共查询到20条相似文献，搜索用时 109 毫秒
1.
Probability theory as logic (or Bayesian probability theory) is a rational inferential methodology that provides a natural
and logically consistent framework for source reconstruction. This methodology fully utilizes the information provided by
a limited number of noisy concentration data obtained from a network of sensors and combines it in a consistent manner with
the available prior knowledge (mathematical representation of relevant physical laws), hence providing a rigorous basis for
the assimilation of this data into models of atmospheric dispersion for the purpose of contaminant source reconstruction.
This paper addresses the application of this framework to the reconstruction of contaminant source distributions consisting
of an unknown number of localized sources, using concentration measurements obtained from a sensor array. To this purpose,
Bayesian probability theory is used to formulate the full joint posterior probability density function for the parameters
of the unknown source distribution. A simulated annealing algorithm, applied in conjunction with a reversible-jump Markov
chain Monte Carlo technique, is used to draw random samples of source distribution models from the posterior probability density
function. The methodology is validated against a real (full-scale) atmospheric dispersion experiment involving a multiple
point source release. 相似文献
2.
In this paper, we study the uncertainty quantification in inverse problems for flows in heterogeneous porous media. Reversible jump Markov chain Monte Carlo algorithms (MCMC) are used for hierarchical modeling of channelized permeability fields. Within each channel, the permeability is assumed to have a log-normal distribution. Uncertainty quantification in history matching is carried out hierarchically by constructing geologic facies boundaries as well as permeability fields within each facies using dynamic data such as production data. The search with Metropolis–Hastings algorithm results in very low acceptance rate, and consequently, the computations are CPU demanding. To speed-up the computations, we use a two-stage MCMC that utilizes upscaled models to screen the proposals. In our numerical results, we assume that the channels intersect the wells and the intersection locations are known. Our results show that the proposed algorithms are capable of capturing the channel boundaries and describe the permeability variations within the channels using dynamic production history at the wells. 相似文献
3.
Markov Chain Monte Carlo (MCMC) methods are often used to probe the posterior probability distribution in inverse problems. This allows for computation of estimates of uncertain system responses conditioned on given observational data by means of approximate integration. However, MCMC methods suffer from the computational complexities in the case of expensive models as in the case of subsurface flow models. Hence, it is of great interest to develop alterative efficient methods utilizing emulators, that are cheap to evaluate, in order to replace the full physics simulator. In the current work, we develop a technique based on sparse response surfaces to represent the flow response within a subsurface reservoir and thus enable efficient exploration of the posterior probability density function and the conditional expectations given the data.Polynomial Chaos Expansion (PCE) is a powerful tool to quantify uncertainty in dynamical systems when there is probabilistic uncertainty in the system parameters. In the context of subsurface flow model, it has been shown to be more accurate and efficient compared with traditional experimental design (ED). PCEs have a significant advantage over other response surfaces as the convergence to the true probability distribution when the order of the PCE is increased can be proved for the random variables with finite variances. However, the major drawback of PCE is related to the curse of dimensionality as the number of terms to be estimated grows drastically with the number of the input random variables. This renders the computational cost of classical PCE schemes unaffordable for reservoir simulation purposes when the deterministic finite element model is expensive to evaluate. To address this issue, we propose the reduced-terms polynomial chaos representation which uses an impact factor to only retain the most relevant terms of the PCE decomposition. Accordingly, the reduced-terms polynomial chaos proxy can be used as the pseudo-simulator for efficient sampling of the probability density function of the uncertain variables.The reduced-terms PCE is evaluated on a two dimensional subsurface flow model with fluvial channels to demonstrate that with a few hundred trial runs of the actual reservoir simulator, it is feasible to construct a polynomial chaos proxy which accurately approximates the posterior distribution of the high permeability zones, in an analytical form. We show that the proxy precision improves with increasing the order of PCE and corresponding increase of the number of initial runs used to estimate the PCE coefficient. 相似文献
4.
