共查询到20条相似文献，搜索用时 234 毫秒
1.
Ensemble-based data assimilation methods have recently become popular for solving reservoir history matching problems, but because of the practical limitation on ensemble size, using localization is necessary to reduce the effect of sampling error and to increase the degrees of freedom for incorporating large amounts of data. Local analysis in the ensemble Kalman filter has been used extensively for very large models in numerical weather prediction. It scales well with the model size and the number of data and is easily parallelized. In the petroleum literature, however, iterative ensemble smoothers with localization of the Kalman gain matrix have become the state-of-the-art approach for ensemble-based history matching. By forming the Kalman gain matrix row-by-row, the analysis step can also be parallelized. Localization regularizes updates to model parameters and state variables using information on the distance between the these variables and the observations. The truncation of small singular values in truncated singular value decomposition (TSVD) at the analysis step provides another type of regularization by projecting updates to dominant directions spanned by the simulated data ensemble. Typically, the combined use of localization and TSVD is necessary for problems with large amounts of data. In this paper, we compare the performance of Kalman gain localization to two forms of local analysis for parameter estimation problems with nonlocal data. The effect of TSVD with different localization methods and with the use of iteration is also analyzed. With several examples, we show that good results can be obtained for all localization methods if the localization range is chosen appropriately, but the optimal localization range differs for the various methods. In general, for local analysis with observation taper, the optimal range is somewhat shorter than the optimal range for other localization methods. Although all methods gave equivalent results when used in an iterative ensemble smoother, the local analysis methods generally converged more quickly than Kalman gain localization when the amount of data is large compared to ensemble size. 相似文献
2.
Using a small ensemble size in the ensemble Kalman filter methodology is efficient for updating numerical reservoir models
but can result in poor updates following spurious correlations between observations and model variables. The most common approach
for reducing the effect of spurious correlations on model updates is multiplication of the estimated covariance by a tapering
function that eliminates all correlations beyond a prespecified distance. Distance-dependent tapering is not always appropriate,
however. In this paper, we describe efficient methods for discriminating between the real and the spurious correlations in
the Kalman gain matrix by using the bootstrap method to assess the confidence level of each element from the Kalman gain matrix.
The new method is tested on a small linear problem, and on a water flooding reservoir history matching problem. For the water
flooding example, a small ensemble size of 30 was used to compute the Kalman gain in both the screened EnKF and standard EnKF
methods. The new method resulted in significantly smaller root mean squared errors of the estimated model parameters and greater
variability in the final updated ensemble. 相似文献
3.
The performance of the Ensemble Kalman Filter method (EnKF) depends on the sample size compared to the dimension of the parameters
space. In real applications insufficient sampling may result in spurious correlations which reduce the accuracy of the filter
with a strong underestimation of the uncertainty. Covariance localization and inflation are common solutions to these problems.
The Ensemble Square Root Filters (ESRF) is also better to estimate uncertainty with respect to the EnKF. In this work we propose
a method that limits the consequences of sampling errors by means of a convenient generation of the initial ensemble. This
regeneration is based on a Stationary Orthogonal-Base Representation (SOBR) obtained via a singular value decomposition of
a stationary covariance matrix estimated from the ensemble. The technique is tested on a 2D single phase reservoir and compared
with the other common techniques. The evaluation is based on a reference solution obtained with a very large ensemble (one
million members) which remove the spurious correlations. The example gives evidence that the SOBR technique is a valid alternative
to reduce the effect of sampling error. In addition, when the SOBR method is applied in combination with the ESRF and inflation,
it gives the best performance in terms of uncertainty estimation and oil production forecast. 相似文献
4.
