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We propose a novel method for seismic noise attenuation by applying nonstationary polynomial fitting (NPF), which can estimate coherent components with amplitude variation along the event.The NPF with time-varying coefficients can adaptively estimate the coherent components.The smoothness of the polynomial coefficients is controlled by shaping regularization.The signal is coherent along the offset axis in a common midpoint (CMP) gather after normal moveout (NMO).We use NPF to estimate the effective signal and thereby to attenuate the random noise.For radial events-like noise such as ground roll, we first employ a radial trace (RT) transform to transform the data to the time-velocity domain.Then the NPF is used to estimate coherent noise in the RT domain.Finally, the coherent noise is adaptively subtracted from the noisy dataset.The proposed method can effectively estimate coherent noise with amplitude variations along the event and there is no need to propose that noise amplitude is constant.Results of synthetic and field data examples show that, compared with conventional methods such as stationary polynomial fitting and low cut filters, the proposed method can effectively suppress seismic noise and preserve the signals.