A review of applying second-generation wavelets for noise removal from remote sensing data

The processing of remotely sensed data includes compression, noise reduction, classification, feature extraction, change detection and any improvement associated with the problems at hand. In the literature, wavelet methods have been widely used for analysing remote sensing images and signals. The second-generation of wavelets, which is designed based on a method called the lifting scheme, is almost a new version of wavelets, and its application in the remote sensing field is fresh. Although first-generation wavelets have been proven to offer effective techniques for processing remotely sensed data, second-generation wavelets are more efficient in some respects, as will be discussed later. The aim of this review paper is to examine all existing studies in the literature related to applying second-generation wavelets for denoising remote sensing data. However, to make a better understanding of the application of wavelet-based denoising methods for remote sensing data, some studies that apply first-generation wavelets are also presented. In the part of hyperspectral data, there is a focus on noise removal from vegetation spectrum.     

Wavelet-vaguelette decomposition as a tool in local geoid determination

Recently, FFT techniques are frequently applied for local gravity field modeling. Compared to FFT wavelet transformation has some advantages: — higher numerical efficiency, — data compression.The disadvantage of wavelets for gravity field modelling is that the resulting equations are sparse, but not diagonal, as in the FFT case.This paper is to show, how this drawback can be overcome by the use of different systems of orthogonal base functions for data analysis and solution synthesis.     

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      

欧美应用地球物理现状——多波地震勘探

随着多道遥测地震仪和三分量数字检波器的问世及数字处理和资料解释技术的进步，众多欧美大学、研究所及油气公司的地球物理学者针对多波地震勘探理论、资料处理模块、纵波对比试验等开展了大量的研究工作。目前深层横波震源技术尚不成熟，大量的多波技术研究仍然是针对转换波。为保证纵波资料质量，一些项目将传统检波器获得的纵波资料与三分量获得的纵波资料进行对比，即用三分量数字检波器采集的同时，仍用传统纵波检波器进行采集。此外，与三维三分量地震勘探相配套的三维多波VSP技术等也处于研究之中。     

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。     

小波分析的应用现状及展望

小波分析具有多分辨分析的特点,在时频两域都具有表征信号局部特征的能力,是一种窗口大小固定不变,但其形状可以改变的时频局部化分析方法。本文从介绍小波分析的发展简史开始,简述小波分析的基本原理,分析和总结小波分析在地球物理勘探、信号和图像处理中的最新应用成果。讨论小波分析目前应用中存在的主要问题,并展望小波分析一些有前景的应用领域。      

Statistical Classification of Different Petrographic Varieties of Aggregates by Means of Near and Mid Infrared Spectra

The increasing interest of the construction aggregates industry in reducing production costs and the costs resulting from improper use of construction materials leads to the question whether it is possible to statistically identify some rock variants by their reflectivity of near-infrared and mid-infrared light. Infrared spectroscopy allows quantitative and qualitative analysis of minerals in a reliable manner, whereas the classification of rocks is complicated by the fact that the optic behavior of minerals forming the rock often appears muted. In addition, minor constituents may dominate the spectrum. Furthermore the relevant spectra form high dimensional data, which are extremely difficult to analyse statistically, especially when curves are very similar. Common methods of multivariate statistics for this type of data, used in chemometric studies, followed by linear discriminant analysis, do not lead to acceptable classification error rates. In this paper wavelets are used in order to reduce dimensionality. As wavelets are better able to mirror local behavior of curves, they are more suitable for selecting characteristic features. The approximation is analyzed in terms of its classification properties using Mahalanobis distance or flexible discriminant analysis.     

构造高阶B-样条正交小波的一个递推算法

Ｂ－样条正交小波在信号分析方面有着重要的应用。由于Ｂ－样条正交小波随着阶次的升高将导致频域内支集缩小，因而分辨信号不同频率成分的能力将大大增强。因此，研究高阶Ｂ－样条正交小波的简便构造方法很有实际意义。本文独立地给出了一个构造高阶Ｂ－样条正交小波的适于计算机数值计算的递推算法，并给出了构造１１阶以下Ｂ－样条正交小波所需的系数，以供读者利用。同时还给出了一个在频域内计算脉冲响应系数的简便方法。     

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。     

Wavelet Analysis of Geophysical Well-log Data of Bombay Offshore Basin, India

Geophysical well-log (bore-hole) data facilitate understanding of the physical properties of the subsurface formations as a function of depth measured in a well. In the present study, the wavelet transformation technique was applied to the well-log data of three wells in the Bombay High oil field, India, in order to identify depths to the tops of oil and/or gas formation zones (pay zones). Continuous wavelet transformation (CWT) was performed on gamma-ray, resistivity, neutron porosity and velocity log data sets in order to determine the space-localization of the oil and/or gas formation zones. The choice of a mother wavelet is important and largely depends on the data under investigation. We have applied a variety of wavelets to the different log data sets to not only identify the depths to the tops of formation zones, but also to determine the optimum wavelet that best characterizes the pay zones. On examination of scalogram plots of each log corresponding to each wavelet for their better resolution in identifying the formation boundaries, we have found that the scalograms corresponding to the Gaus1 wavelet appeared to give the best resolution in identifying the depths of pay zones in all the well-log data sets of all three wells. To further validate the above observation, a histogram analysis of CWT coefficients is made. This showed that, of all the wavelets considered for the present study, Gaus1 wavelet is the most appropriate and optimum for determining the space-localization of pay zones in all the well-log data sets considered in the present study. The depths of pay zones estimated from scalogram plots of logs agree well with those provided by the Oil and Natural Gas Corporation Ltd., India.     

