共查询到20条相似文献，搜索用时 31 毫秒
1.
Thomas Romary 《Computational Geosciences》2010,14(2):343-355
In history matching of lithofacies reservoir model, we attempt to find multiple realizations of lithofacies configuration
that are conditional to dynamic data and representative of the model uncertainty space. This problem can be formalized in
the Bayesian framework. Given a truncated Gaussian model as a prior and the dynamic data with its associated measurement error,
we want to sample from the conditional distribution of the facies given the data. A relevant way to generate conditioned realizations
is to use Markov chains Monte Carlo (MCMC). However, the dimensions of the model and the computational cost of each iteration
are two important pitfalls for the use of MCMC. Furthermore, classical MCMC algorithms mix slowly, that is, they will not
explore the whole support of the posterior in the time of the simulation. In this paper, we extend the methodology already
described in a previous work to the problem of history matching of a Gaussian-related lithofacies reservoir model. We first
show how to drastically reduce the dimension of the problem by using a truncated Karhunen-Loève expansion of the Gaussian
random field underlying the lithofacies model. Moreover, we propose an innovative criterion of the choice of the number of
components based on the connexity function. Then, we show how we improve the mixing properties of classical single MCMC, without
increasing the global computational cost, by the use of parallel interacting Markov chains. Applying the dimension reduction
and this innovative sampling method drastically lowers the number of iterations needed to sample efficiently from the posterior.
We show the encouraging results obtained when applying the methodology to a synthetic history-matching case. 相似文献
2.
Integrating production data under uncertainty by parallel interacting Markov chains on a reduced dimensional space 总被引：2，自引：0，他引：2
Thomas Romary 《Computational Geosciences》2009,13(1):103-122
In oil industry and subsurface hydrology, geostatistical models are often used to represent the porosity or the permeability
field. In history matching of a geostatistical reservoir model, we attempt to find multiple realizations that are conditional
to dynamic data and representative of the model uncertainty space. A relevant way to simulate the conditioned realizations
is by generating Monte Carlo Markov chains (MCMC). The huge dimensions (number of parameters) of the model and the computational
cost of each iteration are two important pitfalls for the use of MCMC. In practice, we have to stop the chain far before it
has browsed the whole support of the posterior probability density function. Furthermore, as the relationship between the
production data and the random field is highly nonlinear, the posterior can be strongly multimodal and the chain may stay
stuck in one of the modes. In this work, we propose a methodology to enhance the sampling properties of classical single MCMC
in history matching. We first show how to reduce the dimension of the problem by using a truncated Karhunen–Loève expansion
of the random field of interest and assess the number of components to be kept. Then, we show how we can improve the mixing
properties of MCMC, without increasing the global computational cost, by using parallel interacting Markov Chains. Finally,
we show the encouraging results obtained when applying the method to a synthetic history matching case. 相似文献
3.
Parameter identification is one of the key elements in the construction of models in geosciences. However, inherent difficulties
such as the instability of ill-posed problems or the presence of multiple local optima may impede the execution of this task.
Regularization methods and Bayesian formulations, such as the maximum a posteriori estimation approach, have been used to
overcome those complications. Nevertheless, in some instances, a more in-depth analysis of the inverse problem is advisable
before obtaining estimates of the optimal parameters. The Markov Chain Monte Carlo (MCMC) methods used in Bayesian inference
have been applied in the last 10 years in several fields of geosciences such as hydrology, geophysics or reservoir engineering.
In the present paper, a compilation of basic tools for inference and a case study illustrating the practical application of
them are given. Firstly, an introduction to the Bayesian approach to the inverse problem is provided together with the most
common sampling algorithms with MCMC chains. Secondly, a series of estimators for quantities of interest, such as the marginal
densities or the normalization constant of the posterior distribution of the parameters, are reviewed. Those reduce the computational
cost significantly, using only the time needed to obtain a sample of the posterior probability density function. The use of
the information theory principles for the experimental design and for the ill-posedness diagnosis is also introduced. Finally,
a case study based on a highly instrumented well test found in the literature is presented. The results obtained are compared
with the ones computed by the maximum likelihood estimation approach. 相似文献
4.
