Abstract
Time-lapse (4D) seismic data provides spatial information about dynamic changes in a reservoir. This information can be used in combination with production data from wells to adjust reservoir models through a history matching procedure. However, quantitative use of 4D seismic data for history matching is generally challenging. This is partly because of the high dimensionality and the large uncertainty associated with the seismic data. To circumvent these difficulties, some methods have been proposed with a focus on reparameterization of seismic attributes and reformulation of seismic objective functions so that the integration of 4D seismic data is more robust and efficient. A distance parameterization of seismic anomalies due to saturation effects was previously proposed to history match reservoir models in combination with the ensemble Kalman filter (EnKF). Because the parameterization reduces both nonlinearity and the effective number of data, an improved functioning of the EnKF could be achieved. The distances measured from simulated fronts to observed fronts were used as innovations in the EnKF such that the same number of simulated measurements is obtained for each simulated model realization. However, it turns out that this definition is not always an effective measure of the actual differences between simulated and observed fronts as we demonstrate through the experiments in this paper. Using concepts from the field of image analysis, we generalize the defined innovations as a directed local Hausdorff distance, providing a one-directional dissimilarity measure (from simulated to observed fluid fronts, or in a broader sense, to detected features in 4D seismic data). A more robust distance parameterization approach is proposed based on the full local Hausdorff distance that measures the distances between observed and simulated fronts in both directions. Additionally, a comparison is made between contour-based and area-based characterizations of the differences between images that are commonly used for shape matching within the field of image analysis. Numerical experiments in a synthetic 2D case and realistic synthetic 3D case based on the Norne field are presented in which improved functioning of the proposed method is demonstrated.