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

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.     

Estimation for partially observed Markov processes

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.     

New Generation of Probabilistic Seismic Hazard Assessment for the Area Cologne/Aachen Considering the Uncertainties of the Input Data

A new earthquake catalogue for central, northern and northwestern Europe with unified M_w magnitudes, in part derived from chi-square maximum likelihood regressions, forms the basis for seismic hazard calculations for the Lower Rhine Embayment. Uncertainties in the various input parameters are introduced, a detailed seismic zonation is performed and a recently developed technique for maximum expected magnitude estimation is adopted and quantified. Applying the logic tree algorithm, resulting hazard values with error estimates are obtained as fractile curves (median, 16% and 84% fractiles and mean) plotted for pga (peak ground acceleration; median values for Cologne 0.7 and 1.2 m/s² for probabilities of exceedence of 10% and 2%, respectively, in 50 years), 0.4 s (0.8 and 1.5 m/s²) and 1.0 s (0.3 and 0.5 m/s²) pseudoacclerations, and intensity (I₀ = 6.5 and 7.2). For the ground motion parameters, rock foundation is assumed. For the area near Cologne and Aachen, maps show the median and 84% fractile hazard for 2% probability of exceedence in 50 years based on pga (maximum median value about 1.5 m/s²), and 0.4 s (>2 m/s²) and 1.0 s (about 0.8 m/s²) pseudoaccelerations, all for rock. The pga 84% fractile map also has a maximum value above 2 m/s² and shows similarities with the median map for 0.4 s. In all maps, the maximum values fall within the area 6.2–6.3° E and 50.8–50.9° N, i.e., east of Aachen.     

Evidence of reworking and resuspension of carbonates during last glacial maximum and early deglacial period along the southwest coast of India

A gravity core collected from the upper slope of southwest of Quilon at a water depth of 776 m (Lat: 8°12′263″N, Long: 76°28′281″E) was analysed for texture (carbonate free), calcium carbonate and organic carbon. Variation in silicic fraction seems to be controlled by silt, i.e., enrichment from 15 ka BP to 10 ka BP and then constant in Holocene. Below 15 ka BP, the silicic fraction gets depleted compared to the Holocene section with a minimum around 21 ka BP. Clay content remains nearly constant except in the Holocene where it shows an enrichment. Carbonate content of less than 63 micron when computed by subtracting coarse fraction content from the total carbonate suggests that the total carbonates are mainly concentrated in the finer fraction. All these carbonate phases show an inverse relationship with silicic fraction except in Holocene. Below 15 ka BP, CaCO₃ dominates in sediments comprising more than 65%, such an increase is also seen in the coarse fraction. Coarse fraction from these sections contains abundant nodular type aggregates encrusting small forams. This period is marked by a high sedimentation rate comparable to Holocene. These parameters suggest that the productivity and precipitation have increased in the Holocene due to the intensification of the southwest monsoon. During the last glacial maximum and early deglacial period the high sedimentation rate indicates redeposition of the carbonates from the existing carbonate lithofacies situated between Quilon and Cape Comorin probably due to the slope instability.     

地震信号的相位恢复及误差分析

常见的几种地震子波有:零相位子波、最小相位子波、最大相位子波和混合相位子波。以不同类型的信号为激发子波,对不同地层模型合成地震道。仅用原始合成地震道记录的振幅谱来恢复原始记录,讨论不同方法下,由于激发子波的不同,对比分析原始记录与恢复记录的差异,及其恢复效果。     

高光谱遥感数据三次光滑样条滤噪

分析了高光谱遥感数据噪声滤波的作用和现状，实现了一种基于三次光滑样条函数的高光谱遥感数据噪声滤波算法，解决了目前高光谱遥感数据噪声滤波算法自适应效果不理想的问题。通过对AVIRIS数据试验，证明此方法简单易行，计算精度高，具有良好的局部自适应拟合能力，并能有效地滤除数据中的噪声，改善数据质量。     

笼状水合物拉曼光谱特征与结构水合数的耦合关系

为了探讨不同气体组分和环境介质对形成笼状结构类型水合物和水合数的影响, 开展了一元体系 (CH4、CO2、C3H8 )和二元体系(CH4 +CO2、CH4 +C3H8、CH4 +N2 )的水合物生成结晶充填过程、结晶构型和动力学特性分析, 并对生成的水合物进行了拉曼光谱分析。结果表明单组分甲烷充填小孔穴 512和大孔穴 512 62 形成Ⅰ型笼状结构水合物(SⅠ), 二氧化碳和丙烷只占据大孔穴 512 64 形成Ⅱ型笼状结构水合物 (SⅡ ); 而二元混合组分中小孔穴中只充填有甲烷, 而没有CO2、N2 和C3H8。应用反褶积的ν1 对称谱带测定了CH4 分子在Ⅰ型结构大孔穴和小孔穴中的相对占有率,并根据谱带的面积比(对应于小孔穴与大孔穴)计算了平衡条件下甲烷水合物孔穴占有率及其耦合的水合数, 认为气体分子的大小不仅影响它所充填的孔穴形态和类型, 而且影响水合物生成的结构类型和水合数。     

基于DMN的高光谱图像分割方法研究

简述高光谱遥感光谱特征体系(包括光谱曲线特征、光谱变换特征和光谱度量特征3个层面)。研究马尔科夫网的概念和方法,生成基于光谱角(SA)特征度量的DMN,并以DMN为证据对高光谱图像进行分割;研究和实验表明基于SA信息的马尔科夫网可以很好地综合高光谱数据空间特征与光谱特征间的关系,为进一步数据处理提供优化控制(其实质是概率神经网络)。最后提出未来应用和研究方向。     

Damaging properties of ground motions and prediction of maximum response of structures based on momentary energy response

Dynamic damaging potential of ground motions must be evaluated by the response behaviour of structures, and it is necessary to indicate what properties of ground motions are most appropriate for evaluation. For that purpose, the behaviour of energy input process and hysteretic energy dissipation are investigated in this study. It is found that the momentary input energy that is an index for the intensity of input energy is related to the characteristics of earthquakes such as cyclic or impulsive, and to the response displacement of structures immediately. On the basis of these results, a procedure is proposed to predict inelastic response displacement of structures by corresponding earthquake input energy to structural dissipated damping and hysteretic energy. In this procedure the earthquake response of structures is recognized as an input and dissipation process of energy, and therefore structural properties and damaging properties of ground motions can be taken into account more generally. Lastly, the studies of the pseudodynamic loading test of reinforced concrete structure specimens subjected to ground motions with different time duration are shown. The purpose of this test is to estimate the damaging properties of ground motions and the accuracy of the proposed prediction procedure. Copyright © 2002 John Wiley & Sons, Ltd.