Yalchin Efendiev Akhil Datta-Gupta Xianlin Ma Bani Mallick 《Mathematical Geosciences》2008,40(2):213-232
In this paper, the Markov Chain Monte Carlo (MCMC) approach is used for sampling of the permeability field conditioned on
the dynamic data. The novelty of the approach consists of using an approximation of the dynamic data based on streamline computations.
The simulations using the streamline approach allows us to obtain analytical approximations in the small neighborhood of the
previously computed dynamic data. Using this approximation, we employ a two-stage MCMC approach. In the first stage, the approximation
of the dynamic data is used to modify the instrumental proposal distribution. The obtained chain correctly samples from the
posterior distribution; the modified Markov chain converges to a steady state corresponding to the posterior distribution.
Moreover, this approximation increases the acceptance rate, and reduces the computational time required for MCMC sampling.
Numerical results are presented. 相似文献
5.
为了开展寒旱山区典型流域融雪径流过程的研究,提高融雪径流模型（SRM）在山区融雪地区的水文过程模拟精度,本文选取新疆提孜那甫河流域作为典型研究区,在SRM径流计算基础上,加入合适的基流数据并进行不确定性分析。考虑4种常见的基流分割方法（数字滤波法、加里宁法、BFI法（滑动最小值法）和HYSEP（hydrograph separation program）法）,基于贝叶斯理论,采用马尔科夫链蒙特卡洛（MCMC）模拟进行参数不确定性分析,对使用不同基流数据SRM的融雪径流模拟表现进行综合评价。分析结果表明,基于加里宁基流分割方法的模型（SRMK）能够最佳地模拟研究区融雪径流过程（纳什系数NSE在识别期和验证期分别为0.866和0.721,大于其他对比模型）。MCMC模拟能够较好地识别SRM参数,获得可靠的参数后验概率分布。当实测降水资料缺乏或其代表性较差时,TRMM（tropical rainfall measuring mission）卫星数据能够描述研究区的降水过程特征。 相似文献
6.
Building of models in the Earth Sciences often requires the solution of an inverse problem: some unknown model parameters need to be calibrated with actual measurements. In most cases, the set of measurements cannot completely and uniquely determine the model parameters; hence multiple models can describe the same data set. Bayesian inverse theory provides a framework for solving this problem. Bayesian methods rely on the fact that the conditional probability of the model parameters given the data (the posterior) is proportional to the likelihood of observing the data and a prior belief expressed as a prior distribution of the model parameters. In case the prior distribution is not Gaussian and the relation between data and parameters (forward model) is strongly non-linear, one has to resort to iterative samplers, often Markov chain Monte Carlo methods, for generating samples that fit the data likelihood and reflect the prior model statistics. While theoretically sound, such methods can be slow to converge, and are often impractical when the forward model is CPU demanding. In this paper, we propose a new sampling method that allows to sample from a variety of priors and condition model parameters to a variety of data types. The method does not rely on the traditional Bayesian decomposition of posterior into likelihood and prior, instead it uses so-called pre-posterior distributions, i.e. the probability of the model parameters given some subset of the data. The use of pre-posterior allows to decompose the data into so-called, “easy data” (or linear data) and “difficult data” (or nonlinear data). The method relies on fast non-iterative sequential simulation to generate model realizations. The difficult data is matched by perturbing an initial realization using a perturbation mechanism termed “probability perturbation.” The probability perturbation method moves the initial guess closer to matching the difficult data, while maintaining the prior model statistics and the conditioning to the linear data. Several examples are used to illustrate the properties of this method. 相似文献
7.
