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1.
Like compositions in general, regionalized compositions present the problem of spurious spatial correlation. To avoid this problem, this paper uses the additive-logratio transformation of regionalized compositions, following techniques introduced over the last few years for the statistical analysis of compositional data. It leads to an appropriate definition of a spatial covariance structure to describe spatial dependence between regionalized variables subject to constant-sum constraints in the case of weak stationarity. To illustrate stated problems, simulated data are used.  相似文献   

2.
One of the most discussed stages in the history of the Baltic Sea is the Ancylus Lake phase. This paper presents detailed information from the Darss Sill threshold area as well as the adjacent basins, i.e. the Mecklenburg Bay and Arkona Basin located in the southwesternmost Baltic. The threshold area was transgressed at the Baltic Ice Lake maximum phase and during the following regression about 10.3 ka BP a river valley was incised in the Darss Sill to a level of 23-24 m below present sea level (b.s.l.). Preboreal sediments in the study area show lowstand basin deposition in the Arkona Basin and the existence of a local lake in Mecklenburg Bay. The lowstand system is followed by the Ancylus Lake transgression that reached a maximum level of 19 m b.s.l. Thus, at the maximum level the water depth was about 5 m over the threshold, and the shore level fall during the Ancylus Lake regression must be in the same range. The Darss Sill area is the key area for drainage of the Ancylus Lake, and if the previously suggested regression of 8-10 m in southeastern Sweden is to be achieved, isostatic rebound must also play a role. The existence of the so-called Dana River in the Darss Sill area cannot be supported by our investigations. We observed no signs of progressive erosion of the Darss Sill area in the Early Holocene, and there are no prograding systems in Mecklenburg Bay that can be related to the Ancylus Lake regression. On the contrary, local lakes developed in Mecklenburg Bay and in the Darss Sill threshold area. In the Darss Sill area, marl was deposited in a lake in the valley that developed after the final drainage of the Baltic Ice Lake. Studies of diatoms and macrofossils, combined with seismic interpretation and radiocarbon dating, provide detailed information about the chronology and the relative shore level of these lake phases as well as about environmental conditions in the lakes.  相似文献   

3.
Estimation of regionalized compositions: A comparison of three methods   总被引：1，自引：0，他引：1  
A regionalized composition is a random vector function whose components are positive and sum to a constant at every point of the sampling region. Consequently, the components of a regionalized composition are necessarily spatially correlated. This spatial dependence—induced by the constant sum constraint—is a spurious spatial correlation and may lead to misinterpretations of statistical analyses. Furthermore, the cross-covariance matrices of the regionalized composition are singular, as is the coefficient matrix of the cokriging system of equations. Three methods of performing estimation or prediction of a regionalized composition at unsampled points are discussed: (1) the direct approach of estimating each variable separately; (2) the basis method, which is applicable only when a random function is available that can he regarded as the size of the regionalized composition under study; (3) the logratio approach, using the additive-log-ratio transformation proposed by J. Aitchison, which allows statistical analysis of compositional data. We present a brief theoretical review of these three methods and compare them using compositional data from the Lyons West Oil Field in Kansas (USA). It is shown that, although there are no important numerical differences, the direct approach leads to invalid results, whereas the basis method and the additive-log-ratio approach are comparable.  相似文献   

4.
Biostratigraphical and palaeoecological analyses of cores along a transect from Femer Belt to the Arkona Basin reveal that North Sea waters began to enter the western Baltic Sea between 8600 and 8400 calibrated years BP. Studies of diatoms indicate that Mecklenburg Bay was characterised by slightly brackish-water conditions between 8400 and 8000 cal. years BP. At around 8000 cal. years BP increasing salinity is indicated by a strong dominance of the diatoms Paralia sulcata and Dimeregramma minor. Some centuries later another diatom assemblage appeared and became dominant in Mecklenburg Bay. This assemblage includes Hyalinella lateripunctata and Pravifusus hyalinus species typical of shallow water areas along the Atlantic coast today. At this time the first marine molluscs made their appearance. The oldest shell of a marine mollusc found in our material is dated to 7600 cal. years BP. The associated assemblage that includes adult specimens of the gastropod Aporrhais pespelicani indicates higher salinities than today.During the Littorina Sea stage a marine diatom flora with P. sulcata, Catenula adhaerens and D. minor crossed the Darss Sill and became widely distributed in the Arkona Basin, Pomeranian Bay and the Baltic Sea proper. In contrast, taxa indicative of the Hyalinella lateripunctata/P. hyalinus assemblage are only found west of the Darss Sill in Femer Belt and Mecklenburg Bay. Apparently, the Darss Sill threshold has been acting as an important salinity border from around 7800 cal. years BP until today.  相似文献   