We consider a Bayesian model for inversion of observed amplitude variation with offset data into lithology/fluid classes, and study in particular how the choice of prior distribution for the lithology/fluid classes influences the inversion results. Two distinct prior distributions are considered, a simple manually specified Markov random field prior with a first-order neighbourhood and a Markov mesh model with a much larger neighbourhood estimated from a training image. They are chosen to model both horizontal connectivity and vertical thickness distribution of the lithology/fluid classes, and are compared on an offshore clastic oil reservoir in the North Sea. We combine both priors with the same linearized Gaussian likelihood function based on a convolved linearized Zoeppritz relation and estimate properties of the resulting two posterior distributions by simulating from these distributions with the Metropolis–Hastings algorithm. The influence of the prior on the marginal posterior probabilities for the lithology/fluid classes is clearly observable, but modest. The importance of the prior on the connectivity properties in the posterior realizations, however, is much stronger. The larger neighbourhood of the Markov mesh prior enables it to identify and model connectivity and curvature much better than what can be done by the first-order neighbourhood Markov random field prior. As a result, we conclude that the posterior realizations based on the Markov mesh prior appear with much higher lateral connectivity, which is geologically plausible. 相似文献
5.
Muhammad Mohsin Gunter Sp?ck Jürgen Pilz 《Stochastic Environmental Research and Risk Assessment (SERRA)》2012,26(7):925-945
A new bivariate pseudo Pareto distribution is proposed, and its distributional characteristics are investigated. The parameters of this distribution are estimated by the moment-, the maximum likelihood- and the Bayesian method. Point estimators of the parameters are presented for different sample sizes. Asymptotic confidence intervals are constructed and the parameter modeling the dependency between two variables is checked. The performance of the different estimation methods is investigated by using the bootstrap method. A Markov Chain Monte Carlo simulation is conducted to estimate the Bayesian posterior distribution for different sample sizes. For illustrative purposes, a real set of drought data is investigated. 相似文献
6.
Franco Macchioli-Grande Fabio Zyserman Leonardo Monachesi Laurence Jouniaux Marina Rosas-Carbajal 《Geophysical Prospecting》2020,68(5):1633-1656
In glacial studies, properties such as glacier thickness and the basement permeability and porosity are key to understand the hydrological and mechanical behaviour of the system. The seismoelectric method could potentially be used to determine key properties of glacial environments. Here we analytically model the generation of seismic and seismoelectric signals by means of a shear horizontal seismic wave source on top of a glacier overlying a porous basement. Considering a one-dimensional setting, we compute the seismic waves and the electrokinetically induced electric field. We then analyse the sensitivity of the seismic and electromagnetic data to relevant model parameters, namely depth of the glacier bottom, porosity, permeability, shear modulus and saturating water salinity of the glacier basement. Moreover, we study the possibility of inferring these key parameters from a set of very low noise synthetic data, adopting a Bayesian framework to pay particular attention to the uncertainty of the model parameters mentioned above. We tackle the resolution of the probabilistic inverse problem with two strategies: (1) we compute the marginal posterior distributions of each model parameter solving multidimensional integrals numerically and (2) we use a Markov chain Monte Carlo algorithm to retrieve a collection of model parameters that follows the posterior probability density function of the model parameters, given the synthetic data set. Both methodologies are able to obtain the marginal distributions of the parameters and estimate their mean and standard deviation. The Markov chain Monte Carlo algorithm performs better in terms of numerical stability and number of iterations needed to characterize the distributions. The inversion of seismic data alone is not able to constrain the values of porosity and permeability further than the prior distribution. In turn, the inversion of the electric data alone, and the joint inversion of seismic and electric data are useful to constrain these parameters as well as other glacial system properties. Furthermore, the joint inversion reduces the uncertainty of the model parameters estimates and provides more accurate results. 相似文献
7.
Youcun Liu Miaojie Lu Xueli Huo Yonghong Hao Hongkai Gao Yan Liu Yonghui Fan Yuhuan Cui Francois Metivier 《水文研究》2016,30(3):424-432
Global climate change models have predicted the intensification of extreme events, and these predictions are already occurring. For disaster management and adaptation of extreme events, it is essential to improve the accuracy of extreme value statistical models. In this study, Bayes' Theorem is introduced to estimate parameters in Generalized Pareto Distribution (GPD), and then the GPD is applied to simulate the distribution of minimum monthly runoff during dry periods in mountain areas of the Ürümqi River, Northwest China. Bayes' Theorem treats parameters as random variables and provides a robust way to convert the prior distribution of parameters into a posterior distribution. Statistical inferences based on posterior distribution can provide a more comprehensive representation of the parameters. An improved Markov Chain Monte Carlo (MCMC) method, which can solve high‐dimensional integral computation in the Bayes equation, is used to generate parameter simulations from the posterior distribution. Model diagnosis plots are made to guarantee the fitted GPD is appropriate. Then based on the GPD with Bayesian parameter estimates, monthly runoff minima corresponding to different return periods can be calculated. The results show that the improved MCMC method is able to make Markov chains converge faster. The monthly runoff minima corresponding to 10a, 25a, 50a and 100a return periods are 0.60 m3/s, 0.44 m3/s, 0.32 m3/s and 0.20 m3/s respectively. The lower boundary of 95% confidence interval of 100a return level is below zero, which implies that the Ürümqi River is likely to cease to flow when 100a return level appears in dry periods. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
8.
