低信噪比地震资料FDOC-seislet变换阈值消噪方法研究

地震数据本质上是时变的,不仅有效同相轴表现出确定性信号的时变特征,而且复杂地表和构造条件以及深部探测环境总是引入时变的非平稳随机噪声.标准的频率-空间域预测滤波只适合压制平面波信号假设下的平稳随机噪声,而处理非平稳地震随机噪声时,需要将数据体分割为小窗口进行分析,但效果不够理想,而传统非预测类随机噪声压制方法往往适应性不高,因此开发能够保护地震信号时变特征的随机噪声压制方法具有重要的工业价值.压缩感知是近年出现的一个新的采样理论,通过开发信号的稀疏特性,已经在地震数据处理中的数据插值以及噪声压制中得到了应用.本文系统地分析了压缩感知理论框架下的地震随机噪声压制问题,建立了阈值消噪的数学反演目标函数;针对时变有效信息具有的可压缩性,利用有限差分算法求解炮检距连续方程,构建有限差分炮检距连续预测算子(FDOC),在seislet变换框架下,提出一种新的快速稀疏变换域———FDOC-seislet变换,实现地震数据的高度稀疏表征;结合非平稳随机噪声不可压缩的特征,提出了一种整形迭代消噪方法,该方法是一种广义的迭代收缩阈值(IST)算法,在无法计算稀疏变换伴随算子的条件下,仍然能够对强噪声环境中的时变有效信息进行有效恢复.通过对模型数据和实际数据的处理,验证了FDOC-seislet稀疏变换域随机噪声迭代压制方法能够在保护复杂构造地震波信息的前提下,有效地衰减原始数据中的强振幅随机噪声干扰.

Seismic random noise attenuation using FDOC-seislet transform and threshold for seismic data with low SNR

In seismic exploration,seismic data are essentially time-varying,not only effective events display time-varying characteristics,but also complex surface and subsurface conditions and deep exploration environment always create time-varying and nonstationary random noise.Industrial standard prediction filter in the frequency-space (f-x) domain can only suppress stationary random noise under the assumption of stationary plane waves,for which cutting data into overlapping windows is a common method to handle nonstationary problem. However,such an approach cannot produce good results.On the other hand,random noise attenuation methods without prediction cannot provide good adaptability for different data.It is important to develop nonstationary random noise suppression methods that are suitable for time-varying characteristics of seismic data.Compressive sensing is a new sampling theory,which has found different applications in seismic data processing,for example,missing data interpolation and noise attenuation.In this paper,we analyze the problem of seismic random noise attenuation under compressive sensing framework and establish the objective function for threshold denoising.Aiming at the compressible characteristics of time-varying seismic signal,we solve the offset continuation equation by using finite difference algorithm to construct a finite-difference offset-continuation operato. Then a new fast sparse transform,FDOC-seislet transform,is proposed under seislet transform framework,which provides a highly sparse representation of seismic signals.According to the feature that nonstationary random noise is less compressible,we propose a new iterative shaping denoising method,a kind of generalized iterative shrinkage threshold methods,which is able to recover the time-varying signal under strong random noise environment,even when the adjoint operator of sparse transform cannot be calculated.Compared with conventional denoising methods,the examples of synthetic and field data demonstrate that the random noise attenuation method based on FDOC-seislet transform and iterative shaping can protect complex seismic signal and attenuate random noise even with strong amplitudes.