Infill-sampling design and the Cost of classification errors

The criterion used to select infill sample locations should depend on the sampling objective. Minimizing the global estimation variance is the most widely used criterion and is suitable for many problems. However, when the objective of the sampling program is to partition an area of interest into zones of high values and zones of low values, minimizing the expected cost of classification errors is a more appropriate criterion. Unlike the global estimation variance, the cost of classification errors incorporates both the sample locations and the sample values into an objective infill-sampling design criterion.     

Sequential sampling to contour an uncertain function

Sampling exploration of uncertain functions to locate critical contour levels is most effective if sampling decisions are made sequentially. A simple sequential exploration strategy, based on pseudo-Bayesian second-moment analysis, is proposed and compared with non-sequential systematic sampling. Repeated application to functions simulated pseudorandomly from stationary random processes on the line and on the plane indicates uniform superiority of the sequential strategy. The method is particularly advantageous when the function of interest,h(X), has an uncertain trend, and in general when the random process that quantifies prior uncertainty onh(X) is highly correlated.     

The effects of sampling design parameters on block selection

Cost-effective spatial sampling strategy requires balancing sampling costs with the expected benefits from improved information. A contaminated site numerical model was used to test various single-phase sampling schemes, which were evaluated based on the quality of block selections from interpolated values. Different sample set sizes, different sampling patterns, and two levels of sampling precision were used. The sample set size was the only one of these factors observed to be significant. Bias was also examined. Modest levels (<20%) had minimal impact; the effects of higher levels of bias varied with the selection level concentration.Although the research described in this article has been supported by the United States Environmental Protection Agency through cooperative agreement CR814701 to the Environmental Research Center of the University of Nevada, Las Vegas, it has not been subjected to Agency review and, therefore, does not necessarily reflect the view of the Agency and no official endorsement should be inferred.     

Geochemical sampling with special reference to environmental risk assessment

We usually conduct environmental investigation through sample study. Therefore, it is essential that samples should be representative, at all time, and of the object be studied. However, the issues of sample representativeness and sampling errors are often neglected by investigators. Based on modem geo-statistics and sampling theory, this paper addresses these issues in more detail and presents a case study related to environmental risk assessment. The issue of sample representativeness can be measured in the following three aspects： （1） whether the sample numbers are large enough to reflect the characteristics of the initial object being studied）; （2） whether the sample mass （or sample volume） is large enough to represent the original site （the local segment being sampled）; （3） whether assay portion is prepared well enough to depict the initial sample. Sample numbers are dictated by the confidence level, the variance of population and the acceptable estimation error as well as the homogeneity and the spatial continuity of population.     

The updated kriging variance and optimal sample design

A number of criteria based on kriging variance calculations may be used for infill sampling design in geologic site characterization. Searching for the best new sample locations from a set of candidate locations can result in excessive computation time if these criteria and the naive rekriging are used. The relative updated kriging estimate and variance for universal kriging estimation are demonstrated as a simple kriging estimate and variance, respectively. The updated kriging variance is demonstrated as the multiplication of two kriging variances. Using these updated kriging variance equations can increase the computational speed for selecting the best new sample locations. The application results for oil rock thickness in an oilfield indicate that minimizing the average relative updated kriging variance is a useful alternative to the other criteria based on kriging variance in optimal infill sampling design for geologic site characterization.     

Some exact sampling distributions for variogram estimators

For equally spaced observations from a one-dimensional, stationary, Gaussian random function, the characteristic function of the usual variogram estimator for a fixed lag k is derived. Because the characteristic function and the probability density function form a Fourier integral pair, it is possible to tabulate the sampling distribution of a function of a using either analytic or numerical methods. An example of one such tabulation is given for an underlying model that is simple transitive.     

Determination of support in soil sampling

Short-range variation of measurements of a soil characteristic is a function of the support (i.e., size, shape, and orientation of the physical sample taken at a sample point) of the soil samples. This short-range variance often shows up as a substantial component of the nugget effect in experimental semivariograms or estimated generalized covariance functions. Proper choice of support may substantially reduce short-range variance (or nugget) of measurements made at sample points and thereby reduce estimation variance in point or block kriging based on these measurements. Appropriate variance formulas and an example are given for determination of support when support is an array of vertical cores (or bucket auger samples) of equal depth and diameter.     

Variance as a function of sample support size

The effect of sample support size on variance is examined and evaluated. Results based on variograms and geostatistics are compared to the classical relationship developed by H. F. Smith in 1938; that is, that the variance is reduced fromV ₁ toV ₁ /n ^b as the support area increases from I ton plots for uniformity trials. The exponentb is between zero and one. Theoretical results are based on use of auxiliary functions and account for the size and shape of the sample support and the overall field geometry. Results are given in terms of approximations by rational functions for ease of calculation. Experimental results for uniformity trials, infiltration measurements, and spectral data from satellites are compared to theoretical and empirical results. Applications include not only uniformity trials, but also measurement theory.     

