Estimation of covariance matrix from geochemical data with observations below detection limits     

Chang-Jo F. Chung 《Mathematical Geology》1993,25(7):851-865

Multivariate statistical analyses have been extensively applied to geochemical measurements to analyze and aid interpretation of the data. Estimation of the covariance matrix of multivariate observations is the first task in multivariate analysis. However, geochemical data for the rare elements, especially Ag, Au, and platinum-group elements, usually contain observations the below detection limits. In particular, Instrumental Neutron Activation Analysis (INAA) for the rare elements produces multilevel and possibly extremely high detection limits depending on the sample weight. Traditionally, in applying multivariate analysis to such incomplete data, the observations below detection limits are first substituted, for example, each observation below the detection limit is replaced by a certain percentage of that limit, and then the standard statistical computer packages or techniques are used to obtain the analysis of the data. If a number of samples with observations below detection limits is small, or the detection limits are relatively near zero, the results may be reasonable and most geological interpretations or conclusions are probably valid. In this paper, a new method is proposed to estimate the covariance matrix from a dataset containing observations below multilevel detection limits by using the marginal maximum likelihood estimation (MMLE) method. For each pair of variables, sayY andZ whose observations containing below detection limits, the proposed method consists of three steps: (i) for each variable separately obtaining the marginal MLE for the means and the variances, , , , and forY andZ: (ii) defining new variables by and and lettingA=C+D andB=C–D, and obtaining MLE for variances, and forA andB; (iii) estimating the correlation coefficient _YZ by and the covariance _YZ by . The procedure is illustrated by using a precious metal geochemical data set from the Fox River Sill, Manitoba, Canada.  相似文献   

参数的期望估计及其在形变分析中的应用   总被引：1，自引：0，他引：1  

黄杰 《华北地震科学》1997,15(2):25-31

利用“参数的期望估计”能准确定位、定量粗差及参数的期望估计不受粗差影响折特殊性质,寻找地壳变形区域和不变形区域,以确定拟稳点,进而进行拟稳变换,分析地菜变,将是一种有效方法。  相似文献   

Estimation for partially observed Markov processes     

M. E. Thompson  T. N. Kaseke 《Stochastic Hydrology and Hydraulics》1995,9(1):33-47

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.  相似文献   

成都城市发展对热岛强度影响的主成份回归分析     

石凤云  唐佑民 《成都信息工程学院学报》1991,(Z1)

本文对成都市总人口、建成区面积等11个因子、作了主成份回归L-S估计和M-估计,讨论了成都城市发展对“热岛”强度的主要影响因子。结果表明,城区房屋建筑面积及总人口数是影响城市气候(气温)的主要因子,其次为城市人口总户数、建成面积等。 文中,对回归方程进行了拟合计算,回归效果比较满意(尤其是稳健回归)。  相似文献   

Comparison of structural and least-squares lines for estimating geologic relations   总被引：1，自引：0，他引：1  

Garnett P. Williams  Brent M. Troutman 《Mathematical Geology》1990,22(8):1027-1049

Two different goals in fitting straight lines to data are to estimate a true linear relation (physical law) and to predict values of the dependent variable with the smallest possible error. Regarding the first goal, a Monte Carlo study indicated that the structural-analysis (SA) method of fitting straight lines to data is superior to the ordinary least-squares (OLS) method for estimating true straight-line relations. Number of data points, slope and intercept of the true relation, and variances of the errors associated with the independent (X) and dependent (Y) variables influence the degree of agreement. For example, differences between the two line-fitting methods decrease as error in X becomes small relative to error in Y. Regarding the second goal—predicting the dependent variable—OLS is better than SA. Again, the difference diminishes as X takes on less error relative to Y. With respect to estimation of slope and intercept and prediction of Y, agreement between Monte Carlo results and large-sample theory was very good for sample sizes of 100, and fair to good for sample sizes of 20. The procedures and error measures are illustrated with two geologic examples.  相似文献   

HP–LT Variscan metamorphism in the Cubito-Moura schists (Ossa-Morena Zone, southern Iberia)     

Guillermo Booth-Rea  Jos Fernando Simancas  Antonio Azor  Jos Miguel Azan  Francisco Gonzlez-Lodeiro  Paulo Fonseca 《Comptes Rendus Geoscience》2006,338(16):1260-1267

Multi-equilibrium thermobarometry shows that low-grade metapelites (Cubito-Moura schists) from the Ossa–Morena Zone underwent HP–LT metamorphism from 340–370 °C at 1.0–0.9 GPa to 400–450 °C at 0.8–0.7 GPa. These HP–LT equilibriums were reached by parageneses including white K mica, chlorite and chloritoid, which define the earliest schistosity (S₁) in these rocks. The main foliation in the schists is a crenulation cleavage (S₂), which developed during decompression from 0.8–0.7 to 0.4–0.3 GPa at increasing temperatures from 400–450 °C to 440–465 °C. Fe³⁺ in chlorite decreased greatly during prograde metamorphism from molar fractions of 0.4 determined in syn-S₁ chlorites down to 0.1 in syn-S₂ chlorites. These new data add to previous findings of eclogites in the Moura schists indicating that a pile of allochtonous rocks situated next to the Beja-Acebuches oceanic amphibolites underwent HP–LT metamorphism during the Variscan orogeny. To cite this article: G. Booth-Rea et al., C. R. Geoscience 338 (2006).  相似文献   

