Spatial variability in petrophysical properties in Upper Maastrichtian chalk outcrops at Stevns Klint, Denmark

The spatial variability of porosity and permeability was determined for a section in the uppermost Maastrichtian chalk exposed in the Sigerslev quarry at Stevns Klint. The aims were threefold: (1) to quantify the spatial variability pattern and its link to geology by applying systematic variogram analysis procedure, (2) to detect potential cyclicity in the petrophysical properties in this pure and overtly homogeneous chalk, and (3) to compare the section with chalk reservoirs in the North Sea in order to asses to what extent this onshore sequence has a potential as an analogue of the offshore, more deeply buried chalk reservoirs. The interval is of comparable stratigraphic age to the uppermost reservoir zones in the Tor Formation of the North Sea chalk reservoirs. The variability and spatial correlation of porosity and permeability in both horizontal and vertical directions are interpreted in a geological context and show indications of small-scale heterogeneity at 15–25 cm scale, but the clear cyclic layering described from other chalk deposits is not recognised at this locality. The investigated outcrop is not a close analogue to North Sea reservoir chalk, but some aspects are common including basic material properties, porosity/permeability trends and the variability pattern. The outcrop has a potential as analogue for some of the onshore subsurface chalk successions at shallow burial depth that form important aquifers.     

Some Results on the Spatial Breakdown Point of Robust Point Estimates of the Variogram

The effect of outliers on estimates of the variogram depends on how they are distributed in space. The ‘spatial breakdown point’ is the largest proportion of observations which can be drawn from some arbitrary contaminating process without destroying a robust variogram estimator, when they are arranged in the most damaging spatial pattern. A numerical method is presented to find the spatial breakdown point for any sample array in two dimensions or more. It is shown by means of some examples that such a numerical approach is needed to determine the spatial breakdown point for two or more dimensions, even on a regular square sample grid, since previous conjectures about the spatial breakdown point in two dimensions do not hold. The ‘average spatial breakdown point’ has been used as a basis for practical guidelines on the intensity of contaminating processes that can be tolerated by robust variogram estimators. It is the largest proportion of contaminating observations in a data set such that the breakdown point of the variance estimator used to obtain point estimates of the variogram is not exceeded by the expected proportion of contaminated pairs of observations over any lag. In this paper the behaviour of the average spatial breakdown point is investigated for cases where the contaminating process is spatially dependent. It is shown that in two dimensions the average spatial breakdown point is 0.25. Finally, the ‘empirical spatial breakdown point’, a tool for the exploratory analysis of spatial data thought to contain outliers, is introduced and demonstrated using data on metal content in the soils of Sheffield, England. The empirical spatial breakdown point of a particular data set can be used to indicate whether the distribution of possible contaminants is likely to undermine a robust variogram estimator.     

Combining ordination techniques and geostatistics to determine the patterns of diatom distributions at Lake Lama, Central Siberia

The patterns of spatial variation of diatom assemblages from surface sediments in Lake Lama were quantified using a combined approach of ordination and geostatistics. The aims were (i) to estimate the amount of variation between diatom assemblages within the lake, (ii) to model the spatial variability of the diatom assemblages and their diversity, and (iii) to map the diatom distributions in the lake. A correspondence analysis (CA) separated the diatom assemblages into a planktonic and a periphytic group. Rheophilic taxa were found within the periphytic group. Variogram analysis showed that only the sample scores of the first CA axis and the Shannon diversity index were spatially structured. The range of spatial correlation was estimated to be 55 km for both variables. The diversity and, to a lesser extent, the sample scores had considerable small-scale variability of about 20 and 3%, respectively. Estimates of the first component of the CA and the Shannon index were derived using block-kriging. The maps of the estimates provided a basis for partitioning Lake Lama according to the spatial structures into an eastern and a western basin, a north–south connection between the basins, and a north–south directed tip at the far eastern end. It was shown that variation in diatom assemblages is mainly spatially structured at the catchment scale and that there is a considerable amount of variation at smaller scales. According to the modeled spatial distribution, the assemblages are most likely affected by the lake size, morphology, and the water and nutrient input introduced by rivers. This has to be taken into account when paleolimnological interpretations are drawn from records of complex lake systems like Lake Lama.     

用几何光学模型对方向变化和直方图建模(英文)

森林和林地的图象二向性反射函数是一个统计函数，较之小尺度的树冠，它更多地用于大尺度的均匀覆盖的地块。用航空象片和高空间分辨率扫描仪数据作的图象热点影响研究在小尺度下显示出很大方差，而且，太阳和观测角度的交互变化进一步增加了这种反射各向异性变化的方差并有规律地继续呈现在分辨率低的图象中，这被称作ＢＲＶＦ或二向性反射方差函数。近年来，作为一种解释结构的手段，高分辨率图象的方向性方差和直方图结构越来越受到重视，这方面的数据也越来越多。这项工作是利用图象方差来解释结构问题（Ｓｔｒａｈｌｅｒ和李小文倡导）的一种延伸，并在过去１５年中由众多人员作了大量工作。在树冠尺度下，森林的直方图和二向反射方差函数可以计算出来，这里利用了近似迭代函数来处理这些数据并和数值积分模拟进行了对比，结果显示可对二向性反射方差函数的测量和引入直方图的各向异性进行准确建模。     

