【作者】 聂鹏飞；

【导师】 李月；

【作者基本信息】 吉林大学 ， 通信与信息系统， 2012， 博士

【副题名】正则化约束下的维纳滤波与方向导数迹变换

【摘要】 随着数字信号处理的产生和快速发展，数字信号处理在生物医学、图像视频、雷达、通信、航空航天以及地球物理探测等领域都有广泛应用。地球物理探测中的地震勘探是资源勘探的主要手段。地震勘探采集的数据往往会受到各种干扰，因此并不能直接用来反演和解释，需要首先进行数字信号处理以提高信噪比，获得精确、可靠的反演和解释结果。从数字信号处理角度讲，地震勘探降噪方法技术的研究始于上世纪六十年代。从数字维纳滤波方法引入地震勘探开始，地震勘探的降噪技术飞速发展，逐渐形成了适用于地震勘探数字信号处理的基本理论与方法系统。地震勘探中的噪声可分为两大类：随机噪声和规则噪声。由于二者性质不同，它们有各自不同的压制方法。所谓的随机噪声就是没有固定频率，在地震整张记录上随机出现，频带很宽，视速度不确定，无一定传播方向的噪声。因而很难利用随机噪声同有效波之间在频率上的差异或传播方向上的差异对其进行压制。维纳滤波是地震勘探随机噪声压制最早也是最经典的方法，但是它要求已知信号或噪声的相关函数或功率谱。实际上，这是很难满足的，因此维纳滤波的实际效果不理想。同时，维纳——霍夫方程是一种不适定问题求解。为了解决维纳——霍夫方程的不适定性，经典的求解方法有频谱因式分解法和伯德——香农法（预白化法）。文中为了改善维纳滤波的上述不足，引入正则化的思想。因为正则化不但是不适定问题求解的普遍方法，而且通过正则项可约束或修正由于相关函数或功率谱估计不准时的滤波响应，使其尽可能的接近维纳滤波的最优解。在一维情况下，文中引入估计信号一阶导数的正则化约束项，推导了在该约束下维纳滤波的冲激响应和频域响应。在正则化参数选取理想情况下，正则化约束下的维纳滤波能完全恢复期望信号，而维纳滤波并不能实现这一点，它会不同程度的影响期望信号的完全恢复。文中根据实际情况讨论了正则化参数的取值，并给出了正则化参数的解析表达，使得正则约束下的维纳滤波能更方便的应用、实现。在二维情况下，引入估计信号梯度的约束项，推导了二维情况下正则化约束维纳滤波的频域响应。文中对二维正则化约束下的维纳滤波只给出了理论上的推导并未进行详细讨论，在后续的研究中将进行进一步的完善。通过理论模型及实际资料处理分析，表明一维正则约束下的维纳滤波去噪能力较维纳滤波强，且对有效信号的损失更小，特别是对于一些频率较高的信号。因此正则约束下的维纳滤波优于维纳滤波，它拓展了维纳滤波理论，提高了其实用性。规则噪声在时间上的出现具有规律性，有明显的运动学特征，具有一定的视频率和视速度，如面波、多次波、声波、工业电等。在陆地地震勘探中，面波是一种主要的规则噪声，它的存在严重的干扰着地震记录的信噪比。因此，面波的压制是地震勘探中重要一环。面波是一种特殊类型的瑞雷波，它产生于近地表的低速带，具有低频、低速、强振幅和频散特性。由于面波的频散特性，在地震记录上它常以近直线形式呈“扫帚状”分布。目前，面波的压制技术很多，包括频域滤波、FK滤波以及Radon变换等。由于面波和有效波（反射波）具有相关性，而且面波的频带和有效波的低频部分频带总有重叠部分，因此在频域或FK域滤波会不同程度的损失低频的有效信号。Radon变换是根据面波在地震记录中具有的线性，把面波变换为Radon域的一个“能量点”，从而使其与有效信号分开。然而由于端点效应的存在，Radon变换并不能完全压制面波。同时，由于Radon域的切除影响会造成有效信号的畸变。迹变换是近年发展起来的一种模式识别方法，在图像的识别上已取得很成功的应用。它是Radon变换的一般形式，其特点是可沿直线取不同的泛函，而Radon变换只是直线上的一种积分运算，即线积分。因此说迹变换是Radon变换的一般形式。文中基于迹变换方法提出一种新的面波压制方法。该方法是函数的方向导数沿直线积分，称其为方向导数迹变换。应用傅里叶变换和希尔伯特变换的特性，文中推导了方向导数迹变换的反变换公式，目的是实现方向导数迹变换域滤波后的有效信号的重建。在计算方向导数迹变换时，在方向导数迹变换域会得到两部分，一部分主要是面波信息，另一部分则主要体现有效信号（相对于前一部分而言）。由于面波和有效信号的Radon变换在Radon域是一个整体，在这一个域中由于端点效应的存在以及面波和少部分有效信号交织在一起，很难精确的确定面波的范围，因此压制面波后会保留面波的端点信息同时会损失一部分有效信号。方向导数迹变换则把面波和有效信号变换为方向导数迹变换域中的两部分，根据这两部能更精确的确定面波的范围，使面波压制更彻底。文中给出了由这两部分确定面波域的公式，并通过大量不同模型的实验给出了公式中参数的选择规律。为了详细的了解面波，文中对面波的产生、传播以及特性进行了详细的讨论。含有面波的理论地震记录的模拟由简单到复杂，应用方向导数迹变换对不同模型进行面波压制处理，通过面波压制前后的波形对比及频谱分析，表明文中提出的方向导数迹变换能对面波进行有效的压制，同时其效果较Radon变换好，因为它对端点效应的处理效果很好。实际资料的处理也验证了方向导数迹变换的有效性，表明方向导数迹变换具有一定的理论研究价值和应用前景。更多还原

