共查询到20条相似文献，搜索用时 31 毫秒
1.
Jeff B. Boisvert Clayton V. Deutsch 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(8):1077-1084
In a spatial property modeling context, the variables of interest to be modeled often display complex nonlinear features.
Techniques to incorporate these nonlinear features, such as multiple point statistics or cummulants, are often complex with
input parameters that are difficult to infer. The methodology proposed in this paper uses a classical vector-based definition
of locally varying anisotropy to characterize nonlinear features and incorporate locally varying anisotropy into numerical
property models. The required input is an exhaustive field of anisotropy orientation and magnitude. The methodology consists
of (1) using the shortest path distance between locations to define the covariance between points in space (2) multidimensional
scaling of the domain to ensure positive definite kriging equations and (3) estimation or simulation with kriging or sequential
Gaussian simulation. The only additional parameter required when kriging or simulating with locally varying anisotropy is
the number of dimensions to retain in multidimensional scaling. The methodology is demonstrated on a CO2 emissions data set for the United States in 2002 and shows an improvement in cross validation results as well as a visual
reproduction of nonlinear features. 相似文献
2.
Xavier Emery 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(2):211-219
The multi-Gaussian model is used in geostatistical applications to predict functions of a regionalized variable and to assess
uncertainty by determining local (conditional to neighboring data) distributions. The model relies on the assumption that
the regionalized variable can be represented by a transform of a Gaussian random field with a known mean value, which is often
a strong requirement. This article presents two variations of the model to account for an uncertain mean value. In the first
one, the mean of the Gaussian random field is regarded as an unknown non-random parameter. In the second model, the mean of
the Gaussian field is regarded as a random variable with a very large prior variance. The properties of the proposed models
are compared in the context of non-linear spatial prediction and uncertainty assessment problems. Algorithms for the conditional
simulation of Gaussian random fields with an uncertain mean are also examined, and problems associated with the selection
of data in a moving neighborhood are discussed. 相似文献
3.
Xavier Emery 《Stochastic Environmental Research and Risk Assessment (SERRA)》2006,20(1-2):53-65
In the geostatistical analysis of regionalized data, the practitioner may not be interested in mapping the unsampled values
of the variable that has been monitored, but in assessing the risk that these values exceed or fall short of a regulatory
threshold. This kind of concern is part of the more general problem of estimating a transfer function of the variable under
study. In this paper, we focus on the multigaussian model, for which the regionalized variable can be represented (up to a
nonlinear transformation) by a Gaussian random field. Two cases are analyzed, depending on whether the mean of this Gaussian
field is considered known or not, which lead to the simple and ordinary multigaussian kriging estimators respectively. Although
both of these estimators are theoretically unbiased, the latter may be preferred to the former for practical applications
since it is robust to a misspecification of the mean value over the domain of interest and also to local fluctuations around
this mean value. An advantage of multigaussian kriging over other nonlinear geostatistical methods such as indicator and disjunctive
kriging is that it makes use of the multivariate distribution of the available data and does not produce order relation violations.
The use of expansions into Hermite polynomials provides three additional results: first, an expression of the multigaussian
kriging estimators in terms of series that can be calculated without numerical integration; second, an expression of the associated
estimation variances; third, the derivation of a disjunctive-type estimator that minimizes the variance of the error when
the mean is unknown. 相似文献
4.
叠前地质统计学反演将随机模拟与叠前反演相结合,不仅可以反演各种储层弹性参数,还提高了反演结果的分辨率.基于联合概率分布的直接序贯协模拟方法可以在原始数据域对数据进行模拟,不需要对数据进行高斯变换,拓展了地质统计学反演的应用范围;而联合概率分布的应用确保了反演参数之间相关性,提高了反演的精度.本文将基于联合概率分布的直接序贯协模拟方法与蒙特卡洛抽样算法相结合,参考全局随机反演策略,提出了基于蒙特卡洛优化算法的全局迭代地质统计学反演方法.为了提高反演的稳定性,我们修改了局部相关系数的计算公式,提出了一种新的基于目标函数的优化局部相关系数计算公式并应用到协模拟之中.模型测试及实际数据应用表明,该方法可以很好的应用于叠前反演之中. 相似文献
5.
