Positive definiteness is not enough

Geostatisticians know that the mathematical functions chosen to represent spatial covariances and variograms must have the appropriate type of positive definiteness, but they may not realize that there are restrictions on the types of covariances and variograms that are compatible with particular distributions. This paper gives some examples showing that (1) the spherical model is not compatible with the multivariate lognormal distribution if the coefficient of variation is 2.0 or more (even in 1-D), and (2) the Gaussian covariance and several other models are not compatible with indicator random functions. As these examples concern quite different types of random functions, it is clear that there is a general problem of compatibility between spatial covariance models (or variograms) and a specified multivariate distribution. The problem arises with all distributions except the multivariate normal, and not just the two cited here. The need for a general theorem giving the necessary and sufficient conditions for a covariance or a variogram to be compatible with a particular distribution is stressed.     

Spatial prediction and ordinary kriging

Suppose data {Z(s _i ):i=1, ..., n} are observed at spatial locations {s _i :i=1, ..., n}. From these data, an unknownZ(s ₀) is to be predicted at a known locations ₀c, or, ifZ(s₀) has a component of measurement error, then a smooth versionS(s ₀) should be predicted. This article considers the assumptions needed to carry out the spatial prediction using ordinary kriging, and looks at how nugget effect, range, and sill of the variogram affect the predictor. It is concluded that certain commonly held interpretations of these variogram parameters should be modified.This paper was presented at MGUS 87 Conference, Redwood City, California, 14 April 1987.     

The equivalence of predictions from universal kriging and intrinsic random-function kriging

A proof is provided that the predictions obtained from kriging based on intrinsic random functions of orderk are identical to those obtained from anappropriate universal kriging model. This is a theoretical result based on known variability measures. It does not imply that people performing traditional universal kriging will get the same predictions as those using intrinsic random functions, because traditionally these methods differ in how variability is modeled. For intrinsic random functions, the same proof shows that predictions do not depend on the specific choice of the generalized covariance function. It is argued that the choice between these methods is really one of modeling and estimating the variability in the data.     

Robustness of variograms and conditioning of kriging matrices

Current ideas of robustness in geostatistics concentrate upon estimation of the experimental variogram. However, predictive algorithms can be very sensitive to small perturbations in data or in the variogram model as well. To quantify this notion of robustness, nearness of variogram models is defined. Closeness of two variogram models is reflected in the sensitivity of their corresponding kriging estimators. The condition number of kriging matrices is shown to play a central role. Various examples are given. The ideas are used to analyze more complex universal kriging systems.Research performed while on leave at Centre de Geóstatistique et de Morphologie Mathématique, Fontainebleau.     

A comparison between cokriging and ordinary kriging: Case study with a polymetallic deposit

Cokriging is applied to the estimation of mineral resources in a polymetallic deposit. Several major steps, which should be taken in using cokriging, are highlighted as necessary practical considerations. The case study is related to an ultramafic copper-nickel deposit. Six elements, Cu, Ni, Au, Ag, Pt, and Pd, occurring in the deposit, are partitioned into three subgroups and the elements within each group are simultaneously estimated on the basis of over 4000 drill assays. A comparison was made between ordinary kriging and cokriging methods through cross-validation. The results show that cokriging has significantly improved the estimates of resources by reducing the overall estimation error by over 15% and the variance of error by over 20%.     

Distribution of kriging error and stationarity of the variogram in a coal property

If a particular distribution for kriging error may be assumed, confidence intervals can be estimated and contract risk can be assessed. Contract risk is defined as the probability that a block grade will exceed some specified limit. In coal mining, this specified limit will be set in a coal sales agreement. A key assumption necessary to implement the geostatistical model is that of local stationarity in the variogram. In a typical project, data limitations prevent a detailed examination of the stationarity assumption. In this paper, the distribution of kriging error and scale of variogram stationarity are examined for a coal property in northern West Virginia.     

Inner product matrices, kriging, and nonparametric estimation of variogram

Two important problems in the practical implementation of kriging are: (1) estimation of the variogram, and (2) estimation of the prediction error. In this paper, a nonparametric estimator of the variogram to circumvent the problem of the precise choice of a variogram model is proposed. Using orthogonal decomposition of the kriging predictor and the prediction error, a method for selecting, what may be considered, a statistical neighborhood is suggested. The prediction error estimates based on this scheme, in fact, reflects the true prediction error, thus leading to proper coverage for the corresponding prediction interval. By simulations and a reanalysis of published data, it is shown that the proposals made in this paper are useful in practice.     