The ensemble Kalman filter has been successfully applied for data assimilation in very large models, including those in reservoir
simulation and weather. Two problems become critical in a standard implementation of the ensemble Kalman filter, however,
when the ensemble size is small. The first is that the ensemble approximation to cross-covariances of model and state variables
to data can indicate the presence of correlations that are not real. These spurious correlations give rise to model or state
variable updates in regions that should not be updated. The second problem is that the number of degrees of freedom in the
ensemble is only as large as the size of the ensemble, so the assimilation of large amounts of precise, independent data is
impossible. Localization of the Kalman gain is almost universal in the weather community, but applications of localization
for the ensemble Kalman filter in porous media flow have been somewhat rare. It has been shown, however, that localization
of updates to regions of non-zero sensitivity or regions of non-zero cross-covariance improves the performance of the EnKF
when the ensemble size is small. Localization is necessary for assimilation of large amounts of independent data. The problem
is to define appropriate localization functions for different types of data and different types of variables. We show that
the knowledge of sensitivity alone is not sufficient for determination of the region of localization. The region depends also
on the prior covariance for model variables and on the past history of data assimilation. Although the goal is to choose localization
functions that are large enough to include the true region of non-zero cross-covariance, for EnKF applications, the choice
of localization function needs to balance the harm done by spurious covariance resulting from small ensembles and the harm
done by excluding real correlations. In this paper, we focus on the distance-based localization and provide insights for choosing
suitable localization functions for data assimilation in multiphase flow problems. In practice, we conclude that it is reasonable
to choose localization functions based on well patterns, that localization function should be larger than regions of non-zero
sensitivity and should extend beyond a single well pattern. 相似文献
5.
集合卡尔曼滤波(Ensemble Kalman Filter,EnKF)作为一种有效的数据同化方法,在众多数值实验中体现优势的同时,也暴露了它使用小集合估计协方差情况下精度较低的缺陷。为了降低取样噪声对协方差估计的干扰并提高滤波精度,应用局域化函数对小集合估计的协方差进行修正,即在协方差矩阵中以舒尔积的形式增加空间距离权重以限制远距离相关。在一个二维理想孔隙承压含水层模型中的运行结果表明,局域化对集合卡尔曼滤波估计地下水参数的修正十分有效,局域化可以很好地过滤小集合估计中噪声的影响,节省计算量的同时又可以防止滤波发散。相关长度较小的水文地质参数(如对数渗透系数)更容易受到噪声的干扰,更有必要进行局域化修正。 相似文献
6.
The ensemble Kalman filter (EnKF), an efficient data assimilation method showing advantages in many numerical experiments, is deficient when used in approximating covariance from an ensemble of small size. Implicit localization is used to add distance-related weight to covariance and filter spurious correlations which weaken the EnKF??s capability to estimate uncertainty correctly. The effect of this kind of localization is studied in two-dimensional (2D) and three-dimensional (3D) synthetic cases. It is found that EnKF with localization can capture reliably both the mean and variance of the hydraulic conductivity field with higher efficiency; it can also greatly stabilize the assimilation process as a small-size ensemble is used. Sensitivity experiments are conducted to explore the effect of localization function format and filter lengths. It is suggested that too long or too short filter lengths will prevent implicit localization from modifying the covariance appropriately. Steep localization functions will greatly disturb local dynamics like the 0-1 function even if the function is continuous; four relatively gentle localization functions succeed in avoiding obvious disturbance to the system and improve estimation. As the degree of localization of the L function increases, the parameter sensitivity becomes weak, making parameter selection easier, but more information may be lost in the assimilation process. 相似文献
7.
