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.     

Peak discharge of a Pleistocene lava-dam outburst flood in Grand Canyon, Arizona, USA

The failure of a lava dam 165,000 yr ago produced the largest known flood on the Colorado River in Grand Canyon. The Hyaloclastite Dam was up to 366 m high, and geochemical evidence linked this structure to outburst-flood deposits that occurred for 32 km downstream. Using the Hyaloclastite outburst-flood deposits as paleostage indicators, we used dam-failure and unsteady flow modeling to estimate a peak discharge and flow hydrograph. Failure of the Hyaloclastite Dam released a maximum 11 × 10⁹ m³ of water in 31 h. Peak discharges, estimated from uncertainty in channel geometry, dam height, and hydraulic characteristics, ranged from 2.3 to 5.3 × 10⁵ m³ s⁻¹ for the Hyaloclastite outburst flood. This discharge is an order of magnitude greater than the largest known discharge on the Colorado River (1.4 × 10⁴ m³ s⁻¹) and the largest peak discharge resulting from failure of a constructed dam in the USA (6.5 × 10⁴ m³ s⁻¹). Moreover, the Hyaloclastite outburst flood is the oldest documented Quaternary flood and one of the largest to have occurred in the continental USA. The peak discharge for this flood ranks in the top 30 floods (>10⁵ m³ s⁻¹) known worldwide and in the top ten largest floods in North America.     

Soil quality changes in land degradation as indicated by soil chemical, biochemical and microbiological properties in a karst area of southwest Guizhou, China

Not only the nutritional status and biological activity but also the soil ecological functioning or soil health has been impacted profoundly by land degradation in the karst area of southwest China where the karst ecosystems are generally considered as extremely vulnerable to land degradation under intensified land-use changes. The objectives of this study are to elucidate the changes in overall soil quality by a holistic approach of soil nutritional, biological activity, and soil health indicators in the karst area as impacted by intense cultivation and vegetation degradation. Topsoil samples were collected on selected eco-tesserae in a sequence of land degradation in a karst area of southwest Guizhou in 2004. The soil nutrient pools of organic carbon (C_org), extractable extracellular carbon (C_ext), total soil nitrogen (N_t), alkali-hydrolyzable nitrogen (N_ah), total phosphorus (P_t), available phosphorus (P_a) were analyzed by wet soil chemistry. The soil biological properties were studied by means of measurements of microbial biomass carbon (both by fumigation–extraction, FE-C_mic, and by calculation from substrate-incubation respiration, SIR-C_mic) of respiration [respiration without addition of substrates, basal respiration (BR), and potential respiration (PR) with substrate-incubation] and of soil enzyme activities (invertase, urease, and alkaline phosphatase). Soil health status was assessed by simple indices of C_mic/C_org and BR/C_mic in conjunction with bacterial community structures determined by polymerase chain reaction and denaturing gradient gel electrophoresis. While the nutritional pool parameters, such as C_org and C_ext, described basically the changes in soil life-supporting capacity with cultivation interference and vegetation declined, those parameters of biological activity such as FE-C_mic, SIR, and SIR-C_mic as well as bacterial community structures measured by molecular method evidenced well the changes in soil functioning for ecosystem health with the land degradation.     

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.     

区域水资源可持续利用的综合评价方法

水资源可持续利用指标体系及评价方法是水资源可持续利用研究的核心问题之一。以复合系统理论为基础,将水资源、社会经济和环境组成的复合系统定义为水资源可持续利用系统(RSWRS系统)。应用Bossel可持续发展基本定向指标框架,建立了水资源可持续利用指标评价体系。应用系统综合评价法,权重采用基于Bossel评分标准,以参考状态的离差平方和最大法计算,建立了以RSWRS系统发展综合指数和发展态势度量模型。以陕西省为例,进行了水资源可持续利用的综合定量评价。     

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.     

Ordovician Graptolite Rhabdosome Complication and Its Implications on Sea Level Changes

A total of four times of rhabdosome complication events, i.e., the lateral branching of graptolite stipes during the Late Middle Ordovician, the secondary branching of graptolite stipes at the earliest Upper Ordovician, the early Qiantangjiangian of Upper Ordovician and the middle Qiantangjiangian, respectively, is discussed in this paper. These events and other adaptation events demonstrate close relationships between a diverse graptolite fauna and sea level changes, and consequently can be employed to study sea level fluctuations. It is safe to conclude that the complication of rhabdosome started at the maximum flooding surface (MFS) and terminated at the beginning of regression.