Multiple-Point Statistics for Training Image Selection

Selecting a training image (TI) that is representative of the target spatial phenomenon (reservoir, mineral deposit, soil type, etc.) is essential for an effective application of multiple-point statistics (MPS) simulation. It is often possible to narrow potential TIs to a general subset based on the available geological knowledge; however, this is largely subjective. A method is presented that compares the distribution of runs and the multiple-point density function from available exploration data and TIs. The difference in the MPS can be used to select the TI that is most representative of the data set. This tool may be applied to further narrow a suite of TIs for a more realistic model of spatial uncertainty. In addition, significant differences between the spatial statistics of local conditioning data and a TI may lead to artifacts in MPS. The utilization of this tool will identify contradictions between conditioning data and TIs. TI selection is demonstrated for a deepwater reservoir with 32 wells.     

河北省遵化平原土壤养分的时空变异特征——变异函数与Kriging插值分析

运用地统计学 ,结合 GIS研究了 2 0年前后河北省遵化县 (市 )土壤表层 ( 0～ 2 0 cm)速效钾、速效磷和有机质 3种养分的时空变异规律。配对样本的 t检验以及 kriging插值的结果表明 ,1 999年土壤速效钾、速效磷和有机质的含量比 1 980年有一定提高。 3种养分的空间分布特征也不同程度地发生了变化。有机质的空间分布特征变化较大 ,其块金值 ( Nugget)与基台值( Sill)之比从 1 980年的 60 %下降到 1 999年的 32 .3% ,变程也由 4.8km变为 2 .7km。速效钾和速效磷的块金值与基台值之比也有一定变化 ,但变程没有太大改变。人类的施肥、耕作措施的改变及土地利用变化是引起土壤养分变化的主要原因。     

Quantifying geological uncertainty for flow and transport modeling in multi-modal heterogeneous formations

In this work, we address the problem of characterizing the heterogeneity and uncertainty of hydraulic properties for complex geological settings. Hereby, we distinguish between two scales of heterogeneity, namely the hydrofacies structure and the intrafacies variability of the hydraulic properties. We employ multiple-point geostatistics to characterize the hydrofacies architecture. The multiple-point statistics are borrowed from a training image that is designed to reflect the prior geological conceptualization. The intrafacies variability of the hydraulic properties is represented using conventional two-point correlation methods, more precisely, spatial covariance models under a multi-Gaussian spatial law. We address the different levels and sources of uncertainty in characterizing the subsurface heterogeneity, and explore their effect on groundwater flow and transport predictions. Typically, uncertainty is assessed by way of many images, termed realizations, of a fixed statistical model. However, in many cases, sampling from a fixed stochastic model does not adequately represent the space of uncertainty. It neglects the uncertainty related to the selection of the stochastic model and the estimation of its input parameters. We acknowledge the uncertainty inherent in the definition of the prior conceptual model of aquifer architecture and in the estimation of global statistics, anisotropy, and correlation scales. Spatial bootstrap is used to assess the uncertainty of the unknown statistical parameters. As an illustrative example, we employ a synthetic field that represents a fluvial setting consisting of an interconnected network of channel sands embedded within finer-grained floodplain material. For this highly non-stationary setting we quantify the groundwater flow and transport model prediction uncertainty for various levels of hydrogeological uncertainty. Results indicate the importance of accurately describing the facies geometry, especially for transport predictions.     

Spatial relationships among species, above-ground biomass, N, and P in degraded grasslands in Ordos Plateau, northwestern China

We chose five communities, representing a mild to severe gradient of grassland desertification in a semi-arid area of Ordos Plateau, northwestern China, to explore the spatial relationships among plant species, above-ground biomass (AGB), and plant nutrients (N and P). Community 1 (C1) was dominated by Stipa bungeana; Community 2 (C2) by a mix of S. bungeana and the shrub Artemisia ordosica; Community 3 (C3) by A. ordosica; Community 4 (C4) by a mix of Cynanchum komarovii and C. komorovii; and Community 5 (C5) by C. komorovii. Quantitative methods, including geostatistics, were used to compare community composition, structure, and indicators of ecosystem function (i.e. AGB, plant N and P) in five 16-m² plots. The highest AGB, plant nitrogen (N) and plant phosphorus (P) were found in lightly degraded community C2. With increasing desertification effects from C3 to C5, the AGB, N, and P decreased significantly while plant density remained unchanged. The spatial variations of AGB were higher in shrub-dominated communities (C1 and C5) than in grass-dominated communities (C2–C4). Strong spatial relationships were detected within and among the communities, with stronger relationships between AGB and density than between AGB and species richness. Spatial patterns of plant N and P were different from those of AGB, reflecting different N and P contents of individual plants and different species that can redistribute soil resources in these communities. The AGB was positively correlated with soil nutrients (TOC, TN, TP, and IN), except for soil AP. We concluded that several specific aspects of ecosystem properties were directly associated with the conversion of the grass and shrub “functional types” in these degraded grasslands.     