Self-affinity dimensions of topography and its implications in morphotectonics: an example from Taiwan

This paper discusses the self-affinity dimensions of landscape surfaces at a short-range scale and the link to morphotectonic features of the young orogenic belts of Taiwan. The variogram method is adopted to estimate such parameters as the fractal dimension (D), the ordinate-intercept (γ) and the range (R) from data subsets of the digital elevation model (DEM) in a moving-window operation. The fractal morphology expressed by D and γ is found to be useful in defining geomorphic provinces that are related to tectonic features. The mountainous terrain is characterized by high gamma values and low fractal dimensions in contrast to the coastal plains where low gamma values and high fractal dimensions are found. A zone, defined by the fractal parameters (2.4<D<2.6 and 0<γ<2.4), is found to coincide with the most tectonically active zone of Taiwan. Active faults often occur at the boundary between landscapes with contrasting fractal patterns. In the flat lowlands along the western coast, the fractal morphology displays a west-facing amphitheatric pattern, which may be related to the indentation of the pre-Miocene Peikang Basement High. The fractal morphology may reflect some subtle changes in surface textures of a landscape sculpted by surface processes, which in turn are influenced by tectonic activities. The surface roughening and diffusive smoothing may concur to shape the landscape surface at the short ranges we discuss in this study.     

Statistical and geostatistical features of streambed hydraulic conductivities in the Platte River, Nebraska

This paper presents streambed hydraulic conductivities of the Platte River from south-central to eastern Nebraska. The hydraulic conductivities were determined from river channels using permeameter tests. The vertical hydraulic conductivities (K _v ) from seven test sites along this river in south-central Nebraska belong to one statistical population. Its mean value is 40.2 m/d. However, the vertical hydraulic conductivities along four transects of the Ashland test site in eastern Nebraska have lower mean values, are statistically different from the K _v values in south-central Nebraska, and belong to two different populations with mean values of 20.7 and 9.1 m/d, respectively. Finer sediments carried from the Loup River and Elkhorn River watersheds to the eastern reach of the Platte River lowers the vertical hydraulic conductivity of the streambed. Correlation coefficients between water depth and K _v values along a test transect indicates a positive correlation – a larger K _v usually occurs in the part of channel with deeper water. Experimental variograms derived from the vertical hydraulic conductivities for several transects across the channels of the Platte River show periodicity of spatial correlation, which likely result from periodic variation of water depth across the channels. The sandy to gravelly streambed contains very local silt and clay layers; spatially continuous low-permeability streambed was not observed in the river channels. The horizontal hydraulic conductivities were larger than the vertical hydraulic conductivities for the same test locations.     

裂隙岩体渗透性空间分布的指示克里格估值

本文较详细介绍了指示克立格估值的基本方法和原理，以指示变异函数为基本工具分析了向家坝坝址区裂隙岩体渗透性空间分布的结构特征，表明该址区裂隙岩体渗透性存在明显的各向异性特征；在此基础上用指示克立格法对未采样点处进行估值，估值结果显示坝址区裂隙岩体渗透性存在明显的壳状渗透结构特征.通过这一实际应用，表明指示克立格法可以较好地描述裂隙岩体渗透性的空间分布规律.     

新20号井水位异常特征分析

运用mapsis软件前兆异常分析中的差分、从属函数和变差对新20号井水位进行异常识别,结果认为:(1)差分、从属函数和变差异常形态均为高值异常;(2)差分和变差对近场M<,s>≥5地震漏报率较高,但有异常出现时,后续往往有地震对应,而从属函数对近场M<,s>≥5映震率为66.7%,对远场M<,s>≥7映震率为71.4%...     

加入多尺度图像纹理的岩性分类

利用遥感图像进行岩性分类,是遥感地质应用的重要方面之一.本文运用地统计学中变差函数提取图像纹理,并与原始的光谱图像相结合用于遥感图像的岩性分类.文章分析了不同尺度的纹理信息对岩性分类的作用,并进一步分析和比较多尺度图像纹理对岩性分类的作用.结果表明,在岩性分类过程中加入不同尺度的纹理信息可不同程度地提高图像的岩性分类精度,而同时加入多尺度的纹理信息,可得到更高的分类精度.将多尺度的图像纹理信息和光谱信息综合,是一种有效的岩性分类方法.     

Exploring a valid model for the variogram of an isotropic spatial process

The variogram is one of the most important tools in the assessment of spatial variability and a crucial parameter for kriging. It is widely known that an estimator for the variogram cannot be used as its representator in some contexts because of its lack of conditional semi negative definiteness. Consequently, once the variogram is estimated, a valid family must be chosen to fit an appropriate model. Under isotropy, this selection is carried out by eye from the observation of the variogram estimated curve. In this paper, a statistical methodology is proposed to explore a valid model for the variogram. The statistic for this approach is based on quadratic forms depending on smoothed random variables which gather the underlying spatial variation. The distribution of the test statistic is approximated by a shifted chi-square distribution. A simulation study is also carried out to check the power and size of the test. Reference bands, as a complementary graphical tool, are calculated. An example from the literature is used to illustrate the methodologies presented.