共查询到20条相似文献，搜索用时 31 毫秒
1.
Numerical representations of multivariate natural phenomena, including characteristics of mineral deposits, petroleum reservoirs
and geo-environmental attributes, need to consider and reproduce the spatial relationships between correlated attributes of
interest. There are, however, only a few methods that can practically jointly simulate large size multivariate fields. This
paper presents a method for the conditional simulation of a non-Gaussian vector random field directly on block support. The
method is derived from the group sequential simulation paradigm and the direct block simulation algorithm which leads to the
efficient joint simulation of large multivariate datasets jointly and directly on the block support. This method is a multistage
process. First, a vector random function is orthogonalized with minimum/maximum autocorrelation factors (MAF). Blocks are
then simulated by performing LU simulation on their discretized points, which are later back-rotated and averaged to yield
the block value. The internal points are then discarded and only the block value is stored in memory to be used for further
conditioning through a joint LU, resulting in the reduction of memory requirements. The method is termed direct block simulation
with MAF or DBMAFSIM. A proof of the concept using an exhaustive data set demonstrates the intricacies and the performance
of the proposed approach. 相似文献
2.
Geostatistical Simulation of Regionalized Pore-Size Distributions Using Min/Max Autocorrelation Factors 总被引：1，自引：0，他引：1
In many fields of the Earth Sciences, one is interested in the distribution of particle or void sizes within samples. Like many other geological attributes, size distributions exhibit spatial variability, and it is convenient to view them within a geostatistical framework, as regionalized functions or curves. Since they rarely conform to simple parametric models, size distributions are best characterized using their raw spectrum as determined experimentally in the form of a series of abundance measures corresponding to a series of discrete size classes. However, the number of classes may be large and the class abundances may be highly cross-correlated. In order to model the spatial variations of discretized size distributions using current geostatistical simulation methods, it is necessary to reduce the number of variables considered and to render them uncorrelated among one another. This is achieved using a principal components-based approach known as Min/Max Autocorrelation Factors (MAF). For a two-structure linear model of coregionalization, the approach has the attractive feature of producing orthogonal factors ranked in order of increasing spatial correlation. Factors consisting largely of noise and exhibiting pure nugget–effect correlation structures are isolated in the lower rankings, and these need not be simulated. The factors to be simulated are those capturing most of the spatial correlation in the data, and they are isolated in the highest rankings. Following a review of MAF theory, the approach is applied to the modeling of pore-size distributions in partially welded tuff. Results of the case study confirm the usefulness of the MAF approach for the simulation of large numbers of coregionalized variables. 相似文献
3.
Generalized Bootstrap Method for Assessment of?Uncertainty in Semivariogram Inference 总被引：1，自引：0，他引：1
The semivariogram and its related function, the covariance, play a central role in classical geostatistics for modeling the average continuity of spatially correlated attributes. Whereas all methods are formulated in terms of the true semivariogram, in practice what can be used are estimated semivariograms and models based on samples. A generalized form of the bootstrap method to properly model spatially correlated data is used to advance knowledge about the reliability of empirical semivariograms and semivariogram models based on a single sample. Among several methods available to generate spatially correlated resamples, we selected a method based on the LU decomposition and used several examples to illustrate the approach. The first one is a synthetic, isotropic, exhaustive sample following a normal distribution, the second example is also a synthetic but following a non-Gaussian random field, and a third empirical sample consists of actual raingauge measurements. Results show wider confidence intervals than those found previously by others with inadequate application of the bootstrap. Also, even for the Gaussian example, distributions for estimated semivariogram values and model parameters are positively skewed. In this sense, bootstrap percentile confidence intervals, which are not centered around the empirical semivariogram and do not require distributional assumptions for its construction, provide an achieved coverage similar to the nominal coverage. The latter cannot be achieved by symmetrical confidence intervals based on the standard error, regardless if the standard error is estimated from a parametric equation or from bootstrap. 相似文献
4.
Conditioning of coefficient matrices of Ordinary Kriging 总被引：1，自引：0，他引：1
R. J. O''Dowd 《Mathematical Geology》1991,23(5):721-739
The solution of a set of linear equations is central to Ordinary Kriging. Computers are commonly applied because of the amount of data and work involved. There has, until recently, been little attention devoted toward the conditioning of kriging matrices. This article considers implications of conditioning upon numerical stability, instead of on robustness which has been the main focus of past work. The effect of properties of the stationary covariance matrix on the conditioning of the kriging matrix is discussed. The relationship between the covariance and autocorrelation functions allows some conclusions about the conditioning of covariance matrices, based on past work in deconvolution. The conditioning of some coefficient matrices of stationary kriging, defined in terms of either the semivariogram or the covariance, is examined. 相似文献
5.
