Uncertainty assessment for reconstructions based on deformable geometry

Hanson, Kenneth M.; Cunningham, G.; McKee, R.J.

doi:10.1002/(sici)1098-1098(1997)8:6<506::aid-ima2>3.0.co;2-e

Cited by 28 publications

(21 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The accuracy of the BIE approach is difficult to assess since it does not provide a direct way of estimating the variances of the parameters. In 1997, Hanson, Cunningham, and McKee [37,38] used Markov chain Monte Carlo to estimate the accuracy of the perimeter for a simple two-dimensional pixel-based object. Though computationally intensive, this is the only work that calculated the true variances of the object parameters instead of just lower bounds.…”

Section: Discussionmentioning

confidence: 99%

Model-based Tomographic Reconstruction Literature Search

Chambers¹,

Lehman²

2005

View full text Add to dashboard Cite

Section: Discussionmentioning

confidence: 99%

Model-based Tomographic Reconstruction Literature Search

Chambers¹,

Lehman²

2005

View full text Add to dashboard Cite

“…Voronoi cells possess very attractive geometrical and computational properties, see [7] . The Neighbourhood Approximation (NA) algarithm was originally developed to solve an inverse problem in earthquake seismology [14] .…”

Section: Voronoi Cells and The Neighbourhood Approximation Algorithmmentioning

confidence: 99%

“…Exploring a multidimensional space is non-trivial . Deterministic [7,8,12] and stochastic [11,13,16] algorithms for history matching have been reported in the literature .…”

Section: Introductionmentioning

confidence: 99%

Prediction under Uncertainty in Reservoir Modeling

Christie¹,

Subbey²,

Sambridge³

2002

ECMOR VIII - 8th European Conference on the Mathematics of Oil Recovery

View full text Add to dashboard Cite

Abstrac tReservoir simulation is routinely employed in the prediction of reservoir performance under different depletion and operating scenarios . Usually, a single history matched model, conditioned to production data, is obtained . The model is then used to forecast fotore production profiles . Since the history match is non-unique, this is essentially an inverse problem. Hence the forecast production profiles are uncertain, although this uncertainty is not usually quantified .This paper presents a new approach for generating uncertain reservoir performance predictions and quantifying the uncertainty associated with forecasting fotore performance . Firstly, we generate multiple reservoir realizations using a new stochastic algorithm . This involves adaptively sampling the model parameter space using an algorithm, which biases the sampling towards regions of good fit . Using the complete ensemble of models generated, we resample from the posterior distribution and quantify the uncertainty associated with forecasting reservoir performance, in a Bayesian framework .To demonstrate the strength of the method in performance prediction, we use an upscaled model to history match fine scale data . We then forecast the fine grid performance using the maximum likelihood model and quantify the uncertainty associated with the predictions . We demonstrate that the maximum likelihood model is highly accurate in reservoir performance prediction .This method differs from other methods for generating multiple reservoir realizations in the following way . Rather than seeking a single global optimum, the algorithm selectively samples parameter space to derive an ensemble of models . These models share the common property of fitting the observed data to some degree of accuracy . This approach is reasonable since the inverse problem is ill-posed . In contrast to other stochastic methods, the algorithm performs a guided search in parameter space by using information derived from the complete ensemble of previously generated models . Hence no external directionality is imposed on the search process .In Bayesian analysis, the posterior probability distribution characterizes the uncertainty in the model parameters estimated from an ensemble of models . Correctly sampling from this distribution is therefore essential for accurate quantification of forecasted reservoir performance . The Neigbourhood algorithm utilizes the nearest neighbor property of the Voronoi cells, together with a Markov Chain Monte Carlo algorithm, in correctly sampling from the posterior probability distribution . IntroductionPetroleum reservoir data is inherently uncertain . The field information is usually sparse and noisy . Part of the data is obtained from cores (-10-17 of the reservoir volume) collected at a finit e

show abstract

“…The expected variance in 8 is the expectation over the ensemble of all such sequences: where 0 = E{v} = E (6). The autocovariance of a sequence is defined as E{(Uk -u)(?&+l-U)}.…”

Section: Statistical Efficiency Of a Mcmc Sequencementioning

confidence: 99%

<title>Posterior sampling with improved efficiency</title>

Hanson

Cunningham

1998

SPIE Proceedings

View full text Add to dashboard Cite

Lob Alamos National hboratoy, an afhrmatlve actbV6qual oppommty employer, I ABSTRACTThe Markov Chain Monte Carlo (MCMC) technique provides a means to generate a random sequence of model realizations that sample the posterior probability distribution of a Bayesian analysis. That sequence may be used to make inferences about the model uncertainties that derive from measurement uncertainties. This paper presents an approach to improving the efficiency of the Metropolis approach to MCMC by incorporating an approximation to the covariance matrix of the posterior distribution. The covariance matrix is approximated using the update formula from the BFGS quasi-Newton optimization algorithm. Examples are given for uncorrelated and correlated multidimensional Gaussian posterior distributions.

show abstract

Uncertainty assessment for reconstructions based on deformable geometry

Cited by 28 publications

References 23 publications

Model-based Tomographic Reconstruction Literature Search

Model-based Tomographic Reconstruction Literature Search

Prediction under Uncertainty in Reservoir Modeling

<title>Posterior sampling with improved efficiency</title>

Contact Info

Product

Resources

About