A Multiscale Method For Data Assimilation

Rafael Jesus de Moraes, Hadi Hajibeygi, Jan Dirk Jansen

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

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In data assimilation problems, various types of data are naturally linked to different spatial resolutions (e.g. seismic and electromagnetic data), and these scales are usually not coincident to the subsurface simulation model scale. Alternatives like down/upscaling of the data and/or the simulation model can be used, but with potential loss of important information. To address this issue, a novel Multiscale (MS) data assimilation method is introduced. The overall idea of the method is to keep uncertain parameters and observed data at their original representation scale, avoiding down/upscaling of any quantity. The method relies on a recently developed mathematical framework to compute adjoint gradients via a MS strategy. The fine-scale uncertain parameters are directly updated and the MS grid is constructed in a resolution that meets the observed data resolution. The advantages of the technique are demonstrated in the assimilation of data represented at a coarser scale than the simulation model. The misfit objective function is constructed to keep the MS nature of the problem. The regularization term is represented at the simulation model (fine) scale, whereas the data misfit term is represented at the observed data (coarse) scale. The performance of the method is demonstrated in synthetic models and compared to down/upscaling strategies. The experiments show that the MS strategy provides advantages 1) on the computational side – expensive operations are only performed at the coarse scale; 2) with respect to accuracy – the matched uncertain parameter distribution is closer to the “truth”; and 3) in the optimization performance – faster convergence behaviour due to faster gradient computation. In conclusion, the newly developed method is capable of providing superior results when compared to strategies that rely on the up/downscaling of the response/observed data, addressing the scale dissimilarity via a robust, consistent MS strategy.
Original languageEnglish
Title of host publication16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018
EditorsD. Gunasekera
Number of pages18
ISBN (Print)9789462822603
Publication statusPublished - 2018
Event16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018: 3–6 September 2018, Barcelona, Spain - Barcelona, Spain
Duration: 3 Sept 20186 Sept 2018
Conference number: 16


Conference16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018
Abbreviated titleECMOR 2018
Internet address

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


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