State estimation in high dimensional systems remains a challenging part of real time analysis. The ensemble Kalman filter addresses this challenge by using Gaussian approximations constructed from a number of samples. This method has been a large success in many applications. Unfortunately, for some cases, Gaussian approximations are no longer valid, and the filter does not work so well. In this paper, we use the idea of the ensemble Kalman filter together with the more theoretically valid particle filter. We outline a Gaussian mixture approach based on shrinking the predicted samples to overcome sample degeneracy, while maintaining non-Gaussian nature. A tuning parameter determines the degree of shrinkage. The computational cost is similar to the ensemble Kalman filter. We compare several filtering methods on three different cases: a target tracking model, the Lorenz 40 model, and a reservoir simulation example conditional on seismic and electromagnetic data.

No abstract

No abstract

Information analysis can be used in the context of reservoir decisions under uncertainty to evaluate whether additional data (e.g., seismic data) are likely to be useful in impacting the decision. Such evaluation of geophysical information sources depends on input modeling assumptions. We studied results for Bayesian inversion and value of information analysis when the input distributions are skewed and non-Gaussian. Reservoir parameters and seismic amplitudes are often skewed and using models that capture the skewness of distributions, the input assumptions are less restrictive and the results are more reliable. We examined the general methodology for value of information analysis using closed skew normal (SN) distributions. As an example, we found a numerical case with porosity and saturation as reservoir variables and computed the value of information for seismic amplitude variation with offset intercept and gradient, all modeled with closed SN distributions. Sensitivity of the value of information analysis to skewness, mean values, accuracy, and correlation parameters is performed. Simulation results showed that fewer degrees of freedom in the reservoir model results in higher value of information, and seismic data are less valuable when seismic measurements are spatially correlated. In our test, the value of information was approximately eight times larger for a spatial-dependent reservoir variable compared with the independent case.

No abstract