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1.
Testing the correctness of the sequential algorithm for simulating Gaussian random fields 总被引：2，自引：2，他引：0
The sequential algorithm is widely used to simulate Gaussian random fields. However, a rigorous application of this algorithm is impractical and some simplifications are required, in particular a moving neighborhood has to be defined. To examine the effect of such restriction on the quality of the realizations, a reference case is presented and several parameters are reviewed, mainly the histogram, variogram, indicator variograms, as well as the ergodic fluctuations in the first and second-order statistics. The study concludes that, even in a favorable case where the simulated domain is large with respect to the range of the model, the realizations may poorly reproduce the second-order statistics and be inconsistent with the stationarity and ergodicity assumptions. Practical tips such as the multiple-grid strategy do not overcome these impediments. Finally, extending the original algorithm by using an ordinary kriging should be avoided, unless an intrinsic random function model is sought after. 相似文献
2.
S. De Iaco M. Palma 《Stochastic Environmental Research and Risk Assessment (SERRA)》2002,16(5):333-341
In geostatistics, stochastic simulation is often used either as an improved interpolation algorithm or as a measure of the
spatial uncertainty. Hence, it is crucial to assess how fast realization-based statistics converge towards model-based statistics
(i.e. histogram, variogram) since in theory such a match is guaranteed only on average over a number of realizations. This
can be strongly affected by the random number generator being used. Moreover, the usual assumption of independence among simulated
realizations of a random process may be affected by the random number generator used. Simulation results, obtained by using
three different random number generators implemented in Geostatistical Software Library (GSLib), are compared. Some practical
aspects are pointed out and some suggestions are given to users of the unconditional LU simulation method. 相似文献
3.
Impact of the simulation algorithm, magnitude of ergodic fluctuations and number of realizations on the spaces of uncertainty of flow properties 总被引：1，自引：1，他引：0
P. Goovaerts 《Stochastic Environmental Research and Risk Assessment (SERRA)》1999,13(3):161-182
Geostatistical simulation algorithms are routinely used to generate conditional realizations of the spatial distribution
of petrophysical properties, which are then fed into complex transfer functions, e.g. a flow simulator, to yield a distribution
of responses, such as the time to recover a given proportion of the oil. This latter distribution, often referred to as the
space of uncertainty, cannot be defined analytically because of the complexity (non-linearity) of transfer functions, but
it can be characterized algorithmically through the generation of many realizations. This paper compares the space of uncertainty
generated by four of the most commonly used algorithms: sequential Gaussian simulation, sequential indicator simulation, p-field simulation and simulated annealing. Conditional to 80 sample permeability values randomly drawn from an exhaustive
40×40 image, 100 realizations of the spatial distribution of permeability values are generated using each algorithm and fed
into a pressure solver and a flow simulator. Principal component analysis is used to display the sets of realizations into
the joint space of uncertainty of the response variables (effective permeability, times to reach 5% and 95% water cuts and
to recover 10% and 50% of the oil). The attenuation of ergodic fluctuations through a rank-preserving transform of permeability
values reduces substantially the extent of the space of uncertainty for sequential indicator simulation and p-field simulation, while improving the prediction of the response variable by the mean of the output distribution. Differences
between simulation algorithms are the most pronounced for long-term responses (95% water cut and 50% oil recovery), with sequential
Gaussian simulation yielding the most accurate prediction. In this example, utilizing more than 20 realizations generally
increases only slightly the size of the space of uncertainty. 相似文献
4.
Estimating threshold-exceeding probability maps of environmental variables with Markov chain random fields 总被引：2，自引：2，他引：0
Weidong Li Chuanrong Zhang Dipak K. Dey Shanqin Wang 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(8):1113-1126
Estimating and mapping spatial uncertainty of environmental variables is crucial for environmental evaluation and decision
making. For a continuous spatial variable, estimation of spatial uncertainty may be conducted in the form of estimating the
probability of (not) exceeding a threshold value. In this paper, we introduced a Markov chain geostatistical approach for
estimating threshold-exceeding probabilities. The differences of this approach compared to the conventional indicator approach
lie with its nonlinear estimators—Markov chain random field models and its incorporation of interclass dependencies through
transiograms. We estimated threshold-exceeding probability maps of clay layer thickness through simulation (i.e., using a
number of realizations simulated by Markov chain sequential simulation) and interpolation (i.e., direct conditional probability
estimation using only the indicator values of sample data), respectively. To evaluate the approach, we also estimated those
probability maps using sequential indicator simulation and indicator kriging interpolation. Our results show that (i) the
Markov chain approach provides an effective alternative for spatial uncertainty assessment of environmental spatial variables
and the probability maps from this approach are more reasonable than those from conventional indicator geostatistics, and
(ii) the probability maps estimated through sequential simulation are more realistic than those through interpolation because
the latter display some uneven transitions caused by spatial structures of the sample data. 相似文献
5.