Smoothing and interpolation by kriging and with splines

Let scalar measurements at distinct points x₁, , x_n be y₁, , y_n.We may look for a smooth function f(x)that goes through or near the points (x_i, y_i).Kriging assumes f(x)is a random function with known (possibly estimable) covariance function (in the simplest case). Splines assume a definition of the smoothness of a nonrandom function f(x).An elementary explanation is given of the fact that spline approximations are special cases of the solution of a kriging problem.     

Geostatistical case studies of the advantages of lognormal-de Wijsian kriging with mean for a base metal mine and a gold mine

Parallel variogram analyses, block kriging, and follow-up studies were effected for the lead content of part of the Prieska copper-zinc ore body and for the gold content of the highly variable Breef in a section of the Loraine gold mine, based first on untransformed values and second on logarithmically transformed values using the lognormal-de Wijsian model. For both models the effect was also analyzed of using the population mean or ignoring it. Practical follow-up comparisons confirm theoretical considerations and show that on these mines conditional biases can be eliminated conveniently by kriging with mean; also that the lognormal-de Wijsian model with mean gives the best results.     

塔里木地块与古亚洲/特提斯构造体系的对接

塔里木盆地为环形山链所环绕,北缘为古亚洲体系的天山弧形山链,南缘为特提斯体系的西昆仑-阿尔金弧形山链。自新元古代晚期以来,塔里木地块及周缘地区经历了古亚洲洋盆和特提斯洋盆的开启、俯冲、闭合以及微陆块多次碰撞造山,发生多期的构造、岩浆及成矿作用。特别是受印度/亚洲碰撞(60~50Ma)以来的近程效应和远程效应影响,使塔里木盆地周缘发生强烈的隆升、缩短及走滑变形,形成了现今复杂的环型造山系,完成了古亚洲体系和特提斯体系与塔里木地块的最终对接。塔里木地块与周缘两大构造体系的焊接是从早古生代开始的。研究表明,早古生代末期塔里木已与西昆仑-阿尔金始特提斯造山系链接一起。此时,塔里木地块东段与中天山增生弧地体碰撞,而西段在晚古生代与中天山增生弧地体碰撞。塔里木盆地周缘早古生代造山系中存在早古生代中期和早古生代晚期的两次造山事件,致使塔里木盆地内映现两个早古生代构造不整合面:晚奥陶世-志留纪之间的角度不整合和中晚泥盆世与早古生代之间的角度不整合。塔里木盆地早古生代的古地理、古环境和古构造研究表明,塔里木早古生代台地位于盆地的中西部,盆地东部为陆缘斜坡和深海/半深海沉积盆地,与南天山早古生代被动陆缘链接。印度/亚洲碰撞导致塔里木盆地西南缘的喜马拉雅西构造结的形成与不断推进,使特提斯构造体系与古亚洲构造体系在西构造结处靠拢及对接,终使塔里木盆地最后定型。     

可变电荷土壤和恒电荷土壤与氢离子相互作用机理

研究了可变电荷土壤和恒电荷土壤与H相互作用的机理，并比较了它们之间的差别，研究结果表明，氢离子输入土壤后可以转化为表面正电荷，可溶性铝和可交换性酸，但是由于土壤的组成和性质不同，不同土壤中H＋三种去向的贡献不同。H＋转化为表面正电荷是由于土壤表面Fe-OH,Al-OH的质子化造成的，因此H＋转化为表面正电荷的能力与土壤中氧化铁的含量密切相关，从而可变电荷土壤中H＋转化为表面正电荷的贡献比恒电荷土壤中的大。H＋转化为可溶性铝的能力与土教育部 的矿物组成密切相关，随着H＋输入量的增加，土壤中可溶性铝的含量也增加。可变电荷土壤中可溶性铝增加的顺序为红壤＞赤红壤＞铁质砖红壤，在H＋的加入量小于15mmol/kg时，黄棕壤的可溶性铝介于红壤和赤红壤之间，当H＋的加入量大于约15mmol/kg时，黄棕壤的可溶性铝略小于赤红壤，棕壤的可溶性铝明显小于红壤和赤红壤，但比铁质砖红壤高，恒电荷土壤的可变性酸量明显大于可变电荷土壤，但从总的看来，H＋加入量的变化对可交换性酸量的影响不大。     

