分数阶S变换:第一部分,理论(英文)

S变换(ST)结合了小波变换和短时傅里叶变换的特性,对信号处理具有良好的局部时频聚集性.分数阶傅里叶变换是一种对非平稳信号分析的工具.本文基于分数阶傅里叶变换和S变换的思想,提出了分数阶S变换(FRST),将S变换从时间-频率域推广到时间-分数阶频率域,推导了它的逆变换公式并研究了其数学性质。分数阶S变换(FRST)具有分数阶傅里叶变换和S变换的优点,增强了S变换对信号处理的灵活性。相比于S变换,分数阶S变换能提高信号时频分辨能力。仿真实验证实了该方法的有效性。     

基于分数阶小波域GSM模型的地震信号随机噪声压制方法

地震信号中的随机噪声是一种干扰波,严重降低了地震信号的信噪比,并影响着资料的后续处理和分析.本文根据地震信号中有效信号和随机噪声的差异,结合分数阶B样条小波变换与高斯尺度混合模型提出了一种地震信号随机噪声压制方法.首先利用分数阶B样条小波变换将含噪地震信号映射到最优分数阶小波时频域内,然后对各小波子带系数分别建立高斯尺度混合模型,由贝叶斯方法估计出源地震信号小波系数,最后使用分数阶B样条小波逆变换重构得到降噪后的地震信号.利用本文方法对合成地震记录和实际地震信号进行降噪处理,实验结果表明本文方法能够有效地压制地震信号中的随机噪声,并且较好地保留了有效信号.     

基于分数域自适应滤波的地震信号去噪方法

提出了一种基于分数域自适应滤波的地震信号去噪方法.先论述了分数阶傅立叶变换(FrFT)的基本原理及分数域滤波的采样与信号重构定理.根据FrFT具有时频旋转特性,分析了时频域信噪重叠情况下实现噪声分离的可行性.通过时频面旋转交互方式求取最佳阶数以及滤波器的带宽,最后利用理想信号与处理结果的相关系数来验证该方法的有效性.合成记录及实际资料的处理结果表明,分数域滤波与常规Fourier变换相比,具有良好的去噪性能,可有效解决时频域信噪重叠的信噪分离难题,达到信号保真与去除噪声的目的.     

分数阶S变换,第二部分:在储层预测及流体识别中的应用（英文）

分数阶S变换(FRST)具有较强的时频聚集性。利用FRST处理地震数据,通过合适的分数阶参数将频率轴旋转到适当位置,即可实现目标地质特征信息的最佳识别。由于不同的地震信号的最优分数阶参数可能不同,因而对整体的分数阶参数的最优估计不利于对多道地震数据的处理。本文首先利用FRST分离出共频率数据体,并利用共频率数据体进行了低频伴影分析,然后提出FRST和盲分离结合的方法,不需要对地震数据的最优分数阶参数进行估计,即可提取识别有效地质特征信息的独立频谱,提高对地震数据的解释效率。仿真实验表明在分数阶时频域内此方法能有效分离出独立的频率信息。将该方法用于实际的地震数据,并与已知井信息进行比对,验证了其有效性。     

基于分数阶傅里叶变换的混合Cadzow滤波法

常规频率域SVD滤波法在随机噪声压制处理时,容易造成弯曲同相轴损伤。针对这一问题,本文提出一种基于分数阶傅里叶变换的混合Cadzow滤波法压制三维地震数据中随机噪声的方法。首先应用分数阶傅里叶变换,将地震数据变换到时频面,再依据Eigenimage滤波法与Cadzow滤波法建立混合的高维Hankel矩阵,然后对其运行奇异值分解,最后通过秩约化的方法来压制随机噪声。此方法用于四川某地区的地震数据处理,结果表明该方法可有效地去除随机噪声,保护有效信号,提高叠后地震数据的信噪比。     