6.
Xavier Emery 《Stochastic Environmental Research and Risk Assessment (SERRA)》2005,19(5):348-360
This work deals with the geostatistical simulation of a family of stationary random field models with bivariate isofactorial
distributions. Such models are defined as the sum of independent random fields with mosaic-type bivariate distributions and
infinitely divisible univariate distributions. For practical applications, dead leaf tessellations are used since they provide
a wide range of models and allow conditioning the realizations to a set of data via an iterative procedure (simulated annealing).
The model parameters can be determined by comparing the data variogram and madogram, and enable to control the spatial connectivity
of the extreme values in the realizations. An illustration to a forest dataset is presented, for which a negative binomial
model is used to characterize the distribution of coniferous trees over a wooded area. 相似文献
7.
The random function is a mathematical model commonly used in the assessment of uncertainty associated with a spatially correlated
attribute that has been partially sampled. There are multiple algorithms for modeling such random functions, all sharing the
requirement of specifying various parameters that have critical influence on the results. The importance of finding ways to
compare the methods and setting parameters to obtain results that better model uncertainty has increased as these algorithms
have grown in number and complexity. Crossvalidation has been used in spatial statistics, mostly in kriging, for the analysis
of mean square errors. An appeal of this approach is its ability to work with the same empirical sample available for running
the algorithms. This paper goes beyond checking estimates by formulating a function sensitive to conditional bias. Under ideal
conditions, such function turns into a straight line, which can be used as a reference for preparing measures of performance.
Applied to kriging, deviations from the ideal line provide sensitivity to the semivariogram lacking in crossvalidation of
kriging errors and are more sensitive to conditional bias than analyses of errors. In terms of stochastic simulation, in addition
to finding better parameters, the deviations allow comparison of the realizations resulting from the applications of different
methods. Examples show improvements of about 30% in the deviations and approximately 10% in the square root of mean square
errors between reasonable starting modelling and the solutions according to the new criteria. 相似文献
8.
A covariance-based model-fitting approach is often considered valid to represent field spatial variability of hydraulic properties. This study examines the representation of geologic heterogeneity in two types of geostatistical models under the same mean and spatial covariance structure, and subsequently its effect on the hydraulic response to a pumping test based on 3D high-resolution numerical simulation and field data. Two geostatistical simulation methods, sequential Gaussian simulation (SGS) and transition probability indicator simulation (TPROGS) were applied to create conditional realizations of alluvial fan aquifer systems in the Lawrence Livermore National Laboratory (LLNL) area. The simulated K fields were then used in a numerical groundwater flow model to simulate a pumping test performed at the LLNL site. Spatial connectivity measures of high-K materials (channel facies) captured connectivity characteristics of each geostatistical model and revealed that the TPROGS model created an aquifer (channel) network having greater lateral connectivity. SGS realizations neglected important geologic structures associated with channel and overbank (levee) facies, even though the covariance model used to create these realizations provided excellent fits to sample covariances computed from exhaustive samplings of TPROGS realizations. Observed drawdown response in monitoring wells during a pumping test and its numerical simulation shows that in an aquifer system with strongly connected network of high-K materials, the Gaussian approach could not reproduce a similar behavior in simulated drawdown response found in TPROGS case. Overall, the simulated drawdown responses demonstrate significant disagreement between TPROGS and SGS realizations. This study showed that important geologic characteristics may not be captured by a spatial covariance model, even if that model is exhaustively determined and closely fits the exponential function. 相似文献
9.
一种模拟随机数字地层模型的方法 总被引：2，自引：1，他引：1
介绍了一种利用计算机生成随机数字地层模型的方法。此方法根据给定的地层厚度及参数统计特性．按截尾正态分布进行随机抽样构建随机分层结构,并对各分层参数随机赋值,完成随机模型的构筑。用此方法可以很容易地在计算机上生成大量符合某种统计特性的随机数字层状地层模型,从而可以在这些模型上进行感兴趣的仿真模拟研究。为展示这一方法的应用,生成了10个第四系随机层状模型,并在这些模型上进行了地震SH波的地震动放大效应数字模拟实验。结果发现随机模型的响应无论在形态特点还是幅值上都与均值模型的响应显著不同,表明用不完全准确的参数模型模拟估计场址地震动响应时必须充分考虑到参数不准导致的误差。 相似文献
10.