多年冻土地基正温输气管道地温场实测及分析

我国有多条油气管道位于多年冻土地区,工程问题层出不穷。因输送介质处于正温状态,其所释放热量对管道周围冻土冻融过程有极大影响。为阐明正温管道对多年冻土温度场及冻融特征的影响,基于西部某多年冻土区正温输气管道现场实验,对管道地基温度场进行了为期1年的现场实测。数据分析表明,多年冻土天然上限为1.5~2.0 m;土体融化期及冻结期分别为6-10月、11-次年5月;监测段多年冻土热量收支基本平衡,属于不稳定冻土,在外界热扰动下极易退化;正温输气管道的存在引起了多年冻土的退化且对其温度场有很大影响,水平方向影响范围约1.5 m,管下最大融深可达7.0 m。同时指出了针对处于临界状态的多年冻土,在基于对其全面、深入了解的基础上,越早考虑相关工程建设带来的热扰动对多年冻土的不利影响,则处置难度越低且损失越小。     

Correlation of Mississippian (Upper Viséan) foraminiferan,conodont, miospore and ammonoid zonal schemes,and correlation with the Asbian–Brigantian boundary in northwest Ireland

The microbiota of the upper Viséan (Asbian–Brigantian) rocks in the Lough Allen Basin in northwest Ireland is analysed. The Middle Mississippian sequence studied extends from the upper part of the Dartry Limestone/Bricklieve Limestone formations of the Tyrone Group to the Carraun Shale Formation of the Leitrim Group. The rocks have been traditionally dated by ammonoid faunas representing the B_2a to P_2c subzones. The Meenymore Formation (base of the Leitrim Group) also contains conodont faunas of the informal partial‐range Mestognathus bipluti zone. The upper Brigantian Lochriea nodosa Conodont Zone was recognized by previous authors in the middle of the Carraun Shale Formation (Ardvarney Limestone Member), where it coincides with upper Brigantian ammonoids of the Lusitanoceras granosus Subzone (P_2a). Foraminifera and algae in the top of the Dartry Limestone Formation are assigned to the upper Cf6γ Foraminifera Subzone (highest Asbian), whereas those in the Meenymore Formation belong to the lower Cf6δ Foraminifera Subzone (lower Brigantian). The Dartry Limestone Formation–Meenymore Formation boundary is thus correlated with the Asbian–Brigantian boundary in northwest Ireland. For the first time, based on new data, a correlation between the ammonoid, miospore, foraminiferan and conodont zonal schemes is demonstrated. The foraminiferans and algae, conodonts and ammonoids are compared with those from other basins in Ireland, northern England, and the German Rhenish Massif. Historically, the Asbian–Brigantian boundary has been correlated with several levels within the P_1a Ammonoid Subzone. However, the new integrated biostratigraphical data indicate that the Asbian–Brigantian boundary in northwest Ireland is probably located within the B_2a Ammonoid Subzone and the NM Miospore Zone, but the scarcity of ammonoids in the Tyrone Group precludes an accurate placement of that boundary within this subzone. Copyright © 2006 John Wiley & Sons, Ltd.     

Sorption and diffusion studies with low molecular weight organic compounds in cementitious systems

The uptake of methanol, ethanol, formaldehyde, acetaldehyde, formic acid and acetic acid by cement paste was determined in hydrating cement after 1 h, 28 d and 390 d hydration. The sorption values determined for formate and acetate were critically assessed by investigating through- and out-diffusion of these compounds in fully hydrated cement paste and their uptake by individual cement phases. Diffusion studies included inverse modelling of four data sets for each compound and an uncertainty analysis based on a Latin hypercube sampling procedure. Solid–liquid distribution ratios determined from the hydration experiments are on the order of 10⁻⁴ m³ kg⁻¹ in the case of alcohols and aldehydes indicating non-specific (very weak) bonding onto the surface of the cement phases, e.g. through hydrogen bonding. Hydration and diffusion studies reveal slightly higher distribution ratios and reversible uptake by cement paste and cement phases in the case of acetate indicating specific adsorption (electrostatic interaction) onto partially positively charged surface sites of the cement phases. Selective binding of a small fraction of formate is evidenced from both sorption and out-diffusion experiments suggesting the presence of sorption sites capable of strongly bonding the anion, presumably by SO₄²⁻/HCOO⁻ replacement in the ettringite structure.     

