基于SW统计量的自适应时频峰值滤波压制地震勘探随机噪声研究

由于金属矿区地震记录中随机噪声性质复杂且信噪比低,常规降噪方法难以达到预期的滤波效果.时频峰值滤波(TFPF)方法是实现低信噪比地震勘探记录中随机噪声压制的有效方法,但其在复杂地震勘探随机噪声下时窗参数优化问题仍难以解决.本文充分利用地震勘探噪声的统计特性,结合Shapiro-Wilk(SW)统计量辨识地震勘探记录中的微弱有效信号,提出基于SW统计量的自适应时频峰值滤波降噪方法(S-TFPF).在S-TFPF方案中,对于有效信号集中区,S-TFPF方法根据信号频率特征,选择有利于信号保持的较短时窗长度;对于噪声集中区,按噪声方差自适应增加时窗长度,增强随机噪声压制能力.S-TFPF应用于合成记录和共炮点记录的滤波结果表明,与传统时频峰值滤波方法相比,S-TFPF方法可以有效抑制低信噪比地震勘探记录中的随机噪声,更好地恢复出同相轴.     

Interpretation of potential fields from inclined dikes in the wavenumber domain

The interpretation of the gravity and magnetic fields from inclined dikes has been studied with artifical data contaminated by various noise components: base level, linear trend, and random noise. A Gaussian window was applied to the data prior to transformation to reduce the influence of noise as demonstrated by an analysis of the horizontal cylinder. The case of the dike is more complicated due to the fact that its spectrum has a number of zeroes at wavenumbers which are inversely related to the width of the dike. Around these wavenumbers, especially the random noise distorts the spectrum making interpretation ambiguous.     

Gamma random field simulation by a covariance matrix transformation method

In studies involving environmental risk assessment, Gaussian random field generators are often used to yield realizations of a Gaussian random field, and then realizations of the non-Gaussian target random field are obtained by an inverse-normal transformation. Such simulation process requires a set of observed data for estimation of the empirical cumulative distribution function (ECDF) and covariance function of the random field under investigation. However, if realizations of a non-Gaussian random field with specific probability density and covariance function are needed, such observed-data-based simulation process will not work when no observed data are available. In this paper we present details of a gamma random field simulation approach which does not require a set of observed data. A key element of the approach lies on the theoretical relationship between the covariance functions of a gamma random field and its corresponding standard normal random field. Through a set of devised simulation scenarios, the proposed technique is shown to be capable of generating realizations of the given gamma random fields.     

Geostatistical simulation of random fields with bivariate isofactorial distributions by adding mosaic models

This work deals with the geostatistical simulation of a family of stationary random field models with bivariate isofactorial distributions. Such models are defined as the sum of independent random fields with mosaic-type bivariate distributions and infinitely divisible univariate distributions. For practical applications, dead leaf tessellations are used since they provide a wide range of models and allow conditioning the realizations to a set of data via an iterative procedure (simulated annealing). The model parameters can be determined by comparing the data variogram and madogram, and enable to control the spatial connectivity of the extreme values in the realizations. An illustration to a forest dataset is presented, for which a negative binomial model is used to characterize the distribution of coniferous trees over a wooded area.     

Bootstrap approaches for spatial data

Generation of replicates of the available data enables the researchers to solve different statistical problems, such as the estimation of standard errors, the inference of parameters or even the approximation of distribution functions. With this aim, Bootstrap approaches are suggested in the current work, specifically designed for their application to spatial data, as they take into account the dependence structure of the underlying random process. The key idea is to construct nonparametric distribution estimators, adapted to the spatial setting, which are distribution functions themselves, associated to discrete or continuous random variables. Then, the Bootstrap samples are obtained by drawing at random from the estimated distribution. Consistency of the suggested approaches will be proved by assuming stationarity from the random process or by relaxing the latter hypothesis to admit a deterministic trend. Numerical studies for simulated data and a real data set, obtained from environmental monitoring, are included to illustrate the application of the proposed Bootstrap methods.     