Field observed performance of slopes can be used to back calculate input parameters of soil properties and evaluate uncertainty of a slope stability analysis model. In this paper, a new probabilistic method is proposed for back analysis of slope failure. The proposed back analysis method is formulated based on Bayes’ theorem and solved using the Markov chain Monte Carlo simulation method with a Metropolis–Hasting algorithm. The method is very flexible as any type of prior distribution can be used. The method is also computationally efficient when a response surface method is employed to approximate the slope stability model. An illustrative example of back analysis of a hypothetical slope failure is presented. Effects of jumping distribution functions and number of samples on the efficiency of Markov chains are studied. It is found that the covariance matrix of the jumping function can be set to be one half of the covariance of the prior distribution to achieve a reasonable acceptance rate and that 80,000 samples seem to be sufficient to obtain robust posterior statistics for the example. It is also found that the correlation of cohesion and friction angle of soil does not affect the posterior statistics and the remediation design of the slope significantly, while the type of the prior distribution seems to have much influence on the remediation design. 相似文献
8.
Different interpretation of sedimentary environments lead to “scenario uncertainty” where the prior reservoir model has a high level of discrete uncertainty. In a real field application, the scenario uncertainty has a considerable effect on flow response uncertainty and makes the uncertainty quantification problem highly nonlinear. We use clustering methods to address the scenario uncertainty. Our approach to cluster analysis is based on the posterior probabilities of models, known as “Bayesian model selection.” Accordingly, we integrate overall possible parameters in each scenario with respect to their corresponding priors to give the measure of how well a model is supported by observations. We propose a cluster-based reduced terms polynomial chaos proxy to efficiently estimate the posterior probability density function under each cluster and calculate the posterior probability of each model. We demonstrate that the convergence rate of the reduced terms polynomial chaos proxy is significantly improved under each cluster comparing to the non-clustered case. We apply the proposed cluster-based polynomial chaos proxy framework to study the plausibility of three training images based on different geological interpretation of the second layer of synthetic Stanford VI reservoir. We demonstrate that the proposed workflow can be efficiently used to calculate the posterior probability of each scenario and also sample from the posterior facies models within each scenario. 相似文献
9.
The Bayesian framework is the standard approach for data assimilation in reservoir modeling. This framework involves characterizing the posterior distribution of geological parameters in terms of a given prior distribution and data from the reservoir dynamics, together with a forward model connecting the space of geological parameters to the data space. Since the posterior distribution quantifies the uncertainty in the geologic parameters of the reservoir, the characterization of the posterior is fundamental for the optimal management of reservoirs. Unfortunately, due to the large-scale highly nonlinear properties of standard reservoir models, characterizing the posterior is computationally prohibitive. Instead, more affordable ad hoc techniques, based on Gaussian approximations, are often used for characterizing the posterior distribution. Evaluating the performance of those Gaussian approximations is typically conducted by assessing their ability at reproducing the truth within the confidence interval provided by the ad hoc technique under consideration. This has the disadvantage of mixing up the approximation properties of the history matching algorithm employed with the information content of the particular observations used, making it hard to evaluate the effect of the ad hoc approximations alone. In this paper, we avoid this disadvantage by comparing the ad hoc techniques with a fully resolved state-of-the-art probing of the Bayesian posterior distribution. The ad hoc techniques whose performance we assess are based on (1) linearization around the maximum a posteriori estimate, (2) randomized maximum likelihood, and (3) ensemble Kalman filter-type methods. In order to fully resolve the posterior distribution, we implement a state-of-the art Markov chain Monte Carlo (MCMC) method that scales well with respect to the dimension of the parameter space, enabling us to study realistic forward models, in two space dimensions, at a high level of grid refinement. Our implementation of the MCMC method provides the gold standard against which the aforementioned Gaussian approximations are assessed. We present numerical synthetic experiments where we quantify the capability of each of the ad hoc Gaussian approximation in reproducing the mean and the variance of the posterior distribution (characterized via MCMC) associated to a data assimilation problem. Both single-phase and two-phase (oil–water) reservoir models are considered so that fundamental differences in the resulting forward operators are highlighted. The main objective of our controlled experiments was to exhibit the substantial discrepancies of the approximation properties of standard ad hoc Gaussian approximations. Numerical investigations of the type we present here will lead to the greater understanding of the cost-efficient, but ad hoc, Bayesian techniques used for data assimilation in petroleum reservoirs and hence ultimately to improved techniques with more accurate uncertainty quantification. 相似文献
10.