The tectonics and mineral systems of Proterozoic Western Australia:Relationships with supercontinents and global secular change

The cratonisation of Western Australia during the Proterozoic overlapped with several key events in the evolution of Earth. These include global oxidation events and glaciations, as well as the assembly,accretionary growth, and breakup of the supercontinents Columbia and Rodinia, culminating in the assembly of Gondwana. Globally, Proterozoic mineral systems evolved in response to the coupled evolution of the atmosphere, hydrosphere, biosphere and lithosphere. Consequently, mineral deposits form preferentially in certain times, but they also require a favourable tectonic setting. For Western Australia a distinct plate-margin mineralisation trend is associated with Columbia, whereas an intraplate mineralisation trend is associated with Rodinia and Gondwana, each with associated deposit types. We compare the current Proterozoic record of ore deposits in Western Australia to the estimated likelihood of oredeposit formation. Overall likelihood is estimated with a simple matrix-based approach that considers two components: The "global secular likelihood" and the "tectonic setting likelihood". This comparative study shows that at least for the studied ore-deposit types, deposits within Western Australia developed at times, and in tectonic settings compatible with global databases. Nevertheless, several deposit types are either absent or poorly-represented relative to the overall likelihood models. Insufficient exploration may partly explain this, but a genuine lack of deposits is also suggested for some deposit types. This may relate either to systemic inadequacies that inhibited ore-deposit formation, or to poor preservation. The systematic understanding on the record of Western Australia helps to understand mineralisation processes within Western Australia and its past connections in Columbia, Rodinia and Gondwana and aids to identify regions of high exploration potential.     

稳定同位素和微量元素在多源多汇体系中地球化学行为的理论模拟

根据地质体系多源多汇的特点,引进了一种新的定量地球化学理论模型,适用于模拟稳定同位素和微量元素在具有多个物质来源和多种分馏途径的地质体系中的变化规律。运用本文多源多汇模型研究岩浆同化-分异结晶过程中微量元素和稳定同位素的行为,所得的结果与前人AFC模型结果一致。运用此多源多汇模型对岩浆水与大气水混合过程中结晶出的石英进行模拟计算,发现其氧同位素组成随着结晶温度的降低而变大。大气中甲烷的产生和消耗有多种途径,是一种多源多汇体系,运用此模型研究它的碳同位素组成,发现其值随着甲烷总量的增多而变大。多源多汇模型不仅从更高的层次上包含了简单分馏模式、多元混合模式和AFC模式,而且可以研究这些模式不能解决的复杂地球化学过程。     

软土中张紧式吸力锚破坏标准模型试验与有限元分析

为了确定软土中张紧式吸力锚的破坏标准,采用自主研发的电动伺服加载装置,在荷载和位移控制方式下进行了张紧式吸力锚在最佳系泊点受静荷载作用的承载力模型试验。结果表明：不同的破坏模式,锚破坏时对应的位移也不同。当锚为竖向破坏时,对应锚沿系泊方向的位移约为0.6倍的锚径;当锚为水平破坏时,对应锚沿系泊方向的位移约为0.3倍的锚径。同时,按照模型试验所得的破坏标准确定的吸力锚的极限承载力与极限分析法的预测结果吻合较好。对足尺锚进行了有限元分析,将分析结果与极限分析法的预测结果进行比较,验证了模型试验所得位移破坏标准的合理性。     

Fault systems and paleostresses in the Vestfirdir Peninsula. Relationships with the Tertiary paleo-rifts of Skagi and Snaefells (Northwest Iceland)

Abstract

The Vestfirdir Peninsula of northwestern Iceland mainly consists of tholeiitic lava flows, 8–14 Ma old, gently dipping to the southeast. A detailed study of strike-slip and normal faulting allowed identification of two main paleostress regimes. Two sets of normal faults were recognized. The largest set trends ENE-WSW to NNE-SSW; the minor set trends NW-SE to WNW-ESE. Concerning the major extension, the reconstruction of paleostress trajectories shows a gradual change in trend from ESE-WNW, in the northern half of the peninsula, to NNW-SSE to the south. The minor extension also shows a gradual change from NNE-SSW to ENE-WSW trends, from north to south. The nearly constant perpendicularity between the major and minor trends of extension is accounted for by permutation of stress axes within the general pattern of extension related to oceanic rifting. The progressive azimuthal change of the major extension trend, from northeast to southwest across the peninsula, is interpreted as the expression of a change in trend of the extinct Skagi-Snaefells rift, a structure that cannot be reconstructed directly through geological mapping. The average trends of extension in the southern Vestfirdir Peninsula, N150°E, suggest a N60°E trend for the ancient Snaefells rift segment. Likewise, the N100–110°E trends of extension in northern Vestfirdir suggest a N10–20°E trend for the Skagi paleo-rift., © Elsevier, Paris     

Multiple overpressure systems and their relationship with hydrocarbon accumulation in the Qikou Depression of the Bohai Bay Basin,China