Mohammadali Tarrahi Siavash Hakim Elahi Behnam Jafarpour 《Computational Geosciences》2016,20(5):929-952
Ensemble methods present a practical framework for parameter estimation, performance prediction, and uncertainty quantification in subsurface flow and transport modeling. In particular, the ensemble Kalman filter (EnKF) has received significant attention for its promising performance in calibrating heterogeneous subsurface flow models. Since an ensemble of model realizations is used to compute the statistical moments needed to perform the EnKF updates, large ensemble sizes are needed to provide accurate updates and uncertainty assessment. However, for realistic problems that involve large-scale models with computationally demanding flow simulation runs, the EnKF implementation is limited to small-sized ensembles. As a result, spurious numerical correlations can develop and lead to inaccurate EnKF updates, which tend to underestimate or even eliminate the ensemble spread. Ad hoc practical remedies, such as localization, local analysis, and covariance inflation schemes, have been developed and applied to reduce the effect of sampling errors due to small ensemble sizes. In this paper, a fast linear approximate forecast method is proposed as an alternative approach to enable the use of large ensemble sizes in operational settings to obtain more improved sample statistics and EnKF updates. The proposed method first clusters a large number of initial geologic model realizations into a small number of groups. A representative member from each group is used to run a full forward flow simulation. The flow predictions for the remaining realizations in each group are approximated by a linearization around the full simulation results of the representative model (centroid) of the respective cluster. The linearization can be performed using either adjoint-based or ensemble-based gradients. Results from several numerical experiments with two-phase and three-phase flow systems in this paper suggest that the proposed method can be applied to improve the EnKF performance in large-scale problems where the number of full simulation is constrained. 相似文献
8.
Combining sensitivities and prior information for covariance localization in the ensemble Kalman filter for petroleum reservoir applications 总被引：1，自引：0，他引：1
Sampling errors can severely degrade the reliability of estimates of conditional means and uncertainty quantification obtained
by the application of the ensemble Kalman filter (EnKF) for data assimilation. A standard recommendation for reducing the
spurious correlations and loss of variance due to sampling errors is to use covariance localization. In distance-based localization,
the prior (forecast) covariance matrix at each data assimilation step is replaced with the Schur product of a correlation
matrix with compact support and the forecast covariance matrix. The most important decision to be made in this localization
procedure is the choice of the critical length(s) used to generate this correlation matrix. Here, we give a simple argument
that the appropriate choice of critical length(s) should be based both on the underlying principal correlation length(s) of
the geological model and the range of the sensitivity matrices. Based on this result, we implement a procedure for covariance
localization and demonstrate with a set of distinctive reservoir history-matching examples that this procedure yields improved
results over the standard EnKF implementation and over covariance localization with other choices of critical length. 相似文献
9.
非线性滤波方法与陆面数据同化 总被引：8，自引：4，他引：4
陆面数据同化研究近几年成为地球科学研究的新兴领域,其中以非线性滤波为代表的数据同化方法发展迅速并得到了广泛应用。在贝叶斯理论框架内,从递推贝叶斯估计理论的角度系统地分析了扩展卡尔曼滤波、无迹卡尔曼滤波、集合卡尔曼滤波、SIR粒子滤波等非线性滤波方法的异同;针对应用比较广泛的集合卡尔曼滤波和SIR粒子滤波应用中存在的问题,论述了几种提高滤波性能的实用方法,如协方差矩阵的Localization方法、协方差矩阵的Inflation方法、双集合卡尔曼滤波方法、扰动集合、扰动大气驱动和模型参数、平方根集合卡尔曼滤波以及粒子滤波算法的改进等。最后总结讨论了各种非线性滤波方法应用中的特点、难点以及各种算法在陆面数据同化中的应用前景和发展方向。 相似文献
10.
To more correctly estimate the error covariance of an evolved state of a nonlinear dynamical system, the second and higher-order
moments of the prior error need to be known. Retrospective optimal interpolation (ROI) may require relatively less information
on the higher-order moments of the prior errors than an ensemble Kalman filter (EnKF) because it uses the initial conditions
as the background states instead of forecasts. Analogous to the extension of a Kalman filter into an EnKF, an ensemble retrospective
optimal interpolation (EnROI) technique was derived using the Monte Carlo method from ROI. In contrast to the deterministic
version of ROI, the background error covariance is represented by a background ensemble in EnROI. By sequentially applying
EnROI to a moving limited analysis window and exploiting the forecast from the average of the background ensemble of EnROI
as a guess field, the computation costs for EnROI can be reduced. In the numerical experiment using a Lorenz-96 model and
a Model-III of Lorenz with a perfect-model assumption, the cost-effectiveness of the suboptimal version of EnROI is demonstrated
to be superior to that of EnKF using perturbed observations. 相似文献
11.
