共查询到20条相似文献，搜索用时 20 毫秒
1.
Estimation or simulation? That is the question 总被引：1，自引：0，他引：1
Jorge Kazuo Yamamoto 《Computational Geosciences》2008,12(4):573-591
The issue of smoothing in kriging has been addressed either by estimation or simulation. The solution via estimation calls
for postprocessing kriging estimates in order to correct the smoothing effect. Stochastic simulation provides equiprobable
images presenting no smoothing and reproducing the covariance model. Consequently, these images reproduce both the sample
histogram and the sample semivariogram. However, there is still a problem, which is the lack of local accuracy of simulated
images. In this paper, a postprocessing algorithm for correcting the smoothing effect of ordinary kriging estimates is compared
with sequential Gaussian simulation realizations. Based on samples drawn from exhaustive data sets, the postprocessing algorithm
is shown to be superior to any individual simulation realization yet, at the expense of providing one deterministic estimate
of the random function. 相似文献
2.
Compensating for estimation smoothing in kriging 总被引：2，自引：0，他引：2
Smoothing is a characteristic inherent to all minimum mean-square-error spatial estimators such as kriging. Cross-validation can be used to detect and model such smoothing. Inversion of the model produces a new estimator—compensated kriging. A numerical comparison based on an exhaustive permeability sampling of a 4-ft2 slab of Berea Sandstone shows that the estimation surface generated by compensated kriging has properties intermediate between those generated by ordinary kriging and stochastic realizations resulting from simulated annealing and sequential Gaussian simulation. The frequency distribution is well reproduced by the compensated kriging surface, which also approximates the experimental semivariogram well—better than ordinary kriging, but not as well as stochastic realizations. Compensated kriging produces surfaces that are more accurate than stochastic realizations, but not as accurate as ordinary kriging. 相似文献
3.
Covariance models provide the basic measure of spatial continuity in geostatistics. Traditionally, a closed-form analytical model is fitted to allow for interpolation of sample Covariance values while ensuring the positive definiteness condition. For cokriging, the modeling task is made even more difficult because of the restriction imposed by the linear coregionalization model. Bochner's theorem maps the positive definite constraints into much simpler constraints on the Fourier transform of the covariance, that is the density spectrum. Accordingly, we propose to transform the experimental (cross) covariance tables into quasidensity spectrum tables using Fast Fourier Transform (FFT). These quasidensity spectrum tables are then smoothed under constraints of positivity and unit sum. A backtransform (FFT) yields permissible (jointly) positive definite (cross) covariance tables. At no point is any analytical modeling called for and the algorithm is not restricted by the linear coregionalization model. A case study shows the proposed covariance modeling to be easier and much faster than the traditional analytical covariance modeling, yet yields comparable kriging or simulation results. 相似文献
4.
Conditional Spectral Simulation with Phase Identification 总被引：2，自引：0，他引：2
Tingting Yao 《Mathematical Geology》1998,30(3):285-308
Spectral simulation is used widely in electrical engineering to generate random fields with a given covariance spectrum. The algorithms used are fast particularly when based on Fast Fourier Transform (FFT). However, because of lack of phase identification, spectral simulation only generates unconditional realizations. Local data conditioning is obtained typically by adding a simulated kriging residual. This conditioning process requires an additional kriging at each simulated node thus forfeiting the speed advantage of FFT. A new algorithm for conditioning is proposed whereby the phase values are determined iteratively to ensure approximative data reproduction while reproducing the frequency spectrum, that is, the covariance model. A case study is presented to demonstrate the algorithm. 相似文献
5.