This work evaluated the spatial variability and distribution of heterogeneous hydraulic conductivity (K) in the Choushui River alluvial fan in Taiwan, using ordinary kriging (OK) and mean and individual sequential Gaussian simulations (SGS). A baseline flow model constructed by upscaling parameters was inversely calibrated to determine the pumping and recharge rates. Simulated heads using different K realizations were then compared with historically measured heads. A global/local simulated error between simulated and measured heads was analysed to assess the different spatial variabilities of various estimated K distributions. The results of a MODFLOW simulation indicate that the OK realization had the smallest sum of absolute mean simulation errors (SAMSE) and the SGS realizations preserved the spatial variability of the measured K fields. Moreover, the SAMSE increases as the spatial variability of the K field increases. The OK realization yields small local simulation errors in the measured K field of moderate magnitude, whereas the SGS realizations have small local simulation errors in the measured K fields, with high and low values. The OK realization of K can be applied to perform a deterministic inverse calibration. The mean SGS method is suggested for constructing a K field when the application focuses on extreme values of estimated parameters and small calibration errors, such as in a simulation of contaminant transport in heterogeneous aquifers. The individual SGS realization is useful in stochastically assessing the spatial uncertainty of highly heterogeneous aquifers. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
11.
Contaminant plumes whose characteristic length is smaller than the horizontal integral scale of the hydraulic conductivity, K, are abundant in shallow, phreatic aquifers. In such cases, the aquifer can be regarded as layered, with K being only a function of the vertical coordinate. The heterogeneity of K has a critical role upon the efficiency of remediation of such sites, for example, by Pump and Treat schemes. The expected efficiency is a random variable, with uncertainty. Quantifying this uncertainty can be of great importance to decision making. In this study, we focus on a case study in the coastal aquifer of Israel and compare two different approaches for constructing realizations of K: continuous and indicator. We observe a significant difference between the constructed realizations, which results in a considerable difference in the predicted remediation efficiency and its uncertainty. Furthermore, we study the effect of conditioning the realizations by a rather limited number of K data points. We find that the conditioning results in a major reduction of the uncertainty. In addition, we compare the results of the transport model to a simplified semi‐analytical solution that is based on assuming radial flow. We find a good agreement with the three‐dimensional numerical model. This result illustrates that the simplified solution can be used for prediction of the remediation efficiency when the flow at the plume vicinity can be regarded as radial. 相似文献
12.
岩相和储层物性参数是油藏表征的重要参数,地震反演是储层表征和油气藏勘探开发的重要手段.随机地震反演通常基于地质统计学理论,能够对不同类型的信息源进行综合,建立具有较高分辨率的储层模型,因而得到广泛关注.其中,概率扰动方法是一种高效的迭代随机反演策略,它能综合考虑多种约束信息,且只需要较少的迭代次数即可获得反演结果.在概率扰动的优化反演策略中,本文有效的联合多点地质统计学与序贯高斯模拟,并结合统计岩石物理理论实现随机反演.首先,通过多点地质统计学随机模拟,获得一系列等可能的岩相模型,扰动更新初始岩相模型后利用相控序贯高斯模拟建立多个储层物性参数模型;然后通过统计岩石物理理论,计算相应的弹性参数;最后,正演得到合成地震记录并与实际地震数据对比,通过概率扰动方法进行迭代,直到获得满足给定误差要求的反演结果.利用多点地质统计学,能够更好地表征储层空间特征.相控序贯高斯模拟的应用,能够有效反映不同岩相中储层物性参数的分布.提出的方法可在较少的迭代次数内同时获得具有较高分辨率的岩相和物性参数反演结果,模型测试和实际数据应用验证了方法的可行性和有效性. 相似文献
13.
A nested workflow of multiple‐point geostatistics (MPG) and sequential Gaussian simulation (SGS) was tested on a study area of 6 km2 located about 20 km northwest of Quebec City, Canada. In order to assess its geological and hydrogeological parameter heterogeneity and to provide tools to evaluate uncertainties in aquifer management, direct and indirect field measurements are used as inputs in the geostatistical simulations to reproduce large and small‐scale heterogeneities. To do so, the lithological information is first associated to equivalent hydrogeological facies (hydrofacies) according to hydraulic properties measured at several wells. Then, heterogeneous hydrofacies (HF) realizations are generated using a prior geological model as training image (TI) with the MPG algorithm. The hydraulic conductivity (K) heterogeneity modeling within each HF is finally computed using SGS algorithm. Different K models are integrated in a finite‐element hydrogeological model to calculate multiple transport simulations. Different scenarios exhibit variations in mass transport path and dispersion associated with the large‐ and small‐scale heterogeneity respectively. Three‐dimensional maps showing the probability of overpassing different thresholds are presented as examples of management tools. 相似文献
14.