Multivariate drought characteristics using trivariate Gaussian and Student t copulas 总被引：4，自引：0，他引：4
This study aims to investigate the changing properties of drought events in Weihe River basin, China, by modeling the multivariate joint distribution of drought duration, severity and peak using trivariate Gaussian and Student t copulas. Monthly precipitations of Xi'an gauge are used to illustrate the meta‐elliptical copula‐based methodology for a single‐station application. Gaussian and Student t copulas are found to produce a better fit comparing with other six symmetrical and asymmetrical Archimedean copulas, and, checked by the goodness‐of‐fit tests based on a modified bootstrap version of Rosenblatt's transformation, both of them are acceptable to model the multivariate joint distribution of drought variables. Gaussian copula, the best fitting, is employed to construct the dependence structures of positively associated drought variables so as to obtain the multivariate joint and conditional probabilities of droughts. A Kendall's return period (KRP) introduced by Salvadori and De Michele (2010) is then adopted to assess the multivariate recurrent properties of drought events, and its spatial distributions indicate that prolonged droughts are likely to break out with rather short recurrence intervals in the whole region, while drought status in the southeast seems to be severer than the northwest. The study is of some merits in terms of multivariate drought modeling using a preferable copula‐based method, the results of which could serve as a reference for regional drought defense and water resources management. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
6.
This paper introduces a new geostatistical model for counting data under a space-time approach using nonhomogeneous Poisson processes, where the random intensity process has an additive formulation with two components: a Gaussian spatial component and a component accounting for the temporal effect. Inferences of interest for the proposed model are obtained under the Bayesian paradigm. To illustrate the usefulness of the proposed model, we first develop a simulation study to test the efficacy of the Markov Chain Monte Carlo (MCMC) method to generate samples for the joint posterior distribution of the model’s parameters. This study shows that the convergence of the MCMC algorithm used to simulate samples for the joint posterior distribution of interest is easily obtained for different scenarios. As a second illustration, the proposed model is applied to a real data set related to ozone air pollution collected in 22 monitoring stations in Mexico City in the 2010 year. The proposed geostatistical model has good performance in the data analysis, in terms of fit to the data and in the identification of the regions with the highest pollution levels, that is, the southwest, the central and the northwest regions of Mexico City. 相似文献
7.
A multidimensional scaling approach to enforce reproduction of transition probabilities in truncated plurigaussian simulation 总被引：2，自引：1，他引：1
Jared L. Deutsch Clayton V. Deutsch 《Stochastic Environmental Research and Risk Assessment (SERRA)》2014,28(3):707-716
Truncated plurigaussian (TPG) simulation is a flexible method for simulating rock types in deposits with complicated ordering structures. The truncation of a multivariate Gaussian distribution controls the proportions and ordering of rock types in the simulation while the variogram for each Gaussian variable controls rock type continuity. The determination of a truncation procedure for complicated geological environments is not trivial. A method for determining the truncation and fitting variograms applicable to any number of rock types and multivariate Gaussian distribution is developed here to address this problem. Multidimensional scaling is applied to place dissimilar categories far apart and similar categories close together. The multivariate space is then mapped using a Voronoi decomposition and rotated to optimize variogram reproduction. A case study simulating geologic layers at a large mineral deposit demonstrates the potential of this method and compares the results with sequential indicator simulation (SIS). Input proportion and transition probability reproduction with TPG is demonstrated to be better than SIS. Variogram reproduction is comparable for both techniques. 相似文献
8.
9.
Amir H. Hosseini Clayton V. Deutsch Kevin W. Biggar Carl A. Mendoza 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(5):735-749
The spatial distribution of residual light non-aqueous phase liquid (LNAPL) is an important factor in reactive solute transport
modeling studies. There is great uncertainty associated with both the areal limits of LNAPL source zones and smaller scale
variability within the areal limits. A statistical approach is proposed to construct a probabilistic model for the spatial
distribution of residual NAPL and it is applied to a site characterized by ultra-violet-induced-cone-penetration testing (CPT–UVIF).
The uncertainty in areal limits is explicitly addressed by a novel distance function (DF) approach. In modeling the small-scale
variability within the areal limits, the CPT–UVIF data are used as primary source of information, while soil texture and distance
to water table are treated as secondary data. Two widely used geostatistical techniques are applied for the data integration,
namely sequential indicator simulation with locally varying means (SIS–LVM) and Bayesian updating (BU). A close match between
the calibrated uncertainty band (UB) and the target probabilities shows the performance of the proposed DF technique in characterization
of uncertainty in the areal limits. A cross-validation study also shows that the integration of the secondary data sources
substantially improves the prediction of contaminated and uncontaminated locations and that the SIS–LVM algorithm gives a
more accurate prediction of residual NAPL contamination. The proposed DF approach is useful in modeling the areal limits of
the non-stationary continuous or categorical random variables, and in providing a prior probability map for source zone sizes
to be used in Monte Carlo simulations of contaminant transport or Monte Carlo type inverse modeling studies. 相似文献
10.