一维溶质运移源(汇)项系数反演的迭代正则化算法

对于多孔介质中发生物理化学反应的溶质运移现象,可以用带有非线性源（汇）项作用的一维对流弥散-反应扩散方程来描述,但方程中反映溶质吸附/解吸附能力的源(汇)项系数往往是未知的. 本文讨论了基于出流端浓度观测数据的源项系数反演问题. 根据Tikhonov正则化和矩阵的奇异值分解系统,建立了一种离散的迭代正则化算法,给出了算法实现步骤.数值模拟结果表明该算法不仅精度高,而且对于数据的随机扰动具有稳定性.最后应用建立的算法反演计算了一个具体的土柱试验源项系数,数值结果也表明文中所构造算法的有效性.     

Random field characteristics of earthquake occurrence and test of earthquake occurrence rate

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低信噪比地震资料FDOC-seislet变换阈值消噪方法研究

地震数据本质上是时变的,不仅有效同相轴表现出确定性信号的时变特征,而且复杂地表和构造条件以及深部探测环境总是引入时变的非平稳随机噪声.标准的频率-空间域预测滤波只适合压制平面波信号假设下的平稳随机噪声,而处理非平稳地震随机噪声时,需要将数据体分割为小窗口进行分析,但效果不够理想,而传统非预测类随机噪声压制方法往往适应性不高,因此开发能够保护地震信号时变特征的随机噪声压制方法具有重要的工业价值.压缩感知是近年出现的一个新的采样理论,通过开发信号的稀疏特性,已经在地震数据处理中的数据插值以及噪声压制中得到了应用.本文系统地分析了压缩感知理论框架下的地震随机噪声压制问题,建立了阈值消噪的数学反演目标函数;针对时变有效信息具有的可压缩性,利用有限差分算法求解炮检距连续方程,构建有限差分炮检距连续预测算子(FDOC),在seislet变换框架下,提出一种新的快速稀疏变换域———FDOC-seislet变换,实现地震数据的高度稀疏表征;结合非平稳随机噪声不可压缩的特征,提出了一种整形迭代消噪方法,该方法是一种广义的迭代收缩阈值(IST)算法,在无法计算稀疏变换伴随算子的条件下,仍然能够对强噪声环境中的时变有效信息进行有效恢复.通过对模型数据和实际数据的处理,验证了FDOC-seislet稀疏变换域随机噪声迭代压制方法能够在保护复杂构造地震波信息的前提下,有效地衰减原始数据中的强振幅随机噪声干扰.     

基于脉冲检测的混合震源数据分离

混合震源采集技术相对于传统地震数据采集具有改善成像质量、提高采集效率的优势.减小混合炮中单炮之间的随机延时范围能够有效的提高采集效率,但这也给之后的混采数据分离带来了影响.混采数据经伪分离后非共炮域数据中的混叠噪声明显更加集中,不利于对混叠噪声进行压制.本文提出基于脉冲检测方法对混采数据进行分离,并且与迭代的多级中值滤波方法作对比,时间延时范围较大时,两种方法都能得到很好的分离结果;时间延时范围较小时,本文方法能更有效的去除混叠噪声,同时也能更好的保留细节信息.实际数据计算结果表明,本文方法一定程度上还能够有效压制其他随机噪声.     

Porosity of bimodal and trimodal sediment mixtures

This study focuses on the prediction of the porosity of nonuniform sediment mixtures,considering the effects of particle packing.A random particle packing model has been developed for the porosity of bimodal mixtures by extending the existing random particle filling theory.Coefficients in the developed model are calibrated by fitting the model to measured data for a variety of bimodal mixtures,including spherical glass particles,rounded quarry grains,and natural sediments.The model coefficients ...     

Application of random sets to model uncertainties of natural entities extracted from remote sensing images

Remotely sensed images as a major data source to observe the earth, have been extensively integrated into spatial-temporal analysis in environmental research. Information on spatial distribution and spatial-temporal dynamic of natural entities recorded by series of images, however, usually bears various kinds of uncertainties. To deepen our insight into the uncertainties that are inherent in these observations of natural phenomena from images, a general data modeling methodology is developed to embrace different kinds of uncertainties. The aim of this paper is to propose a random set method for uncertainty modeling of spatial objects extracted from images in environmental study. Basic concepts of random set theory are introduced and primary random spatial data types are defined based on them. The method has been applied to dynamic wetland monitoring in the Poyang Lake national nature reserve in China. Four Landsat images have been used to monitor grassland and vegetation patches. Their broad gradual boundaries are represented by random sets, and their statistical mean and median are estimated. Random sets are well suited to estimate these boundaries. We conclude that our method based on random set theory has a potential to serve as a general framework in uncertainty modeling and is applicable in a spatial environmental analysis.     