Relation between two common localisation methods for the EnKF 总被引：3，自引：0，他引：3
This study investigates the relation between two common localisation methods in ensemble Kalman filter (EnKF) systems: covariance
localisation and local analysis. Both methods are popular in large-scale applications with the EnKF. The case of local observations
with non-correlated errors is considered. Both methods are formulated in terms of tapering of ensemble anomalies, which provides
a framework for their comparison. Based on analytical considerations and experimental evidence, we conclude that in practice
the two methods should yield very similar results, so that the choice between them should be based on other criteria, such
as numerical effectiveness and scalability. 相似文献
12.
The ensemble Kalman filter (EnKF) has been successfully applied to data assimilation in steam-assisted gravity drainage (SAGD) process, but applications of localization for the EnKF in the SAGD process have not been studied. Distance-based localization has been reported to be very efficient for assimilation of large amounts of independent data with a small ensemble in water flooding process, but it is not applicable to the SAGD process, since in the SAGD process, oil is produced mainly from the transition zone steam chamber to cold oil instead of the regions around the producer. As the oil production rate is mainly affected by the temperature distribution in the transition zone, temperature-based localization was proposed for automatic history matching of the SAGD process. The regions of the localization function were determined through sensitivity analysis by using a large ensemble with 1000 members. The sensitivity analysis indicated that the regions of cross-correlations between oil production and state variables are much wider than the correlations between production data and model variables. To choose localization regions that are large enough to include the true regions of non-zero cross-covariance, the localization function is defined based on the regions of non-zero covariances of production data to state variables. The non-zero covariances between production data and state variables are distributed in accordance with the steam chamber. This makes the definition of a universal localization function for different state variables easier. Based on the cross-correlation analysis, the temperature range in which oil production is contributed is determined, and beyond or below this range, the localization function reduces from one, and at the critical temperature or steam temperature, the localization function reduces to zero. The temperature-based localization function was obtained through modifying the distance-based localization function. Localization is applied to covariance of data with permeability, saturation, and temperature, as well as the covariance of data with data. A small ensemble (10 ensemble members) was employed in several case studies. Without localization, the variability in the ensemble collapsed very quickly and lost the ability to assimilate later data. The mean variance of model variables dropped dramatically by 95 %, and there was almost no variability in ensemble forecasts, while the prediction was far from the reference with data mismatch keeping up at a high level. At least 50 ensemble members are needed to keep the qualities of matches and forecasts, which significantly increases the computation time. The EnKF with temperature-based localization is able to avoid the collapse of ensemble variability with a small ensemble (10 members), which saves the computation time and gives better history match and prediction results. 相似文献
13.
Estimating observation error covariance matrix of seismic data from a perspective of image denoising
Estimating observation error covariance matrix properly is a key step towards successful seismic history matching. Typically, observation errors of seismic data are spatially correlated; therefore, the observation error covariance matrix is non-diagonal. Estimating such a non-diagonal covariance matrix is the focus of the current study. We decompose the estimation into two steps: (1) estimate observation errors and (2) construct covariance matrix based on the estimated observation errors. Our focus is on step (1), whereas at step (2) we use a procedure similar to that in Aanonsen et al. 2003. In Aanonsen et al. 2003, step (1) is carried out using a local moving average algorithm. By treating seismic data as an image, this algorithm can be interpreted as a discrete convolution between an image and a rectangular window function. Following the perspective of image processing, we consider three types of image denoising methods, namely, local moving average with different window functions (as an extension of the method in Aanonsen et al. 2003), non-local means denoising and wavelet denoising. The performance of these three algorithms is compared using both synthetic and field seismic data. It is found that, in our investigated cases, the wavelet denoising method leads to the best performance in most of the time. 相似文献
14.