M.A. Wibrin P. Bogaert D. Fasbender 《Stochastic Environmental Research and Risk Assessment (SERRA)》2006,20(6):423-433
Due to the fast pace increasing availability and diversity of information sources in environmental sciences, there is a real need of sound statistical mapping techniques for using them jointly inside a unique theoretical framework. As these information sources may vary both with respect to their nature (continuous vs. categorical or qualitative), their spatial density as well as their intrinsic quality (soft vs. hard data), the design of such techniques is a challenging issue. In this paper, an efficient method for combining spatially non-exhaustive categorical and continuous data in a mapping context is proposed, based on the Bayesian maximum entropy paradigm. This approach relies first on the definition of a mixed random field, that can account for a stochastic link between categorical and continuous random fields through the use of a cross-covariance function. When incorporating general knowledge about the first- and second-order moments of these fields, it is shown that, under mild hypotheses, their joint distribution can be expressed as a mixture of conditional Gaussian prior distributions, with parameters estimation that can be obtained from entropy maximization. A posterior distribution that incorporates the various (soft or hard) continuous and categorical data at hand can then be obtained by a straightforward conditionalization step. The use and potential of the method is illustrated by the way of a simulated case study. A comparison with few common geostatistical methods in some limit cases also emphasizes their similarities and differences, both from the theoretical and practical viewpoints. As expected, adding categorical information may significantly improve the spatial prediction of a continuous variable, making this approach powerful and very promising. 相似文献
11.
Camilla Zacché da Silva João Felipe Costa 《Stochastic Environmental Research and Risk Assessment (SERRA)》2014,28(8):1929-1938
There are many situations in the mining industry where grade estimation of multiple correlated variables is required. The resulting model is expected to reproduce the data correlation, but there is no guarantee that the correlation observed among data will be reproduced by the model if the variables are independently estimated by kriging, and the correlation is not explicitly taken into account. The best geostatistical approach to address this estimation problem is to use co-kriging, which requires both cross and direct covariance modeling of all variables. However, the co-kriging method is labor-intensive when the problem involves more than three attributes. An alternative is to decorrelate the variables and estimate each one independently, using, for instance, the minimum/maximum autocorrelation factors (MAF) approach. This method involves the application of a linear transformation to the correlated variables, transforming the original data into a space where they are uncorrelated. The resulting transformed data can be individually estimated using kriging, avoiding the use of the linear model of coregionalization. Once the kriging has been performed, the MAF estimates are back-transformed to the original data space, re-establishing their correlation.The methodology is illustrated in a case study where there are two variables with correlation coefficient, ρ = ?0.98. The MAF transformation was applied in combination with ordinary kriging (herein denoted as KMAF). Co-kriging was performed to provide a benchmark for comparing the results obtained through KMAF. The results obtained by co-kriging and KMAF showed less than 1 % average deviation between the two block models. 相似文献
12.
Planar waves events recorded in a seismic array can be represented as lines in the Fourier domain. However, in the real world, seismic events usually have curvature or amplitude variability, which means that their Fourier transforms are no longer strictly linear but rather occupy conic regions of the Fourier domain that are narrow at low frequencies but broaden at high frequencies where the effect of curvature becomes more pronounced. One can consider these regions as localised “signal cones”. In this work, we consider a space–time variable signal cone to model the seismic data. The variability of the signal cone is obtained through scaling, slanting, and translation of the kernel for cone‐limited (C‐limited) functions (functions whose Fourier transform lives within a cone) or C‐Gaussian function (a multivariate function whose Fourier transform decays exponentially with respect to slowness and frequency), which constitutes our dictionary. We find a discrete number of scaling, slanting, and translation parameters from a continuum by optimally matching the data. This is a non‐linear optimisation problem, which we address by a fixed‐point method that utilises a variable projection method with ?1 constraints on the linear parameters and bound constraints on the non‐linear parameters. We observe that slow decay and oscillatory behaviour of the kernel for C‐limited functions constitute bottlenecks for the optimisation problem, which we partially overcome by the C‐Gaussian function. We demonstrate our method through an interpolation example. We present the interpolation result using the estimated parameters obtained from the proposed method and compare it with those obtained using sparsity‐promoting curvelet decomposition, matching pursuit Fourier interpolation, and sparsity‐promoting plane‐wave decomposition methods. 相似文献
13.