Pressure measurements using drill stem tests and estimates from log data calculation indicate that three vertically stacked regional pressure compartments exist in the Qikou Depression of Bohai Bay Basin, N. China. The compartments comprise hydrostatic, upper weak, and lower overpressure systems. Laterally, overpressure (pressure coefficient > 1.2) occurs in the deeper areas and weakens gradually from the centre to the margin of the depression. The accumulation of oil and gas exhibits the interesting characteristics of oil‐bearing layers above gas‐bearing layers in the Qikou Depression. The pattern can be accounted for by the evolution of overpressure system, the maturity process of the source rock and the main fault activity. In the late Dongying Formation (Ed, 30 Ma), the lower overpressure system began to form shape, and the hydrocarbon sources generated a large volume of oil. However, because there was no migration pathway, the oil only accumulated in the original strata. In the late Guantao Formation (Ng, 12 Ma), the gas was generated, the upper overpressure system formed gradually, and the activity of the main fault gradually increased. Then, the overpressure pushed the early gathered oil to flow from the lower overpressure system into the upper overpressure system. Afterwards, the activity of the main fault decreased again and remains weak until now. Thus, later generated natural gas cannot keep migrating along the main fault and can only accumulate in the lower overpressure system. Copyright © 2014 John Wiley & Sons, Ltd.     

Characterization of water bursting and discharge into underground mines with multilayered groundwater flow systems in the North China coal basin

A conceptual framework for characterization of water bursting and discharge into underground mines with multilayered groundwater flow systems is presented, based on the features of the site conditions and analyses of the water bursting and mine inundation events of the North China coal basin. Comprehensive analyses of the hydrogeological conditions for establishment of the three-dimensional groundwater flow systems of the North China coal basin revealed different vertical hydraulic connection paths or channels. These connections include karst collapse columns, fault or fracture zones, buried weathering zones, and fracture networks in aquitards, within the multilayered groundwater flow systems. Also examined, was the effect of the primary features of the flow system and those different connection paths on water bursting and discharge into the underground coal mines. It was demonstrated that appropriately identifying and adequately understanding the three-dimensional multilayered groundwater flow systems and those various vertical hydraulic connection mechanisms are critical for appropriately preventing water bursting hazards and predicting water discharge into underground mines. A valuable guideline is presented on characterization of water bursting and discharge into underground mines with multilayered groundwater flow systems.

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Resumen Un cadre de travail conceptuel pour la caractérisation du jaillissement et de la vidange des eaux dans les mines à plusieurs niveaux d'écoulement est présenté, basé sur les conditions et l'analyse sur site du jaillissement des eaux et des inondations dans les bassins charbonneux du Nord de la Chine. L'analyse compréhensive des conditions hydrogéologiques des systèmes d'écoulement tridimensionnel de ces bassins, révèle des trajets ou des chenaux qui sont autant de connections hydrauliques verticales. Ces connections comprennent des effondrement karstiques en colonne, des zones de fractures et de failles, des zones d'altération, des réseaux de fractures dans les aquitards, dans le système hydrogéologique multicouche. L'influence des caractéristiques primaires du système d'écoulement et de ces différentes connections sur le jaillissement et la vidange dans les mines, est également examiné. Il a été démontré que l'identification appropriée et la compréhension adéquate du système d'écoulement souterrain multicouche et tridimensionnel, et des mécanismes variés de connection hydraulique verticale est critiquée pour prévenir de manière appropriée les risques de jaillissement et de vidange dans les mines. Des guidelines valorisables sont présentées, pour la caractérisation du jaillissement et de la vidange dans de tels systèmes.

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Résumé Se presenta un marco conceptual para la de caracterización de la despresurización y descarga de agua a minas subterráneas con sistemas de acuíferos de múltiples niveles, el cual se basa en las condiciones del sitio, análisis de la despresurización de agua e inundaciones de minas en la cuenca de carbón del norte de la China.Un análisis comprehensivo de las condiciones hidrogeológicas para el establecimiento de los sistemas de flujo de agua de tri-dimensionales en la cuenca de carbón del norte de la China ha revelado diferentes canales hidráulicos verticales. Estas conexiones incluyen columnas de karst colapsadas, fallas o zonas de fracturas, zonas de regalita hundida y redes de fracturas en zonas de poca permeabilidad dentro de los sistemas de flujo de múltiples niveles.También se investigó el efecto de los rasgos primarios del sistema de flujo y los diferentes canales conectivos sobre la despresurización y descarga de agua a minas subterráneas. Se demostró que el entendimiento e identificación adecuada de los sistemas de acuíferos de múltiples niveles en tres dimensiones es crítico para prevenir apropiadamente la despresurización y descarga de agua a minas subterráneas. Se presentan lineamientos valiosos en relación con la despresurización y descarga de agua a minas subterráneas en sistemas de flujo de múltiple nivel.