地球物理学报  2015, Vol. 58 Issue (12): 4559-4567 PDF

Elimination of seismic random noise based on the SW statistic adaptive TFPF
LIN Hong-Bo , MA Hai-Tao, LI Yue, SHAO Dong-Yang
Department of Information Engineering, Jilin University, Changchun 130012, China
Abstract: Owing to complex properties of random noise in raw data in metal mine and low signal-to-noise ratio (SNR), it is extremely difficult for conventional denoising methods to obtain expected filtering results. Time-frequency peak filtering (TFPF) is an effective method to eliminate seismic random noise in seismic data at low SNR. However, the selection of window length of TFPF significantly affects the performance in signal preserving and seismic random noise attenuation. The conventional TFPF using a fixed window length usually obtains unbiased signal estimation by using a short window length, but it leads to relatively poor performance of seismic random noise attenuation. Therefore, it is crucial to adapt the window length for TFPF according to the characteristics of signal and noise, respectively.
Taking statistical property of seismic random noise into account, we propose a Shapiro-Wilk (SW) statistic based adaptive time-frequency peak filtering (S-TFPF) to suppress seismic random noise in seismic data at low SNR. The SW test, a statistical method for the measurement of Gaussianity of time series, is introduced into TFPF method. Based on the assumption that seismic random noise usually is white Gaussian noise and seismic signals are non-Gaussian, the SW statistics of seismic random noise are different from those of seismic signals. Therefore, the seismic signals in seismic data can be identified by means of the SW statistics. Furthermore, Gaussianization of seismic data is done by applying a band-pass filter to seismic data, which makes complex seismic random noise Gaussian and keep seismic signals. As a result, the accuracy of identification of valid signals under complex seismic random noise is improved based on SW statistics. Then, adaptively adjusting window length of S-TFPF is implemented based on the SW statistics. In this algorithm, the window length of S-TFPF in the signal-dominant segment are set according to the frequencies of signals to preserve signals, whereas the window length of S-TFPF for noise-dominant segment increases with the variance of noise increasing, so as to completely eliminate seismic random noise.
The Gaussianity of seismic noise data is investigated by SW test and the performance of new method is analyzed on synthetic data and field data. The SW test result show that most seismic random noise are non-Gaussian noise and their SW statistics are lower than but close to the SW statistic of ideal Gaussian noise. The significant difference of the SW statistics exists between random noise and seismic signals. However, the difference of SW statistic of noisy seismic data decreases, because signals are contaminated by seismic random noise and properties of seismic random noise are complex. After preprocessing seismic data by means of Gaussianization, the SW statistics of seismic random noise becomes closer to 1 and the SW statistics of seismic signals slightly decrease, which leads to an accurate segmenting of seismic signal and seismic random noise. Then the adaptive window length of the S-TFPF is obtained based on the SW statistics and apply to processing synthetic and field seismic data. The results show that the S-TFPF method better keeps the amplitude and frequency component of filtered seismic signals than the TFPF. Furthermore, the filtered seismic data obtained by the S-TFPF has higher SNR and lower mean square error comparing with the TFPF. Application to the field data shows that the filtered seismic data by using S-TFPF has less background noise and more continuous seismic events.
The proposed method improves the adaptability of window length of the TFPF using SW statistics of seismic data. In the new method, the window length can be adapted at different segments of seismic data according to characteristics of seismic signals and statistical property of seismic random noise, respectively, thus reducing the bias of seismic signal estimation and improving denoising performance of the TFPF. The results of synthetic and field data demonstrate the practicability and effectiveness of the S-TFPF method.
Key words: Seismic signal processing     SW test     Random noise     Adaptive     Time-frequency peak filtering
﻿ 1 引言

2 时频峰值滤波原理

3 基于SW统计量的自适应TFPF 3.1 SW检验

SW检验算法是检验随机序列非高斯性的统计学方法(Shapiro and Wilk，1965).其基本思想是在数据服从正态分布的假设下，利用线性回归计算SW检验统计量，度量待测数据顺序统计量与标准高斯分布顺序统计量的相关程度.相关程度越高，待 测数据越近似服从正态分布.SW检验统计量定义为

 图 1 地震勘探随机噪声记录 Fig. 1 Seismic random noise data

 图 2 地震勘探噪声高斯性检验结果 Fig. 2 The result of Gaussianity test of seismic random noise

 图 3 地震勘探噪声高斯性检验统计量 Fig. 3 The statistic of Gaussianity test for seismic random noise

 图 4 含噪信号高斯检验统计量 (a)含实际噪声的合成记录；(b)含噪记录高斯性统计量W. Fig. 4 SW statistic of noisy signal (a)Ricker wavelet with field seismic noise；(b)Values of SW statistic of noisy signal.
3.2 基于SW的自适应TFPF

4 地震数据处理 4.1 合成地震勘探记录

 图 5 含噪合成记录 (a)合成记录；(b)含噪记录. Fig. 5 Noisy synthetic seismic data (a)Synthetic data；(b)Noisy data.

 图 6 含噪合成记录降噪结果 (a)TFPF结果；(b)S-TFPF降噪结果；(c)第25道滤波结果波形对比；(d)第25道滤波结果幅度谱对比. Fig. 6 Filtering result of noisy synthetic data (a)Result of TFPF；(b)Result of S-TFPF；(c)Comparison of waveforms of the 25th filtered trace；(d)Comparison of spectra of the 25th filtered trace.

4.2 实际地震勘探记录

 图 7 某矿区实际记录 Fig. 7 Field data from some area

 图 8 实际地震勘探记录滤波结果 (a)时频峰值滤波结果；(b)本文方法的滤波结果. Fig. 8 Filtering data of field seismic data (a)Result of using TFPF；(b)Result of using S-TFPF.

5 结论

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