A system and method perform structure-preserving smoothing (SPS) using a data adaptive method for smoothing 3D post-stacked seismic attributes which reduces random noise while preserving the structure without prior computation of its orientation. The data is smoothed within a neighborhood sub-window along a set of predefined orientations, and the best smoothing result is then selected for output. The orientation corresponding to the best result often approximates the true structure orientation embedded in the data, so that the embedded structure is thus preserved. The SPS method can also be combined with median, alpha-trim, symmetric near neighbor, or edge-preserving filters. The SPS method is an effective way to reduce random noise and eliminate noise footprints, and to enhance coherence and curvature attributes.