Correcting the Smoothing Effect of Ordinary Kriging Estimates 总被引：2，自引：0，他引：2
Jorge Kazuo Yamamoto 《Mathematical Geology》2005,37(1):69-94
The smoothing effect of ordinary kriging is a well-known dangerous effect associated with this estimation technique. Consequently kriging estimates do not reproduce both histogram and semivariogram model of sample data. A four-step procedure for correcting the smoothing effect of ordinary kriging estimates is shown to be efficient for the reproduction of histogram and semivariogram without loss of local accuracy. Furthermore, this procedure provides a unique map sharing both local and global accuracies. Ordinary kriging with a proper correction for smoothing effect can be revitalized as a reliable estimation method that allows a better use of the available information. 相似文献
6.
Generalized sequential kriging (GSK) for heterogeneous cell size: property modeling without matrices
J. A. Vargas-Guzmán 《Computational Geosciences》2010,14(1):207-215
Sequential kriging avoids the use of matrices and resolves the issue of unstable solutions. It allows for stepwise ways to
get joint estimations and cosimulations that are equivalent to the simultaneous solution. The approach is proposed as the
solution for geocellular modeling with variable cell size from heterogeneous structural properties (HSPs) as required for
modeling with structural constraints. Rock properties are controlled by structural domains, regions, and structural geology
parameters. In some cases, rock properties are cross-correlated to formation thickness, curvature of structures, and other
structural attributes. Cell thickness may be proportional to formation thickness and may enter as a conditioning property
in the estimation of rock property parameters for simulation. In addition, cell volume controls the upscaling of covariance
structures (i.e., regularized variograms). Structural properties are priorly modeled. Perturbation response functions (PRFs)
are computed for each cell vs all possible sample point locations to facilitate sequential kriging. Upscaled PRFs are modified
following conditional updating after each new data value is included in the estimation of parameters. Generalized sequential
kriging is expected to become the main tool for real-time spatial modeling of 3D cellular models with HSP. In addition, some
new developments related to the sequential kriging algorithm are included. Sequential kriging can be used for the estimation
of parameters for simulation in the so-called unstructured grids. 相似文献
7.
The Second-Order Stationary Universal Kriging Model Revisited 总被引：3，自引：0，他引：3
Universal kriging originally was developed for problems of spatial interpolation if a drift seemed to be justified to model the experimental data. But its use has been questioned in relation to the bias of the estimated underlying variogram (variogram of the residuals), and furthermore universal kriging came to be considered an old-fashioned method after the theory of intrinsic random functions was developed. In this paper the model is reexamined together with methods for handling problems in the inference of parameters. The efficiency of the inference of covariance parameters is shown in terms of bias, variance, and mean square error of the sampling distribution obtained by Monte Carlo simulation for three different estimators (maximum likelihood, bias corrected maximum likelihood, and restricted maximum likelihood). It is shown that unbiased estimates for the covariance parameters may be obtained but if the number of samples is small there can be no guarantee of good estimates (estimates close to the true value) because the sampling variance usually is large. This problem is not specific to the universal kriging model but rather arises in any model where parameters are inferred from experimental data. The validity of the estimates may be evaluated statistically as a risk function as is shown in this paper. 相似文献
8.
Spatial declustering weights 总被引：1，自引：0，他引：1
G. Bourgault 《Mathematical Geology》1997,29(2):277-290
Because of autocorrelation and spatial clustering, all data within a given dataset have not the same statistical weight for
estimation of global statistics such mean, variance, or quantiles of the population distribution. A measure of redundancy
(or nonredundancy) of any given regionalized random variable Z(uα)within any given set (of size N) of random variables is proposed. It is defined as the ratio of the determinant of the N X Ncorrelation matrix to the determinant of the (N - 1) X (N - 1)correlation matrix excluding random variable Z(uα).This ratio measures the increase in redundancy when adding the random variable Z(uα)to the (N - 1 )remainder. It can be used as declustering weight for any outcome (datum) z(uα). When the redundancy matrix is a kriging covariance matrix, the proposed ratio is the crossvalidation simple kriging variance.
The covariance of the uniform scores of the clustered data is proposed as a redundancy measure robust with respect to data
clustering. 相似文献
9.
