GNMF小波谱分离在地震勘探噪声压制中的应用

Application of GNMF wavelet spectral unmixing in seismic noise suppression

地震勘探资料噪声压制及信噪比提高是整个地震勘探信号处理过程中的重要任务,随着地震勘探深度的增加及其复杂性,人们对地震数据质量的要求越来越高.勘探环境的复杂化使得采集到的地震资料中有效信号被大量噪声淹没,无法清晰辨识,严重影响后续的数据处理与解释.小波去噪是地震勘探中常用且发展较成熟的一种方法,但是其涉及到的阈值函数选取问题一直令人困扰,虽然已有多种阈值函数被提出,但仍存在各自的缺陷.本文利用小波分解在时域及频域良好的信号细节体现特性,引入模式识别中的非负矩阵分解(NMF)谱分离思想,针对小波系数阈值优化问题,提出了一种小波域图非负矩阵分解(GNMF)消噪算法.该方法首先在小波分解基础上,利用GNMF算法实现小波分解系数谱中信号分量与噪声分量的谱分离,然后通过反变换重构各分离子谱对应的子信号,最后利用K均值聚类算法将得到的多个子信号划分为信号类及噪声类,最终得到重构信号及分离噪声.合成记录和实际地震资料的消噪结果验证了新方法在提高信号与噪声分离准确性和精度方面的有效性,同时新方法避免了阈值选取造成的噪声压制不理想或有效成分损失问题.与小波消噪结果的对比及数值分析也说明了新方法在噪声压制及有效成分保持方面的优势.

Seismic noise suppression and signal-to-noise ratio（SNR）improvement is an important task in the process of seismic signal processing.With the development of seismic exploration in depth and complexity,the requirement of the quality of seismic data is becoming higher.The complexity of acquisition environment makes seismic data mixed with a lot of noise,which makes the effective signal difficult to identify.It directly affects the follow-up data processing and interpretation process.Wavelet denoising is a common and mature method,which is used in seismic exploration.However,the selection of threshold function is always a troubling problem,which hindering its performance.Although many improved methods have been proposed,they still had some shortcomings,respectively.The proposed method applies the popular graph nonnegative matrix factorization（GNMF）spectral separation theory to seismic random noise suppression.In the constraint function of GNMF,an additional item is added to the conventional constraint function of NMF,which plays an important role in the performance and accuracy improvement of GNMF for the wavelet coefficients spectrums unmixing.It makes full use of the wavelet decomposition characteristics that embodiment the details of the signals in time domain and frequency domain.The novel method first uses GNMF to separate the wavelet coefficient spectrums into some sub-spectrums,and then reconstructs the corresponding sub-signals from these sub-spectrums through inverse transform.Then,it classifies the sub signals into signal class and noise class by K-mean clustering algorithm.The sum of the sub-signals in signal class is the effective signal and the sum of the sub-signals in noise class is the separated noise.The novel method effectively improves the accuracy and precision of separation signal and noise in the spectral space.Meanwhile,it avoids the worse noise suppression or serious energy loss problems,which is caused by threshold selection.The experimental results on synthetic records and actual seismic data both show the effectiveness and advantages of the proposed algorithm in the aspect of noise suppression and effective composition maintain.Firstly,based on wavelet decomposition,GNMF algorithm is used to decompose the signal components and the noise components.Then,the sub signals are decomposed into signal and noise by using K means clustering algorithm.A new method avoids the problem of noise suppression caused by the threshold selection and the loss of the effective components.Meanwhile,the effectiveness of the method in improving the accuracy and precision of the signal and noise separation is verified.Compared with the results of wavelet de-noising,the proposed method is more effective and has great advantages in noise suppression and effective maintenance.In order to solve the problem of threshold selection in wavelet denoising method,the wavelet method is applied to the optimization problem of wavelet coefficient threshold in time domain and frequency domain.A novel method based upon GNMF is proposed.The novel method resolves the problem of the threshold selection in the traditional wavelet de-noising method and it can suppress the noise and protects the effective signal components effectively.The simulation and real data results both show that the novel wavelet denoising method has obvious advantages over the traditional wavelet de-noising method.