全球变化中土壤信息系统的研究进展

地理信息系统（GIS）支持下的土壤信息系统（SIS）在评价土地生产能力、土地退化的现状、速率和风险以及全球变化研究中具有重要意义。简述了国内外SIS的研究进展,包括FAO世界土壤图的出版和修正、数字化世界土壤资源数据库（SDB）的建立、土壤—土地数字化数据库（SOTER）在全世界的进展、世界土壤排放清单（WISE）的发展以及美国和我国的SIS进展情况。在此基础上简介了土壤属性空间变异性的研究方法———地形分析和地质统计学,并指出地质统计学与GIS的结合将是未来的发展趋势。     

A treatise on the use of geostatistics for the characterization of nonrenewable resources

Five decades of geostatistical development are reviewed to summarize the state of the art for spatial interpolation vis-à-vis kriging or a form thereof. Although a search of the literature reveals a variety of kriging methods, there are but two infrastructures for geostatistical interpolation: simple cokriging, for estimating a single variable using two variables, and generalized cokriging, for estimating one or more variables using the same number of variables that are estimated. The many forms of kriging are varieties of these two interpolation infrastructures. This notion is emphasized to aid the selection of an appropriate interpolation model for a nonrenewable resource. These models are discussed, and literature for the models and for applicable software is cited. Additionally, all aspects of spatial interpolation are discussed, including the adequacy of spatial sampling, distribution characteristics of spatial samples, semivariograms, search parameters, and selection of interpolation models in conformance with spatial data characteristics. Finally, the relationship between interpolation and raster-based geographic information systems is emphasized.     

Geostatistical estimation of signal-to-noise ratios for spectral vegetation indices

In the past 40 years, many spectral vegetation indices have been developed to quantify vegetation biophysical parameters. An ideal vegetation index should contain the maximum level of signal related to specific biophysical characteristics and the minimum level of noise such as background soil influences and atmospheric effects. However, accurate quantification of signal and noise in a vegetation index remains a challenge, because it requires a large number of field measurements or laboratory experiments. In this study, we applied a geostatistical method to estimate signal-to-noise ratio (S/N) for spectral vegetation indices. Based on the sample semivariogram of vegetation index images, we used the standardized noise to quantify the noise component of vegetation indices. In a case study in the grasslands and shrublands of the western United States, we demonstrated the geostatistical method for evaluating S/N for a series of soil-adjusted vegetation indices derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor. The soil-adjusted vegetation indices were found to have higher S/N values than the traditional normalized difference vegetation index (NDVI) and simple ratio (SR) in the sparsely vegetated areas. This study shows that the proposed geostatistical analysis can constitute an efficient technique for estimating signal and noise components in vegetation indices.     

Optimal selection of number and location of rainfall gauges for areal rainfall estimation using geostatistics and simulated annealing

This paper presents a method for establishing an optimal network design for the estimation of areal averages of rainfall events. The problem consists of minimising an objective function which includes both the accuracy of the areal mean estimation (as expressed by the kriging variance of estimation) and the economic cost of the data collection. The well known geostatistical variance-reduction method is used in combination with simulated annealing as an algorithm of minimisation. This methodology has several advantages which will be demonstrated in this paper. Several synthetic examples are shown in order to illustrate the performance of the methodology in two different optimisation problems: the optimal selection of a subset from a set of stations that already exist and the optimal augmentation of a previously existing network.     

Defining probability of saturation with indicator kriging on hard and soft data

In humid, well-vegetated areas, such as in the northeastern US, runoff is most commonly generated from relatively small portions of the landscape becoming completely saturated, however, little is known about the spatial and temporal behavior of these saturated regions. Indicator kriging provides a way to use traditional water table data to quantify probability of saturation to evaluate predicted spatial distributions of runoff generation risk, especially for the new generation of water quality models incorporating saturation excess runoff theory. When spatial measurements of a variable are transformed to binary indicators (i.e., 1 if above a given threshold value and 0 if below) and the resulting indicator semivariogram is modeled, indicator kriging produces the probability of the measured variable to exceed the threshold value. Indicator kriging gives quantified probability of saturation or, consistent with saturation excess runoff theory, runoff generation risk with depth to water table as the variable and the threshold set near the soil surface. The probability of saturation for a 120 m × 180 m hillslope based upon 43 measurements of depth to water table is investigated with indicator semivariograms for six storm events. The indicator semivariograms show high spatial structure in saturated regions with large antecedent rainfall conditions. The temporal structure of the data is used to generate interpolated (soft) data to supplement measured (hard) data. This improved the spatial structure of the indicator semivariograms for lower antecedent rainfall conditions. Probability of saturation was evaluated through indicator kriging incorporating soft data showing, based on this preliminary study, highly connected regions of saturation as expected for the wet season (April through May) in the Catskill Mountain region of New York State. Supplementation of hard data with soft data incorporates physical hydrology of the hillslope to capture significant patterns not available when using hard data alone for indicator kriging. With the need for water quality models incorporating appropriate runoff generation risk estimates on the rise, this manner of data will lay the groundwork for future model evaluation and development.