We present a method of using classical wavelet-based multiresolution analysis to separate scales in model and observations during data assimilation with the ensemble Kalman filter. In many applications, the underlying physics of a phenomena involve the interaction of features at multiple scales. Blending of observational and model error across scales can result in large forecast inaccuracies since large errors at one scale are interpreted as inexact data at all scales due to the misrepresentation of observational error. Our method uses a partitioning of the range of the observation operator into separate observation scales. This naturally induces a transformation of the observation covariance and we put forward several algorithms to efficiently compute the transformed covariance. Another advantage of our multiresolution ensemble Kalman filter is that scales can be weighted independently to adjust each scale’s affect on the forecast. To demonstrate feasibility, we present applications to a one-dimensional Kuramoto-Sivashinsky (K–S) model with scale-dependent observation noise and an application involving the forecasting of solar photospheric flux. The solar flux application uses the Air Force Data Assimilative Photospheric Transport (ADAPT) model which has model and observation error exhibiting strong scale dependence. Results using our multiresolution ensemble Kalman filter show significant improvement in solar forecast error compared to traditional ensemble Kalman filtering. 相似文献
15.
集合—变分数据同化方法的发展与应用 总被引：3，自引：0，他引：3
近年来,集合—变分数据同化方法已成为大气数据同化领域研究的热点问题.该方法能够综合利用集合卡尔曼滤波和变分同化的优势,是实现“集合预报和数据同化一体化”的有效途径.在分析变分同化和集合卡尔曼滤波优缺点的基础上引出集合—变分数据同化的概念;按照不同实现方式,将集合—变分同化分为协方差线性组合和增加控制变量2类,介绍了相应的研究进展,并将集合—变分同化概念拓展;然后介绍了集合—变分同化在英美两国的应用;最后回顾了集合—变分同化研究的主要问题,展望了未来的发展趋势. 相似文献
16.
17.
重质非水相有机污染物(DNAPL)泄漏到地下后,其运移与分布特征受渗透率非均质性影响显著。为刻画DNAPL污染源区结构特征,需进行参数估计以描述水文地质参数的非均质性。本研究构建了基于集合卡尔曼滤波方法(EnKF)与多相流运移模型的同化方案,通过融合DNAPL饱和度观测数据推估非均质介质渗透率空间分布。通过二维砂箱实际与理想算例,验证了同化方法的推估效果,并探讨了不同因素对同化的影响。研究结果表明:基于EnKF方法同化饱和度观测资料可有效地推估非均质渗透率场;参数推估精度随观测时空密度的增大而提高;观测点位置分布对同化效果有所影响,布置在污染集中区域的观测数据对于参数估计具有较高的数据价值。 相似文献
18.
In this work, we present an efficient matrix-free ensemble Kalman filter (EnKF) algorithm for the assimilation of large data
sets. The EnKF has increasingly become an essential tool for data assimilation of numerical models. It is an attractive assimilation
method because it can evolve the model covariance matrix for a non-linear model, through the use of an ensemble of model states,
and it is easy to implement for any numerical model. Nevertheless, the computational cost of the EnKF can increase significantly
for cases involving the assimilation of large data sets. As more data become available for assimilation, a potential bottleneck
in most EnKF algorithms involves the operation of the Kalman gain matrix. To reduce the complexity and cost of assimilating
large data sets, a matrix-free EnKF algorithm is proposed. The algorithm uses an efficient matrix-free linear solver, based
on the Sherman–Morrison formulas, to solve the implicit linear system within the Kalman gain matrix and compute the analysis.
Numerical experiments with a two-dimensional shallow water model on the sphere are presented, where results show the matrix-free
implementation outperforming an singular value decomposition-based implementation in computational time. 相似文献
19.
Generalized covariance functions in estimation 总被引：3，自引：0，他引：3
Peter K. Kitanidis 《Mathematical Geology》1993,25(5):525-540
I discuss the role of generalized covariance functions in best linear unbiased estimation and methods for their selection. It is shown that the experimental variogram (or covariance function) of the detrended data can be used to obtain a preliminary estimate of the generalized covariance function without iterations and I discuss the advantages of other parameter estimation methods. 相似文献
20.