Distance parameterization for efficient seismic history matching the ensemble Kalman Filters

The availability of multiple history matched models is essential for proper handling of uncertainty in determining the optimal development of producing hydrocarbon fields. The ensemble Kalman Filter in particular is becoming recognized as an efficient method for quantitative conditioning of multiple models to history data. It is known, however, that the ensemble Kalman Filter (EnKF) may have problems with finding solutions in history matching cases that are highly nonlinear and involve very large numbers of data, such is typical when time-lapse seismic surveys are available. Recently, a parameterization of seismic anomalies due to saturation effects was proposed in terms of arrival times of fronts that reduces both nonlinearity and the effective number of data. A disadvantage of the arameterization in terms of arrival times is that it requires imulation of models beyond the update time. An alternative istance parameterization is proposed here for flood fronts, or more generally, for isolines of arbitrary seismic attributes representing a front that removes the need for additional simulation time. An accurate fast marching method for solution of the Eikonal equation in Cartesian grids is used to calculate distances between observed and simulated fronts, which are used as innovations in the EnKF. Experiments are presented that demonstrate the functioning of the method in synthetic 2D and realistic 3D cases. Results are compared with those resulting from use of saturation data, as they could potentially be inverted from seismic data, with and without localization. The proposed algorithm significantly reduces the number of data while still capturing the essential information. It furthermore removes the need for seismic inversion when the oil-water front is only identified, and it produces a more favorable distribution of simulated data, leading to a very efficient and improved functioning of the EnKF.