Transfer function-noise modeling and spatial interpolation to evaluate the risk of extreme (shallow) water-table levels in the Brazilian Cerrados

Water regimes in the Brazilian Cerrados are sensitive to climatological disturbances and human intervention. The risk that critical water-table levels are exceeded over long periods of time can be estimated by applying stochastic methods in modeling the dynamic relationship between water levels and driving forces such as precipitation and evapotranspiration. In this study, a transfer function-noise model, the so called PIRFICT-model, is applied to estimate the dynamic relationship between water-table depth and precipitation surplus/deficit in a watershed with a groundwater monitoring scheme in the Brazilian Cerrados. Critical limits were defined for a period in the Cerrados agricultural calendar, the end of the rainy season, when extremely shallow levels (<0.5-m depth) can pose a risk to plant health and machinery before harvesting. By simulating time-series models, the risk of exceeding critical thresholds during a continuous period of time (e.g. 10 days) is described by probability levels. These simulated probabilities were interpolated spatially using universal kriging, incorporating information related to the drainage basin from a digital elevation model. The resulting map reduced model uncertainty. Three areas were defined as presenting potential risk at the end of the rainy season. These areas deserve attention with respect to water-management and land-use planning.     

多点地质统计学：理论、应用与展望

本文系统地介绍了多点地质统计学的基本原理及方法，并以我国渤海湾盆地某区块新近系明化镇组河流相储层为例，进行了多点统计学随机建模的实例分析。多点地质统计学为储层随机建模的国际前沿研究方向，该方法综合了基于象元的方法易忠实条件数据以及基于目标的方法易再现目标几何形态的优点，同时克服了传统基于变差函数的二点统计学不能表达复杂空间结构和再现目标几何形态的不足。通过理论与实例研究，分析了目前多点统计学尚存在的问题(包括训练图像平稳性问题、目标连续性问题以及综合软信息的问题等)及未来发展的方向。     

Numerical modeling of the effects of beach slope on water-table fluctuation in the unconfined aquifer of Donghai Island,China

Beach slope is an important factor influencing the tide-induced water-table fluctuation in coastal unconfined aquifers. However, research about the effect of beach slope on water-table fluctuation is limited, especially for gentle slopes. To understand the effect of beach slope on beach groundwater dynamics, a numerical model, calibrated with field monitoring data from Donghai Island (China), was built to simulate the observed water-table fluctuation. Sensitivity analysis was performed to assess the sensitivity of water-table fluctuation to the parameters and conceptualization of the model. The analysis indicated that the water-table fluctuation was especially sensitive to the hydraulic conductivity and specific yield, and the horizontal length of the model domain could affect the amplitude of the water-table fluctuation. Moreover, it is found that the variation of the amplitude is more evident when the beach-slope angle changes in the range from 1.5 to 45°, especially in the range from 1.5 to 5°. Understanding the effect of beach slope on tide-induced water-table dynamics could help modelers deal with the slope better in their beach groundwater flow models.     

Modeling water-table fluctuations in a sloping aquifer with random hydraulic conductivity

To prevent environmental problems like water logging and increase in soil salinity which are responsible for the degradation of the top productive soils, an optimum ditch drainage design is required. For this purpose a knowledge of the spatio-temporal variation of the water table is essential. In this study the spatio-temporal variation of the water table in a sloping ditch drainage system has been modeled from a stochastic point of view, incorporating randomness in hydraulic conductivity to get the expression for the mean and the standard deviation of the water-table height. The hydraulic conductivity has been considered to be a realization of a log-normal distribution. Application of these expressions in the prediction of mean water-table variation with the associated error bounds has been demonstrated with the help of a ditch drainage problem of a sloping aquifer. The sensitivity analysis has also been carried out to see the effect of variability in the hydraulic conductivity on the water-table fluctuations. The error bounds quantified on the water-table height will thus help in the decision-making process for proper drainage design.     