5.
Jensen, J. B., Bennike, O., Witkowski, A., Lemke, W. & Kuijpers, A. 1997 (September): The Baltic Ice Lake in the southwestern Baltic: sequence-, chrono- and biostratigraphy. Boreas , Vol. 26, pp. 217–236. Oslo. ISSN 0300–9483.
This multidisciplinary study focuses on late-glacial deposits in the Mecklenburg Bay -Arkona Basin area. The sequence stratigraphical method has been used on shallow seismic and lithological data, in combination with biostratigraphical work and radiocarbon dating. Glacial-till deposits underlie sediments from two Baltic Ice Lake phases. Varved clay deposits from the initial phase cover the deepest parts of the basins. A prograding delta is observed at the western margin of the Arkona Basin, prograding from the Darss Sill area. The delta system is possibly related to a highstand dated at 12.8 ka. A maximum transgression level around 20 m below present sea level (b.s.l.) is inferred, followed by a drop in water level and formation of lowstand features. The final ice lake phase is characterized by a new transgression. The transgression maximum as observed in the Mecklenburg Bay is represented by transgressive and highstand deltaic deposits. These also indicate a maximum shore level of 20 m b.s.l. The deltaic sediments that contain macroscopic plant remains and diatoms have yielded Younger Dryas ages. Mapping of the late-glacial morphology of the Darss Sill area reveals a threshold at 23 to 24 m b.s.l. This means that the Baltic Ice Lake highstand phases inundated the Darss Sill, which implies that the westernmost extension of the Baltic Ice Lake reached as far as Kiel Bay. Forced regressive coastal deposits at the western margin of the Arkona Basin mark a lowstand level of around 40 m b.s.l. caused by the final drainage of the Baltic Ice Lake. The lowstand deposits predate lacustrine deposits from the Ancylus Lake, which date to approximately 9.6 ka BP.  相似文献   

6.
Updating of Population Parameters and Credibility of Discriminant Analysis   总被引：1，自引：0，他引：1  
The uncertainty of classification in discriminant analysis may result from the original characteristics of the phenomena studied, the approach of inferring population parameters, and the credibility of the parameters which are estimated by geologist or statistician. A credibility function and a significance function are proposed. Both can be used to appraise the uncertainty of classification. The former is involved with the uncertainty resulting from the errors in the reward-penalty matrix, while the latter may be involved with the uncertainty resulting from the original characteristics of the phenomena studied and the statistical approach. Inappropriate classified results may be originated from the bias estimates of population parameters (mean vector and covariance matrix), which are estimated by bias samples. These bias estimates can be updated by constraining the varying region of the mean vector. The equations for updating Bayesian estimates of the mean vector and the covariance matrix are demonstrated if the mean vector is restricted to a subregion of the entire real space. Results for a gas reservoir indicate that the discriminant rules based on the updated equations are more efficient than the traditional discriminant rules.  相似文献   

7.

Problems with compositional data, like spurious correlation and negative bias, are well known in the Geosciences. Not so well known is the fact that the same problems appear when dealing with regionalized compositions. Here, these problems are illustrated, and a solution, based on the principle of working in coordinates using orthonormal logratio representations, is presented. This approach offers a tool for standard geostatistical studies. One of the advantages the method has is that it allows the usual inconsistencies with indicator kriging to be overcome through simplicial indicator kriging. A general way of modelling crossvariograms of coordinates, based on the matrix valued variation variogram, is discussed. In summary, the main aspects related to the modelling and analysis of regionalized compositions have had satisfactory solutions found for them. The proposed methodology is illustrated with public data from a survey concerning arsenic contamination in underground water in Bangladesh.

  相似文献   

8.
Spatial declustering weights   总被引：1，自引：0，他引：1  
Because of autocorrelation and spatial clustering, all data within a given dataset have not the same statistical weight for estimation of global statistics such mean, variance, or quantiles of the population distribution. A measure of redundancy (or nonredundancy) of any given regionalized random variable Z(uα)within any given set (of size N) of random variables is proposed. It is defined as the ratio of the determinant of the N X Ncorrelation matrix to the determinant of the (N - 1) X (N - 1)correlation matrix excluding random variable Z(uα).This ratio measures the increase in redundancy when adding the random variable Z(uα)to the (N - 1 )remainder. It can be used as declustering weight for any outcome (datum) z(uα). When the redundancy matrix is a kriging covariance matrix, the proposed ratio is the crossvalidation simple kriging variance. The covariance of the uniform scores of the clustered data is proposed as a redundancy measure robust with respect to data clustering.  相似文献   

9.
A discriminant technique based on mixture models is presented to be applied when observations are a sample of a mixture of compositions with each component following an additive logistic normal distribution on the d-dimensional simplex. The efficiency of this discriminant technique is compared empirically with the efficiency of the standard discriminant technique based on logcontrast. Simulated compositional data and a real dataset are used to carry out these comparisons.  相似文献   

