﻿ 基于自适应阈值RCSST变换的金属矿山地地区地震信号随机噪声消减
 地球物理学报  2019, Vol. 62 Issue (10): 4020-4027 PDF

Reduction of seismic random noise in mountainous metallic mines based on adaptive threshold RCSST
ZHENG Sheng, MA HaiTao, LI Yue
Department of Information and Engineering, Jilin University, Changchun 130012, China
Abstract: The suppression of random noise in seismic data is an essential step in processing of seismic signals. However, as the exploration environment is becoming more and more complicated, the energy of valid signals gets weaker and the Signal to Noise Ratio(SNR)of seismic data is much lower which brings great difficulty to seismic data processing and interpretation. In order to solve this problem, a Shearlet transform denoising algorithm based on adaptive threshold recursive cycle spinning is proposed in view of the exploration environment of metal mines in Yunnan mountainous regions. In this algorithm, the Shearlet transform is combined with recursive cycle spinning. By virtue of multiscale and multidirection features of Shearlet transform, the seismic signals are transformed into different scales and directions. Then, we propose a new adaptive threshold to prevent the coefficients being killed excessively and protect the amplitude of the effective signals. Experiments show that this adaptive threshold RCSST algorithm can overcome the disadvantages of conventional Shearlet transform denoising algorithm and protect the amplitude of signals effectively. Application to of simulative and real seismic data in Yunnan mountainous regions with low SNR demonstrates that this algorithm can suppress the random noises effectively and protect the amplitude of valid signals.
Keywords: Low SNR seismic signals    Random noise suppression    Shearlet transform    Recursive cycle spinning    Adaptive threshold
0 引言

1 Shearlet变换原理及其去噪原理 1.1 Shearlet变换的原理

Shearlet变换理论是基于复小波变换的(Guo et al., 2004, 2006), L2(R2)是闭区间R2的平方可积函数，当维数n=2时，函数fL2(R2)的连续Shearlet变换定义为

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 图 1 不同a和s时的频域支撑 Fig. 1 Frequency domain support of for different values of a and s
1.2 基于阈值的Shearlet去噪原理

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 图 2 基于不同阈值的TST算法去噪结果 Fig. 2 Denoising results of the TST algorithm with different thresholds

2 基于RCSST的自适应阈值去噪 2.1 阈值的改进

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2.2 RCSST的基本原理

Cycle Spinning(CS)算法是由Caifman和Donoho等提出的(Eslami and Radha, 2003), 首先是对地震资料的行和列进行循环平移，改变不连续点位置，然后对平移后的地震信号进行变换去噪处理，最后将去噪后的地震资料反向平移，并且叠加平均，但是取平均值通常并不能达到最优化运算，为了获得更好的去噪效果，本文采用递归循环平移(RCS)，此即CS的递归形式(Fletcher et al., 2002), 其对于虚假同向轴的抑制效果要好于CS的线性平均，并且在一定的约束条件下保证收敛性, 该过程可以表示如下：

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(1) 取k=0, 为待处理的地震资料，设定递归次数K.

(2) 计算平移量xy(x=y=kmodN)，根据xy的值对进行循环平移.

(3) 对平移后的地震信号进行Shearlet变换从而获得不同尺度不同方向的系数.

(4) 对不同尺度不同方向的系数用自适应阈值进行处理.阈值函数定义为

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(5) 对上式得到的进行Shearlet反变换, 并对反变换的结果进行反向平移，得到去噪后的结果.

(6) 如果k=K，跳出循环并输出去噪结果，否则，令, k=k+1, 返回步骤2.

3 实验结果 3.1 地震仿真模型实验分析

 图 3 模拟地震资料的去噪结果对比 (a)纯净信号；(b)含噪信号；(c) TST算法去噪结果；(d) CSST算法去噪结果；(e) RCSST算法去噪结果. Fig. 3 Comparison of denoising results for synthetic seismic data using different methods (a) Pure; (b) Noisy record; (c) Denoising by TST; (d) Denoising by CSST; (e) Denoising by RCSST.

 图 4 随机噪声时域波形和频谱比较 (a)单道时域波形对比；(b)单道频谱对比. Fig. 4 Comparison of waveforms and frequency spectra of random noise (a) Waveforms of time-domain at single trace; (b) Frequency spectrum at single trace.

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3.2 实际地震资料实验分析

 图 5 实际地震资料的去噪结果对比 (a)原始地震信号；(b) TST算法去噪结果；(c) CSST算法去噪结果；(d) RCSST算法去噪结果. Fig. 5 Denoising results of real seismic data by different methods (a) Original seismic data; (b) By TST; (c) By CSST; (d) By RCSST.

 图 6 局部放大图 (a)原始地震信号；(b) TST算法去噪结果；(c) CSST算法去噪结果；(d) RCSST算法去噪结果. Fig. 6 Local enlarged view of denosing between traces 25-85 and travel time 150-450 ms by different methods (a) Original seismic data; (b) By TST; (c) By CSST; (d) By RCSST.
4 结论

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