A fast method with tunable accuracy is proposed to estimate errors and uncertainties in pore-scale and Digital Rock Physics (DRP) problems. The overall predictivity of these studies can be, in fact, hindered by many factors including sample heterogeneity, computational and imaging limitations, model inadequacy and not perfectly known physical parameters. The typical objective of pore-scale studies is the estimation of macroscopic effective parameters such as permeability, effective diffusivity and hydrodynamic dispersion. However, these are often non-deterministic quantities (i.e., results obtained for specific pore-scale sample and setup are not totally reproducible by another “equivalent” sample and setup). The stochastic nature can arise due to the multi-scale heterogeneity, the computational and experimental limitations in considering large samples, and the complexity of the physical models. These approximations, in fact, introduce an error that, being dependent on a large number of complex factors, can be modeled as random. We propose a general simulation tool, based on multilevel Monte Carlo, that can reduce drastically the computational cost needed for computing accurate statistics of effective parameters and other quantities of interest, under any of these random errors. This is, to our knowledge, the first attempt to include Uncertainty Quantification (UQ) in pore-scale physics and simulation. The method can also provide estimates of the discretization error and it is tested on three-dimensional transport problems in heterogeneous materials, where the sampling procedure is done by generation algorithms able to reproduce realistic consolidated and unconsolidated random sphere and ellipsoid packings and arrangements. A totally automatic workflow is developed in an open-source code [1], that include rigid body physics and random packing algorithms, unstructured mesh discretization, finite volume solvers, extrapolation and post-processing techniques. The proposed method can be efficiently used in many porous media applications for problems such as stochastic homogenization/upscaling, propagation of uncertainty from microscopic fluid and rock properties to macro-scale parameters, robust estimation of Representative Elementary Volume size for arbitrary physics. 相似文献
15.
太湖富营养化条件下影响蓝藻水华的主导气象因子 总被引：2，自引：2，他引：0
利用2004-2018年卫星遥感解译的太湖蓝藻水华信息构建蓝藻综合指数,采用随机森林机器学习算法分析同期气象因子与蓝藻水华综合指数的关系,定量评估影响蓝藻水华的主要气象因子特征变量的重要性度量和贡献率.结果表明,在光、温、水、风等主要气象要素中,气温对蓝藻水华综合指数起着主导的作用,其次是风速和降水,日照时间的影响或可忽略.其中气温条件中重要性度量最大的是年平均气温,其次是冬、春季节的平均气温;风速因子中影响较大的是7月份的平均风速;水分条件中主导因子是9月累计降水量.优选的随机森林模型模拟值与实际蓝藻水华综合指数的变化趋势基本一致,拟合优度为0.91,通过0.01显著性检验,随机森林模型模拟效果较好.用随机森林模型模拟值对太湖蓝藻水华分等级评估,模型模拟精度达到了86.7%,其中5个重度等级年份模型模拟结果完全一致,中度等级的6个年份模型模拟值有5年与之相符,中度以上等级的模拟精度达90.9%,模型能够反映气象因子对蓝藻水华综合指数的综合影响,对中、重度蓝藻水华的模拟效果更好.随机森林模型有助于理解富营养化状态下影响蓝藻水华的主导气象因子,利用气象因子的可预测性可以促进蓝藻水华预测预警能力的提升. 相似文献
16.
For good groundwater flow and solute transport numerical modeling, it is important to characterize the formation properties. In this paper, we analyze the performance and important implementation details of a new approach for stochastic inverse modeling called inverse sequential simulation (iSS). This approach is capable of characterizing conductivity fields with heterogeneity patterns difficult to capture by standard multiGaussian-based inverse approaches. The method is based on the multivariate sequential simulation principle, but the covariances and cross-covariances used to compute the local conditional probability distributions are computed by simple co-kriging which are derived from an ensemble of conductivity and piezometric head fields, in a similar manner as the experimental covariances are computed in an ensemble Kalman filtering. A sensitivity analysis is performed on a synthetic aquifer regarding the number of members of the ensemble of realizations, the number of conditioning data, the number of piezometers at which piezometric heads are observed, and the number of nodes retained within the search neighborhood at the moment of computing the local conditional probabilities. The results show the importance of having a sufficiently large number of all of the mentioned parameters for the algorithm to characterize properly hydraulic conductivity fields with clear non-multiGaussian features. 相似文献
17.