Reservoir description using dynamic parameterisation selection with a combined stochastic and gradient search     

Lars Kristian Nielsen  Sam Subbey  Mike Christie  Trond Mannseth 《Computational Geosciences》2006,10(3):321-342

There is a correspondence between flow in a reservoir and large scale permeability trends. This correspondence can be derived by constraining reservoir models using observed production data. One of the challenges in deriving the permeability distribution of a field using production data involves determination of the scale of resolution of the permeability. The Adaptive Multiscale Estimation (AME) seeks to overcome the problems related to choosing the resolution of the permeability field by a dynamic parameterisation selection. The standard AME uses a gradient algorithm in solving several optimisation problems with increasing permeability resolution. This paper presents a hybrid algorithm which combines a gradient search and a stochastic algorithm to improve the robustness of the dynamic parameterisation selection. At low dimension, we use the stochastic algorithm to generate several optimised models. We use information from all these produced models to find new optimal refinements, and start out new optimisations with several unequally suggested parameterisations. At higher dimensions we change to a gradient-type optimiser, where the initial solution is chosen from the ensemble of models suggested by the stochastic algorithm. The selection is based on a predefined criterion. We demonstrate the robustness of the hybrid algorithm on sample synthetic cases, which most of them were considered insolvable using the standard AME algorithm.  相似文献   

Mais comment s'écoule donc un glacier ? Aperçu historique     

Frédérique Rémy  Laurent Testut 《Comptes Rendus Geoscience》2006,338(5):368-385

Ice and snow have often helped physicists understand the world. On the contrary it has taken them a very long time to understand the flow of the glaciers. Naturalists only began to take an interest in glaciers at the beginning of the 19th century during the last phase of glacier advances. When the glacier flow from the upslope direction became obvious, it was then necessary to understand how it flowed. It was only in 1840, the year of the Antarctica ice sheet discovery by Dumont d'Urville, that two books laid the basis for the future field of glaciology: one by Agassiz on the ice age and glaciers, the other one by canon Rendu on glacier theory. During the 19th century, ice flow theories, adopted by most of the leading scientists, were based on melting/refreezing processes. Even though the word ‘fluid’ was first used in 1773 to describe ice, more the 130 years would have to go by before the laws of fluid mechanics were applied to ice. Even now, the parameter of Glen's law, which is used by glaciologists to model ice deformation, can take a very wide range of values, so that no unique ice flow law has yet been defined. To cite this article: F. Rémy, L. Testut, C. R. Geoscience 338 (2006).  相似文献   

Water temperature behaviour in the River Loire since 1976 and 1881     

Florentina Moatar  Joël Gailhard 《Comptes Rendus Geoscience》2006,338(5):319-328

Analysis of monthly mean river temperatures, recorded on an hourly basis in the middle reaches of the Loire since 1976, allows reconstruction by multiple linear regression of the annual, spring and summer water temperatures from equivalent information on air temperatures and river discharge. Since 1881, the average annual and summer temperatures of the Loire have risen by approximately 0.8?°C, this increase accelerating since the late 1980s due to the rise in air temperature and also to lower discharge rates. In addition, the thermal regime in the Orleans to Blois reach is considerably affected by the inflow of groundwater from the Calcaires de Beauce aquifer, as shown by the summer energy balance. To cite this article: F. Moatar, J. Gailhard, C. R. Geoscience 338 (2006).  相似文献   

Sur les anomalies structurales de l'anticlinal de l'oued Bahloul de Tunisie : héritage tectonique et plissement cisaillant de couverture     

Ahmed Saadi  Noureddine Boukadi  Ali Gaaya 《Comptes Rendus Geoscience》2006,338(9):650-657

The Oued Bahloul structure exists in the central Atlas of Tunisia. This structure is oriented N70 and it shows a very particular geometry characterized by: (i) an important disharmony between the northern and the southern flanks; (ii) a dissymmetry between the east and the west parts of the structure; (iii) several gaps and progressive unconformities present in the Cretaceous and Eocene series.Three major tectonic directions characterize this structure: (i) the N120 appears in the western part of the anticline; (ii) some north–south faults distinguish the oriental part; (iii) the strike fault, which is confirmed by seismic data, affects the central part of this anticline. To cite this article: A. Saadi et al., C. R. Geoscience 338 (2006).  相似文献