Goovaerts P 《Mathematical Geology》2008,40(1):101-128
This paper presents a methodology to conduct geostatistical variography and interpolation on areal data measured over geographical units (or blocks) with different sizes and shapes, while accounting for heterogeneous weight or kernel functions within those units. The deconvolution method is iterative and seeks the pointsupport model that minimizes the difference between the theoretically regularized semivariogram model and the model fitted to areal data. This model is then used in area-to-point (ATP) kriging to map the spatial distribution of the attribute of interest within each geographical unit. The coherence constraint ensures that the weighted average of kriged estimates equals the areal datum.This approach is illustrated using health data (cancer rates aggregated at the county level) and population density surface as a kernel function. Simulations are conducted over two regions with contrasting county geographies: the state of Indiana and four states in the Western United States. In both regions, the deconvolution approach yields a point support semivariogram model that is reasonably close to the semivariogram of simulated point values. The use of this model in ATP kriging yields a more accurate prediction than a na?ve point kriging of areal data that simply collapses each county into its geographic centroid. ATP kriging reduces the smoothing effect and is robust with respect to small differences in the point support semivariogram model. Important features of the point-support semivariogram, such as the nugget effect, can never be fully validated from areal data. The user may want to narrow down the set of solutions based on his knowledge of the phenomenon (e.g., set the nugget effect to zero). The approach presented avoids the visual bias associated with the interpretation of choropleth maps and should facilitate the analysis of relationships between variables measured over different spatial supports. 相似文献
6.
Oscar Rondon 《Mathematical Geosciences》2012,44(4):469-504
Multivariate conditional simulation is used to assess the multivariate grade risk in mineral deposits. With the presence of several spatially correlated attributes, it is important to ensure that their joint simulation is carried out properly and that the observed spatial correlation is reproduced in the realizations. The method of minimum/maximum autocorrelation factors (MAF) is a well established and practical technique that can be used for this purpose. MAF offers tremendous advantages over standard full cosimulation, principal component analysis, and stepwise techniques. In what follows, a detailed review of the MAF technique, its applications, and examples are provided to guide the practitioner on its use. 相似文献
7.
8.
Pierre Goovaerts 《Mathematical Geosciences》2008,40(1):101-128
This paper presents a methodology to conduct geostatistical variography and interpolation on areal data measured over geographical units (or blocks) with different sizes and shapes, while accounting for heterogeneous weight or kernel functions within those units. The deconvolution method is iterative and seeks the point-support model that minimizes the difference between the theoretically regularized semivariogram model and the model fitted to areal data. This model is then used in area-to-point (ATP) kriging to map the spatial distribution of the attribute of interest within each geographical unit. The coherence constraint ensures that the weighted average of kriged estimates equals the areal datum.This approach is illustrated using health data (cancer rates aggregated at the county level) and population density surface as a kernel function. Simulations are conducted over two regions with contrasting county geographies: the state of Indiana and four states in the Western United States. In both regions, the deconvolution approach yields a point support semivariogram model that is reasonably close to the semivariogram of simulated point values. The use of this model in ATP kriging yields a more accurate prediction than a naïve point kriging of areal data that simply collapses each county into its geographic centroid. ATP kriging reduces the smoothing effect and is robust with respect to small differences in the point support semivariogram model. Important features of the point-support semivariogram, such as the nugget effect, can never be fully validated from areal data. The user may want to narrow down the set of solutions based on his knowledge of the phenomenon (e.g., set the nugget effect to zero). The approach presented avoids the visual bias associated with the interpretation of choropleth maps and should facilitate the analysis of relationships between variables measured over different spatial supports. 相似文献
9.
Joint geostatistical simulation techniques are used to quantify uncertainty for spatially correlated attributes, including mineral deposits, petroleum reservoirs, hydrogeological horizons, environmental contaminants. Existing joint simulation methods consider only second-order spatial statistics and Gaussian processes. Motivated by the presence of relatively large datasets for multiple correlated variables that typically are available from mineral deposits and the effects of complex spatial connectivity between grades on the subsequent use of simulated realizations, this paper presents a new approach for the joint high-order simulation of spatially correlated random fields. First, a vector random function is orthogonalized with a new decorrelation algorithm into independent factors using the so-termed diagonal domination condition of high-order cumulants. Each of the factors is then simulated independently using a high-order univariate simulation method on the basis of high-order spatial cumulants and Legendre polynomials. Finally, attributes of interest are reconstructed through the back-transformation of the simulated factors. In contrast to state-of-the-art methods, the decorrelation step of the proposed approach not only considers the covariance matrix, but also high-order statistics to obtain independent non-Gaussian factors. The intricacies of the application of the proposed method are shown with a dataset from a multi-element iron ore deposit. The application shows the reproduction of high-order spatial statistics of available data by the jointly simulated attributes. 相似文献
10.