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
9.
Modeling the stochastic dependence of air pollution index data 总被引：1，自引：1，他引：0
The air pollution index (API) is a common tool, which is often used for determining the quality of air in the environment. In this study, a discrete-time Markov chain model is applied for describing the stochastic behaviour of API data. The study reported in this paper is conducted based on the data collected from Klang city in Malaysia for a period of 3 years (2012–2014). Based on the API data, we considered a five-state Markov chain for depicting the five different states of the air pollution. We identified the Markov chain is an ergodic Markov chain and determined the limiting distribution for each state of the air pollution. In addition, we have identified the mean first passage time from one state to another. Based on the limiting distribution and the mean return time, we found that the risk of occurrences for unhealthy events is small. However, the risk remains notably troubling. Therefore, the standard of air quality in Klang falls within a margin that is considered healthy for human beings. 相似文献
10.
In this paper, we investigate the information content in “nanosensors” with limited functionality that might be injected into a reservoir or an aquifer to provide information on the spatial distribution of properties. The two types of sensors that we consider are sensors that can potentially measure pressure at various times during transport, and sensors can be located in space by perturbations in electrical, magnetic, or acoustic properties. The intent of the study is to determine the resolution of estimates of properties that can be obtained from various combinations of sensors, various frequencies of observations, and various specifications on sensor precision.Our goal is to investigate the resolution of model estimates for various types of measurements. For this, we compute linearized estimates of the sensitivity of the observations to the porosity and permeability assuming gaussian errors in the pressure and location observations. Because the flow is one-dimensional and incompressible, observations of location are sensitive to the porosity between the injection location and the sensor location, while the location of particles is sensitive to the effective permeability over the entire interval from injector to producer. When only the pressure is measured but the location of the sensor is unknown, as might be the situation for a threshold sensor, the pressure is sensitive to both permeability and porosity only in the region between the injector and sensor.In addition to the linearized sensitivity and resolution analyses, Markov chain Monte Carlo sampling is used to estimate the posterior pdf for model variables for realistic (non-Gaussian) likelihood models. For a Markov chain of length one million samples approximately 200-500 independent samples are generated for uncertainty and resolution assessment. Results from the MCMC analysis are not in conflict with the linearized analysis. 相似文献
11.
In geophysical inverse problems, the posterior model can be analytically assessed only in case of linear forward operators, Gaussian, Gaussian mixture, or generalized Gaussian prior models, continuous model properties, and Gaussian-distributed noise contaminating the observed data. For this reason, one of the major challenges of seismic inversion is to derive reliable uncertainty appraisals in cases of complex prior models, non-linear forward operators and mixed discrete-continuous model parameters. We present two amplitude versus angle inversion strategies for the joint estimation of elastic properties and litho-fluid facies from pre-stack seismic data in case of non-parametric mixture prior distributions and non-linear forward modellings. The first strategy is a two-dimensional target-oriented inversion that inverts the amplitude versus angle responses of the target reflections by adopting the single-interface full Zoeppritz equations. The second is an interval-oriented approach that inverts the pre-stack seismic responses along a given time interval using a one-dimensional convolutional forward modelling still based on the Zoeppritz equations. In both approaches, the model vector includes the facies sequence and the elastic properties of P-wave velocity, S-wave velocity and density. The distribution of the elastic properties at each common-mid-point location (for the target-oriented approach) or at each time-sample position (for the time-interval approach) is assumed to be multimodal with as many modes as the number of litho-fluid facies considered. In this context, an analytical expression of the posterior model is no more available. For this reason, we adopt a Markov chain Monte Carlo algorithm to numerically evaluate the posterior uncertainties. With the aim of speeding up the convergence of the probabilistic sampling, we adopt a specific recipe that includes multiple chains, a parallel tempering strategy, a delayed rejection updating scheme and hybridizes the standard Metropolis–Hasting algorithm with the more advanced differential evolution Markov chain method. For the lack of available field seismic data, we validate the two implemented algorithms by inverting synthetic seismic data derived on the basis of realistic subsurface models and actual well log data. The two approaches are also benchmarked against two analytical inversion approaches that assume Gaussian-mixture-distributed elastic parameters. The final predictions and the convergence analysis of the two implemented methods proved that our approaches retrieve reliable estimations and accurate uncertainties quantifications with a reasonable computational effort. 相似文献
12.