投入式水位检测系统在煤田及水文勘探中的应用

由压力传感器、温度传感器、流量传感器、单片机和计算机共同组成投入式水位检测系统。在抽水试验过程中,单片机自动化采集各传感器传输来的数据,并根据压力传感器测得的压力数据运用水静力学基本方程式计算出动态水位;利用超声波流量计和热电偶一体化温度变送器测得瞬时流量和水温的变化情况;测试全过程实现了自动化动态采集试验数据,达到无人值守的目的。投入式水位检测系统克服了以往采取的响钟法等方法的操作繁琐、劳动强度大、测量误差大等缺欠,解决了大降深抽水试验水位监测的难题,使得几个人就可完成群井抽水试验,形成水位、流量和水温变化的数据库。现场应用表明,该系统测量精度高,运行状态良好,有一定的发展前景。     

多点地质统计学建模的发展趋势

从算法研究、训练图像处理和实际应用三个方面详细解剖了国内外多点地质统计学的发展历程,在此基础上,分析了多点地质统计学主流的几种算法的核心原理、适用范围及优缺点,以此来对储层建模的发展趋势作出展望。目前,多点地质统计学虽是随机建模的一种前沿研究热点,但由于其尚未成熟,仍需对建模算法进行研究。为此,在前人研究的基础上,重点分析了多点地质统计学的发展趋势：合理处理训练图像;合理利用软信息;选择合适的相似性方法;选择合适的标准化方法;合理利用平稳性;算法间的耦合;选择合适的过滤器;拓展缝洞型碳酸盐岩模拟。最后,提出多点地质统计学在储层建模方面,应从增加储层的模拟区域、提高模拟精度、扩大储层相的模拟范围和提高计算机模拟效率等方面进行改进。     

Spatial dynamics of soil salinity under arid and semi-arid conditions: geological and environmental implications

Salinity is a highly important problem in arid and semi-arid regions. Consequently, the analysis of soil salinity plays a crucial role in environmental sciences. Environmental variables show spatial variability and statistical tools able to analyze and describe the spatial dependence and quantify the scale and intensity of the spatial variation are needed. Moreover, the spatial prediction has special importance for agricultural transformation of the land or for environmental restoration (selection of the most appropriate species adapted to soil salinity). In this paper we propose a methodological framework based on geostatistics to model the spatial dynamics of soil salinity measurements to further analyze the case of a region in southeastern Spain.     

不同方法下土壤重金属元素空问最大变异距离研究——以浙江上虞为例

从地质统计学和全域型空间自相关分析两种途径探讨浙江上虞市土壤重金属的空间变异情况。研究结果表明，空间分析法得到的上虞市重金属空间变程比地质统计学法得到的空间变程更为直观和稳定；但空间分析法的准确程度依赖于空间间隔的大小，不同的空间间隔计算量有很大的不同，随着间隔的逐渐减小，计算量成倍增加。地质统计学法能快速得到空间变程，还能推测空间变异程度，用优化的拟合模型得到的结果更为准确。     

Matheronian geostatistics—Quo vadis?

Components of geostatistical estimation, developed as a method for ore deposit assessment, are discussed in detail. The assumption that spatial observations can be treated as a stochastic process is judged to be an inappropriate model for natural data. Problems of semivariogram formulation are reviewed, and this method is considered to be inadequate for estimating the function being sought. Characteristics of bivariate interpolation are summarized, highlighting kriging limitations as an interpolation method. Limitations are similar to those of inverse distance weighted observations interpolation. Attention is drawn to the local bias of kriging and misplaced claims that it is an “optimal” interpolation method. The so-called “estimation variance,” interpreted as providing confidence limits for estimation of mining blocks, is shown to be meaningless as an index of local variation. The claim that geostatistics constitutes a “new science” is examined in detail. Such novelties as exist in the method are shown to transgress accepted principles of scientific inference. Stochastic modeling in general is discussed, and purposes of the approach emphasized. For the purpose of detailed quantitative assessment it can provide only prediction qualified by hypothesis at best. Such an approach should play no part in ore deposit assessment where the need is for local detailed inventories; these can only be achieved properly through local deterministic methods, where prediction is purely deductive.     

土壤水分空间插值的克里金平滑效应修正方法

地统计学的普通克里金法是研究土壤水分空间变异特性和描绘其空间分布的有效方法。但与其它建立在最小二乘标准上的插值方法一样,普通克里金法也存在着平滑效应问题,即估计值的变异程度比实际要小,从而导致估计值往往不能反映出土壤水分真实的空间变化特征。结合实际的土壤水分监测数据,采用Yamamoto提出的一套针对普通克里金估计值进行后处理的方法,较好地解决了普通克里金法平滑效应的问题,在保证局部估计值精度的同时,重现了土壤含水率在空间的分布与变化特征。     

Spatial Modeling Techniques for Characterizing Geomaterials:Deterministic vs.Stochastic Modeling for Single-Variable and Multivariate Analyses

