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We propose a method for extracting automatically and simultaneously the quasi-horizontal surfaces in three-dimensional (3-D) seismic data. The proposed algorithm identifies connected sets of points which form surfaces in 3-D space. To improve reliability, this algorithm takes into consideration the relative positions of all horizons, and uses globally self-consistent connectivity criteria which respect the temporal order of horizon creation. The first stage of the algorithm consists of the preliminary estimation of the local direction of each horizon at each point of the 3-D space. The second stage consists of smoothing the signal along the detected layer structure to reduce noise. The last stage consists of the simultaneous building of all 3-D horizons. The output of the processing is a set of 3-D horizons represented by a series of triangulated surfaces.