通过地震反演数据识别岩性,是地震反演的一项基本任务.由于不同岩性的弹性参数范围常常存在一定程度的重叠,所以给岩性识别带来了很大的困难.本文以叠前反演的弹性参数为基础,通过马尔科夫随机场(Markov Random Field简写为MRF)建立先验模型,按照解释好的测井资料,对不同岩性的弹性参数进行统计,得到计算所需的参数,在贝叶斯(Bayesian)框架下建立岩性分类的目标函数,达到岩性识别的目的.通过马尔科夫随机场建立先验模型,能够建立相邻点间的相互作用关系,得到横向上延续的岩性剖面.本文使用一个楔形模型和Marmousi Ⅱ模型对该方法进行了测试,结果表明,该方法有效可行.同时,本文通过加入误差的方法,检验了反演存在误差对识别结果的影响. 相似文献
13.
14.
In this paper we propose a method for the characterization of naturally fractured reservoirs by quantitative integration of seismic and production data. The method is based on a consistent theoretical frame work to model both effective hydraulic and elastic properties of fractured porous media and a (non‐linear) Bayesian method of inversion that provides information about uncertainties as well as mean (or maximum likelihood) values. We model a fractured reservoir as a porous medium containing a single set of vertical fractures characterized by an unknown fracture density, azimuthal orientation and aperture. We then look at the problem of fracture parameter estimation as a non‐linear inverse problem and try to estimate the unknown fracture parameters by joint inversion of seismic amplitude versus angle and azimuth data and dynamic production data. Once the fracture parameters have been estimated the corresponding effective stiffness and permeability tensors can be estimated using consistent models. A synthetic example is provided to clearly explain and test the workflow. It shows that seismic and production data complement each other, in the sense that the seismic data resolve a non‐uniqueness in the fracture orientation and the production data help to recover the true fracture aperture and permeability, because production data are more sensitive to the fracture aperture than the seismic data. 相似文献
15.
The coupling upscaling finite element method is developed for solving the coupling problems of deformation and consolidation of heterogeneous saturated porous media under external loading conditions. The method couples two kinds of fully developed methodologies together, i.e., the numerical techniques developed for calculating the apparent and effective physical properties of the heterogeneous media and the upscaling techniques developed for simulating the fluid flow and mass transport properties in heterogeneous porous media. Equivalent permeability tensors and equivalent elastic modulus tensors are calculated for every coarse grid block in the coarse-scale model of the heterogeneous saturated porous media. Moreover, an oversampling technique is introduced to improve the calculation accuracy of the equivalent elastic modulus tensors. A numerical integration process is performed over the fine mesh within every coarse grid element to capture the small scale information induced by non-uniform scalar field properties such as density, compressibility, etc. Numerical experiments are carried out to examine the accuracy of the developed method. It shows that the numerical results obtained by the coupling upscaling finite element method on the coarse-scale models fit fairly well with the reference solutions obtained by traditional finite element method on the fine-scale models. Moreover, this method gets more accurate coarse-scale results than the previously developed coupling multiscale finite element method for solving this kind of coupling problems though it cannot recover the fine-scale solutions. At the same time, the method developed reduces dramatically the computing effort in both CPU time and memory for solving the transient problems, and therefore more large and computational-demanding coupling problems can be solved by computers. 相似文献
16.
随机地震反演关键参数优选和效果分析(英文) 总被引：2，自引：0，他引：2
随机地震反演技术是将地质统计理论和地震反演相结合的反演方法,它将地震资料、测井资料和地质统计学信息融合为地下模型的后验概率分布,利用马尔科夫链蒙特卡洛(MCMC)方法对该后验概率分布采样,通过综合分析多个采样结果来研究后验概率分布的性质,进而认识地下情况。本文首先介绍了随机地震反演的原理,然后对影响随机地震反演效果的四个关键参数,即地震资料信噪比、变差函数、后验概率分布的样本个数和井网密度进行分析并给出其优化原则。资料分析表明地震资料信噪比控制地震资料和地质统计规律对反演结果的约束程度,变差函数影响反演结果的平滑程度,后验概率分布的样本个数决定样本统计特征的可靠性,而参与反演的井网密度则影响反演的不确定性。最后通过对比试验工区随机地震反演和基于模型的确定性地震反演结果,指出随机地震反演可以给出更符合地下实际情况的模型。 相似文献
17.
