Ensemble Kalman Filter Adjusted to Time-Lapse Seismic Data

Time-lapse seismic data are frequently used in History Matching of reservoir production data. The Ensemble Kalman Filter (EnKF) is a method that conditions on observations as they appear. It uses an n-member ensemble of representations of reservoir characteristics and conditions them on production data. However, if the dimension of the production data is greater than the number of ensemble members, rank problems may arise and the EnKF solution might break down. The dimension of seismic data is vast and exceeds the number ensemble members in realistic models. We propose a hierarchical model, phrased in a consistent Bayesian setting, to account for these problems. The model incorporates prior information about the expected level and heterogeneity of the solution.<br>The hierarchical model is implemented on simple synthetic examples and they show promising results.<br>