共查询到20条相似文献，搜索用时 31 毫秒
1.
Gilles Bourgault 《Mathematical Geosciences》2014,46(7):841-868
A multivariate probability transformation between random variables, known as the Nataf transformation, is shown to be the appropriate transformation for multi-Gaussian kriging. It assumes a diagonal Jacobian matrix for the transformation of the random variables between the original space and the Gaussian space. This allows writing the probability transformation between the local conditional probability density function in the original space and the local conditional Gaussian probability density function in the Gaussian space as a ratio equal to the ratio of their respective marginal distributions. Under stationarity, the marginal distribution in the original space is modeled from the data histogram. The stationary marginal standard Gaussian distribution is obtained from the normal scores of the data and the local conditional Gaussian distribution is modeled from the kriging mean and kriging variance of the normal scores of the data. The equality of ratios of distributions has the same form as the Bayes’ rule and the assumption of stationarity of the data histogram can be re-interpreted as the gathering of the prior distribution. Multi-Gaussian kriging can be re-interpreted as an updating of the data histogram by a Gaussian likelihood. The Bayes’ rule allows for an even more general interpretation of spatial estimation in terms of equality for the ratio of the conditional distribution over the marginal distribution in the original data uncertainty space with the same ratio for a model of uncertainty with a distribution that can be modeled using the mean and variance from direct kriging of the original data values. It is based on the principle of conservation of probability ratio and no transformation is required. The local conditional distribution has a variance that is data dependent. When used in sequential simulation mode, it reproduces histogram and variogram of the data, thus providing a new approach for direct simulation in the original value space. 相似文献
2.
Denis Marcotte 《Mathematical Geology》1995,27(6):749-762
Conditional simulation with data subject to measurement error has received little attention in the geostatistical literature. The treatment of measurement error in simulation must be different from its treatment in estimation. Two approaches are examined: pre- and post-simulation filtering of data measurement error. The pre-simulation filtering is shown to be inefficient. The post-simulation filtering performs best. It is done by factorial kriging and a modified version of factorial kriging which ensures predetermined theoretical variance for the filtered data. It also is shown that the theoretical variogram of the filtered data reproduces the underlying variogram (i.e., without noise) almost perfectly. A simulation with a high level of correlated noise is used for validation and comparison. The post-simulation filtered values show an experimental variogram in agreement with the previously identified underlying variogram. Moreover, the filtered image compares well with the true image. The theoretical variogram corresponding to the post-simulation filter can be computed beforehand. Thus, the size of the simulation grid and of the filter neighborhood can be adjusted to ensure good reproduction of the underlying variogram. 相似文献
3.
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
4.
G. Bourgault 《Mathematical Geology》1994,26(6):733-752
In geostatistics, factorial kriging is often proposed to filter noise. This filter is built from a linear model which is ideally suited to a Gaussian signal with additive independent noise. Robustness of the performance of factorial kriging is evaluated in less congenial situations. Three different types of noise are considered all perturbing a lognormally distributed signal. The first noise model is independent of the signal. The second noise model is heteroscedastic; its variance depends on the signal, yet noise and signal are uncorrelated. The third noise model is both heteroscedastic and linearly correlated with the signal. In ideal conditions, exhaustive sampling and additive independent noise, factorial kriging succeeds to reproduce the spatial patterns of high signal values. This score remains good in presence of heteroscedastic noise variance but falls quickly in presence of noise-to-signal correlation as soon as the sample becomes sparser. 相似文献
5.
《Applied Geochemistry》1999,14(1):133-145
Three univariate geostatistical methods of estimation are applied to a geochemical data set. The studied methods are: ordinary kriging (cross-validation), factorial kriging, and indicator kriging. These techniques use the probabilistic and spatial behaviour of geochemical variables, giving a tool for identifying potential anomalous areas to locate mineralization. Ordinary kriging is easy to apply and to interpret the results. It has the advantage of using the same experimental grid points for its estimates, and no additional grid points are needed. Factorial kriging decomposes the raw variable into as many components as there are identified structures in the variogram. This, however, is a complex method and its application is more difficult than that of ordinary or indicator kriging. The main advantages of indicator kriging are that data are used by their rank order, being more robust about outlier values, and that the presentation of results is simple. Nevertheless, indicator kriging is incapable of separating anomalous values and the high values from the background, which have a behaviour different to the anomaly. In this work, the results of the application of these 3 kriging methods to a set of mineral exploration data obtained from a geochemical survey carried out in NW Spain are presented. This area is characterised by the presence of Au mineral occurrences. The kriging methods were applied to As, considered as a pathfinder of Au in this area. Numerical treatment of Au is not applicable, because it presents most values equal to the detection limit, and a series of extreme values. The results of the application of ordinary kriging, factorial kriging and indicator kriging to As make possible the location of a series of rich values, sited along a N–S shear zone, considered a structure related to the presence of Au. 相似文献
6.
