基于f-x域时频非凸正则化低秩矩阵近似的共偏移距道集去噪方法

随机噪声压制是地震数据处理的关键环节,而时频稀疏低秩近似算法逐道处理地震数据过程中无法利用信号的道间相干性。为此,将时频稀疏低秩近似与f-x域去噪结合,提出一种f-x域时频非凸正则化低秩矩阵近似算法。该算法对f-x域中每一单频分量作时频分解后,再对时频系数矩阵作低秩矩阵近似计算,能够利用信号和噪声的时频谱差异实现非平稳信号去噪处理。与共炮点道集和共中心点道集相比,共偏移距道集具有平缓甚至接近水平的同相轴结构,基本满足f-x域去噪的线性同相轴假设前提,建议将所提算法应用于共偏移距道集去噪处理。通过数值模拟和实际地震数据试算,证明本文方法能够有效压制随机噪声,同时保持有效信号不被损害。

Random noise attenuation of common offset gathers by f-x low-rank matrix approximation with nonconvex regularization

Random noise attenuation played an important role in the seismic data processing. The low-rank estimation of the seismic signal in the time-frequency domain is essentially a trace-by-trace process, which cannot exploit the channel-to-channel coherence of the signal. We propose a novel random noise attenuation based on f-x low-rank matrix approximation with nonconvex regularization. Firstly, the noisy seismic data is transformed into the f-x domain by Fourier transform. Then, the time-frequency method is employed to decompose each discrete frequency slice. Finally, we estimate the sparse low-rank matrix from the obtained noisy matrix. This method enables the denoising of non-stationary signals by exploiting the spectral differences between signal and noise. Compared with the common shot and mid-point gathers, the common offset gather is characterized by flat events, which basically satisfies the assumption of linear events for f-x domain denoising, and it is suggested that the proposed algorithm should be applied to the common offset gather. Synthetic and real data sets demonstrate the performance of our proposed method in random noise suppression and preserving more useful energy.