Markov链模型在储层随机建模中的作用越来越受到关注,但其多用于类型属性(岩相、沉积相、沉积亚相等)的模拟,对于连续型属性(孔隙度、渗透率、含油气饱和度等)的模拟还比较困难.本文提出用Markov链模型相控建模方法模拟连续型属性的思路,即首先用Markov链模型模拟出类型属性,其次在类型属性约束下模拟出连续型属性,从而解决连续型属性不能产生突变边界的问题.最后应用此方法进行了模拟实验,模拟结果显示不同岩相中孔隙度差异较大,而同种岩相中孔隙度变化较小,证明了此方法的可靠性和适用性. 相似文献
18.
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
19.
Identification of rock boundaries and structural features from well log response is a fundamental problem in geological field studies. However, in a complex geologic situation, such as in the presence of crystalline rocks where metamorphisms lead to facies changes, it is not easy to discern accurate information from well log data using conventional artificial neural network (ANN) methods. Moreover inferences drawn by such methods are also found to be ambiguous because of the strong overlapping of well log signals, which are generally tainted with deceptive noise. Here, we have developed an alternative ANN approach based on Bayesian statistics using the concept of Hybrid Monte Carlo (HMC)/Markov Chain Monte Carlo (MCMC) inversion scheme for modeling the German Continental Deep Drilling Program (KTB) well log data. MCMC algorithm draws an independent and identically distributed (i.i.d) sample by Markov Chain simulation technique from posterior probability distribution using the principle of statistical mechanics in Hamiltonian dynamics. In this algorithm, each trajectory is updated by approximating the Hamiltonian differential equations through a leapfrog discrimination scheme. We examined the stability and efficiency of the HMC-based approach on “noisy” data assorted with different levels of colored noise. We also perform uncertainty analysis by estimating standard deviation (STD) error map of a posteriori covariance matrix at the network output of three types of lithofacies over the entire length of the litho section of KTB. Our analyses demonstrate that the HMC-based approach renders robust means for classification of complex lithofacies successions from the KTB borehole noisy signals, and hence may provide a useful guide for understanding the crustal inhomogeneity and structural discontinuity in many other tectonically critical and complex regions. 相似文献
20.
Despite their apparent high dimensionality, spatially distributed hydraulic properties of geologic formations can often be compactly (sparsely) described in a properly designed basis. Hence, the estimation of high-dimensional subsurface flow properties from dynamic performance and monitoring data can be formulated and solved as a sparse reconstruction inverse problem. Recent advances in statistical signal processing, formalized under the compressed sensing paradigm, provide important guidelines on formulating and solving sparse inverse problems, primarily for linear models and using a deterministic framework. Given the uncertainty in describing subsurface physical properties, even after integration of the dynamic data, it is important to develop a practical sparse Bayesian inversion approach to enable uncertainty quantification. In this paper, we use sparse geologic dictionaries to compactly represent uncertain subsurface flow properties and develop a practical sparse Bayesian method for effective data integration and uncertainty quantification. The multi-Gaussian assumption that is widely used in classical probabilistic inverse theory is not appropriate for representing sparse prior models. Following the results presented by the compressed sensing paradigm, the Laplace (or double exponential) probability distribution is found to be more suitable for representing sparse parameters. However, combining Laplace priors with the frequently used Gaussian likelihood functions leads to neither a Laplace nor a Gaussian posterior distribution, which complicates the analytical characterization of the posterior. Here, we first express the form of the Maximum A-Posteriori (MAP) estimate for Laplace priors and then use the Monte-Carlo-based Randomize Maximum Likelihood (RML) method to generate approximate samples from the posterior distribution. The proposed Sparse RML (SpRML) approximate sampling approach can be used to assess the uncertainty in the calibrated model with a relatively modest computational complexity. We demonstrate the suitability and effectiveness of the SpRML formulation using a series of numerical experiments of two-phase flow systems in both Gaussian and non-Gaussian property distributions in petroleum reservoirs and successfully apply the method to an adapted version of the PUNQ-S3 benchmark reservoir model. 相似文献