Xavier Emery 《Mathematical Geology》2003,35(6):699-718
This paper presents a methodology for assessing local probability distributions by disjunctive kriging when the available data set contains some imprecise measurements, like noisy or soft information or interval constraints. The basic idea consists in replacing the set of imprecise data by a set of pseudohard data simulated from their posterior distribution; an iterative algorithm based on the Gibbs sampler is proposed to achieve such a simulation step. The whole procedure is repeated many times and the final result is the average of the disjunctive kriging estimates computed from each simulated data set. Being data-independent, the kriging weights need to be calculated only once, which enables fast computing. The simulation procedure requires encoding each datum as a pre-posterior distribution and assuming a Markov property to allow the updating of pre-posterior distributions into posterior ones. Although it suffers some imperfections, disjunctive kriging turns out to be a much more flexible approach than conditional expectation, because of the vast class of models that allows its computation, namely isofactorial models. 相似文献
7.
This study uses factorial and indicator kriging methods with a geographic information system (GIS), to overlay and delineate the variation and pollution sources of soil heavy metals in fields in the north of Changhua County, Taiwan. Accordingly, the spatial variation and pollution probability patterns of soil cadmium, chromium and copper are estimated to support further environmental monitoring, remediation and planning. The overlay maps of industrial plants, irrigation channels and kriging estimates, constitute a GIS. This reveals that the short- and long-range variations and soil pollution by Cd, Cr and Cu strongly corresponded to the locations of irrigation systems and industrial plants in the area of study. The maps also verify most locations of suspected pollution sources from the GIS database. Moreover, the probability spatial patterns estimated by indicator kriging, based on the pollution thresholds of Cd, Cr and Cu, were also highly correlated with irrigation channels and industrial plants. The GIS, with factorial and indicator kriging under different combinations of variations and pollution probabilities of soil Cd, Cr and Cu, provide alternative scenarios for delineating the areas that contain high variation and high pollution probability of these heavy metals, to enable decision makers to identify pollution sources, and to further investigate and remedy soil pollution. 相似文献
8.
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
9.
Arnon Karnieli Dr. 《GeoJournal》1990,22(4):391-398
The classical methods for interpolating and spatial averaging of precipitation fields fail to quantify the accuracy of the estimate. On the other hand, kriging is an interpolation method for predicting values of regionalized variables at points (punctual kriging) or average values over an area (block kriging).This paper demonstrates the use of the kriging method for mapping and evaluating precipitation data for the State of Arizona. Using 158 rain gauge stations with 30 years or more of record, the precipitation over the state has been modeled as a realization of a two dimensional random field taking into consideration the spatial variability conditions.Three data sets have been used: (1) the mean annual precipitation over the state; (2) the mean summer rainy season; and (3) the mean winter rainy season. Validation of the empirical semi-variogram for a constant drift case indicated that the exponential model was appropriate for all the data sets. In addition to a global kriging analysis, the data have been examined under an anisotropic assumption which reflects the topographic structure of the state. 相似文献
10.
An Experimental Comparison of Ordinary and Universal Kriging and Inverse Distance Weighting 总被引：17，自引：0，他引：17
A factorial, computational experiment was conducted to compare the spatial interpolation accuracy of ordinary and universal kriging and two types of inverse squared-distance weighting. The experiment considered, in addition to these four interpolation methods, the effects of four data and sampling characteristics: surface type, sampling pattern, noise level, and strength of small-scale spatial correlation. Interpolation accuracy was measured by the natural logarithm of the mean squared interpolation error. Main effects of all five factors, all two-factor interactions, and several three-factor interactions were highly statistically significant. Among numerous findings, the most striking was that the two kriging methods were substantially superior to the inverse distance weighting methods over all levels of surface type, sampling pattern, noise, and correlation. 相似文献
11.
