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We have developed a new method of stacking NMO-corrected or migrated seismic data using local correlation. We substitute local correlation for the weight value in statistically weighted stacking and then use soft thresholding to make the stacking selective. Because weights are derived from the input data, our method can be regarded as a nonlinear filter. Synthetic and field data examples confirm that our approach can be significantly more effective than other weighted stacking methods in improving S/N and suppressing distortions resulting from prestack processing. Seismic stacking using local correlation can give a poor result if the quality of the reference trace is very poor. Because the coherency enhancement from local correlation is not based on physics, one should use this approach with caution when aiming to preserve physically meaningful amplitudes.