Directional Wavelets and a Wavelet Variogram for Two-Dimensional Data

This paper describes two new approaches that can be used to compute the two-dimensional experimental wavelet variogram. They are based on an extension from earlier work in one dimension. The methods are powerful 2D generalizations of the 1D variogram that use one- and two-dimensional filters to remove different types of trend present in the data and to provide information on the underlying variation simultaneously. In particular, the two-dimensional filtering method is effective in removing polynomial trend with filters having a simple structure. These methods are tested with simulated fields and microrelief data, and generate results similar to those of the ordinary method of moments variogram. Furthermore, from a filtering point of view, the variogram can be viewed in terms of a convolution of the data with a filter, which is computed fast in O(NLogN) number of operations in the frequency domain. We can also generate images of the filtered data corresponding to the nugget effect, sill and range of the variogram. This in turn provides additional tools to analyze the data further.     

用双正交小波实现有限脉冲信号的滤波

小波分析是一种时间-频率的分析方法，它具有多分辨分析的特点，而且在时频两域都具有表征信号局部特征的功能，因此被称为数学中的“显微镜”。紧支撑正交小波除了Haar小波外不具有线性相位，因此用双正交样条小波和Mallat塔式算法对有限脉冲信号进行了分解与重构。基于小波变换相当于频率域的带通滤波原理，尝试了在时间域对有限脉冲信号利用小波变换进行了滤波，并用一个数学模型做验证，基本上压制了需要消除的波形，并在其中讨论了双正交样条小波的阶次问题。     

Automatic identification of fake patterns caused by short-width wavelets in seismic data

Despite the popularity of using the Haar wavelet filter in many applications, it sometimes introduces fake patterns into the multi resolution analysis (MRA) of seismic data. In this work, we compared different wavelet filters to demonstrate that these patterns are fake and not part of the original waveforms and to show that they are a result of using the Haar wavelet filter as a short-width wavelet. To achieve this, many seismic waveforms from two different sources: the Egyptian National Seismic Network (ENSN) and the High Sensitivity Seismograph Network Japan (Hi-net) are used with different wavelet filters. We propose an algorithm based on an autoregressive (AR) model to detect these patterns automatically and fully.     

Image Filtering by Factorial Kriging—Sensitivity analysis and application to Gloria side-scan sonar images

Factorial Kriging (FK) is a data- dependent spatial filtering method that can be used to remove both independent and correlated noise on geological images as well as to enhance lineaments for subsequent geological interpretation. The spatial variability of signal, noise, and lineaments, characterized by a variogram model, have been used explicitly in calculating FK filter coefficients that are equivalent to the kriging weighting coefficients. This is in contrast to the conventional spatial filtering method by predefined, data-independent filters, such as Gaussian and Sobel filters. The geostatistically optimal FK filter coefficients, however, do not guarantee an optimal filtering effect, if filter geometry (size and shape) are not properly selected. The selection of filter geometry has been investigated by examining the sensitivity of the FK filter coefficients to changes in filter size as well as variogram characteristics, such as nugget effect, type, range of influence, and anisotropy. The efficiency of data-dependent FK filtering relative to data-independent spatial filters has been evaluated through simulated stochastic images by two examples. In the first example, both FK and data-independent filters are used to remove white noise in simulated images. FK filtering results in a less blurring effect than the data-independent fillers, even for a filter size as large as 9 × 9. In the second example, FK and data-independent filters are compared relative to the extraction of lineaments and components showing anisotropic variability. It was determined that square windows of the filter mask are effective only for removing Isotropie components or white noise. A nonsquare windows must be used if anisotropic components are to be filtered out. FK filtering for lineament enhancement is shown to be resistant to image noise, whereas data-independent filters are sensitive to the presence of noise. We also have applied the FK filtering to the GLORIA side-scan sonar image from the Gulf of Mexico, illustrating that FK is superior to the data-independent filters in removing noise and enhancing lineaments. The case study also demonstrate that variogram analysis and FK filtering can be used for large images if a spectral analysis and optimal filter design in the frequency domain is prohibitive because of a large memory requirement.     