On the bias and sampling variation of the harmonic average

We derive the bias and sampling variation of the harmonic average. These expressions, based on the lognormal distribution, are validated using Monte Carlo and jackknife analysis of field data. The average has a positive bias. The sampling variation results suggest that, for moderate to large sample sizes, the harmonic average is no more variable than the arithmetic average if the medium is appropriately sampled.     

The combination of sampling and kriging in the regional estimation of coal resources

Two-dimensional systematic sampling of small plots followed by the kriging of those plots may be employed to obtain regional estimates of coal resources and measures of the accuracy of the estimates. The use of sampling makes large savings in computation possible. Two case studies involving the estimation of coal tonnage are discussed.     

Adding bounds to kriging

The ordinary kriging interpolation algorithm is extended by the inclusion of explicit lower and upper bounds on the estimate. The associated estimation variance is written as the ordinary kriging variance plus a non-negative correction term.     

动态Kriging方法

在空间Ｋｒｉｇｉｎｇ方法的基础上，考虑了地下水系统的状态变量在时间上的自相关关系，并建立了反应变量动态特征的动态Ｋｒｉｇｉｎｇ方法，并对该方法的应用范围和使用步骤进行了讨论。     

Design criteria for roadway supports to resist dynamic loads

Summary Conditions under which dynamic loads occur in mines are briefly described and the special vulnerability of roadways in coal mines to fail under dynamic load is considered. A method for assessment of shock load energy anticipated is proposed, based on the volume of rock and the velocity of rock particles induced by rapid rock failure and/or seismic tremors. Case examples from Upper Silesian coal mines are given and the safety factor of steel supports against the shock energy from rockbursts is discussed. The shock energy damping ability of various parts of steel supports and support systems is calculated as a basis for rational support design. Results of six mine experiments where various types of roadway support were installed and then loaded dynamically by blasting within surrounding rocks are discussed.     

涪陵页岩气田加密井轨道优化设计技术

为了进一步降低涪陵页岩气田加密调整井的施工难度,提高钻井速度,针对涪陵工区的地质特点,开展加密井轨道优化设计技术研究。页岩气三维轨道设计主要有五点六段制、斜面圆弧六段制、双二维等三种类型,本文通过定向段长、摩阻、扭矩等指标对比优选,得出斜面圆弧三维轨道设计更适合涪陵工区加密井轨道设计。为了优化斜面圆弧三维轨道设计参数,本文以一口三维水平井为例进行轨道优化,通过对比不同造斜点、造斜率情况下摩阻和扭矩的变化规律,以摩阻扭矩最小为优化目标,优选造斜点和造斜率,为涪陵页岩气田加密井轨道优化设计提供借鉴。     

A neural network approach to geostatistical simulation

Neural networks offer a non-algorithmic approach to geostatistical simulation with the possibility of automatic recognition of correlation structure. The paper gives a brief overview of neural networks and describes a feedforward, back-propagation network for geostatistical simulation. The operation of the network is illustrated with two simple one-dimensional examples which can be followed through with hand calculations to give an insight into the operation of the network. The convergence of the network is described in terms of the variogram calculated from the values at each of the output nodes at each iteration.     

海洋沉积地层多功能取样钻具研制

目前,海洋钻探取心主要采用提钻或绳索打捞的方式获取岩心。随着对取心质量和采取率要求越来越高,再加上海底沉积层变化多样,单一的取样器具已经不能满足当前的取样需要。为此,本文研制了一种海洋沉积地层多功能取样钻具,能够根据海底地层性质,开展低扰动、高品质的取样操作。通过海洋钻进取样试验表明,针对海底的淤泥、粘土及砂质地层,超前取样钻具、液压剪切取样钻具和半合管取样钻具能够有效获取海底的沉积层岩样,平均采取率为73.34%。研制的多功能取样钻具采用超前取样和液压压入取样技术,降低了对沉积物岩心的扰动,提升了岩心品质和采取率,为下一步的工程化应用奠定了基础。     

A geostatistical approach to predicting the washability characteristics of coal in situ

The washability characteristics of coal are dependent on two basic relations: the ash assay vs. relative density curve, and the distribution by weight of the relative densities of coal particles. Armstrong and Whitmore (1980) demonstrated that the ash content and the yield of coal floating at a particular density can be predicted with reasonable accuracy using a simple inverse proportionality relation for the ash assay vs. density curve and a lognormal model for the distribution. In this paper, geostatistical techniques are used in conjunction with the two models to predict the washability characteristics of coal in situ.     

Guidelines to locate and protect high-quality groundwater in Baiyu Mountain area of China

The Baiyu Mountain area has the most shortage of water in the Ordos Basin of China. The majority of the groundwater is in the Luohe water-bearing formation, which is characterized by high total dissolved solids (TDS). The concentration of TDS can be as high as 10.45 g/l, which makes the water unsuitable for either potable or irrigation purpose. The dominant ions in the groundwater are SO^2–₄·Cl^–. The maximum concentrations of SO^2–₄ and Cl^– are 3,170 and 3,830 mg/l, respectively. The areas with low TDS groundwater are in Jingbian and Zhidan counties. However, nitrogen pollution caused by human and agriculture activities is a significant threat to the protection of fresh water in these counties.