Victor Ginting Felipe Pereira Michael Presho Shaochang Wo 《Computational Geosciences》2011,15(4):691-707
In this paper, we develop a procedure for subsurface characterization of a fractured porous medium. The characterization involves
sampling from a representation of a fracture’s permeability that has been suitably adjusted to the dynamic tracer cut measurement
data. We propose to use a type of dual-porosity, dual-permeability model for tracer flow. This model is built into the Markov
chain Monte Carlo (MCMC) method in which the permeability is sampled. The Bayesian statistical framework is used to set the
acceptance criteria of these samples and is enforced through sampling from the posterior distribution of the permeability
fields conditioned to dynamic tracer cut data. In order to get a sample from the distribution, we must solve a series of problems
which requires a fine-scale solution of the dual model. As direct MCMC is a costly method with the possibility of a low acceptance
rate, we introduce a two-stage MCMC alternative which requires a suitable coarse-scale solution method of the dual model.
With this filtering process, we are able to decrease our computational time as well as increase the proposal acceptance rate.
A number of numerical examples are presented to illustrate the performance of the method. 相似文献
11.
A Bayesian linear inversion methodology based on Gaussian mixture models and its application to geophysical inverse problems are presented in this paper. The proposed inverse method is based on a Bayesian approach under the assumptions of a Gaussian mixture random field for the prior model and a Gaussian linear likelihood function. The model for the latent discrete variable is defined to be a stationary first-order Markov chain. In this approach, a recursive exact solution to an approximation of the posterior distribution of the inverse problem is proposed. A Markov chain Monte Carlo algorithm can be used to efficiently simulate realizations from the correct posterior model. Two inversion studies based on real well log data are presented, and the main results are the posterior distributions of the reservoir properties of interest, the corresponding predictions and prediction intervals, and a set of conditional realizations. The first application is a seismic inversion study for the prediction of lithological facies, P- and S-impedance, where an improvement of 30% in the root-mean-square error of the predictions compared to the traditional Gaussian inversion is obtained. The second application is a rock physics inversion study for the prediction of lithological facies, porosity, and clay volume, where predictions slightly improve compared to the Gaussian inversion approach. 相似文献
12.
In many applications in flows through porous media, one needs to determine the properties of subsurface to detect, monitor, or predict the actions of natural or induced forces. Here, we focus on two important subsurface properties: rock permeability and porosity. A Bayesian approach using a Markov Chain Monte Carlo (MCMC) algorithm is well suited for reconstructing the spatial distribution of permeability and porosity, and quantifying associated uncertainty in these properties. A crucial step in this approach is the computation of a likelihood function, which involves solving a possibly nonlinear system of partial differential equations. The computation time for the likelihood function limits the number of MCMC iterations that can be performed in a practical period of time. This affects the consistency of the posterior distribution of permeability and porosity obtained by MCMC exploration. To speed-up the posterior exploration, we can use a prefetching technique, which relies on the fact that multiple likelihoods of possible states into the future in an MCMC chain can be computed ahead of time. In this paper, we show that the prefetching technique implemented on multiple processors can make the Bayesian approach computationally tractable for subsurface characterization and prediction of porous media flows. 相似文献
13.
Bayesian lithology/fluid inversion—comparison of two algorithms 总被引：1，自引：0，他引：1
Algorithms for inversion of seismic prestack AVO data into lithology-fluid classes in a vertical profile are evaluated. The
inversion is defined in a Bayesian setting where the prior model for the lithology-fluid classes is a Markov chain, and the
likelihood model relates seismic data and elastic material properties to these classes. The likelihood model is approximated
such that the posterior model can be calculated recursively using the extremely efficient forward–backward algorithm. The
impact of the approximation in the likelihood model is evaluated empirically by comparing results from the approximate approach
with results generated from the exact posterior model. The exact posterior is assessed by sampling using a sophisticated Markov
chain Monte Carlo simulation algorithm. The simulation algorithm is iterative, and it requires considerable computer resources.