10.
This work focuses on the characterization of the central tendency of a sample of compositional data. It provides new results about theoretical properties of means and covariance functions for compositional data, with an axiomatic perspective. Original results that shed new light on geostatistical modeling of compositional data are presented. As a first result, it is shown that the weighted arithmetic mean is the only central tendency characteristic satisfying a small set of axioms, namely continuity, reflexivity, and marginal stability. Moreover, this set of axioms also implies that the weights must be identical for all parts of the composition. This result has deep consequences for spatial multivariate covariance modeling of compositional data. In a geostatistical setting, it is shown as a second result that the proportional model of covariance functions (i.e., the product of a covariance matrix and a single correlation function) is the only model that provides identical kriging weights for all components of the compositional data. As a consequence of these two results, the proportional model of covariance function is the only covariance model compatible with reflexivity and marginal stability.  相似文献   

11.
Multi-element analyses of more than 600 panned heavy-mineral concentrate samples from the Jameson Land area of central East Greenland were investigated by discriminant analysis which, combined with an a priori knowledge of the geology, was used to assist interpretation and classification the data. The importance of sample density, and the method and degree of sample grouping were investigated. Also the effect of using either the within-covariance or the pooled covariance matrices in the discriminant functions was studied.Discriminant analysis assumes the element concentrations to be normally distributed and that equality of within-covariances exists. These assumptions were not always met, and this was probably the main reason why one-third of the samples could not be classified. However, the study shows that interpretation of the data, although it is historical and forms only part of a regional reconnaissance survey, benefits from the application of discriminant analysis.  相似文献   

12.
To avoid spurious spatial correlation when analyzing the spatial covariance structure of regionalized compositions, additive-log-ratio transformation can be used. Here, the additive-log-ratio cokriging estimator, derived in a natural way from this transformation, is shown to be invariant under permutation of components of the untransformed regionalized composition. It leads, as expected, to an exact interpolation. As original data, predicted values of the regionalized composition at unknown points add up to the same constant c and lie between 0 and c.  相似文献   

13.
In this work, we present an efficient matrix-free ensemble Kalman filter (EnKF) algorithm for the assimilation of large data sets. The EnKF has increasingly become an essential tool for data assimilation of numerical models. It is an attractive assimilation method because it can evolve the model covariance matrix for a non-linear model, through the use of an ensemble of model states, and it is easy to implement for any numerical model. Nevertheless, the computational cost of the EnKF can increase significantly for cases involving the assimilation of large data sets. As more data become available for assimilation, a potential bottleneck in most EnKF algorithms involves the operation of the Kalman gain matrix. To reduce the complexity and cost of assimilating large data sets, a matrix-free EnKF algorithm is proposed. The algorithm uses an efficient matrix-free linear solver, based on the Sherman–Morrison formulas, to solve the implicit linear system within the Kalman gain matrix and compute the analysis. Numerical experiments with a two-dimensional shallow water model on the sphere are presented, where results show the matrix-free implementation outperforming an singular value decomposition-based implementation in computational time.  相似文献   

14.
The parameters of covariance functions (or variograms) of regionalized variables must be determined before linear unbiased estimation can be applied. This work examines the problem of minimum-variance unbiased quadratic estimation of the parameters of ordinary or generalized covariance functions of regionalized variables. Attention is limited to covariance functions that are linear in the parameters and the normality assumption is invoked when fourth moments of the data need to be calculated. The main contributions of this work are (1) it shows when and in what sense minimum-variance unbiased quadratic estimation can be achieved, and (2) it yields a well-founded, practicable, and easy-to-automate methodology for the estimation of parameters of covariance functions. Results of simulation studies are very encouraging.  相似文献   

15.
Zones of mixing between shallow groundwaters of different composition were unravelled by “two-way regionalized classification,” a technique based on correspondence analysis (CA), cluster analysis (ClA) and discriminant analysis (DA), aided by gridding, map-overlay and contouring tools. The shallow groundwaters are from a granitoid plutonite in the Fundão region (central Portugal). Correspondence analysis detected three natural clusters in the working dataset: 1, weathering; 2, domestic effluents; 3, fertilizers. Cluster analysis set an alternative distribution of the samples by the three clusters. Group memberships obtained by correspondence analysis and by cluster analysis were optimized by discriminant analysis, gridded over the entire Fundão region, and converted into “two-way regionalized classification” memberships as follows: codes 1, 2 or 3 were used when classification by correspondence analysis and cluster analysis produced the same results; code 0 when the grid node was first assigned to cluster 1 and then to cluster 2 or vice versa (mixing between weathering and effluents); code 4 in the other cases (mixing between agriculture and the other influences). Code-3 areas were systematically surrounded by code-4 areas, an observation attributed to hydrodynamic dispersion. Accordingly, the extent of code-4 areas in two orthogonal directions was assumed proportional to the longitudinal and transverse dispersivities of local soils. The results (0.7–16.8 and 0.4–4.3 m, respectively) are acceptable at the macroscopic scale. The ratios between longitudinal and transverse dispersivities (1.2–11.1) are also in agreement with results obtained by other studies.  相似文献   

