NDLI: Levenberg–Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification

Content Provider	Springer Nature Link
Author	Chen, Yan Oliver, Dean S.
Copyright Year	2013
Abstract	The use of the ensemble smoother (ES) instead of the ensemble Kalman filter increases the nonlinearity of the update step during data assimilation and the need for iterative assimilation methods. A previous version of the iterative ensemble smoother based on Gauss–Newton formulation was able to match data relatively well but only after a large number of iterations. A multiple data assimilation method (MDA) was generally more efficient for large problems but lacked ability to continue “iterating” if the data mismatch was too large. In this paper, we develop an efficient, iterative ensemble smoother algorithm based on the Levenberg–Marquardt (LM) method of regularizing the update direction and choosing the step length. The incorporation of the LM damping parameter reduces the tendency to add model roughness at early iterations when the update step is highly nonlinear, as it often is when all data are assimilated simultaneously. In addition, the ensemble approximation of the Hessian is modified in a way that simplifies computation and increases stability. We also report on a simplified algorithm in which the model mismatch term in the updating equation is neglected. We thoroughly evaluated the new algorithm based on the modified LM method, LM-ensemble randomized maximum likelihood (LM-EnRML), and the simplified version of the algorithm, LM-EnRML (approx), on three test cases. The first is a highly nonlinear single-variable problem for which results can be compared against the true conditional pdf. The second test case is a one-dimensional two-phase flow problem in which the permeability of 31 grid cells is uncertain. In this case, Markov chain Monte Carlo results are available for comparison with ensemble-based results. The third test case is the Brugge benchmark case with both 10 and 20 years of history. The efficiency and quality of results of the new algorithms were compared with the standard ES (without iteration), the ensemble-based Gauss–Newton formulation, the standard ensemble-based LM formulation, and the MDA. Because of the high level of nonlinearity, the standard ES performed poorly on all test cases. The MDA often performed well, especially at early iterations where the reduction in data mismatch was quite rapid. The best results, however, were always achieved with the new iterative ensemble smoother algorithms, LM-EnRML and LM-EnRML (approx).
Starting Page	689
Ending Page	703
Page Count	15
File Format	PDF
ISSN	14200597
Journal	Computational Geosciences
Volume Number	17
Issue Number	4
e-ISSN	15731499
Language	English
Publisher	Springer Netherlands
Publisher Date	2013-05-08
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Ensemble randomized maximum likelihood method Ensemble Kalman filter Iterative ensemble smoother Ensemble smoother Levenberg–Marquardt Iterative EnKF Earth Sciences Geotechnical Engineering & Applied Earth Sciences Hydrogeology Mathematical Modeling and Industrial Mathematics Soil Science & Conservation
Content Type	Text
Resource Type	Article
Subject	Computers in Earth Sciences Computational Theory and Mathematics Computer Science Applications Computational Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Conditioning Truncated Pluri-Gaussian Models to Facies Observations in Ensemble-Kalman-Based Data Assimilation

Investigation of the sampling performance of ensemble-based methods with a simple reservoir model

Ensemble Randomized Maximum Likelihood Method as an Iterative Ensemble Smoother

Monte Carlo simulation of permeability fields and reservoir performance predictions with SVD parameterization in RML compared with EnKF

Ensemble-based conditioning of reservoir models to seismic data

A parallel ensemble-based framework for reservoir history matching and uncertainty characterization

An iterative ensemble Kalman filter for reservoir engineering applications

Bayesian estimation of reservoir properties—effects of uncertainty quantification of 4D seismic data

A probabilistic parametrization for geological uncertainty estimation using the ensemble Kalman filter (EnKF)

Levenberg–Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification

Similar Documents

Conditioning Truncated Pluri-Gaussian Models to Facies Observations in Ensemble-Kalman-Based Data Assimilation

Investigation of the sampling performance of ensemble-based methods with a simple reservoir model

Ensemble Randomized Maximum Likelihood Method as an Iterative Ensemble Smoother

Monte Carlo simulation of permeability fields and reservoir performance predictions with SVD parameterization in RML compared with EnKF

Ensemble-based conditioning of reservoir models to seismic data

A parallel ensemble-based framework for reservoir history matching and uncertainty characterization

An iterative ensemble Kalman filter for reservoir engineering applications

Bayesian estimation of reservoir properties—effects of uncertainty quantification of 4D seismic data

A probabilistic parametrization for geological uncertainty estimation using the ensemble Kalman filter (EnKF)

Levenberg–Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification