﻿ 丘陵地带地震资料随机噪声压制新技术:高阶加权阈值函数的Shearlet变换
 地球物理学报  2019, Vol. 62 Issue (10): 4039-4046 PDF

The new technology for suppression of hilly land seismic random noise: Shearlet transform and the high order weighted threshold function
DONG XinTong, MA HaiTao, LI Yue
Department of Information and Engineering, Jilin University, Changchun 130012, China
Abstract: As the seismic exploration environment is becoming more and more complicated, the SNR (Signal to Noise Ratio) of the obtained seismic data is much lower than before, the conventional method can not suppress the random noises effectively. Shearlet transform is a new multi-scale and multi-direction time frequency analysis method, the Shearlet transform has huge advantages in sparse representation characteristic and direction sensitivity, so Shearlet transform is suitable for seismic data processing. In conventional Shearlet denoising method, the hard threshold function is applied to choose the Shearlet coefficients. However, through hard threshold function, many valid signals are eliminated when the random noises are suppressed. This phenomenon leads to the appearance of false axis. In order to solve this problem, we propose the high order weighted threshold function, this new proposed threshold function has better continuity than hard threshold function and overcome the disadvantage of soft threshold function. Experiment shows the new method can eliminate the random noise of simulative seismic data and hilly land actual seismic data effectively and retain the amplitude of valid signals.
Keywords: Low SNR seismic signals    Random noise suppression    Shearlet transform    High order weighted threshold function
0 引言

1 Shearlet变换基本原理

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2 高阶加权阈值函数原理

2.1 对阈值加权处理方法

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c(i, j)表示Shearlet系数，c′(i, j)表示经过阈值函数处理的Shearlet系数，sgn()表示符号函数，σ表示噪声的标准差，N表示地震资料的大小.

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 图 1 三种阈值函数的示意图(注：横坐标-50到50的灰色加粗线条代表五种阈值函数图像的重叠部分) Fig. 1 The schematic of three threshold function (Note: the gray line in the x-coordinate -50 to 50 represents the overlaps of the images of the five threshold functions)

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2.2 误差理论分析

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2.3 本文算法大致流程

(a) 分解：对需要处理的低信噪比地震信号进行Shearlet变换.

(b) 新的阈值函数处理：在Shearlet域利用高阶加权阈值函数对系数进行阈值收缩处理.

(c) 反变换：对处理后的Shearlet系数进行Shearlet反变换，得到去噪后的地震资料.

3 仿真实验及结果 3.1 模拟实验

 图 2 模拟信号的去噪结果图 (a)原始信号；(b)含噪信号；(c)基于小波变换的阈值去噪；(d) Shearlet硬阈值去噪；(e)本文算法去噪结果. Fig. 2 The denoising results of simulation signals (a) Original Signal; (b) Noisy record; (c) Result of wavelet transform; (d) Result of hard threshold Shearlet transform; (e) Result of the proposed algorithm.

 图 3 单道波形和频谱对比 (a)单道时域波形对比；(b)频谱对比. Fig. 3 The comparison of waveform and spectrum in a single trace (a) Waveform of the result of single trace; (b) Spectrum of the result of single trace.

3.2 野外地震记录处理

 图 4 实际地震信号去噪结果 (a)原始信号; (b)基于小波变换的阈值去噪; (c) Shearlet硬阈值去噪; (d)本文算法去噪结果. Fig. 4 The denoising results of the field seismic data (a) Original Signal; (b) Result of wavelet transform; (c) Result of hard threshold Shearlet transform; (d) Result of the proposed algorithm.

 图 5 局部放大图 (a)原始信号; (b)基于小波变换的阈值去噪; (c) Shearlet硬阈值去噪; (d)本文算法去噪结果. Fig. 5 The partial enlarged image (a) Original Signal; (b) Result of wavelet transform; (c) Result of hard threshold Shearlet transform; (d) Result of the proposed algorithm.
4 结论与讨论

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