Linear geophysical inversion via the discrete cosine pseudo‐inverse: application to potential fields 
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下载免费PDF全文 J.L. Fernández‐Martínez Z. Fernández‐Muñiz J.L.G. Pallero S. Bonvalot 《Geophysical Prospecting》2017,65(Z1):94-111
In this paper, we present a methodology to perform geophysical inversion of large‐scale linear systems via a covariance‐free orthogonal transformation: the discrete cosine transform. The methodology consists of compressing the matrix of the linear system as a digital image and using the interesting properties of orthogonal transformations to define an approximation of the Moore–Penrose pseudo‐inverse. This methodology is also highly scalable since the model reduction achieved by these techniques increases with the number of parameters of the linear system involved due to the high correlation needed for these parameters to accomplish very detailed forward predictions and allows for a very fast computation of the inverse problem solution. We show the application of this methodology to a simple synthetic two‐dimensional gravimetric problem for different dimensionalities and different levels of white Gaussian noise and to a synthetic linear system whose system matrix has been generated via geostatistical simulation to produce a random field with a given spatial correlation. The numerical results show that the discrete cosine transform pseudo‐inverse outperforms the classical least‐squares techniques, mainly in the presence of noise, since the solutions that are obtained are more stable and fit the observed data with the lowest root‐mean‐square error. Besides, we show that model reduction is a very effective way of parameter regularisation when the conditioning of the reduced discrete cosine transform matrix is taken into account. We finally show its application to the inversion of a real gravity profile in the Atacama Desert (north Chile) obtaining very successful results in this non‐linear inverse problem. The methodology presented here has a general character and can be applied to solve any linear and non‐linear inverse problems (through linearisation) arising in technology and, particularly, in geophysics, independently of the geophysical model discretisation and dimensionality. Nevertheless, the results shown in this paper are better in the case of ill‐conditioned inverse problems for which the matrix compression is more efficient. In that sense, a natural extension of this methodology would be its application to the set of normal equations. 相似文献
14.
We describe an objective method for evaluating the spatial distribution of water equivalents of the snow cover within a small catchment. Regression analysis is used to quantify the relationship between elevation, presence or absence of forest, and potential direct solar radiation as independent variables and water equivalent as measured at a number of sites. First, this regression relationship is used to interpolate water equivalent data all over the basin area. Then we interpolate the residuals of the regression using a geostatistical approach. Superimposing the results obtained by interpolating the regression relationship and the interpolated residuals eventually yields the water equivalent distribution over the test area. The advantages of the interpolation method used lie in the optimal (effective, unbiased) estimation of the interpolated values as well as in the possibility to quantify the associated estimation variances. 相似文献
15.
W. A. Woodward S. R. Sain H. L. Gray B. Zhao M. D. Fisk 《Pure and Applied Geophysics》2002,159(4):889-903
—?We consider the problem of multivariate outlier testing for purposes of distinguishing seismic signals of underground nuclear events from training samples based on non-nuclear seismic events when certain data are missing. We consider the case in which the training data follow a multivariate normal distribution. Assume a potential outlier is observed on which k features of interest are measured. Assume further that the available training set of n observations on these k features is available but that some of the observations in the training data have missing features. The approach currently used in practice is to perform the outlier testing using a generalized likelihood ratio test procedure based only on the data vectors in the training data with complete data. When there is a substantial amount of missing data within the training set, use of this strategy may lead to a loss of valuable information. An alternative procedure is to incorporate all n of the data vectors in the training data using the EM algorithm to appropriately handle the missing data in the training set. Resampling methods are used to find appropriate critical regions. We use simulation results and analysis of models fit to Pg/Lg ratios for the WMQ station in China to compare these two strategies for dealing with missing data. 相似文献
16.
17.
Environmental data are commonly constrained by a detection limit (DL) because of the restriction of experimental apparatus. In particular due to the changes of experimental units or assay methods, the observed data are often cut off by more than one DL. Measurements below the DLs are typically replaced by an arbitrary value such as zeros, half of DLs, or DLs for convenience of analysis. However, this method is widely considered unreliable and prone to bias. In contrast, maximum likelihood estimation (MLE) method for censored data has been developed for better performance and statistical justification. However, the existing MLE methods seldom address the multivariate context of censored environmental data especially for water quality. This paper proposes using a mixture model to flexibly approximate the underlying distribution of the observed data due to its good approximation capability and generation mechanism. In particular, Gaussian mixture model (GMM) is mainly focused in this study. To cope with the censored data with multiple DLs, an expectation–maximization (EM) algorithm in a multivariate setting is developed. The proposed statistical analysis approach is verified from both the simulated data and real water quality data. 相似文献
18.
