laboratory tests at 16 locations in shallow, inshore waters of Hong Kong. The method involved classification (cluster analysis using the Bray–Curtis similarity index) and ordination (multi-dimensional scaling) of infaunal patterns and the use of multiple discriminant analysis to relate groupings of the locations to the selected environmental and toxicity data. Analysis of the combined sediment physical, biological, chemical and toxicity dataset by stepwise multiple discriminant analysis allowed identification of those variables most sensitive for discriminating location groups. The use of multiple discriminant analysis in sediment quality characterization was evaluated against the Sediment Quality Triad approach and other statistical techniques.