Seven realistic evaluation models are defined, from which synthetic seismic data are generated. Using identical seismic data,
the approximate marginal posterior is calculated and the exact marginal posterior is assessed. It is concluded that the approximate
likelihood model preserves 50% to 90% of the information content in the exact likelihood model. 相似文献
14.
In real-time flood warning systems, sufficient lead-time is important for people to take suitable actions. Rainfall forecasting is one of the ways commonly used to extend the lead-time for catchments with short response time. However, an accurate forecast of rainfall is still difficult for hydrologists using the present deterministic model. Therefore, a probability-based rainfall forecasting model, based on Markov chain, was proposed in this study. The rainfall can be forecast one to three hours in advance for a specified nonexceeding probability using the transition probability matrix of rainfall state. In this study, the nonexceeding probability, which was hourly updated on the basis of development or decay of rainfall processes, was taken as a dominant variable parameter. The accuracy of rainfall forecasting one to three hours in advance is concluded from the application of this model to four recording rain gauges. A lumped rainfall-runoff forecasting model derived from a transfer function was further applied in unison with this rainfall forecasting model to forecast flows one to four hours in advance. The results of combination of these two models show good performance with agreement between the observed and forecast hydrographs. 相似文献
15.
The chemical zoning profile in metamorphic minerals is often used to deduce the pressure–temperature (P–T) history of rock. However, it remains difficult to restore detailed paths from zoned minerals because thermobarometric evaluation
of metamorphic conditions involves several uncertainties, including measurement errors and geological noise. We propose a
new stochastic framework for estimating precise P–T paths from a chemical zoning structure using the Markov random field (MRF) model, which is a type of Bayesian stochastic
method that is often applied to image analysis. The continuity of pressure and temperature during mineral growth is incorporated
by Gaussian Markov chains as prior probabilities in order to apply the MRF model to the P–T path inversion. The most probable P–T path can be obtained by maximizing the posterior probability of the sequential set of P and T given the observed compositions of zoned minerals. Synthetic P–T inversion tests were conducted in order to investigate the effectiveness and validity of the proposed model from zoned Mg–Fe–Ca
garnet in the divariant KNCFMASH system. In the present study, the steepest descent method was implemented in order to maximize
the posterior probability using the Markov chain Monte Carlo algorithm. The proposed method successfully reproduced the detailed
shape of the synthetic P–T path by eliminating appropriately the statistical compositional noises without operator’s subjectivity and prior knowledge.
It was also used to simultaneously evaluate the uncertainty of pressure, temperature, and mineral compositions for all measurement
points. The MRF method may have potential to deal with several geological uncertainties, which cause cumbersome systematic
errors, by its Bayesian approach and flexible formalism, so that it comprises potentially powerful tools for various inverse
problems in petrology. 相似文献
16.
Comparing the Gradual Deformation with the Probability Perturbation Method for Solving Inverse Problems 总被引：1，自引：0，他引：1
Jef Caers 《Mathematical Geology》2007,39(1):27-52
Inverse problems are ubiquitous in the Earth Sciences. Many such problems are ill-posed in the sense that multiple solutions
can be found that match the data to be inverted. To impose restrictions on these solutions, a prior distribution of the model
parameters is required. In a spatial context this prior model can be as simple as a Multi-Gaussian law with prior covariance
matrix, or could come in the form of a complex training image describing the prior statistics of the model parameters. In
this paper, two methods for generating inverse solutions constrained to such prior model are compared. The gradual deformation
method treats the problem of finding inverse solution as an optimization problem. Using a perturbation mechanism, the gradual
deformation method searches (optimizes) in the prior model space for those solutions that match the data to be inverted. The
perturbation mechanism guarantees that the prior model statistics are honored. However, it is shown with a simple example
that this perturbation method does not necessarily draw accurately samples from a given posterior distribution when the inverse
problem is framed within a Bayesian context. On the other hand, the probability perturbation method approaches the inverse
problem as a data integration problem. This method explicitly deals with the problem of combining prior probabilities with
pre-posterior probabilities derived from the data. It is shown that the sampling properties of the probability perturbation
method approach the accuracy of well-known Markov chain Monte Carlo samplers such as the rejection sampler. The paper uses
simple examples to illustrate the clear differences between these two methods 相似文献
17.