Many types of structural systems that undergo cycles of inelastic deformation under severe natural hazard loadings exhibit ‘pinching’ of hysteresis loops. In this paper, a generally pinching hysteretic restoring force model—an extension of the Bouc–Wen differential hysteresis model—is used in stochastic equivalent linearization of single-degree-of-freedom structural systems. The severity and rate of pinching are controlled by the hysteretic energy dissipation and the pinching level can be specified to match experimental data. Under white noise excitations, estimates of reponse statistics from linearization are shown to compare favourably with those from Monte Carlo simulation. Numerical studies on the sensitivity of the accuracy of response statistics obtained by linearization to changes in the hysteresis parameters showed that, for a range of practical cases, the linearization method can be used in lieu of simulation and that, in low-frequency systems, some hysteresis parameters may be set to a constant value a priori to reduce the number of model parameters that needs to be estimated or identified, and to simplify further random vibration analysis and/or performance evaluation studies. 相似文献
18.
Jun-Jih Liou Yuan-Fong Su Jie-Lun Chiang Ke-Sheng Cheng 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(2):235-251
In studies involving environmental risk assessment, Gaussian random field generators are often used to yield realizations
of a Gaussian random field, and then realizations of the non-Gaussian target random field are obtained by an inverse-normal
transformation. Such simulation process requires a set of observed data for estimation of the empirical cumulative distribution
function (ECDF) and covariance function of the random field under investigation. However, if realizations of a non-Gaussian
random field with specific probability density and covariance function are needed, such observed-data-based simulation process
will not work when no observed data are available. In this paper we present details of a gamma random field simulation approach
which does not require a set of observed data. A key element of the approach lies on the theoretical relationship between
the covariance functions of a gamma random field and its corresponding standard normal random field. Through a set of devised
simulation scenarios, the proposed technique is shown to be capable of generating realizations of the given gamma random fields. 相似文献
19.
The plurigaussian model is used in mining engineering, oil reservoir characterization, hydrology and environmental sciences to simulate the layout of geological domains in the subsurface, while reproducing their spatial continuity and dependence relationships. However, this model is well-established only in the stationary case, when the spatial distribution of the domains is homogeneous in space, and suffers from theoretical and practical impediments in the non-stationary case. To overcome these limitations, this paper proposes extending the model to the truncation of intrinsic random fields of order k with Gaussian generalized increments, which allows reproducing spatial trends in the distribution of the geological domains. Methodological tools and algorithms are presented to infer the model parameters and to construct realizations of the geological domains conditioned to existing data. The proposal is illustrated with the simulation of rock type domains in an ore deposit in order to demonstrate its applicability. Despite the limited number of conditioning data, the results show a remarkable agreement between the simulated domains and the lithological model interpreted by geologists, while the conventional stationary plurigaussian model turns out to be unsuccessful. 相似文献
20.
From past seismic events such as the 1995 Kobe (Hyogoken-Nanbu) and 2001 Nisqually earthquakes, it was found that liquefaction-induced lateral spread has caused significant damage to structures such as buildings and bridges, in addition to underground utility facilities like pipelines. In this respect, seaport facilities are particularly vulnerable to these liquefaction-related damages, because they are usually constructed on poorly consolidated natural deposit or fills. This study investigates the effect of the liquefaction and lateral spread on the seismic response of caisson type quay walls. For this purpose, 2D nonlinear dynamic analyses of soil–structure system are carried out with the aid of finite difference software, FLAC. The unique feature of this study lies in the fact that the 2D soil system is idealized as homogeneous non-Gaussian random field. A simulation algorithm is then used to generate a set of digital realizations of 2D random field sample. Each realization is used for the dynamic analysis to generate a unique response of the soil–structure system. Repeating this analysis for the entire set of realizations, the probabilistic nature of the response is characterized in the Monte Carlo sense. This result based on random field is compared with the response obtained under the uniform field assumption with the mean value of soil property. The comparison shows that in general the uniform model provides unconservative result compared with the response from the random field model due to nonlinear behavior of the soil–structure system. It is also found that the consideration of spatial variation of soil can capture the dispersion of observed response of quay walls. 相似文献