Another look at anisotropy in geostatistics 总被引：3，自引：0，他引：3
Dale L. Zimmerman 《Mathematical Geology》1993,25(4):453-470
A thorough geostatistical data analysis includes a careful study of how the data's second-order variation, as characterized by the semivariogram, depends on the relative orientation of data locations. If the semivariogram depends on only the (Euclidean) distance between locations, then the semivariogram is isotropic; otherwise, it is anisotropic. In this article, I take another look at the modeling of anisotropy in geostatistics. A new, more specific classification of types of anisotropy is proposed. More importantly, some heretofore inadequately understood implications of the dependence of various semivariogram attributes on direction are discussed, and the wisdom of some current practices for modeling the direction-dependence of these attributes is questioned. 相似文献
11.
传统的路基压实质量均匀性评价方法均基于变异系数等概率统计指标,未能考虑检测数据的空间分布特性,难以准确评价路基压实质量的不均匀性。基于地统计学理论,建立半变异函数模型描述连续压实检测数据的空间变异性,采用指数模型对半变异函数曲线进行最优拟合,并提出偏基台值C作为路基压实均匀性控制指标。分别采用地统计方法与传统数理统计法对沪昆客运专线芷江试验段的路基进行压实均匀性评价。结果表明：在压路机振动频率波动或存在压实薄弱区域的情况下,与传统数理统计指标变异系数Cv相比,地统计指标C可消除系统误差等随机性因素对均匀性评价结果的影响,更能客观反映不同工况下的填筑土体在空间上的不均匀压实状态,其结果为铁路路基压实均匀性评价提供了新的思路。 相似文献
12.
Kriging-based geostatistical models require a semivariogram model. Next to the initial decision of stationarity, the choice of an appropriate semivariogram model is the most important decision in a geostatistical study. Common practice consists of fitting experimental semivariograms with a nested combination of proven models such as the spherical, exponential, and Gaussian models. These models work well in most cases; however, there are some shapes found in practice that are difficult to fit. We introduce a family of semivariogram models that are based on geometric shapes, analogous to the spherical semivariogram, that are known to be conditional negative definite and provide additional flexibility to fit semivariograms encountered in practice. A methodology to calculate the associated geometric shapes to match semivariograms defined in any number of directions is presented. Greater flexibility is available through the application of these geometric semivariogram models. 相似文献
13.
This paper presents novel visualization techniques to simplify representation of the fourth‐order material stiffness tensor as a set of three‐dimensional geometric objects. Stiffness visualization aids in understanding the complex stiffness characteristics of highly non‐linear constitutive models including modelled material anisotropy and loading path dependent stiffness variation. Stiffness visualization is relevant for understanding the relationship of material stiffness to global behaviour in the analysis of a boundary value problem. The spherical pulse stiffness visualization method, developed in the acoustics field, is extended to visualize stiffness of geomaterials using three three‐dimensional objects. This method is limited to relatively simple constitutive models with symmetric stiffness matrices insensitive to loading magnitude and direction. A strain dependent stiffness visualization method is developed that allows the examination of material stiffness for a range of loading directions and is suitable for highly non‐linear and path dependent material models. The proposed stiffness visualization can be represented as 3‐D, 2‐D and 1‐D objects. The visualization technique is used to represent material stiffness and its evolution during simulated soil laboratory tests and deep excavation construction. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
14.
Pierre Petitgas Mathieu Woillez Mathieu Doray Jacques Rivoirard 《Mathematical Geosciences》2018,50(2):187-208
Marine research survey data on fish stocks often show a small proportion of very high-density values, as for many environmental data. This makes the estimation of second-order statistics, such as the variance and the variogram, non-robust. The high fish density values are generated by fish aggregative behaviour, which may vary greatly at small scale in time and space. The high values are thus imprecisely known, both in their spatial occurrence and order of magnitude. To map such data, three indicator-based geostatistical methods were considered, the top-cut model, min–max autocorrelation factors (MAF) of indicators, and multiple indicator kriging. In the top-cut and MAF approaches, the variable is decomposed into components and the most continuous ones (those corresponding to the low and medium values) are used to guide the mapping. The methods are proposed as alternatives to ordinary kriging when the variogram is difficult to estimate. The methods are detailed and applied on a spatial data set of anchovy densities derived from a typical fish stock acoustic survey performed in the Bay of Biscay, which show a few high-density values distributed in small spatial patches and also as solitary events. The model performances are analyzed by cross-validating the data and comparing the kriged maps. Results are compared to ordinary kriging as a base case. The top-cut model had the best cross-validation performance. The indicator-based models allowed mapping high-value areas with small spatial extent, in contrast to ordinary kriging. Practical guidelines for implementing the indicator-based methods are provided. 相似文献
15.
