Efficient Implementation of an Iterative Ensemble Smoother for Data Assimilation and Reservoir History Matching

Evensen, Geir; Raanes, Patrick; Stordal, Andreas S.; Hove, Joakim

doi:10.3389/fams.2019.00047

Cited by 33 publications

(27 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We can instead try techniques which better handle departures from linearity. For instance, the iterative ensemble Kalman smoother (e.g., Evensen et al, 2019) is a useful candidate to solve this problem.…”

Section: Summary and Future Workmentioning

confidence: 99%

Assimilation of atmospheric infrasound data to constrain tropospheric and stratospheric winds

Amezcua

Näsholm

Blixt

et al. 2020

Quart J Royal Meteoro Soc

View full text Add to dashboard Cite

This data assimilation study exploits infrasound from explosions to probe an atmospheric wind component from the ground up to stratospheric altitudes. Planned explosions of old ammunition in Finland generate transient infrasound waves that travel through the atmosphere. These waves are partially reflected back towards the ground from stratospheric levels, and are detected at a receiver station located in northern Norway at 178 km almost due north from the explosion site. The difference between the true horizontal direction towards the source and the backazimuth direction (the horizontal direction of arrival) of the incoming infrasound wavefronts, in combination with the pulse propagation time, are exploited to provide an estimate of the average cross‐wind component in the penetrated atmosphere. We perform offline assimilation experiments with an ensemble Kalman filter and these observations, using the ERA5 ensemble reanalysis atmospheric product as background (prior) for the wind at different vertical levels. We demonstrate that information from both sources can be combined to obtain analysis (posterior) estimates of cross‐winds at different vertical levels of the atmospheric slice between the explosion site and the recording station. The assimilation makes greatest impact at the 12–60 km levels, with some changes with respect to the prior of the order of 0.1–1.0 m·s−1, which is a magnitude larger than the typical standard deviation of the ERA5 background. The reduction of background variance in the higher levels often reached 2–5%. This is the first published study demonstrating techniques to implement assimilation of infrasound data into atmospheric models. It paves the way for further exploration in the use of infrasound observations – especially natural and continuous sources – to probe the middle atmospheric dynamics and to assimilate these data into atmospheric model products.

show abstract

Section: Summary and Future Workmentioning

confidence: 99%

Assimilation of atmospheric infrasound data to constrain tropospheric and stratospheric winds

Amezcua

Näsholm

Blixt

et al. 2020

Quart J Royal Meteoro Soc

View full text Add to dashboard Cite

show abstract

“…For computing the Ensemble Smoother (ES) or Iterative Ensemble Smoother (IES) solutions, see [3,9,10,12,24], where the two last papers present new subspace-EnRML algorithm used in this work (see Algorithm 1). The method computes for each ensemble member z j , the following iteration for iterate number i,…”

Section: Subspace Enrml Solutionmentioning

confidence: 99%

“…It is possible to approximately compute the inversion in line number 13 to a cost of O(mN 2 ) operations by using the ensemble subspace algorithm discussed in [7,8,12] (and see also the discussion in the following section).…”

Section: Subspace Enrml Solutionmentioning

confidence: 99%

“…The cost of integrating the model is proportional to the number of time steps, n t . With each time step requiring n c n computations, the total cost of the ensemble integration is Nn t n c n. For nonlinear models, the number of timesteps is likely much larger than N, and the number of computations per time step can be several times n. All other computations in this algorithm are linear in the number of measurements, m, and the number of state variables, n. For the detailed derivation of the subspace EnRML algorithm, see [12,24].…”

Section: Subspace Enrml Solutionmentioning

confidence: 99%

“…In Algorithm 1, we have represented the measurement errorcovariance matrix by an ensemble of measurement perturbations, E. The inversion is in this case computed using ensemble subspace scheme as was proposed by Evensen [7] and further discussed in Evensen [8] and recently in Evensen [12]. This scheme projects the measurement error perturbations onto the ensemble subspace and computes the pseudo inverse of the following factorization…”

Section: Ensemble Subspace Inversionmentioning

confidence: 99%

See 2 more Smart Citations

Formulating the history matching problem with consistent error statistics

Evensen

2021

Comput Geosci

Self Cite

View full text Add to dashboard Cite

It is common to formulate the history-matching problem using Bayes’ theorem. From Bayes’, the conditional probability density function (pdf) of the uncertain model parameters is proportional to the prior pdf of the model parameters, multiplied by the likelihood of the measurements. The static model parameters are random variables characterizing the reservoir model while the observations include, e.g., historical rates of oil, gas, and water produced from the wells. The reservoir prediction model is assumed perfect, and there are no errors besides those in the static parameters. However, this formulation is flawed. The historical rate data only approximately represent the real production of the reservoir and contain errors. History-matching methods usually take these errors into account in the conditioning but neglect them when forcing the simulation model by the observed rates during the historical integration. Thus, the model prediction depends on some of the same data used in the conditioning. The paper presents a formulation of Bayes’ theorem that considers the data dependency of the simulation model. In the new formulation, one must update both the poorly known model parameters and the rate-data errors. The result is an improved posterior ensemble of prediction models that better cover the observations with more substantial and realistic uncertainty. The implementation accounts correctly for correlated measurement errors and demonstrates the critical role of these correlations in reducing the update’s magnitude. The paper also shows the consistency of the subspace inversion scheme by Evensen (Ocean Dyn. 54, 539–560 2004) in the case with correlated measurement errors and demonstrates its accuracy when using a “larger” ensemble of perturbations to represent the measurement error covariance matrix.

show abstract

Novel iterative ensemble smoothers derived from a class of generalized cost functions

Luo

2021

Comput Geosci

View full text Add to dashboard Cite

Iterative ensemble smoothers (IES) are among the state-of-the-art approaches to solving history matching problems. From an optimization-theoretic point of view, these algorithms can be derived by solving certain stochastic nonlinear-least-squares problems. In a broader picture, history matching is essentially an inverse problem, which is often ill-posed and may not possess a unique solution. To mitigate the ill-posedness, in the course of solving an inverse problem, prior knowledge and domain experience are often incorporated, as a regularization term, into a suitable cost function within a respective optimization problem. Whereas in the inverse theory there is a rich class of inversion algorithms resulting from various choices of regularized cost functions, there are few ensemble data assimilation algorithms (including IES) which in their practical uses are implemented in a form beyond nonlinear-least-squares. This work aims to narrow this noticed gap. Specifically, we consider a class of more generalized cost functions, and establish a unified formula that can be used to construct a corresponding group of novel ensemble data assimilation algorithms, called generalized IES (GIES), in a principled and systematic way. For demonstration, we choose a subset (up to 30 +) of the GIES algorithms derived from the unified formula, and apply them to two history matching problems. Experiment results indicate that many of the tested GIES algorithms exhibit superior performance to that of an original IES developed in a previous work, showcasing the potential benefit of designing new ensemble data assimilation algorithms through the proposed framework.

show abstract

Efficient Implementation of an Iterative Ensemble Smoother for Data Assimilation and Reservoir History Matching

Cited by 33 publications

References 18 publications

Assimilation of atmospheric infrasound data to constrain tropospheric and stratospheric winds

Assimilation of atmospheric infrasound data to constrain tropospheric and stratospheric winds

Formulating the history matching problem with consistent error statistics

Novel iterative ensemble smoothers derived from a class of generalized cost functions

Contact Info

Product

Resources

About