基于B-样条的双正交小波的构造

紧支集正交小波除Haar基外不具有对称性或反对称性。讨论基于B -样条的双正交小波的构造 ,这种双正交小波同时具有紧支集和对称性的特点     

Recovery of source time function approximations by homomorphic deconvolution of broad-band-recorded teleseismic body waves

An improved method of interactive cepstral analysis and homomorphic deconvolution is employed to recover basic wavelets, representing an approximation of source time functions, from broad-band records of teleseismic body waves radiated from nine events in the subducting lithosphere of the Kurile arc. The depths of the events ranged from 5 to 131 km. Five of them occurred above the slab of the subduction, and four inside the slab. The recovered wavelets of the deepest event correspond to an explosive/implosive-like source, and those of three shallow events are similar to the theoretical shapes for simple kinematic dislocation models. The recovered wavelets of two events inside the slab and some of the obtained impulse traces exhibit anomalies the explanation of which is at present beyond the abilities of the authors. The direction of the continuation of the study is outlined.     

胶结结构性土统一硬化模型

结构性土颗粒间的胶结使试样剪切破坏最终应力比高于相应重塑土,也限制了试样剪切时体积应变的自由发挥。在考虑结构垮塌为主的结构性土统一硬化(UH)模型基础上,将应力空间中静止的临界状态线扩展为动态的移动临界状态线。据此,通过建立新的屈服面方程并修正剪胀方程,将结构性土统一硬化(UH)模型扩展为胶结结构性土统一硬化(UH)模型。相对于原模型,新模型增加了1个模型参数,即初始胶结应力,反映土颗粒之间的初始胶结作用。通过4种结构性土试验数据与模型预测对照表明：所提模型能够较合理地描述结构性土等向压缩、常规三轴排水与不排水剪切等特性。     

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。     

天津海积软土结合水固结分析

当前近代海积软土工程沉降分析仍以传统的太沙基单向渗透固结理论为基础。而海积软土有其特殊工程地质性质 ,如 :高孔隙比、高含水量、高压缩性、低渗透性 ,计算结果很难与实际情况相符合。本文从微观角度入手 ,根据压汞和SEM资料分析影响软土固结的本质因素 ;最后借助单向压缩实验 ,对比理论固结曲线与试验压缩曲线 ,分析产生偏差的原因 ,阐述了海积软土固结机制 ,提出结合水固结新概念。     

基于匹配追踪时—频分解技术的辫状河道油藏储层预测简

The braided channel sedimentary sand is a kind of common oil reservoir, which is characteristic of poor regularity structure and complicated oil water relation. Seismic trace can be remodeled by wavelet decomposition, namely seismic trace is decomposed into a series of different attribute wavelets. The different reflection is obtained by the different attribute wavelets, thus prediction accuracy of braided channel sedimentary sand is improved. The seismic signal treated by matching pursuit method has good focusing capability of instantaneous spectrum, based on which the seismic signal is simply and rapidly remodeled by time frequency decomposition. The seismic data of Kendong 701 area were processed based on matching pursuit time frequency decomposition. The results showed that the interpretability of oil reservoir was improved and the seismic reflection characteristics and drilling data were well related. The braided channel sedimentary sands of Minghuazheng and Guantao group strata in Kendong 701 area were predicted, and the results showed that the reservoir distribution had the obvious braided channel features. Based on the predictions, three wells were located and the prediction and drilled results were consistent.     

联合数据压缩技术在地震勘探中的应用

对于“海量”的地震数据,一般压缩方法的效果不好。利用离散余弦变换编码和离散小波变换编码的联合压缩技术,对地震勘探数据进行了压缩处理,结果表明:本压缩方法能提高压缩比,保留更多的地震信号中细节信息,具有良好的压缩性能和很好的计算性能。联合压缩技术对于不同的地震数据压缩都有效果,但是压缩比不尽相同。     

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。     

Ultraspectral sounder data compression review

Ultraspectral sounders provide an enormous amount of measurements to advance our knowledge of weather and climate applications. The use of robust data compression techniques will be beneficial for ultraspectral data transfer and archiving. This paper reviews the progress in lossless compression of ultraspectral sounder data. Various transform-based, prediction-based, and clustering-based compression methods are covered. Also studied is a preprocessing scheme for data reordering to improve compression gains. All the coding experiments are performed on the ultraspectral compression benchmark dataset collected from the NASA Atmospheric Infrared Sounder (AIRS) observations.     

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。