空间局部加权回归自适应TFPF

Spatial locally weighted regression adaptive time-frequency peak filtering

时频峰值滤波(TFPF)算法是一种非常有效的去噪方法.但是传统的TFPF采用的单一窗长,并且仅沿时间方向进行滤波,忽略了信号的空间信息,并且TFPF近似等效成一个时不变的低通滤波器,不能追踪快速变化的信号.针对这些问题,引入空间局部加权回归自适应TFPF(SLWR-ATFPF).鉴于随机噪声在各个位置的方向随机性,以及有效信号在各个位置的方向确定性,首先利用空间局部加权回归(SLWR),对含噪信号进行空间加权,从而使加权之后的信号包含空间信息.然后,再引入凸集和Viterbi的思想,对空间加权之后的信号进行自适应滤波.从而,完成时空域二维自适应滤波.将SLWR-ATFPF应用于合成记录和实际的共炮点记录,实验结果表明,改进的方法与原算法相比,能够在压制低信噪比(SNR)随机噪声的同时更好地保留有效信号.

The time-frequency peak filtering（TFPF）algorithm is an effective method for random noise attenuation.Recently,TFPF has been widely applied to seismic random noise attenuation.Whereas,TFPF still has some shortcomings.（1）The conventional TFPF uses a fixed window length for all frequency components.As a consequence,serious loss of the valid information or insufficient suppression of the noise is unavoidable.（2）TFPF carries out filtering only along the time direction,which lacks consideration of the spatial correlation.（3）TFPF is approximately equivalent to a time-invariant low-pass filer,which means that the frequency components of signal higher than some cut-off frequency would be attenuated.To solve these problems,we introduce the spatial locally weighted regression adaptive TFPF（SLWR-ATFPF）.Due to the randomness of the random noise at each location and the definiteness of the valid signal at each location,we first apply the spatial locally weighted regression（SLWR）to achieve the space weighting of the noisy signal,which would make the signal contain spatial information.Then,we introduce the idea of convex sets and the Viterbi′s algorithm to finish the adaptive filtering of the spatially weighted signal.Finally,we complete the spatiotemporal adaptive filtering.To verify the feasibility and effectiveness of the proposed approach,we use synthetic and real seismic records to test it.Through the comparison of waveforms and spectrums,it is easy to see that SLWR-ATFPF could preserve valid signals,including peaks and troughs more effectively.Moreover,the results of SLWR-ATFPF are closer to the noise-free signal both on high-and lowfrequency components.In the real seismic record,the results of SLWR-ATFPF recover the reflection events more continuously and smoothly.In addition,some originally buried events are revealed clearly.SLWR-ATFPF as an improvement method of TFPF could achieve better random noise attenuation and higher continuity and clarity of reflection events than conventional TFPF and adaptive TFPF（ATFPF）.Therefore,this method has large applied space.