The majority of geostatistical estimation and simulation algorithms rely on a covariance model as the sole characteristic of the spatial distribution of the attribute under study. The limitation to a single covariance implicitly calls for a multivariate Gaussian model for either the attribute itself or for its normal scores transform. The Gaussian model could be justified on the basis that it is both analytically simple and it is a maximum entropy model, i.e., a model that minimizes unwarranted structural properties. As a consequence, the Gaussian model also maximizes spatial disorder (beyond the imposed covariance) which can cause flow simulation results performed on multiple stochastic images to be very similar; thus, the space of response uncertainty could be too narrow entailing a misleading sense of safety. The ability of the sole covariance to adequately describe spatial distributions for flow studies, and the assumption that maximum spatial disorder amounts to either no additional information or a safe prior hypothesis are questioned. This paper attempts to clarify the link between entropy and spatial disorder and to provide, through a detailed case study, an appreciation for the impact of entropy of prior random function models on the resulting response distributions. 相似文献
10.
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
11.
The majority of geostatistical estimation and simulation algorithms rely on a covariance model as the sole characteristic of the spatial distribution of the attribute under study. The limitation to a single covariance implicitly calls for a multivariate Gaussian model for either the attribute itself or for its normal scores transform. The Gaussian model could be justified on the basis that it is both analytically simple and it is a maximum entropy model, i.e., a model that minimizes unwarranted structural properties. As a consequence, the Gaussian model also maximizes spatial disorder (beyond the imposed covariance) which can cause flow simulation results performed on multiple stochastic images to be very similar; thus, the space of response uncertainty could be too narrow entailing a misleading sense of safety. The ability of the sole covariance to adequately describe spatial distributions for flow studies, and the assumption that maximum spatial disorder amounts to either no additional information or a safe prior hypothesis are questioned. This paper attempts to clarify the link between entropy and spatial disorder and to provide, through a detailed case study, an appreciation for the impact of entropy of prior random function models on the resulting response distributions. 相似文献
12.
Application of universal kriging for estimation of earthquake ground motion: Statistical significance of results 总被引：1，自引：0，他引：1
Universal kriging is compared with ordinary kriging for estimation of earthquake ground motion. Ordinary kriging is based on a stationary random function model; universal kriging is based on a nonstationary random function model representing first-order drift. Accuracy of universal kriging is compared with that for ordinary kriging; cross-validation is used as the basis for comparison. Hypothesis testing on these results shows that accuracy obtained using universal kriging is not significantly different from accuracy obtained using ordinary kriging. Tests based on normal distribution assumptions are applied to errors measured in the cross-validation procedure;t andF tests reveal no evidence to suggest universal and ordinary kriging are different for estimation of earthquake ground motion. Nonparametric hypothesis tests applied to these errors and jackknife statistics yield the same conclusion: universal and ordinary kriging are not significantly different for this application as determined by a cross-validation procedure. These results are based on application to four independent data sets (four different seismic events). 相似文献
13.
