Uncertainty as the overlap of alternate conditional distributions

An important task in modern geostatistics is the assessment and quantification of resource and reserve uncertainty. This uncertainty is valuable support information for many management decisions. Uncertainty at specific locations and uncertainty in the global resource is of interest. There are many different methods to build models of uncertainty, including Kriging, Cokriging, and Inverse Distance. Each method leads to different results. A method is proposed to combine local uncertainties predicted by different models to obtain a combined measure of uncertainty that combines good features of each alternative. The new estimator is the overlap of alternate conditional distributions.     

大陆岩石圈对扩张机制的响应—辽蒙地质走廊中—新生代火山活动的时空分布

选择辽西为中心,以近东西向延伸800km的辽蒙地质走廊为研究区,通过年代学研究,确认130Ma以来的中、新生代火山活动对称分布的时空格局,具有“中间老、两侧新”的特点,而且随着时间的推移,软流圈来源的岩浆向东西两侧侧向流动,岩浆来源不断加深。在此基础上提出“软流圈底辟体上涌和水平侧向流动”的模式。     

Changing grading of soil: effect on critical states

Examples of situations are presented where the grading of a soil changes during its lifetime either by crushing of particles leading to an increase of fine material or by slow transport of fine particles with seepage leading to a decrease of fine material. Such grading changes influence the basic constitutive properties of the soil, in particular properties such as critical states which are dependent on the available range of densities of packing. Discrete element modelling is used to show the dependence of critical state conditions on grading and the way in which the particle assembly seeks out new critical state conditions as the grading changes.     

中强地震前后能量分布的自仿射特性

根据简化的地震波传播理论,“漫化”地震能量在空间的分配,减弱能量空间分布概率的极端情形及消除统计域为“空”的情形,由此构造类似于二维ｆＢｍ的地震能量空间分布概率曲面。与起伏不平的地形相似,由于基在水平方向及垂直方向的变化不是等比例的,因而这一分形曲面可能是统计自仿射的。     

Microlites and "nanolites" in rhyolitic glass: microstructural and chemical characterization

 We used transmission electron microscopy (TEM) and scanning electron microscopy (SEM) to study magmatic crystals in the Ben Lomond rhyolite lava dome, Taupo Volcanic Center, New Zealand. Using TEM and SEM to investigate the size distributions of these crystals, we identified three size populations: microphenocrysts (>1.2 μm wide), microlites (>0.6 μm wide), and smaller crystals (<0.6 μm wide) which we term "nanolites". The predominant mineral phases of the microlites and nanolites are augites, pigeonites, and hypersthenes. The compositions and microstructures within these pyroxenes indicate disequilibrium crystallization at approximately 850–900  °C and undercoolings as high as 300  °C from equilibrium crystallization temperatures. Complex microstructures resulting from subsolidus reactions in augite and pigeonite are consistent with moderate cooling rates within the upper obsidian layer of the Ben Lomond rhyolite dome. This study demonstrates the existence of sub-micron magmatic crystals in a rhyolite and illustrates the potential of TEM to provide unique information about the crystallization and cooling histories of glassy volcanic rocks. Received: May 8, 1995 / Accepted: November 27, 1995     

Bayesian estimation of seismic hazard for two sites in Switzerland

Seismic hazard analysis is based on data and models, which both are imprecise and uncertain. Especially the interpretation of historical information into earthquake parameters, e.g. earthquake size and location, yields ambiguous and imprecise data. Models based on probability distributions have been developed in order to quantify and represent these uncertainties. Nevertheless, the majority of the procedures applied in seismic hazard assessment do not take into account these uncertainties, nor do they show the variance of the results. Therefore, a procedure based on Bayesian statistics was developed to estimate return periods for different ground motion intensities (MSK scale).Bayesian techniques provide a mathematical model to estimate the distribution of random variables in presence of uncertainties. The developed method estimates the probability distribution of the number of occurrences in a Poisson process described by the parameter . The input data are the historical occurrences of intensities for a particular site, represented by a discrete probability distribution for each earthquake. The calculation of these historical occurrences requires a careful preparation of all input parameters, i.e. a modelling of their uncertainties. The obtained results show that the variance of the recurrence rate is smaller in regions with higher seismic activity than in less active regions. It can also be demonstrated that long return periods cannot be estimated with confidence, because the time period of observation is too short. This indicates that the long return periods obtained by seismic source methods only reflects the delineated seismic sources and the chosen earthquake size distribution law.     

Estimation of statistical parameters for censored lognormal hydraulic conductivity measurements

Field tests of hydraulic conductivity (e.g., injection test, pumping test, etc.) in low permeability formations are subject to censoring due to the detection limit of the instruments used. An iterative method of estimating the mean and variance of hydraulic conductivity data with a presumed log-normal distribution function is presented. This method accounts for the data that are actually below the lower detection limit (called truncated data) and thus gives distribution parameters that are more representative for the underlying distribution. The proposed method is then tested on two simulated normally distributed random datasets having different variances. The results show that the means and variances estimated by the proposed method are very accurate. Finally, the method is used to estimate the mean and variance of hydraulic conductivity data from single hole water injection tests in a fractured geological formation.     

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.     

大别杂岩中混合岩的矿物空间分布研究

介绍了矿物空间分布研究的基本原理及两种统计方法(接触频数法和线切法)。作者对混合岩矿物空间分布的研究表明:(1)前人提出的统计方法存在方法上的缺陷和应用上的局限性,作者推导出矿物接触类型的概率公式;(2)部分浅色体中矿物显示聚集分布的特征,而绝大部分的浅色体中矿物具有分散分布的特点。结合质量平衡和地球化学研究认为:大别杂岩中主体混合岩成因机制是重熔和交代作用。