O. Jaquet 《Mathematical Geology》1989,21(7):683-691
A regionalized variable, thickness of the reservoir layer, from a gas field is decomposed by factorial kriging analysis. Maps of the obtained components may be associated with depositional environments that are favorable for petroleum exploration. 相似文献
12.
On unbiased backtransform of lognormal kriging estimates 总被引：4，自引：0，他引：4
Jorge Kazuo Yamamoto 《Computational Geosciences》2007,11(3):219-234
Lognormal kriging is an estimation technique that was devised for handling highly skewed data distributions. This technique
takes advantage of a logarithmic transformation that reduces the data variance. However, backtransformed lognormal kriging
estimates are biased because the nonbias term is totally dependent on a semivariogram model. This paper proposes a new approach
for backtransforming lognormal kriging estimates that not only presents none of the problems reported in the literature but
also reproduces the sample histogram and, consequently, the sample mean. 相似文献
13.
A Simple Approach to Account for Radial Flow and Boundary Conditions When Kriging Hydraulic Head Fields for Confined Aquifers 总被引：2，自引：0，他引：2
The estimation and mapping of realistic hydraulic head fields, hence of flow paths, is a major goal of many hydrogeological studies. The most widely used method to obtain reliable head fields is the inverse approach. This approach relies on the numerical approximation of the flow equation and requires specifying boundary conditions and the transmissivity of each grid element. Boundary conditions are often unknown or poorly known, yet they impose a strong signature on the head fields obtained by inverse analysis. A simpler alternative to the inverse approach is the direct kriging of the head field using the measurements obtained at observation wells. The kriging must be modified to incorporate the available information. Use of the dual kriging formalism enables simultaneously estimating the head field, the aquifer mean transmissivity, and the regional hydraulic gradient from head data in steady or transient state conditions. In transient state conditions, an estimate of the storage coefficient can be obtained. We test the approach on simple analytical cases, on synthetic cases with solutions obtained numerically using a finite element flow simulator, and on a real aquifer. For homogeneous aquifers, infinite or bounded, the kriging estimate retrieves the exact solution of the head field, the exact hydrogeological parameters and the flow net. With heterogeneous aquifers, kriging accurately estimates the head field with prediction errors of the same magnitude as typical head measurement errors. The transmissivities are also accurately estimated by kriging. Moreover, if inversion is required, the kriged head along boundaries can be used as realistic boundary conditions for flow simulation. 相似文献
14.
Kriging Prediction Intervals Based on Semiparametric Bootstrap 总被引：1，自引：0，他引：1
Kriging is a widely used method for prediction, which, given observations of a (spatial) process, yields the best linear unbiased
predictor of the process at a new location. The construction of corresponding prediction intervals typically relies on Gaussian
assumptions. Here we show that the distribution of kriging predictors for non-Gaussian processes may be far from Gaussian,
even asymptotically. This emphasizes the need for other ways to construct prediction intervals. We propose a semiparametric
bootstrap method with focus on the ordinary kriging predictor. No distributional assumptions about the data generating process
are needed. A simulation study for Gaussian as well as lognormal processes shows that the semiparametric bootstrap method
works well. For the lognormal process we see significant improvement in coverage probability compared to traditional methods
relying on Gaussian assumptions. 相似文献
15.
A thorough understanding of the characteristics of transmissivity makes groundwater deterministic models more accurate. These
transmissivity data characteristics occasionally possess a complicated spatial variation over an investigated site. This study
presents both geostatistical estimation and conditional simulation methods to generate spatial transmissivity maps. The measured
transmissivity data from the Dulliu area in Yun-Lin county, Taiwan, is used as the case study. The spatial transmissivity
maps are simulated by using sequential Gaussian simulation (SGS), and estimated by using natural log ordinary kriging and
ordinary kriging. Estimation and simulation results indicate that SGS can reproduce the spatial structure of the investigated
data. Furthermore, displaying a low spatial variability does not allow the ordinary kriging and natural log kriging estimates
to fit the spatial structure and small-scale variation for the investigated data. The maps of kriging estimates are smoother
than those of other simulations. A SGS with multiple realizations has significant advantages over ordinary kriging and even
natural log kriging techniques at a site with a high variation in investigated data. These results are displayed in geographic
information systems (GIS) as basic information for further groundwater study.
Received: 27 August 1999 · Accepted: 22 February 2000 相似文献
16.