【Abstract】 With the generation and rapid development of digital signal processing, it is widelyused in the biomedicine, image video, radar, communication, aerospace and geophysicalexploration and so on. Seismic exploration is the primary exploration method in geophysics.Seismic data which are contaminated by noise can’t be directly used for inversion andinterpretation. In order to obtain results of the inversion and interpretations more accurateand reliable, the signal to noise ratio of seismic data need to be improved by digital signalprocessing.From the perspective of digital signal processing, seismic noise reduction methods andtechniques of research began in the 1960s. From the beginning of digital Wiener filteringmethod introduced to seismic exploration, denoise technology rapidly developed andgradually formed the basic theory of digital signal processing in seismic. Seismic noiseincludes random noise and coherent noise. The random noise has not fixed frequency,certain apparent velocity and direction of propagation and it appears random in the entireseismic record. Its frequency band is very wide. So it is difficult to attenuate by thedifference of frequency and direction of propagationbetween the random noise andreflected signal.Wiener filter is the earliest and most classic method to suppress random noise inseismic. It require to known the correlation or spectrum characteristics of signal and noise.In fact, it is difficult to obtain the correlation or spectral, so the result of Wiener filter is notsatisfactory. At the same time, Wiener-Hoff equation is an ill-posed problem. In order toovercome the ill-posed, the classic method for solving Wiener-Hoff equation includes thespectral factorization and Bode-Shannon method (pre-whitening method). The thinking ofregularization is introduced to improve these shortcomings of Wiener filter in this thesis.The regularization is the general method for solving the ill-posed problem. At the sametime, the Wiener filter response can be constrained by regularization term when thecorrelation or spectrum is estimated inaccurately. The goal is to let the filter response asclose as possible to the optimal Wiener filter response. In the one-dimensional case, weproposed the regularization constraint term about the first derivative of estimated signal. We derived the impulse response and frequency response of Wiener filter under theconstraint. The regularization parameter is discussed and given the analysis formula withthe actual. The analysis formula makes the regularization constraint Wiener filter moreeasily achieved. In the two-dimensional case, we proposed the regularization constraintterm about the gradient of estimated signal. We derived the constraint Wiener filterfrequency response in the thesis. We test the 1D constraint Wiener filter with synthetic andactual data, the results show that 1D constraint Wiener filter has more force capacity indenoising than Wiener filter. The reflection signal loss less after 1D constraint Wienerfiltering than after Wiener filtering, especially for high frequency signal.The coherent noise has significant kinematic characteristics, certain frequency andapparent velocity. Such as ground-roll, multiple, sound, and industrial electricity, etc.Ground-roll is main coherent noise in land seismic exploration. It’s serious interferencewith the signal to noise ratio. Therefore, the suppression of ground-roll is an important partin seismic exploration.Ground roll is a particular type of Rayleigh wave that occurs in the zone of lowvelocity near the surface and has high amplitude, low frequency and low velocity. Groundroll is also dispersive and its distribution likes a broom in the form of near a straight line.Current processing methods of eliminating ground roll include frequency filtering, FKfiltering and Radon transform and so on. The correlation between ground roll and reflectedsignal and the frequency band which is always overlaped, lead to the reflection signallossing with different degrees in frequency filtering or FK filtering. Radon transform isbased on the linear of Ground roll in seismic records. In Radon domain, ground roll is“energy point”, it can be clearly separated form reflection signal. However, due to theendpoint effect and cut-off, the ground-roll can not completely suppressed and thereflection signal is distorted.Trace transform is a developing pattern recognition method in recent years. It has beensuccessfully used for object recognition. The Radon transform is a special case of the Tracetransform, that is to say trace transform is the generalization of Radon transform. Its featureis that the different functional defined on the line set can be choose. But the Radontransform is an integral operation on the line set.In the thesis a new method based on trace transform is proposed for suppressingground roll. This method is integral operation of directional derivative of function along the line set, called directional derivative trace transform. The inverse directional derivativetrace transform is derived by using the properties of Fourier transform and Hilberttransform. Its purpose is to reconstruct the original function. The directional derivativetrace transform of seismic records is composed of two parts, one part mainly is representground roll; the other part mainly is represent reflection signal (relative to the first part). Inthe Radon domain the ground roll and reflection signal is a whole. Because of the endpointeffect and the overlaps of ground roll and a few reflection signals, it is difficult toaccurately determine the scope of the ground roll. So the ground roll can’t be completelysuppressed. The endpoint of ground roll will remaining and few reflection signals will alsobe suppressed. However, in the trace domain the seismic record consists of two parts.According to the two parts ground roll can be more accurately determined, which makes theground roll suppressed more thoroughly. In the thesis presents the formula of determiningthe scope of ground roll is presented and the law of choice parameter is illustrated byexperiments of different models.In order to understand the ground roll in detail, the ground roll generation, propagationand characteristics are discussed in detail in the thesis. The seismic record that containsground roll is simulated from simply to complexly. Using the directional derivative tracetransform to suppress the ground roll in difference models. The analysis of waveform andspectrum before and after ground roll attenuation shows that the proposed method caneffectively suppress the ground roll and the effect is better than Radon transform. Theeffectiveness of the proposed method is also proved by law data processing.更多还原