基于分数阶拉普拉斯算子解耦的黏声介质地震正演模拟与逆时偏移

时间域常Q黏声波方程,由于含分数阶时间导数项,数值求解需要大量内存,计算效率低,不利于地震偏移的实施.通过一系列近似,可将该方程简化为介质频散效应和衰减效应解耦的分数阶拉普拉斯算子黏声波方程,数值求解内存需求少,计算效率高.本文采用交错网格有限差分逼近时间导数,改进的伪谱法计算空间导数,PML吸收边界去除边界反射,对该方程进行数值离散和地震正演模拟,开展地震数据的黏声介质逆时偏移,实现波场逆时延拓过程中同时完成频散校正和衰减补偿.改善深层构造的成像精度,数值结果表明,基于分数阶拉普拉斯算子解耦的黏声介质地震正演模拟与逆时偏移可大幅度提高地震模拟计算效率,偏移剖面明显优于常规声波偏移剖面,极大改善深层构造的成像品质.     

地震分倒频处理技术

为刻画地震信号的局部层次特征,提高复杂地质体的地震分辨率,本文利用倒谱变换能够提高分辨率的特点,结合短时傅里叶变换,构造了倒时-频变换算法,并提出地震分倒频处理技术.文中对地震分倒频处理技术的公式推导、算法设计、分倒频处理技术提高地震纵向分辨率的机理进行了详细研究.设计出了适合三维地震资料处理的软件,并从理论上阐述了地震分倒频处理技术能够提高地震分辨率.利用倒时-频变换对多分量线性调谐信号模型做倒时-频分析,可以得到良好的时频分辨率.实际三维地震资料计算表明,该方法能够提高地震纵向分辨率,且计算效率高,适合大规模三维地震资料的处理.     

基于时频分析与分数阶最优控制网络的地震数据噪声压制

在复杂的地表环境,地震勘探采集到的实际地震资料信噪比较低,分辨率较差,接收的噪声能量较强,与有效信号存在频谱的重叠.常规的消噪手段很难在保证有效信号幅值的同时,还兼顾噪声压制的效果.本文采用基于分数阶最优控制(Fractional Optimal Control)理论建立的深度学习神经网络——FOCNet来压制地震数据噪声,并恢复微弱同相轴.不同于传统深度学习网络(DCNN)算法大多为基于经验的网络设计,FOCNet具有坚实的数理基础,它从动态系统的最优控制角度阐述了网络的原理,并采用长期记忆的方式增强了网络的稳定性,提高了系统对噪声的消减能力.针对地震数据有效信号在低频带与噪声重叠严重,且FOCNet对数据中、高频信息保留更好这一情况,本文提出了一种基于理想时频分析与FOCNet相结合的算法(TF-FOCNet)来压制地震噪声,提取有效信号.该算法通过理想时频分析,针对性的提取信噪重叠的低频目标数据成分,并与数据的中、高频成分一起送入网络中进行处理并融合,完成噪声的压制,增强了低频信息的保留能力.模拟及实际的实验结果验证了算法在随机噪声、面波压制及微弱信号恢复上的有效性和优越性.     

同步挤压广义S变换在南海油气识别中的应用

受窗函数的影响,短时傅里叶变换、小波变换、S变换等传统时频分析方法的分辨率不高.为了提高信号时频变换分辨率,发展了同步挤压小波变换算法;该算法将信号的时频谱值向其中心频率位置挤压,改善了信号时频分析结果,使得信号时频分辨率得到了很大的提升.但由于传统算法时窗固定,处理缺乏灵活性;因此,本文对S变换窗函数进行扩展,提出了同步挤压广义S变换.通过自适应窗函数挤压信号在S域的时频谱值,提高了算法的灵活性和时频分析聚焦能力.运用同步挤压广义S变换对南海某工区实际地震数据进行分频处理,结果显示含油气层能量随着频率的增加而逐渐衰减.因此,使用同步挤压广义S变换对地震数据进行分析处理,不仅可以对储层含油气性进行准确的检测,还可以对地层进行精确的标定.     

