The Ensemble Kalman Filter (EnKF), in combination with travel-time parameterization, provides a robust and flexible method for quantitative multi-model history matching to time-lapse seismic data. A disadvantage of the parameterization in terms of travel-times is that it requires simulation of models beyond the update time. A new distance parameterization is proposed for fronts, or more generally, for isolines of arbitrary seismic attributes, that circumvents the necessity of 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 subsequently used as innovations in the EnKF. Experiments are presented that demonstrate the functioning of the method in synthetic 1D and 2D cases that include uncertain model properties, and merging or multiple secondary fronts. Results are compared with those resulting from direct use of saturation data. The proposed algorithm significantly reduces the number of data while still capturing the essential information, it removes the need for seismic inversion when the oil-water front is identified only, and it produces a more favorable distribution of simulated data, leading to improved functioning of the EnKF.