R. J. Yao J. S. Yang P. Gao H. B. Shao G. M. Liu S. P. Yu 《Environmental Earth Sciences》2014,71(1):233-243
Soil salinity has been known to be problematic to land productivity and environment in the lower Yellow River Delta due to the presence of a shallow, saline water table and marine sediments. Spatial information on soil salinity has gained increasing importance for the demand of management and sustainable utilization of arable land in this area. Apparent electrical conductivity, as measured by electromagnetic induction instrument in a fairly quick manner, has succeeded in mapping soil salinity and many other soil physical and chemical properties from field to regional scales. This was done based on the correlation that existed between apparent electrical conductivity and many other soil properties. In this paper, four spatial prediction methods, i.e., local polynomial, inverse distance weighed, ordinary kriging and universal kriging, were employed to estimate field-scale apparent electrical conductivity with the aid of an electromagnetic induction instrument (type EM38). The spatial patterns estimated by the four methods using EM38 survey datasets of various sample sizes were compared with those generated by each method using the entire sample size. Spatial similarity was evaluated using difference index (DI) between the maps created using various sample sizes (i.e., target maps) and the maps generated with the entire sample size (i.e., the reference map). The results indicated that universal kriging had the best performance owing to the inclusion of residuals and spatial detrending in the kriging system. DI showed that spatial similarity between the target and reference maps of apparent electrical conductivity decreased with the reduction in sample size for each prediction method. Under the same reduction in sample size, the method retaining the most spatial similarity was universal kriging, followed by ordinary kriging, inverse distance weighed, and local polynomial. Approximately, 70 % of total survey data essentially met the need for retaining 90 % details of the reference map for universal kriging and ordinary kriging methods. This conclusion was that OK and UK were two most appropriate methods for spatial estimation of apparent electrical conductivity as they were robust with the reduction in sample size. 相似文献
14.
G. Bourgault 《Mathematical Geosciences》1997,29(2):277-290
Because of autocorrelation and spatial clustering, all data within a given dataset have not the same statistical weight for estimation of global statistics such mean, variance, or quantiles of the population distribution. A measure of redundancy (or nonredundancy) of any given regionalized random variable Z(uα)within any given set (of size N) of random variables is proposed. It is defined as the ratio of the determinant of the N X Ncorrelation matrix to the determinant of the (N - 1) X (N - 1)correlation matrix excluding random variable Z(uα).This ratio measures the increase in redundancy when adding the random variable Z(uα)to the (N - 1 )remainder. It can be used as declustering weight for any outcome (datum) z(uα). When the redundancy matrix is a kriging covariance matrix, the proposed ratio is the crossvalidation simple kriging variance. The covariance of the uniform scores of the clustered data is proposed as a redundancy measure robust with respect to data clustering. 相似文献
15.
Looking at kriging problems with huge numbers of estimation points and measurements, computational power and storage capacities
often pose heavy limitations to the maximum manageable problem size. In the past, a list of FFT-based algorithms for matrix
operations have been developed. They allow extremely fast convolution, superposition and inversion of covariance matrices
under certain conditions. If adequately used in kriging problems, these algorithms lead to drastic speedup and reductions
in storage requirements without changing the kriging estimator. However, they require second-order stationary covariance functions,
estimation on regular grids, and the measurements must also form a regular grid. In this study, we show how to alleviate these
rather heavy and many times unrealistic restrictions. Stationarity can be generalized to intrinsicity and beyond, if decomposing
kriging problems into the sum of a stationary problem and a formally decoupled regression task. We use universal kriging,
because it covers arbitrary forms of unknown drift and all cases of generalized covariance functions. Even more general, we
use an extension to uncertain rather than unknown drift coefficients. The sampling locations may now be irregular, but must
form a subset of the estimation grid. Finally, we present asymptotically exact but fast approximations to the estimation variance
and point out application to conditional simulation, cokriging and sequential kriging. The drastic gain in computational and
storage efficiency is demonstrated in test cases. Especially high-resolution and data-rich fields such as rainfall interpolation
from radar measurements or seismic or other geophysical inversion can benefit from these improvements. 相似文献
16.
Geostatistics provides a suite of methods, summarized as kriging, to analyze a finite data set to describe a continuous property of the Earth. Kriging methods consist of moving window optimum estimation techniques, which are based on a least-squares principle and use a spatial structure function, usually the variogram. Applications of kriging techniques have become increasingly wide-spread, with ordinary kriging and universal kriging being the most popular ones. The dependence of the final map or model on the input, however, is not generally understood. Herein we demonstrate how changes in the kriging parameters and the neighborhood search affect the cartographic result. Principles are illustrated through a glaciological study. The objective is to map ice thickness and subglacial topography of Storglaciären, Kebnekaise Massif, northern Sweden, from several sets of radio-echo soundings and hot water drillings. New maps are presented. 相似文献
17.
