Accounting for Parameter Uncertainty in Reservoir Uncertainty Assessment: The Conditional Finite-Domain Approach

An important aim of modern geostatistical modeling is to quantify uncertainty in geological systems. Geostatistical modeling requires many input parameters. The input univariate distribution or histogram is perhaps the most important. A new method for assessing uncertainty in the histogram, particularly uncertainty in the mean, is presented. This method, referred to as the conditional finite-domain (CFD) approach, accounts for the size of the domain and the local conditioning data. It is a stochastic approach based on a multivariate Gaussian distribution. The CFD approach is shown to be convergent, design independent, and parameterization invariant. The performance of the CFD approach is illustrated in a case study focusing on the impact of the number of data and the range of correlation on the limiting uncertainty in the parameters. The spatial bootstrap method and CFD approach are compared. As the number of data increases, uncertainty in the sample mean decreases in both the spatial bootstrap and the CFD. Contrary to spatial bootstrap, uncertainty in the sample mean in the CFD approach decreases as the range of correlation increases. This is a direct result of the conditioning data being more correlated to unsampled locations in the finite domain. The sensitivity of the limiting uncertainty relative to the variogram and the variable limits are also discussed.     

D型耗能器偏心支撑结构的抗震性能试验研究

偏心支撑结构是一种高烈度地震区高层建筑钢结构合理的抗侧力体系,本文针对目前偏心支撑结构存在的不足,提出一种新型的框架支撑形式——耗能器偏心支撑;并将该单斜杆(D型)耗能器偏心支撑与支撑斜杆上不加设耗能器的D型偏心支撑结构进行了对比试验。验证了该新型框架支撑形式不仅可以减少耗能梁段吸收的地震能量,而且可以减小耗能梁段的破坏程度,从而减少震后修复工作量;它具有很好的变形能力和足够的抗侧移能力。文中同时给出了设计方法,并提出了改进措施。     

Statistical analysis of metallic anomaly patterns at former air force bombing ranges

This paper summarizes the findings of a statistical analysis of the locations of metallic anomalies detected at the Pueblo Precision Bombing Range Number 2 in Otero County, Colorado, and at the Victorville Precision Bombing Range in San Bernardino County, California. The purpose of the study is to explore whether statistical properties of the pattern of anomaly locations can be used to discriminate areas likely to contain unexploded ordnance (UXO) left over from previous bombing practice from those unlikely to contain UXO. Techniques for discriminating areas with and without UXO are needed because historic records have left an incomplete account of previous military training activities, so that locations historically used for target practice are often unknown. This study differs from previous research on metallic anomaly data at former military training ranges in that it analyzes the spatial pattern of the discrete locations of the anomalies, rather than the average number of anomalies per unit area. The results indicate that differences in spatial pattern may be a distinguishing feature between areas that were used for target practice and those that are unlikely to contain UXO, even when a large number of ferrous rocks and other inert metallic anomalies are present. We found that at both of the former bombing ranges, the anomaly patterns in sample areas that are distant from all known bombing targets are consistent with a complete spatial randomness pattern, while those near the target areas fit a radially symmetric, bivariate Gaussian pattern. Furthermore, anomaly location patterns generated by surveys with airborne metal detectors have the same statistical properties as the patterns generated by surveys with on-ground detectors, even though the airborne systems detect only a subset of the anomalies found by the ground-based detectors. Thus, pattern information revealed by airborne surveys with metal detectors may be useful in identifying areas where careful searches for UXO are needed.

Kriging插值和序贯高斯条件模拟算法的对比分析

本文对Kriging插值与序贯高斯条件模拟值的算法联系进行了推导,并将两种计算结果和原始数据的统计参数作了对比。结果表明,Monto-carlo方法求得的序贯高斯条件模拟值经数学变换后等同于已知数据和此前模拟数据共同参与的Kriging插值结果与一个随机偏差的和,该随机偏差的均值为0,方差为Kriging误差方差。最优性条件导致Kriging插值结果的方差较原始数据降低了1个Kriging误差方差,造成Kriging平滑效应,其空间变异函数值降低,但自协方差函数值不变。序贯高斯条件模拟避免了平滑效应,其方差、变异函数和自协方差函数均不变,而其模拟值的误差方差较Kriging误差方差增加了1倍,表明1次随机模拟值的误差比Kriging插值大。然而,多次随机模拟值的平均值与Kriging插值的地理制图效果近似,可以弥补局部估值误差大的不足。因此,在应用中,Kriging插值是提供局部最优估计的方法,但却低估了全局的空间变异。而序贯高斯条件模拟的优点,在于提供若干等可能概率的模拟结果以进行估值的不确定性评价,并再现全局的空间可变性。     

Spatial pattern of grassland aboveground biomass and its environmental controls in the Eurasian steppe

