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The attenuation of linear coherent noise is a persistent problem in seismic processing and imaging. Traditional methods utilize the differences in frequency, wavenumber or amplitude between useful signals and noise to separate them. However, in some cases, the differences are too small to be distinguished, and the traditional method are limited or even invalid. So we introduce mathematical morphological filter to attenuate the linear coherent noise utilize the differences in the shape of seismic waves. In the seismic exploration, we can see that the same linear coherent noises exist in some different common shot gathers. After investigation, we find that the trajectories of linear coherent noises in the common offset gather are horizontal continuous ones. So we implement the MMF attenuation the linear noises in the common offset gathers by using the horizontal consistency. And apply the proposed method on field seismic to show the excellent performance.