The improvement of the Morlet wavelet for multi-period analysis of climate data

The multi-level dynamics of an atmosphere system exhibits temporal structures in different types of climate data. This article addresses two issues in multi-period analysis of climate data. Firstly, the advantages of the modified Morlet wavelet transform (MMWT) for analyzing multi-period structure of time series over Morlet wavelet transform (MWT) are emphasized. Secondly, the multi-period issues of temperature data are studied with MMWT through four steps: the four dominant periods of 60 year temperature data are determined with the wavelet variance; by analyzing the real part of MMWT, the warm and cold stages of the temperature data at different scales are determined, and the time intervals of the warm and cold interchange are singled out; the amplitude of each periodic component is quantitatively characterized by the amplitude of wavelet coefficients; the most intensive oscillation time intervals are computed by the squared modulus of the MMWT (MMPS).     

复小波频谱分析方法及在储层预测中的应用

针对短时窗傅立叶变换频谱分析方法存在窗函数选取不确定、分辨率固定、频谱分析精度较低等问题,采用了复小波分析方法对地震信号进行时频分析,选择复Morlet小波作为分析小波,对地震信号进行复小波变换,并将尺度域转换到频率域,获得了不同频率的时频特征水平切片;用理论模型说明了复小波频谱分析精度明显高于傅立叶变换的频谱分析.对新疆某油田实际资料的处理结果表明,复小波频谱分析能细致地反映储层的分布、位置及形态,其效果优于短时窗傅立叶变换方法.     

小波变换在确定桩裂缝、断桩及浅部缺陷中的应用

利用小波变换多分辨率分析的Mallat二进小波快速算法,引入Db5小波对桩身具有裂缝、断桩及浅部缺陷的基桩桩顶瞬态响应曲线进行多尺度小波变换。从小波变换结果的高尺度部分可以明显地发现缺陷反射波和桩底反射波,进而精确地确定缺陷位置,为补救措施的制定提供依据。     

基于不同小波变换与同态滤波结合的CBERS-02B卫星CCD图像的薄云去除

卫星CCD图像的去云处理对遥感信息的增强与提取有重要的意义,尤其是在云覆盖严重的低纬度地区。为去除CBERS-02B卫星CCD图像中薄云的影响,分别使用Mallat和à trous 2种小波变换对图像进行分解;利用同态滤波对2种小波分解图像的低频系数进行处理,衰减其低频信息;将处理后的小波低频系数与分解的高频系数进行小波重构,从而达到去云的目的。定量分析基于Mallat和à trous小波变换结合同态滤波法的去云结果表明,经à trous小波变换结合同态滤波法的去云影像所包含信息量大,细节信息丰富,去云效果较好。     

小波分析和RBF神经网络在地基沉降预测中的应用研究

地基沉降是一种危害很大的环境灾害。地基沉降的监测数据经常受降雨及工程施工等诸多外界因素的干扰,故而在沉降曲线中存在许多数据突变点。为此,提出基于小波分析与RBF神经网络相结合的新的地基沉降预测方法,首先采用小波分析对对原始监测数据进行数据去噪处理,进而得到反映实际变化的地基沉降曲线,然后采用径向基函数（RBF）神经网络方法对其进行预测,为工程设计提供依据。最后结合工程实例分析,通过多种小波去噪与预测结果的对比研究,表明3次B样条小波的去噪及预测效果最好,与实测值能较好地吻合,具有较好的工程应用前景。     

基于小波包分析的地震资料联合去噪方法研究

在地震记录中,随机噪声严重影响了有效信号的提取,为此必须进行消噪处理。这里首先使用小波包变换对不同频段的信号进行精细分离,有效信号和噪声经小波包分解后,其小波包系数将表现出不同特性,然后根据这种不同特性进行去噪处理,对小波包分析法处理后的剩余地震信号再进行KL(Karhunen-Loeve)变换,提取相关有效信号,最后对提取的有效信号进行中值滤波处理,进一步去除剩余噪声。经合成地震剖面和实际地震剖面处理实验证明,小波包分析、KL变换和中值滤波联合去噪方法,能有效地消除较强的随机噪声,提高地震剖面信噪比和分辨率。     

探地雷达小波的构造及在提高雷达信号分辨率中的应用

从理论上详细分析了探地雷达子波的形成机理,提出了一种构造探地雷达小波函数的方法。与Cauchy小波及Morlet小波相比,以这种小波作为基本小波,应用于探地雷达实际资料处理中,在提高探地雷达剖面分辨率的同时,还能保持较高的信噪比      

基于动态子波估计的吸收系数提取方法

在基于褶积模型的子波提取中,大多假设地震子波为最小相位性质。虽然在地震资料处理中进行了相位转换和Q补偿处理,但从实际地震记录中提取的地震子波,大多也表现为混合相位性质。提取吸收系数大多采用地震记录谱模拟方法,即用地震记录振幅谱平滑代替子波振幅谱,这样就会存在一个误差项,给以常规方法提取的吸收系数地震剖面属性解释带来更多的不确定性。针对以上问题,在地震叠偏剖面上,动态计算地震子波的振幅谱和相位谱,可得到任意相位性质的地震子波,采用谱比法并应用相位项提取较准确的吸收系数。利用动态子波提取的吸收系数剖面,精细显示出储层中含油气和未含油气区域的明显差异,结合嘉陵江组一段动态吸收系数平面图分析,为工区储层的精细解释提供了一种精确的方法。     

利用位场连续复小波变换识辨磁场源(上)

对国外最新研究位场连续复小波变换理论的一系列文章进行了系统总结与高度概括，并利用水平面磁荷模型的垂直分量对齐次位场小波变换系数与位场导数向上延拓的等价关系进行了详细推导与归纳。基于Poisson半群核构成一类柯西小波，它将对位场的求导以及位场向上延拓这两种运算相结合，形成一简单算子，在作用于齐次场源的位场时，其小波变换系数与位场导数向上延拓是等同的，并服从小波变换双尺度规律。利用位场小波变换系数模沿极值轴线的变化特征分别反演磁场源的形态、埋深、倾角，同时利用其相位反演磁倾角。此法实用于重磁资料自动化处理与解释。     

二代小波变换在重力场源分离中的应用

野外采集的重力数据是地下各类地质体重力场的叠加反映,如何有效地分离深源场和浅源场是重力资料处理中的一项重要内容。基于二代小波变换基本理论,在一维的基础上,给出了二维Haar预测算子的构造方法,并利用密度模型正演模拟,证明了二代小波变换实现多尺度分解的有效性,并以苏北某地区重力数据为例,应用二代小波变换开展浅部和深部重力异常场的分离。结果表明,该方法简单实用,在重力数据的场源分离中可以发挥重要的作用,对研究区域性断裂构造特征、划分构造单元、圈定隆坳格局等方面的地质问题具有参考价值。     

地震道的奇性检测与提高分辨率

地震道蕴涵有丰富的奇性特征,而地震子波的起跳点是形成地震道奇性特征的主要原因。样条函数是间段性和连续性的对立统一体。对于地震道,子波起跳点(波至)具有某种意义上的间断性。针对地震道的奇性特征,应用了奇性检测算法,具体过程为:首先以样条函数为尺度函数,构造一个低通滤波器,采用小波包的思想,定义一个算子,使低频分量逐步迭代地从原始信号中分离出,便可以对地震道信号进行奇性分解。经过理论模型和实际资料的处理,能显著提高分辨率,对于面波的去除也很理想;此算法没有任何假设条件的约束。     