16.
Bayesian updating methods provide an alternate philosophy to the characterization of the input variables of a stochastic mathematical model. Here, a priori values of statistical parameters are assumed on subjective grounds or by analysis of a data base from a geologically similar area. As measurements become available during site investigations, updated estimates of parameters characterizing spatial variability are generated. However, in solving the traditional updating equations, an updated covariance matrix may be generated that is not positive-definite, particularly when observed data errors are small. In addition, measurements may indicate that initial estimates of the statistical parameters are poor. The traditional procedure does not have a facility to revise the parameter estimates before the update is carried out. alternatively, Bayesian updating can be viewed as a linear inverse problem that minimizes a weighted combination of solution simplicity and data misfit. Depending on the weight given to the a priori information, a different solution is generated. A Bayesian updating procedure for log-conductivity interpolation that uses a singular value decomposition (SVD) is presented. An efficient and stable algorithm is outlined that computes the updated log-conductivity field and the a posteriori covariance of the estimated values (estimation errors). In addition, an information density matrix is constructed that indicates how well predicted data match observations. Analysis of this matrix indicates the relative importance of the observed data. The SVD updating procedure is used to interpolate the log-conductivity fields of a series of hypothetical aquifers to demonstrate pitfalls and possibilities of the method.  相似文献   

17.
Bayesian updating methods provide an alternate philosophy to the characterization of the input variables of a stochastic mathematical model. Here, a priori values of statistical parameters are assumed on subjective grounds or by analysis of a data base from a geologically similar area. As measurements become available during site investigations, updated estimates of parameters characterizing spatial variability are generated. However, in solving the traditional updating equations, an updated covariance matrix may be generated that is not positive-definite, particularly when observed data errors are small. In addition, measurements may indicate that initial estimates of the statistical parameters are poor. The traditional procedure does not have a facility to revise the parameter estimates before the update is carried out. alternatively, Bayesian updating can be viewed as a linear inverse problem that minimizes a weighted combination of solution simplicity and data misfit. Depending on the weight given to the a priori information, a different solution is generated. A Bayesian updating procedure for log-conductivity interpolation that uses a singular value decomposition (SVD) is presented. An efficient and stable algorithm is outlined that computes the updated log-conductivity field and the a posteriori covariance of the estimated values (estimation errors). In addition, an information density matrix is constructed that indicates how well predicted data match observations. Analysis of this matrix indicates the relative importance of the observed data. The SVD updating procedure is used to interpolate the log-conductivity fields of a series of hypothetical aquifers to demonstrate pitfalls and possibilities of the method.  相似文献   

18.
The statistical analysis of compositional data is based on determining an appropriate transformation from the simplex to real space. Possible transfonnations and outliers strongly interact: parameters of transformations may be influenced particularly by outliers, and the result of goodness-of-fit tests will reflect their presence. Thus, the identification of outliers in compositional datasets and the selection of an appropriate transformation of the same data, are problems that cannot be separated. A robust method for outlier detection together with the likelihood of transformed data is presented as a first approach to solve those problems when the additive-logratio and multivariate Box-Cox transformations are used. Three examples illustrate the proposed methodology.  相似文献   

19.
Because of autocorrelation and spatial clustering, all data within a given dataset have not the same statistical weight for estimation of global statistics such mean, variance, or quantiles of the population distribution. A measure of redundancy (or nonredundancy) of any given regionalized random variable Z(uα)within any given set (of size N) of random variables is proposed. It is defined as the ratio of the determinant of the N X Ncorrelation matrix to the determinant of the (N - 1) X (N - 1)correlation matrix excluding random variable Z(uα).This ratio measures the increase in redundancy when adding the random variable Z(uα)to the (N - 1 )remainder. It can be used as declustering weight for any outcome (datum) z(uα). When the redundancy matrix is a kriging covariance matrix, the proposed ratio is the crossvalidation simple kriging variance. The covariance of the uniform scores of the clustered data is proposed as a redundancy measure robust with respect to data clustering.  相似文献   

20.
各向异性研究是当令地震学研究领域中重要课题之一；三分量地震资料中各向异性的检测是各向异性理论研究成果解决地球科学实际问题的重要桥梁。本文简要描述了各向异性介质中横波分裂现象，分别介绍了现有的四种主要检测技术，即偏振图法、协方差拒阵法、质，点振动分辨率法及传输矩阵法，并对这四种技术作了一定的评述。  相似文献   

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