Sample data in the Earth and environmental sciences are limited in quantity and sampling location and therefore, sophisticated spatial modeling techniques are indispensable for accurate imaging of complicated structures and properties of geomaterials. This paper presents several effective methods that are grouped into two categories depending on the nature of regionalized data used. Type I data originate from plural populations and type II data satisfy the prerequisite of stationarity and have distinct spatial correlations. For the type I data, three methods are shown to be effective and demonstrated to produce plausible results: (1) a spline-based method, (2) a combination of a spline-based method with a stochastic simulation, and (3) a neural network method. Geostatistics proves to be a powerful tool for type II data. Three new approaches of geostatistics are presented with case studies: an application to directional data such as fracture, multi-scale modeling that incorporates a scaling law, and space-time joint analysis for multivariate data. Methods for improving the contribution of such spatial modeling to Earth and environmental sciences are also discussed and future important problems to be solved are summarized.      

Probabilistic and spatial liquefaction analysis using CPT data: a case study for Alameda County site

Soil liquefaction is one of the major concerns causing damage to the structures in saturated sand deposits during earthquakes. Simplified methods for the assessment of liquefaction potential rely on the limit states that are generally established with built-in conservatism and a great deal of subjectivity. Well-known SPT- and CPT-based methods are widely used in the design practice for this purpose due to their simplicity and reasonable predictive capability. However, these methods do not account for various sources of uncertainties explicitly. Moreover, evaluations are made only at the locations of test results and are generalized for the whole region, which may not give accurate results where spatial variation of soil properties is significant. The present study focuses on the probabilistic evaluation of liquefaction potential of Alameda County site, California, considering spatial variation of soil indices related to CPT soundings. A stochastic soil model is adopted for this purpose using random field theory and principles of geostatistics by developing 2D exponential correlation functions. It has been observed that the probability of liquefaction is significantly underestimated as much as 34 %, if the spatial dependence of soil indices is not considered. Further, the effect of spatial variation is more prominent in low-level earthquakes compared to the high-level earthquakes, showing a 41.5 % deviation for magnitude 8.1 and a 60.5 % deviation for magnitude 5.0 earthquake at a depth of 10 m.     

3D矿床建模技术在数字矿产勘查中的应用

为弥补现有数字矿床建模技术在地质矿产勘查处理和应用中的不足,从原始勘查数据建库及标准化、多指标单工程矿体自动圈定、基于语义识别的剖面矿体的连接与外推、矿体表面和品位建模、基于剖面矿体线框模型构建矿体表面模型及基于TIN+Octree数据结构和地质统计学理论建立矿体的空间属性模型等5个方面总结提出一套面向地质矿产勘查业务处理的矿床建模流程和总体技术解决方案.提高了地质矿产勘查研究精度,为进一步的矿山开采提供可靠的数据模型.      

基于转移概率地质统计的淮南顾桥矿区松散层含水介质刻画

含水介质的空间分布及其非均质性对地下水流和溶质运移有着重要的影响。以淮南顾桥矿区作为研究对象,为了刻画矿区松散层含水介质的空间分布,使用转移概率地质统计方法建立含水介质的随机模型,对矿区水文地质结构的空间连续性和空间变异性进行表征;并将随机模拟得到的顾桥矿区含水介质剖面图与矿区原始水文地质剖面进行对比。结果表明,基于转移概率地质统计模拟方法可以比较准确地刻画矿区的水文地质结构;模拟剖面与原始水文地质剖面的比较显示模拟结果与实际含水介质空间分布情况有较好的一致性,转移概率地质统计方法在对含水介质非均质性刻画中具有较好的适用性。     

多点地质统计学建模研究进展

从精细油藏描述中地质建模的意义和现状入手,介绍了多点地质统计学建模研究现状及其与传统地质建模方法的差 异。以辽河盆地西部凹陷某蒸汽驱试验区为例,分析了多点地质统计学建模中建模的基础、训练图像的建立、多点地质统计学 建模与传统地质建模相比所具有的优势等内容。指出多点地质统计学在井间预测方面具有明显优于其他传统建模方法的特 点。在文献调研基础上,结合自身工作实践,探讨了多点地质统计学建模目前存在的问题和未来的发展方向。指出未来多点 地质统计学建模的发展方向主要包括多信息综合地质成因分析基础上的训练图像获取、多点地质统计学算法进行改进和完善 和多点地质统计学建模方法应用领域的扩大等。     

Direct Multiple-Point Geostatistical Simulation of Edge Properties for Modeling Thin Irregularly Shaped Surfaces

