171 research outputs found
Multiscale model diagnostics
No full textI consider the problem of model diagnostics, that is, the problem of criticizing a model prior to history matching by comparing data to an ensemble of simulated data based on the prior model (prior predictions). If the data are not deemed as a credible prior prediction by the model diagnostics, some settings of the model should be changed before history matching is attempted. I particularly target methodologies that are computationally feasible for large models with large amounts of data. A multiscale methodology, that can be applied to analyze differences between data and prior predictions in a scale-by-scale fashion, is proposed for this purpose. The methodology is computationally inexpensive, straightforward to apply, and can handle correlated observation errors without making approximations. The multiscale methodology is tested on a set of toy models, on two simplistic reservoir models with synthetic data, and on real data and prior predictions from the Norne field. The tests include comparisons with a previously published method (termed the Mahalanobis methodology in this paper). For the Norne case, both methodologies led to the same decisions regarding whether to accept or discard the data as a credible prior prediction. The multiscale methodology led to correct decisions for the toy models and the simplistic reservoir models. For these models, the Mahalanobis methodology either led to incorrect decisions, and/or was unstable with respect to selection of the ensemble of prior predictions.publishedVersio
Assimilation of multiple linearly dependent data vectors
No full textAssimilation of a sequence of linearly dependent data vectors, {dl}Ll=1 such that dl=BldLL−1l=1 , is considered for a parameter estimation problem. Such a data sequence can occur, for example, in the context of multilevel data assimilation. Since some information is used several times when linearly dependent data vectors are assimilated, the associated data-error covariances must be modified. I develop a condition that the modified covariances must satisfy in order to sample correctly from the posterior probability density function of the uncertain parameter in the linear-Gaussian case. It is shown that this condition is a generalization of the well-known condition that must be satisfied when assimilating the same data vector multiple times. I also briefly discuss some qualitative and computational issues related to practical use of the developed condition.publishedVersio
Identification of geothermal reservoirs from ensemble-based Bayesian inversion of 3D MT data
No full text
Feasibility of simplified integral equation modeling of low-frequency marine CSEM with a resistive target
No full textWe have assessed the accuracy of a simplified integral equation (SIE) modeling approach for marine controlledsource electromagnetics (CSEM) with low applied frequencies and a resistive target. The most computationally intensive part of rigorous integral equation (IE) modeling is the computation of the anomalous electric field within the target itself. This leads to amatrix problem with a dense coefficient matrix. It is well known that, in general, the presence of many grid cells creates a computational disadvantage for densematrix methods compared to sparse-matrix methods. The SIE approach replaces the dense-matrix part of rigorous IE modeling by sparse-matrix calculations based on an approximation of Maxwell’s equations. The approximation is justified theoretically if a certain dimensionless parameter β is small. As opposed to approximations of the Born type, the validity of the SIE approach does not rely on the anomalous field to be small in comparison with the background field in the target region. We have calculated β for a range of parameter values typical for marine CSEM, and compared the SIE approach numerically to the rigorous IE method and to the quasi-linear (QL) and quasi-analytic (QA) approximate solutions. It is found that the SIE approach is very accurate for small β, corresponding to frequencies in the lower range of those typical for marine CSEM for petroleum exploration. In addition, the SIE approach is found to be significantly more accurate than the QL and QA approximations for small β
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