Spatial analyses of groundwater levels using universal kriging 总被引：6，自引：0，他引：6
For water levels, generally a non-stationary variable, the technique of universal kriging is applied in preference to ordinary
kriging as the interpolation method. Each set of data in every sector can fit different empirical semivariogram models since
they have different spatial structures. These models can be classified as circular, spherical, tetraspherical, pentaspherical,
exponential, gaussian, rational quadratic, hole effect, K-bessel, J-bessel and stable. This study aims to determine which
of these empirical semivariogram models will be best matched with the experimental models obtained from groundwater-table
values collected from Mustafakemalpasa left bank irrigation scheme in 2002. The model having the least error was selected
by comparing the observed water-table values with the values predicted by empirical semivariogram models. It was determined
that the rational quadratic empirical semivariogram model is the best fitted model for the studied irrigation area. 相似文献
16.
Zekai Sen 《Mathematical Geology》1989,21(8):891-903
The cumulative semivariogram approach is proposed for modeling regionalized variables in the geological sciences. This semivariogram is defined as the successive summation of half-squared differences which are ranked according to the ascending order of distances extracted from all possible pairs of sample locations within a region. This procedure is useful especially when sampling points are irregularly distributed within the study area. Cumulative semivariograms possess all of the objective properties of classical semivariograms. Classical semivariogram models are evaluated on the basis of the cumulative semivariogram methodology. Model parameter estimation procedures are simplified with the use of arithmetic, semilogarithmic, or double-logarithmic papers. Plots of cumulative semivariogram values vs. corresponding distances may scatter along a straight line on one of these papers, which facilitates model identification as well as parameter estimation. Straight lines are fitted to the cumulative semivariogram scatter diagram by classical linear regression analysis. Finally, applications of the methodology are presented for some groundwater data recorded in the sedimentary basins of the Kingdom of Saudi Arabia. 相似文献
17.
地质统计学是用于模拟土体固有空间变异性的方法之一,以变差函数为工具,采用Kriging插值提供未采样点处土工参数值的最优线性无偏估计。将地质统计学方法应用于宿-新（宿迁至新沂）高速公路某试验段内孔压静力触探（piezocone penetration test,CPTU）锥尖阻力qt空间变异性研究中,采用回归分析移除数据中的趋势项,从而获得具有弱平稳性的残差数据。指数型理论变差函数能够准确描述试验段内土体的连续空间变异性特征。根据估计结果,试验段内锥尖阻力qt残差的变程具有显著各向异性,在水平方向和竖直方向分别为4.05 m和1.2 m。采用普通Kriging插值结合趋势分析,绘制了qt在试验段的空间分布图和平面投影图,用于指导工程实践。结果表明,普通Kriging插值的估计结果能够与试验段内实测资料形成较好的对比,仅仅在部分极值变化和远离采样点的位置处估计值可靠性会降低。 相似文献
18.
19.
矿产信息是各种成矿相关信息的综合体现,为了有效地提取成矿预测综合信息,有必要客观地筛选原始观测信息,突出成矿密切相关的致矿因子。粗糙集不需要数据的附加信息或先验知识,在知识库分类能力不变的前提条件下,删除无关或不重要的属性,能对决策系统进行有效约简。提出基于粗糙集理论进行集成化预测模型研究的新方法,基于粗糙集思想提取与成矿密切相关的特征矿化信息,获取最佳变量组合及区间值,并将其作为参量建立预测模型,结合经典矿床统计预测聚类方法确定代判临界值,及特征分析方法对矿产资源进行定量预测,确立了8个成矿有利单元,与研究区勘查工程资料基本吻合,表明该方法能够有效降噪,简化模型,为靶区预测提供准确的依据。 相似文献
20.
A parametric study of robustness of kriging variance as a function of range and relative nugget effect for a spherical semivariogram 总被引：1，自引：0，他引：1
P. I. Brooker 《Mathematical Geology》1986,18(5):477-488
In geostatistics, an estimation of blocks of a deposit is reported along with the variance of error made in their estimation. This calculation is based on the model chosen for the semivariogram of the deposit so that mistakes in its estimation can manifest themselves in the perception of accuracy with which blocks are known. Changes in kriging variance resulting from various amounts of error in modeling the relative nugget effect and range of the semivariogram are investigated for an extensive set of spherical semivariograms. 相似文献