地震勘探信号时频分析方法对比与应用分析

针对地震勘探信号,对非平稳信号时频分析几种适效方法:短时Fourier变换、小波变换、S变换、Wigner分布、平滑伪Wigner分布、锥形核时频分布、AOK(adaptive optimum kernel,自适应最优核函数)分布等进行对比与应用研究.在阐明各种方法基本原理的基础上,进行数值分析与应用研究.首先对非平稳地震勘探模拟信号进行试算及时频属性提取,结合各类方法的信号表示理论,在时频局部化的精度和交叉项抑制等方面对计算结果进行对比分析;进一步应用于实际二维地震数据,提取瞬时频率和瞬时带宽等时频属性,进行比较研究.研究表明:对于地震勘探信号,就本文涉及的几种时频分析方法而言,AOK分布是时频局部化精度最高、交叉项抑制最好、时频匹配最优的方法,值得在地震勘探信号分析和地震属性提取、频谱分解等应用中深入研究和应用.     

The optimal fractional Gabor transform based on the adaptive window function and its application

We designed the window function of the optimal Gabor transform based on the time-frequency rotation property of the fractional Fourier transform. Thus, we obtained the adaptive optimal Gabor transform in the fractional domain and improved the time-frequency concentration of the Gabor transform. The algorithm first searches for the optimal rotation factor, then performs the p-th FrFT of the signal and, finally, performs time and frequency analysis of the FrFT result. Finally, the algorithm rotates the plane in the fractional domain back to the normal time-frequency plane. This promotes the application of FrFT in the field of high-resolution reservoir prediction. Additionally, we proposed an adaptive search method for the optimal rotation factor using the Parseval principle in the fractional domain, which simplifies the algorithm. We carried out spectrum decomposition of the seismic signal, which showed that the instantaneous frequency slices obtained by the proposed algorithm are superior to the ones obtained by the traditional Gabor transform. The adaptive time frequency analysis is of great significance to seismic signal processing.     

Properties of an improved Gabor wavelet transform and its applications to seismic signal processing and interpretation

This paper presents an analytical study of the complete transform of improved Gabor wavelets (IGWs), and discusses its application to the processing and interpretation of seismic signals. The complete Gabor wavelet transform has the following properties. First, unlike the conventional transform, the improved Gabor wavelet transform (IGWT) maps time domain signals to the time-frequency domain instead of the time-scale domain. Second, the IGW’s dominant frequency is fixed, so the transform can perform signal frequency division, where the dominant frequency components of the extracted sub-band signal carry essentially the same information as the corresponding components of the original signal, and the subband signal bandwidth can be regulated effectively by the transform’s resolution factor. Third, a time-frequency filter consisting of an IGWT and its inverse transform can accurately locate target areas in the time-frequency field and perform filtering in a given time-frequency range. The complete IGW transform’s properties are investigated using simulation experiments and test cases, showing positive results for seismic signal processing and interpretation, such as enhancing seismic signal resolution, permitting signal frequency division, and allowing small faults to be identified.     

A method for absorption compensation based on adaptive molecular decomposition

In this paper, we present a new method for seismic stratigraphic absorption compensation based on the adaptive molecular decomposition. Using this method, we can remove most of the effects resulting from wavelets truncation and interference which usually exist in the common time-frequency absorption compensation method. Based on the assumption that the amplitude spectrum of the source wavelet is smooth, we first construct a set of adaptive Gabor frames based on the time-variant properties of the seismic signal to transform the signal into the time-frequency domain and then extract the slowly varying component (the wavelet’s time-varying amplitude spectrum) in each window in the time-frequency domain. Then we invert the absorption compensation filter parameters with an objective function defined using the correlation coefficients in each window to get the corresponding compensation filters. Finally, we use these filters to compensate the time-frequency spectrum in each window and then transform the time-frequency spectrum to the time domain to obtain the absorption-compensated signal. By using adaptive molecular decomposition, this method can adapt to isolated and overlapped seismic signals from the complex layers in the inhomogeneous viscoelastic medium. The viability of the method is verified by synthetic and real data sets.     

