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Uncertainty in Training-Image Based Inversion of Hydraulic Head Data Constrained to ERT Data : Workflow and Case Study
Hermans, Thomas; Nguyen, Frédéric; Caers, Jef
2015
 

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Keywords :
prior uncertainty; Popper-Bayes; training image; geological scenario; electrical resistivity tomography; probability perturbation method
Abstract :
[en] In inverse problems, investigating the relationship between data and prior models and the uncertainty related to the posterior distribution of model parameters are as important as matching the data. In recent years, many efforts have been done to assess the posterior distribution of a given problem with reasonable computational costs through inversion techniques such as McMC. The derived posterior distribution is always dependent on the prior distribution. However, most of the studies ignore modeling the prior with realistic uncertainty. In this paper, we propose a workflow to assess the uncertainty of inversion of hydraulic heads data through the addition of electrical resistivity tomography (ERT) constraining data. The workflow is divided in three successive steps: 1) Construction of prior: we generate multiple alternative geological scenarios from literature data (architecture of facies) as well as site specific data (proportions of facies). Spatial uncertainty within each scenario is integrated hierarchically through geostatistics (multiple-point statistics simulation of facies constrained by ERT data as soft data). 2) Validation of prior scenarios: we transform prior facies scenarios into resistivity distribution scenarios through forward and inverse modeling. The scenarios are validated by comparison with field ERT data. The comparison is made through distance calculation and projection into a low dimensional space to calculate the probability of each scenario given field ERT data. 3) Matching dynamical data: we use the probability perturbation method, within each scenario, to integrate hydraulic heads to our models. We account for scenario probabilities, calculated in 2, in determining how many models per scenario we have to consider for building a reliable posterior distribution. The method is first applied on synthetic cases where the "true" model is known. Then, it is apllied a field case study in an alluvial aquifer (Belgium) where we consider prior uncertainty related to the type of elements (gravel channels or bars) and to their size. This study shows the importance of considering the uncertainty of the prior in inverse problems as it has a strong influence on model predictions and decision-making problems.
Research center :
Fondation Roi Baudouin - Prix Ernest Dubois
Disciplines :
Geological, petroleum & mining engineering
Author, co-author :
Hermans, Thomas ;  Université de Liège > Département ArGEnCo > Géophysique appliquée
Nguyen, Frédéric ;  Université de Liège > Département ArGEnCo > Géophysique appliquée
Caers, Jef;  Stanford University > Stanford Center for Reservoir Forecasting
Language :
English
Title :
Uncertainty in Training-Image Based Inversion of Hydraulic Head Data Constrained to ERT Data : Workflow and Case Study
Publication date :
06 May 2015
Event name :
Stanford Canter for Reservoir Forecasting Annual Meeting
Event organizer :
Stanford Center for Reservoir Forecasting
Event place :
Menlo Park, United States - California
Event date :
May 6 to May 7 2015
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Available on ORBi :
since 06 May 2015

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