Predictive filtering (PF) in the frequency domain is one of the most widely used denoising algorithms in seismic data processing. PF is based on the assumption of linear or planar events in the time-space domain. In traditional PF methods, a predictive filter is fixed across the spatial dimension, which cannot deal with spatial variations in seismic data well. To handle the curved events, the predictive filter is either applied in local windows or extended into a nonstationary version. The regularized nonstationary autoregression (RNAR) method can be treated as a nonstationary extension of traditional PF, in which the predictive filter coefficients are variable in different spatial locations. This highly underdetermined inverse problem is solved by shaping regularization with a smoothness constraint in space. We further extend the RNAR method to the more general case, in which we can apply more constraints to the filter coefficients according to the features of seismic data. First, apart from the smoothness in space, we also apply a smoothing constraint in frequency, considering the coherency of the coefficients in the frequency dimension. Second, we apply a frequency-dependent smoothing radius in the spatial dimension to better take advantage of the nonstationarity of seismic data in the frequency axis and to better deal with noise. The effectiveness of our method is validated using several synthetic and field data examples.

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用于地震随机噪声抑制的非平稳预测滤波—教程

频域中的预测滤波（PF）是地震数据处理中使用最广泛的降噪算法之一。PF基于时空域中线性或平面事件的假设。在传统的PF方法中，预测滤波器在整个空间维度上都是固定的，无法很好地处理地震数据中的空间变化。为了处理弯曲事件，可将预测过滤器应用于本地窗口或扩展为非平稳版本。正则化的非平稳自回归（RNAR）方法可以被视为传统PF的非平稳扩展，其中预测滤波器系数在不同的空间位置上是可变的。这个高度不确定的反问题是通过在空间中具有平滑约束的形状正则化来解决的。我们进一步将RNAR方法扩展到更一般的情况，在这种情况下，我们可以根据地震数据的特征对滤波器系数施加更多约束。首先，除了空间上的平滑度之外，我们还考虑了频率维度上系数的相干性，对频率应用了平滑约束。其次，我们在空间维度上应用频率相关的平滑半径，以更好地利用地震数据在频率轴上的非平稳性并更好地处理噪声。我们的方法的有效性通过使用几个综合和现场数据示例进行了验证。考虑频率维度中系数的相干性。其次，我们在空间维度上应用频率相关的平滑半径，以更好地利用地震数据在频率轴上的非平稳性并更好地处理噪声。我们的方法的有效性通过使用几个综合和现场数据示例进行了验证。考虑频率维度中系数的相干性。其次，我们在空间维度上应用频率相关的平滑半径，以更好地利用地震数据在频率轴上的非平稳性并更好地处理噪声。我们的方法的有效性通过使用几个综合和现场数据示例进行了验证。