基于Shearlet变换的自适应地震资料随机噪声压制

Seismic random noise adaptive suppression based on the Shearlet transform

传统的阈值选取方法是对所有变换域系数使用统一阈值,但对Shearlet变换而言,各尺度、各方向的有效信号和噪声均存在差异,因此全局硬阈值存在一定局限性;局部阈值可根据一定范围内的系数分布情况确定。针对地震数据去噪过程中传统阈值选取方法的局限性,通过改进自适应阈值函数压制随机噪声,在局部阈值的基础上改进贝叶斯阈值,形成一种适用于Shearlet变换的自适应阈值函数。具体做法为:将信噪比与阈值函数有机关联,并将信噪比作为阈值设定的因素,即不同的信噪比的权值系数不同,可以自适应求取不同尺度阈值,从而最大限度地改善去噪效果,避免有效信号损失,实现自适应去噪。模型试算与实际资料去噪效果表明,在保证有效信号不受损失的情况下,所提方法可恢复被噪声掩盖的弱信号,有效改善去噪效果。

Conventional thresholding methods use a unified threshold for all the transform domain coefficients.However for Shearlet transform,signals and noises in all the scales and directions are different,so a global hard threshold has some limits.Aiming at these limits,a random noise suppression is proposed with improved adaptive threshold functions.On the basis of local threshold,the Bayesian threshold is improved to form an adaptive threshold function suitable for the Shearlet transform.A relation between the signal-to-noise ratio(SNR)and threshold functions is built.Different SNRs have different weighting coefficients to adaptively calculate different thresholds.So seismic signals are preserved and the denoising is greatly improved.Tests on model and real data show that the proposed method can effectively suppress random noise and highlight weak signals.