Brendon A. Bradley 《地震工程与结构动力学》2010,39(12):1321-1342
A generalized conditional intensity measure (GCIM) approach is proposed for use in the holistic selection of ground motions for any form of seismic response analysis. The essence of the method is the construction of the multivariate distribution of any set of ground‐motion intensity measures conditioned on the occurrence of a specific ground‐motion intensity measure (commonly obtained from probabilistic seismic hazard analysis). The approach therefore allows any number of ground‐motion intensity measures identified as important in a particular seismic response problem to be considered. A holistic method of ground‐motion selection is also proposed based on the statistical comparison, for each intensity measure, of the empirical distribution of the ground‐motion suite with the ‘target’ GCIM distribution. A simple procedure to estimate the magnitude of potential bias in the results of seismic response analyses when the ground‐motion suite does not conform to the GCIM distribution is also demonstrated. The combination of these three features of the approach make it entirely holistic in that: any level of complexity in ground‐motion selection for any seismic response analysis can be exercised; users explicitly understand the simplifications made in the selected suite of ground motions; and an approximate estimate of any bias associated with such simplifications is obtained. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
19.
Geostatistical seismic inversion for non‐stationary patterns using direct sequential simulation and co‐simulation 下载免费PDF全文
下载免费PDF全文 Hamid Sabeti Ali Moradzadeh Faramarz Doulati Ardejani Leonardo Azevedo Amilcar Soares Pedro Pereira Ruben Nunes 《Geophysical Prospecting》2017,65(Z1):25-48
Geostatistical seismic inversion methods are routinely used in reservoir characterisation studies because of their potential to infer the spatial distribution of the petro‐elastic properties of interest (e.g., density, elastic, and acoustic impedance) along with the associated spatial uncertainty. Within the geostatistical seismic inversion framework, the retrieved inverse elastic models are conditioned by a global probability distribution function and a global spatial continuity model as estimated from the available well‐log data for the entire inversion grid. However, the spatial distribution of the real subsurface elastic properties is complex, heterogeneous, and, in many cases, non‐stationary since they directly depend on the subsurface geology, i.e., the spatial distribution of the facies of interest. In these complex geological settings, the application of a single distribution function and a spatial continuity model is not enough to properly model the natural variability of the elastic properties of interest. In this study, we propose a three‐dimensional geostatistical inversion technique that is able to incorporate the reservoir's heterogeneities. This method uses a traditional geostatistical seismic inversion conditioned by local multi‐distribution functions and spatial continuity models under non‐stationary conditions. The procedure of the proposed methodology is based on a zonation criterion along the vertical direction of the reservoir grid. Each zone can be defined by conventional seismic interpretation, with the identification of the main seismic units and significant variations of seismic amplitudes. The proposed method was applied to a highly non‐stationary synthetic seismic dataset with different levels of noise. The results of this work clearly show the advantages of the proposed method against conventional geostatistical seismic inversion procedures. It is important to highlight the impact of this technique in terms of higher convergence between real and inverted reflection seismic data and the more realistic approximation towards the real subsurface geology comparing with traditional techniques. 相似文献
20.
Compositional Bayesian indicator estimation 总被引：1，自引：1，他引：0
Carolina Guardiola-Albert Eulogio Pardo-Ig��zquiza 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(6):835-849
Indicator kriging is widely used for mapping spatial binary variables and for estimating the global and local spatial distributions
of variables in geosciences. For continuous random variables, indicator kriging gives an estimate of the cumulative distribution
function, for a given threshold, which is then the estimate of a probability. Like any other kriging procedure, indicator
kriging provides an estimation variance that, although not often used in applications, should be taken into account as it
assesses the uncertainty of the estimate. An alternative approach to indicator estimation is proposed in this paper. In this
alternative approach the complete probability density function of the indicator estimate is evaluated. The procedure is described
in a Bayesian framework, using a multivariate Gaussian likelihood and an a priori distribution which are both combined according
to Bayes theorem in order to obtain a posterior distribution for the indicator estimate. From this posterior distribution,
point estimates, interval estimates and uncertainty measures can be obtained. Among the point estimates, the median of the
posterior distribution is the maximum entropy estimate because there is a fifty-fifty chance of the unknown value of the estimate
being larger or smaller than the median; that is, there is maximum uncertainty in the choice between two alternatives. Thus
in some sense, the latter is an indicator estimator, alternative to the kriging estimator, that includes its own uncertainty.
On the other hand, the mode of the posterior distribution estimator, assuming a uniform prior, is coincidental with the simple
kriging estimator. Additionally, because the indicator estimate can be considered as a two-part composition which domain of
definition is the simplex, the method is extended to compositional Bayesian indicator estimation. Bayesian indicator estimation
and compositional Bayesian indicator estimation are illustrated with an environmental case study in which the probability
of the content of a geochemical element in soil being over a particular threshold is of interest. The computer codes and its
user guides are public domain and freely available. 相似文献