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It is common in ensemble-based methods of history matching to evaluate the adequacy of the initial ensemble of models through visual comparison between actual observations and data predictions prior to data assimilation. If the model is appropriate, then the observed data should look plausible when compared to the distribution of realizations of simulated data. The principle of data coverage alone is, however, not an effective method for model criticism, as coverage can often be obtained by increasing the variability in a single model parameter. In this paper, we propose a methodology for determining the suitability of a model before data assimilation, particularly aimed for real cases with large numbers of model parameters, large amounts of data, and correlated observation errors. This model diagnostic is based on an approximation of the Mahalanobis distance between the observations and the ensemble of predictions in high-dimensional spaces. We applied our methodology to two different examples: a Gaussian example which shows that our shrinkage estimate of the covariance matrix is a better discriminator of outliers than the pseudo-inverse and a diagonal approximation of this matrix; and an example using data from the Norne field. In this second test, we used actual production, repeat formation tester, and inverted seismic data to evaluate the suitability of the initial reservoir simulation model and seismic model. Despite the good data coverage, our model diagnostic suggested that model improvement was necessary. After modifying the model, it was validated against the observations and is now ready for history matching to production and seismic data. This shows that the proposed methodology for the evaluation of the adequacy of the model is suitable for large realistic problems.

Data assimilation methods often assume perfect models and uncorrelated observation error. The assumption of a perfect model is probably always wrong for applications to real systems, and since model error is known to generally induce correlated effective observation errors, then the common assumption of uncorrelated observation errors is probably almost always wrong, too. The standard approach to dealing with correlated observation errors, which simply ignores the correlation, leads to suboptimal assimilation of observations. In this paper, we examine the consequences of model errors on assimilation of seismic data. We show how to recognize the existence of correlated error through model diagnostics modified for large numbers of data, how to estimate the correlation in the error, and how to use a model with correlated errors in a perturbed observation form of an iterative ensemble smoother to improve the quantification of a posteriori uncertainty. The methodologies for each of these aspects have been developed to allow application to problems with very large number of model parameters and large amounts of data with correlated observation error. We applied the methodologies to a small toy problem with linear relationship between data and model parameters, and to synthetic seismic data from the Norne Field model. To provide a controlled investigation in the seismic example, we investigate an application of data assimilation with two sources of model error-errors in seismic resolution and errors in the petro-elastic model. Both types of model errors result in effectively correlated observation errors, which must be accounted for in the data assimilation scheme. Although the data are synthetic, parameters of the seismic resolution and the observation noise are estimated from the actual inverted acoustic impedance data. Using a structured approach, we are able to assimilate approximately 115,000 observations with correlated total observation error efficiently without neglecting correlations. We show that the application of this methodology leads to less overfitting to the observations, and results in an ensemble estimate with smaller spread than the initial ensemble of predictions, but that the final estimate of uncertainty is consistent with the truth.

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