基于广义Beta小波稀疏域混合约束优化的地震去噪方法研究

Seismic random noise reduction via generalized beta wavelet and mixed norm

地震随机噪声压制是鄂尔多斯盆地黄土塬、沙漠、戈壁滩等复杂地表区域低信噪比地震资料处理的一项重要任务.稀疏反演去噪是地震随机噪声压制的常用方法之一.ℓ_(1)范数和全变分(Total Variation,TV)正则化是稀疏变换域去噪方法中常用的两种正则化项.但是,ℓ_(1)范数是对ℓ_(0)范数的松弛,难以提供更稀疏的去噪结果;基于TV正则化项的方法容易引起阶梯状异常结果.因此,为了避免上述缺点,本文提出了一种基于广义Beta小波稀疏域混合范数优化的地震随机噪声压制方法和算法流程实现.首先利用广义Beta小波紧标架加快计算,获得具有更高局域化性的稀疏时频表示.其次是引入包括ℓp范数和TV正则化的混合约束项,克服单一正则化项的缺点.最后,利用鄂尔多斯盆地黄土塬区的合成地震数据、三维叠后地震数据和共反射点道集数据验证了本文去噪方法的有效性.结果表明:本文提出的去噪方法既能够有效抑制随机噪声、显著提高信噪比,让地震同相轴连续光滑;又能够准确保护有效信号,保持波组间的相对幅值,突出有利微小断层和含油气层的振幅形态.

Seismic random noise reduction is an important task in seismic data processing at the Chinese Ordos loess plateau area,which benefits the geologic structure interpretation and further reservoir prediction.The sparse inversion is one of the widely used tools for seismic random noise reduction,which is often solved via the sparse approximation with a regularization term.Theℓ_(1) norm and Total Variation(TV)regularization are two commonly used techniques in the sparse transform-based random noise reduction methods.However,theℓ_(1) norm is only a relaxation of theℓ_(0) norm,which cannot always provide a sparse result.The TV-based methods may lead to an undesirable staircase result.To avoid these disadvantages,we propose a workflow for seismic random noise reduction by using a sparse representation(i.e.the Continuous Wavelet Transform,CWT)with a mixed norm regularization.In the implementation,the Generalized Beta Wavelet(GBW)is first adopted as the basic wavelet of the CWT to better match seismic wavelets and then obtain a more localized time-frequency representation.It should be noted that the GBW can easily constitute a tight frame,which saves the calculation time when solving the proposed optimization model.Then,the mixed norm regularization,including theℓp norm and the TV regularization,is introduced in this paper,which not only overcomes the disadvantages of the two regularization solvers,but also accurately preserves the valid seismic reflections.Finally,synthetic data,3D post-stack field data and Common Reflection Point(CRP)gather data examples from the Ordos Basin are adopted to demonstrate the effectiveness of the proposed workflow.The denoising results denote that the proposed method can suppress some random noise to improve the signal-to-noise ratio and protect the continuity of the seismic events.Furthermore,the proposed method can maintain the real amplitude of seismic signals to highlight the small-scale faults and the potential oil and gas reservoirs.