基于三参数小波变换的地震瞬时属性计算方法及应用

为提高地震瞬时属性的计算精度,针对薄层反射地震信号含有快速变化的振幅和频率分量的特点,研究了新的分析小波即三参数小波,基于三参数小波变换,提出了在相空间计算地震瞬时属性的方法。三参数小波有三个可调参数,对信号做小波分析时有很高的自由度,能够很好地匹配地震子波或给定的有效信号,三参数小波与BMSW小波或其他小波相比,具有更好的时域局部化性质。实际地震资料的应用效果表明,三参数小波变换地震瞬时属性比Hilbert变换瞬时属性有更高的信噪比和分辨率,基于三参数小波变换的地震瞬时属性分析方法是识别薄层砂体的有效手段。     

基于岩石声发射信号的指数衰减型小波基构造

通过对小波变换中原函数与小波基函数关系描述发现,通用小波基函数Morlet小波、Marr小波、DOG小波、Haar小波、Daubechies小波等在满足容许条件的基础上,光滑性和紧支撑性不能同时具备的问题。在用小波分析方法研究岩石声发射信号中,困难的是找到合适的小波基函数。根据试验所得岩石声发射信号特征,采用冲击脉冲作用于二阶弱阻尼振动单位脉冲函数作为岩石声发射信号小波分析的基础函数。为拟合岩石声发射信号,提出3个构造条件,并逐一证明、优化,最后构造出带有岩石特征参数的小波基函数。经应用验证,新构造的小波基函数在处理岩石声发射信号方面比通用小波基函数更具优势,为小波分析在岩石声发射方面应用奠定了理论基础。     

井约束下的小波变换提高地震资料分辨率

小波变换同时有在时间域和频率域对信号进行局部化的特点，使其在地震资料处理中越来越发挥较大的作用。小波变换增频的幅度与地震资料有效频带的宽度有直接联系，即地震资料的有效频带越宽，剖面主频增加的幅度也就越大。通过理论和实际资料的应用表明，在井声波曲线的约束下，利用小波变换提高地震资料分辨率的幅度可以得到合理控制，大大增加了资料的可信度。     

Comparison of mineralization pattern of geochemical data in spatial and position-scale domain using new DWT- PCA approach

In the current research to determine the mineralization pattern and discuss the mineralization components, the information of position - scale domain of geochemical data has been analyzed. A new method is proposed based on coupling discrete wavelet transforms (DWT) and principal component analysis (PCA) for mineralization elements forecasting applications. The results of this study indicate the potential of DWT–PCA method for geochemical data processing. Wavelet transform (WT), as a multi-spectral analysis method, can decompose the spatial and temporal signals into different frequencies. The features of mineralization can be identified using the position - scale domain of geochemical data that may not be achievable in spatial domain. The geochemical data from the Dalli region have been processed in the spatial domain using PCA. The surface geochemical data of 30 elements have been transformed to position–scale domain using two-dimensional discrete wavelet transform (2DDWT). Wavelet functions (WFs) of Haar, Coiflet2, Biorthogonal3.3 and Symlet7 have been applied separately to decompose the geochemical data to high and low frequencies in one level. To obtain more accurate and complete information of mineralization, a new index has been presented based on wavelet coefficients. Based on this new index, significant results have been obtained by using PCA of the index. The coefficients distribution map (CDM) as a new exploratory criterion has been generated based on 2DDWT to show the geochemical distribution map (GDM). Finally, the results of WT have been compared with the results of spatial domain and the best method of wavelet for interpretation of geochemical data has been introduced. The results of geochemical data analysis by DWT–PCA approach have been confirmed by the exploratory drillings in the study area.     

二维连续复小波变换识别重力场源

利用旋转反投影法由位场一维连续母小波构造出二维连续母小波,同时也给出了位场中适应性非常强的矢量分析母小波和张量分析母小波。在理论模型上(直方棱柱体和球体)进行了二维连续小波变换,估计了场源的尺度指数,通过尺度指数与欧拉结构指数关系式得到场源的欧拉结构指数,由此可以识别出重力场源的类型,成功地实现了重力场源的快速反演。此法实用于重磁资料快速自动化处理、反演与解释。