Abstract: Due to the interference of stochastic noise, the effective signal of seismic exploration is usually covered and thus is difficult to be identified; meanwhile, it is difficult to distinguish the stochastic noise and effective signal in the time domain. As a new type of multi-scale and multi-directional time-frequency analysis method, Shearlet transform possesses the optimal sparse representation capacity, localization characteristics and directional sensibility. When the stochastic noise is removed by Shearlet transform, effective signals can be retained to the maximum degree, and the signal-to-noise ratio of seismic data can be effectively improved. Aiming at the deficiency in traditional Shearlet transform threshold de-noising method unable to change with the scale and direction, the adaptive threshold changing with the scale and direction is proposed, able to adapt to the difference in noise levels of different scales and directions. The adaptive threshold algorithm based on Shearlet transform and de-noising method based on wavelet transform can be used to de-noise the theoretical and actual seismic data respectively. It can be known by contrast that the adaptive threshold algorithm based on Shearlet transform has the stronger de-noising capacity, able to reserve the effective signal to the utmost extent.

Key words: Shearlet transform, adaptive threshold, stochastic noise, sparsity, signal-to-noise ratio

摘要： 由于随机噪声的干扰，地震勘探的有效信号经常淹没其中难以识别，且在时间域难以分离随机噪声和有效信号。Shearlet变换是一种新的多尺度多方向时频分析方法，具有最优的稀疏表示能力、局部化特征和方向敏感性。Shearlet变换在去除随机噪声的同时，能够最大限度地保留有效信号，可以有效地提高地震数据的信噪比。针对传统的Shearlet变换阈值去噪方法不能随尺度和方向变化的不足，提出了随尺度和方向变化的自适应阈值，可以同时适应不同尺度和方向噪声水平的差异。利用Shearlet变换的自适应阈值算法与小波变换去噪方法，分别对理论和实际地震数据进行去噪。对比可知，Shearlet变换的自适应阈值算法具有更强的去噪能力，并能够最大限度地保留有效信号。

关键词: Shearlet变换, 自适应阈值, 随机噪声, 稀疏性, 信噪比