以多重分形理论为基础,对中天山乌拉斯台地区铜多金属元素的岩屑测量数据,采用C-A法获得铜多金属的异常下限值,将其作为阈值进行指示克里格插值,绘制研究区的铜多金属地球化学异常图。研究显示,基于该方法获得的Cu矿化异常高值区主要集中在华力西早期第三侵入次的石英闪长岩和花岗闪长岩岩体中,受北西向和次级北东向断裂构造控制明显,该异常区可以作为寻找热液型铜多金属矿产的重要远景区。该方法对于地球化学数据空间变异性强烈的地区,较之普通克里格插值法具有更好的地球化学异常识别能力和高值信息重建能力,所得结果的最高累计频率值范围与已知矿化点的空间位置吻合度更高,在地球化学异常信息提取工作中具有推广意义。 相似文献
17.
Direct Sequential Simulation and Cosimulation 总被引：7，自引：0，他引：7
Amilcar Soares 《Mathematical Geology》2001,33(8):911-926
Sequential simulation of a continuous variable usually requires its transformation into a binary or a Gaussian variable, giving rise to the classical algorithms of sequential indicator simulation or sequential Gaussian simulation. Journel (1994) showed that the sequential simulation of a continuous variable, without any prior transformation, succeeded in reproducing the covariance model, provided that the simulated values are drawn from local distributions centered at the simple kriging estimates with a variance corresponding to the simple kriging estimation variance. Unfortunately, it does not reproduce the histogram of the original variable, which is one of the basic requirements of any simulation method. This has been the most serious limitation to the practical application of the direct simulation approach. In this paper, a new approach for the direct sequential simulation is proposed. The idea is to use the local sk estimates of the mean and variance, not to define the local cdf but to sample from the global cdf. Simulated values of original variable are drawn from intervals of the global cdf, which are calculated with the local estimates of the mean and variance. One of the main advantages of the direct sequential simulation method is that it allows joint simulation of N
v variables without any transformation. A set of examples of direct simulation and cosimulation are presented. 相似文献
18.
Masoud Monjezi Majid Rajabalizadeh Kashani Mohammad Ataei 《Arabian Journal of Geosciences》2013,6(1):123-128
Grade estimation is very important in designing open pits. In the process of grade estimation, underestimation can result in loss of economic ore, whereas overestimation would unnecessarily increase stripping ratio. Normally, kriging method, which suffers from underestimation and/or overestimation due to smoothing effect, is used for grade estimation. To overcome drawbacks of the kriging method, more efficient techniques such as conditional simulation can be applied. In this paper, utilizing sequential Gaussian conditional simulation, grade models were constructed for Sungun copper deposit situated in the North West of Iran. According to the obtained results, it was observed that conditional simulation can effectively cope with the weakness of kriging method. Also, it was observed that as compared to the kriging method, grade distribution, resulted from the conditional simulation, is almost identical to that of the real exploration data. Accordingly, using conditional simulation, the amount of mineable ore was significantly increased, and also, average net present value as the mines’ most important economic indicator was improved by 40%. 相似文献
19.
20.
Maria Vigsnes Odd Kolbjørnsen Vera Louise Hauge Pål Dahle Petter Abrahamsen 《Mathematical Geosciences》2017,49(5):619-634
Unknown values of a random field can be predicted from observed data using kriging. As data sets grow in size, the computation times become large. To facilitate kriging with large data sets, an approximation where the kriging is performed in sub-segments with common data neighborhoods has been developed. It is shown how the accuracy of the approximation can be controlled by increasing the common data neighborhood. For four different variograms, it is shown how large the data neighborhoods must be to get an accuracy below a chosen threshold, and how much faster these calculations are compared to the kriging where all data are used. Provided that variogram ranges are small compared to the domain of interest, kriging with common data neighborhoods provides excellent speed-ups (2–40) while maintaining high numerical accuracy. Results are presented both for data neighborhoods where the neighborhoods are the same for all sub-segments, and data neighborhoods where the neighborhoods are adapted to fit the data densities around the sub-segments. Kriging in sub-segments with common data neighborhoods is well suited for parallelization and the speed-up is almost linear in the number of threads. A comparison is made to the widely used moving neighborhood approach. It is demonstrated that the accuracy of the moving neighborhood approach can be poor and that computational speed can be slow compared to kriging with common data neighborhoods. 相似文献