P. Goovaerts 《Mathematical Geology》1998,30(5):511-534
This paper presents both estimation and simulation as optimization problems that differ in the optimization criteria, minimization of a local expected loss for estimation and reproduction of global statistics (semivariogram, histogram) for simulation. An intermediate approach is proposed whereby an initial random image is gradually modified using simulated annealing so as to better match both local and global constraints. The relative weights of the different constraints in the objective function allow the user to strike a balance between smoothness of the estimated map and reproduction of spatial variability by simulated maps. The procedure is illustrated using a synthetic dataset. The proposed approach is shown to enhance the influence of observations on neighboring simulated values, hence the final realizations appear to be better conditioned to the sample information. It also produces maps that are more accurate (smaller prediction error) than stochastic simulation ignoring local constraints, but not as accurate as E-type estimation. Flow simulation results show that accounting for local constraints yields, on average, smaller errors in production forecast than a smooth estimated map or a simulated map that reproduces only the histogram and semivariogram. The approach thus reduces the risk associated with the use of a single realization for forecasting and planning. 相似文献
18.
Obtaining accurate geological boundaries and assessing the uncertainty in these limits are critical for effective ore resource and reserve estimation. The uncertainty in the extent of an ore body can be the largest source of uncertainty in ore resource estimation when drilling is sparse. These limits are traditionally interpreted deterministically and it can be difficult to quantify uncertainty in the boundary and its impact on ore tonnage. The proposed methodology is to consider stochastic modeling of the ore boundary with a distance function recoding of the available data. This technique is modified to incorporate non-stationarities in the form of a locally varying anisotropy field used in kriging and sequential Gaussian simulation. Implementing locally varying anisotropy kriging retains the geologically realistic features of a deterministic model while allowing for a stochastic assessment of uncertainty. A case study of a gold deposit in Northern Canada is used to demonstrate the methodology. The proposed technique generates realistic, curvilinear geological boundary models and allows for an assessment of the uncertainty in the model. 相似文献
19.
Geostatistics provides a suite of methods, summarized as kriging, to analyze a finite data set to describe a continuous property of the Earth. Kriging methods consist of moving window optimum estimation techniques, which are based on a least-squares principle and use a spatial structure function, usually the variogram. Applications of kriging techniques have become increasingly wide-spread, with ordinary kriging and universal kriging being the most popular ones. The dependence of the final map or model on the input, however, is not generally understood. Herein we demonstrate how changes in the kriging parameters and the neighborhood search affect the cartographic result. Principles are illustrated through a glaciological study. The objective is to map ice thickness and subglacial topography of Storglaciären, Kebnekaise Massif, northern Sweden, from several sets of radio-echo soundings and hot water drillings. New maps are presented. 相似文献
20.
In the linear model of coregionalization (LMC), when applicable to the experimental direct variograms and the experimental
cross variogram computed for two random functions, the variability of and relationships between the random functions are modeled
with the same basis functions. In particular, structural correlations can be defined from entries of sill matrices (coregionalization
matrices) under second-order stationarity. In this article, modified t-tests are proposed for assessing the statistical significance of estimated structural correlations. Their specific aspects
and fundamental differences, compared with an existing modified t-test for global correlation analysis with spatial data, are discussed via estimated effective sample sizes, in relation to
the superimposition of random structural components, the range of autocorrelation, the presence of correlation at another
structure, and the sampling scheme. Accordingly, simulation results are presented for one structure versus two structures
(one without and the other with autocorrelation). The performance of tests is shown to be related to the uncertainty associated
with the estimation of variogram model parameters (range, sill matrix entries), because these are involved in the test statistic
and the degrees of freedom of the associated t-distribution through the estimated effective sample size. Under the second-order stationarity and LMC assumptions, the proposed
tests are generally valid. 相似文献