Vibrator Data Denoising Based on Fractional Wavelet Transform

In this paper, a novel data denoising method is proposed for seismic exploration with a vibrator which produces a chirp-like signal. The method is based on fractional wavelet transform (FRWT), which is similar to the fractional Fourier transform (FRFT). It can represent signals in the fractional domain, and has the advantages of multi-resolution analysis as the wavelet transform (WT). The fractional wavelet transform can process the reflective chirp signal as pulse seismic signal and decompose it into multi-resolution domain to denoise. Compared with other methods, FRWT can offer wavelet transform for signal analysis in the timefractional-frequency plane which is suitable for processing vibratory seismic data. It can not only achieve better denoising performance, but also improve the quality and continuity of the reflection syncphase axis.     

基于反射地震记录变子波模型提高地震记录分辨率

本文给出了地震记录变子波模型的一种近似数学表达式．基于该表达式研究了反射系数序列不满足白噪假设和子波在地下传播时发生变化这两种情况下地震道谱的组成及结构,讨论了谱白化及反褶积方法在这两种情况下效果不佳的原因．然后基于变子波模型,提出了一种新的提高地震记录分辨率的方法：第一步,用自适应于地震记录的Gabor分子窗把地震记录恰当地划分成若干片断,每段内信号近似平稳,然后将地震记录变换到时间-频率域;第二步,在变换域对每个分子窗内信号的振幅谱进行处理以拓宽频带;最后把处理后的时间-频率域函数反变换回时间域得到提高分辨率后的结果．本文提出的方法具有能较好地适用于反射系数不满足白噪假设的情况及提高分辨率后的地震记录能较好地保持原地震记录的相对能量关系等优点,模型和实际资料算例结果均表明,本文方法在拓宽地震资料频带及保持地震记录局部能量相对关系方面均明显优于谱白化方法．     

几种时频分析方法的比较和实际应用

地震信号往往是非线性非平稳的,时频分析技术能同时展示信号在时间域和频率域的局部化特征。本文研究4种时频分析方法:短时傅里叶变换(STFT)、小波变换、广义S变换和Wigner-Ville分布。在理论上运用雷克子波模拟地震记录进行时频分析对比,发现广义S变换具有相对较好的时频聚焦性以及较好的交叉项抑制性。为了验证这一理论,我们分别在两个工区做了实际的地震实验,分析并阐述4种时频分析方法的优缺点,同时也验证广义S变换的优越性。      

Effects of Gabor transform parameters on signa time-frequency resolution

In this paper, it is described that the time-frequency resolution of geophysical signals is affected by the time window function attenuation coefficient and sampling interval and how such effects are eliminated effectively. Improving the signal resolution is the key to signal time-frequency analysis processing and has wide use in geophysical data processing and extraction of attribute parameters. In this paper, authors research the effects of the attenuation coefficient choice of the Gabor transform window function and sampling interval on signal resolution. Unsuitable parameters not only decrease the signal resolution on the frequency spectrum but also miss the signals. It is essential to first give the optimum window and range of parameters through time-frequency analysis simulation using the Gabor transform. In the paper, the suggestions about the range and choice of the optimum sampling interval and processing methods of general seismic signals are given.     

Gabor变换参数对信号时频分辨率的影响

窗函数的衰减系数和采样间隔究竟对地球物理信号时频分辨率造成多大的影响,如何才能更好地消除这种影响,是该文的主要出发点。提高分辨率是信号时频分析处理的关键,在地球物理数据处理和属性参数提取等方面具有重要作用和广泛应用。该文研究了Gabor变换窗函数衰减系数选择正确与否和采样间隔对信号分辨率的影响。参数选择不当,不仅降低信号时频谱的分辨率,甚至要丢失信号。在用Gabor变换作时频分析时,通过模拟计算预先给出最佳窗函数和最佳参数范围是十分必要的。文中还给出了常规地震信号最佳采样间隔的范围和选择、处理方法。