Vegetation biomass is an important component of terrestrial ecosystem carbon stocks. Grasslands are one of the most widespread biomes worldwideplaying an important role in global carbon cycling. Thereforestudying spatial patterns of biomass and their correlations to environment in grasslands is fundamental to quantifying terrestrial carbon budgets. The Eurasian steppean important part of global grasslandsis the largest and relatively well preserved grassland in the world. In this studywe analyzed the spatial pattern of aboveground biomass(AGB)and correlations of AGB to its environment in the Eurasian steppe by meta-analysis. AGB data used in this study were derived from the harvesting method and were obtained from three data sources(literatureglobal NPP database at the Oak Ridge National Laboratory Distributed Active Archive Center(ORNL)some data provided by other researchers). Our results demonstrated that:(1) as for the Eurasian steppe overallthe spatial variation in AGB exhibited significant horizontal and vertical zonality. In detailAGB showed an inverted parabola curve with the latitude and with the elevationwhile a parabola curve with the longitude. In additionthe spatial pattern of AGB had marked horizontal zonality in the Black Sea-Kazakhstan steppe subregion and the Mongolian Plateau steppe subregionwhile horizontal and vertical zonality in the Tibetan Plateau alpine steppe subregion.(2) Of the examined environmental variablesthe spatial variation of AGB was related to mean annual precipitation(MAP)mean annual temperature(MAT)mean annual solar radiation(MAR)soil Gravel contentsoil p H and soil organic content(SOC) at the depth of 0–30 cm. NeverthelessMAP dominated spatial patterns of AGB in the Eurasian steppe and its three subregions.(3) A Gaussian function was found between AGB and MAP in the Eurasian steppe overallwhich was primarily determined by unique patterns of grasslands and environment in the Tibetan Plateau. AGB was significantly positively related to MAP in the Black Sea-Kazakhstan steppe subregion(elevation 3000 m)the Mongolian Plateau steppe subregion(elevation 3000 m) and the surface(elevation ≥ 4800 m) of the Tibetan Plateau. Neverthelessthe spatial variation in AGB exhibited a Gaussian function curve with the increasing MAP in the east and southeast margins(elevation 4800 m) of the Tibetan Plateau. This study provided more knowledge of spatial patterns of AGB and their environmental controls in grasslands than previous studies only conducted in local regions like the Inner Mongolian temperate grasslandthe Tibetan Plateau alpine grasslandetc.     

室内地磁基准图构建的优化算法研究

对比分析4种室内地磁基准图的构建算法,选取两种场景进行实验,并采用均方差、交叉验证法、积分均方误差等评价指标进行分析。结果表明,协同克里金插值算法有更高的精度,但构建速度较慢;标准高斯过程回归有更快的构建速度,但精度略低。因此,对于有高精度需求的场合可采用协同克里金算法;对于实时性要求高的情况,标准高斯过程回归更能满足需求。     

Permissibility of fractal exponents and models of band-limited two-point functions for fGn and fBm random fields

The fractional Gaussian noise (fGn) and fractional Brownian motion (fBm) random field models have many applications in the environmental sciences. An issue of practical interest is the permissible range and the relations between different fractal exponents used to characterize these processes. Here we derive the bounds of the covariance exponent for fGn and the Hurst exponent for fBm based on the permissibility theorem by Bochner. We exploit the theoretical constraints on the spectral density to construct explicit two-point (covariance and structure) functions that are band-limited fractals with smooth cutoffs. Such functions are useful for modeling a gradual cutoff of power-law correlations. We also point out certain peculiarities of the relations between fractal exponents imposed by the mathematical bounds. Reliable estimation of the correlation and Hurst exponents typically requires measurements over a large range of scales (more than 3 orders of magnitude). For isotropic fractals and partially isotropic self-affine processes the dimensionality curse is partially lifted by estimating the exponent from measurements along fixed directions. We derive relations between the fractal exponents and the one-dimensional spectral density exponents, and we illustrate the relations using measurements of paper roughness.The author would like to acknowledge helpful comments from two anonymous referees.     

Entropy and spatial disorder

The majority of geostatistical estimation and simulation algorithms rely on a covariance model as the sole characteristic of the spatial distribution of the attribute under study. The limitation to a single covariance implicitly calls for a multivariate Gaussian model for either the attribute itself or for its normal scores transform. The Gaussian model could be justified on the basis that it is both analytically simple and it is a maximum entropy model, i.e., a model that minimizes unwarranted structural properties. As a consequence, the Gaussian model also maximizes spatial disorder (beyond the imposed covariance) which can cause flow simulation results performed on multiple stochastic images to be very similar; thus, the space of response uncertainty could be too narrow entailing a misleading sense of safety. The ability of the sole covariance to adequately describe spatial distributions for flow studies, and the assumption that maximum spatial disorder amounts to either no additional information or a safe prior hypothesis are questioned. This paper attempts to clarify the link between entropy and spatial disorder and to provide, through a detailed case study, an appreciation for the impact of entropy of prior random function models on the resulting response distributions.     

Simple and Ordinary Multigaussian Kriging for Estimating Recoverable Reserves

Multigaussian kriging is used in geostatistical applications to assess the recoverable reserves in ore deposits, or the probability for a contaminant to exceed a critical threshold. However, in general, the estimates have to be calculated by a numerical integration (Monte Carlo approach). In this paper, we propose analytical expressions to compute the multigaussian kriging estimator and its estimation variance, thanks to polynomial expansions. Three extensions are then considered, which are essential for mining and environmental applications: accounting for an unknown and locally varying mean (local stationarity), accounting for a block-support correction, and estimating spatial averages. All these extensions can be combined; they generalize several known techniques like ordinary lognormal kriging and uniform conditioning by a Gaussian value. An application of the concepts to a porphyry copper deposit shows that the proposed “ordinary multigaussian kriging” approach leads to more realistic estimates of the recoverable reserves than the conventional methods (disjunctive and simple multigaussian krigings), in particular in the nonmineralized undersampled areas.