Thin, irregularly shaped surfaces such as clay drapes often have a major control on flow and transport in heterogeneous porous media. Clay drapes are often complex, curvilinear three-dimensional surfaces and display a very complex spatial distribution. Variogram-based stochastic approaches are also often not able to describe the spatial distribution of clay drapes since complex, curvilinear, continuous, and interconnected structures cannot be characterized using only two-point statistics. Multiple-point geostatistics aims to overcome the limitations of the variogram. The premise of multiple-point geostatistics is to move beyond two-point correlations between variables and to obtain (cross) correlation moments at three or more locations at a time using training images to characterize the patterns of geological heterogeneity. Multiple-point geostatistics can reproduce thin irregularly shaped surfaces such as clay drapes, but this is often computationally very intensive. This paper describes and applies a methodology to simulate thin, irregularly shaped surfaces with a smaller CPU and RAM demand than the conventional multiple-point statistical methods. The proposed method uses edge properties for indicating the presence of thin irregularly shaped surfaces. Instead of pixel values, edge properties indicating the presence of irregularly shaped surfaces are simulated using snesim. This method allows direct simulation of edge properties instead of pixel properties to make it possible to perform multiple-point geostatistical simulations with a larger cell size and thus a smaller computation time and memory demand. This method is particularly valuable for three-dimensional applications of multiple-point geostatistics.     

Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium)

Sedimentological processes often result in complex three-dimensional subsurface heterogeneity of hydrogeological parameter values. Variogram-based stochastic approaches are often not able to describe heterogeneity in such complex geological environments. This work shows how multiple-point geostatistics can be applied in a realistic hydrogeological application to determine the impact of complex geological heterogeneity on groundwater flow and transport. The approach is applied to a real aquifer in Belgium that exhibits a complex sedimentary heterogeneity and anisotropy. A training image is constructed based on geological and hydrogeological field data. Multiple-point statistics are borrowed from this training image to simulate hydrofacies occurrence, while intrafacies permeability variability is simulated using conventional variogram-based geostatistical methods. The simulated hydraulic conductivity realizations are used as input to a groundwater flow and transport model to investigate the effect of small-scale sedimentary heterogeneity on contaminant plume migration. Results show that small-scale sedimentary heterogeneity has a significant effect on contaminant transport in the studied aquifer. The uncertainty on the spatial facies distribution and intrafacies hydraulic conductivity distribution results in a significant uncertainty on the calculated concentration distribution. Comparison with standard variogram-based techniques shows that multiple-point geostatistics allow better reproduction of irregularly shaped low-permeability clay drapes that influence solute transport.     

Enhancement of aquifer vulnerability indexing using the analytic-element method

Indexing methods are used for the evaluation of aquifer vulnerability and establishing guidelines for the protection of ground-water resources. The principle of the indexing method is to rank influences on groundwater to determine overall vulnerability of an aquifer to contamination. The analytic element method (AEM) of ground-water flow modeling is used to enhance indexing methods by rapidly calculating a potentiometric surface based primarily on surface-water features. This potentiometric map is combined with a digital-elevation model to produce a map of water-table depth. This is an improvement over simple water-table interpolation methods. It is physically based, properly representing surface-water features, hydraulic boundaries, and changes in hydraulic conductivity. The AEM software, SPLIT, is used to improve an aquifer vulnerability assessment for a valley-fill aquifer in western New York State. A GIS-based graphical user interface allows automated conversion of hydrography vector data into analytic elements.     

The effects of geological heterogeneities and piezometric fluctuations on groundwater flow and chemistry in a hard-rock aquifer, southern India

Crystalline aquifers of semi-arid southern India represent a vital water resource for farming communities. A field study is described that characterizes the hydrodynamic functioning of intensively exploited crystalline aquifers at local scale based on detailed well monitoring during one hydrological year. The main results show large water-table fluctuations caused by monsoon recharge and pumping, high spatial variability in well discharges, and a decrease of well yields as the water table decreases. Groundwater chemistry is also spatially variable with the existence of aquifer compartments within which mixing occurs. The observed variability and compartmentalization is explained by geological heterogeneities which play a major role in controlling groundwater flow and connectivity in the aquifer. The position of the water table within the fracture network will determine the degree of connectivity between aquifer compartments and well discharge. The presented aquifer conceptual model suggests several consequences: (1) over-exploitation leads to a drop in well discharge, (2) intensive pumping may contribute to the hydraulic containment of contaminants, (3) groundwater quality is highly variable even at local scale, (4) geological discontinuities may be used to assist in the location of drinking-supply wells, (5) modeling should integrate threshold effects due to water-table fluctuations.