为快速准确地求解突发性水污染溯源问题,在微分进化与蒙特卡罗基础上提出了一种新的溯源方法。该方法将溯源问题视为贝叶斯估计问题,推导出污染源强度、位置和排放时刻等未知参数的后验概率密度函数;结合微分进化和蒙特卡罗模拟方法对后验概率分布进行采样,进而估计出这些未知参数,确定污染源项。通过算例与贝叶斯-蒙特卡罗方法进行对比,结果表明:该方法可使迭代次数有效缩减3/4,污染源强度、位置和排放时刻的平均相对误差分别减少1.23%、2.23%和4.15%,均值误差分别降低0.39%、0.83%和1.49%,其稳定性和可靠性明显高于贝叶斯-蒙特卡罗方法,能较好地识别突发性水污染源,为解决突发水污染事件中的追踪溯源难点问题提供了新的思路和方法。 相似文献
18.
System reliability analysis of slopes using multilayer perceptron and radial basis function networks 
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下载免费PDF全文 This paper presents a system reliability analysis method for soil slopes on the basis of artificial neural networks with computer experiments. Two types of artificial neural networks, multilayer perceptrop (MLP) and radial basis function networks (RBFNs), are tested on the studied problems. Computer experiments are adopted to generate samples for constructing the response surfaces. On the basis of the samples, MLP and RBFN are used for establishing the response surface to approximate the limit state function, and Monte Carlo simulation is performed via the MLP and RBFN response surfaces to estimate the system failure probability of slopes. Experimental results on 3 examples show the effectiveness of the proposed methodology. 相似文献
19.
Although a slope may have numerous potential slip surfaces, its failure probability is often governed by several representative slip surfaces (RSSs). Previous efforts mainly focus on the identification of circular RSSs based on limit equilibrium methods. In this paper, a method is suggested to identify RSSs of arbitrary shape based on the shear strength reduction method. Monte Carlo simulation is used to generate a large number potential slip surfaces. The RSSs are identified through analyzing the failure domains represented by these samples. A kriging-based response surface model is employed to enhance the computational efficiency. These examples shows that the RSSs may not always be circular, and that the suggested method can effectively locate the RSSs without making prior assumptions about the shape of the slip surfaces. For the examples investigated, the system failure probabilities computed based on the shear strength reduction method are comparable to, but not the same as those computed based on the limit equilibrium methods. The suggested method significantly extends our capability for identifying non-circular RSSs and hence probabilistic slope stability analysis involving non-circular slip surfaces. 相似文献
20.
基于MCMC法的非饱和土渗流参数随机反分析 总被引：2，自引：0，他引：2
基于贝叶斯理论,以马尔可夫链蒙特卡罗方法（Markov chain Monte Carlo Simulation, MCMC法）的自适应差分演化Metropolis算法为参数后验分布抽样计算方法,建立利用时变测试数据的参数随机反分析及模型预测方法。以香港东涌某天然坡地降雨入渗测试为算例,采用自适应差分演化Metropolis算法对时变降雨条件下非饱和土一维渗流模型参数进行随机反分析,研究参数后验分布的统计特性,并分别对校准期和验证期内模型预测孔压和实测值进行比较。研究结果表明,DREAM算法得到的各随机变量后验分布标准差较先验分布均显著减小;经过实测孔压数据的校准,模型计算精度很高,校准期内95%总置信区间的覆盖率达到0.964;验证期第2～4个阶段95%总置信区间的覆盖率分别为0.52、0.79和0.79,模型预测结果与实测值吻合程度较高。 相似文献