压制空间非平稳地震勘探随机噪声的ROAD径向时频峰值滤波算法

径向时频峰值滤波算法是一种有效保持低信噪比地震勘探记录中反射同相轴的随机噪声压制方法,但该算法对空间非平稳地震勘探随机噪声压制效果不理想.本文研究空间非平稳地震勘探随机噪声,即各道噪声功率不同的地震勘探随机噪声,其在径向滤波轨线上表征近似脉冲噪声,在径向时频峰值滤波过程中干扰相邻道滤波结果.为了减小空间非平稳随机噪声的影响,本文提出一种基于绝对级差统计量(ROAD)的径向时频峰值滤波随机噪声压制方法.该方法首先根据径向轨线上信号的绝对级差统计量检测空间非平稳地震勘探随机噪声,然后结合局部时频峰值滤波和径向时频峰值滤波压制地震勘探记录中的随机噪声.将ROAD径向时频峰值滤波方法应用于合成记录和实际共炮点地震记录,结果表明ROAD径向时频峰值滤波方法可以压制空间非平稳地震勘探随机噪声且不损害有效信号,有效抑制随机噪声空间非平稳对滤波结果的影响.与径向时频峰值滤波相比,ROAD径向时频峰值滤波方法更适用于空间非平稳地震勘探随机噪声压制.     

Multi-Gaussian kriging and simulation in the presence of an uncertain mean value

The multi-Gaussian model is used in geostatistical applications to predict functions of a regionalized variable and to assess uncertainty by determining local (conditional to neighboring data) distributions. The model relies on the assumption that the regionalized variable can be represented by a transform of a Gaussian random field with a known mean value, which is often a strong requirement. This article presents two variations of the model to account for an uncertain mean value. In the first one, the mean of the Gaussian random field is regarded as an unknown non-random parameter. In the second model, the mean of the Gaussian field is regarded as a random variable with a very large prior variance. The properties of the proposed models are compared in the context of non-linear spatial prediction and uncertainty assessment problems. Algorithms for the conditional simulation of Gaussian random fields with an uncertain mean are also examined, and problems associated with the selection of data in a moving neighborhood are discussed.     

Widely linear denoising of multicomponent seismic data

Seismic data processing is a challenging task, especially when dealing with vector-valued datasets. These data are characterized by correlated components, where different levels of uncorrelated random noise corrupt each one of the components. Mitigating such noise while preserving the signal of interest is a primary goal in the seismic-processing workflow. The frequency-space deconvolution is a well-known linear prediction technique, which is commonly used for random noise suppression. This paper represents vector-field seismic data through quaternion arrays and shows how to mitigate random noise by proposing the extension of the frequency-space deconvolution to its hypercomplex version, the quaternion frequency-space deconvolution. It also shows how a widely linear prediction model exploits the correlation between data components of improper signals. The widely linear scheme, named widely-linear quaternion frequency-space deconvolution, produces longer prediction filters, which have enhanced signal preservation capabilities shown through synthetic and field vector-valued data examples.     

一种神经网络改进小波的地震数据随机噪声去除方法

地震资料的有效信号反射弱,且易受多次波的影响,不可避免地存在随机噪声干扰。提出一种基于神经网络改进小波的地震数据随机噪声去除方法,采用神经网络模型,识别出随机噪声信号,对该信号进行小波包分解,获取多类别随机噪声信号,采用级联BP神经网络模型提取出多类别随机噪声信号,实现地震数据的随机信号压制。实验结果显示,这种改进小波方法对地震数据随机噪声信号的去噪效果较好,在复杂沉积地质结构被探测介质的地震数据随机噪声压制方面具有较强的适用性。     

Incorporation of a Non-linear Image Filtering Technique for Noise Reduction in Seismic Data

Seismic noise is a fundamental part of seismic data which cannot be avoided when conducting any seismic survey. It consists of coherent and random noise. Noise removal or filtering is one of the major concerns in the field of seismic processing. In this paper, we introduce an image filtering technique based on a detection-estimation algorithm for Gaussian and random noise removal in seismic data, namely the trilateral filter, based on a statistic called rank-ordered absolute differences. The non-linear and adaptive behaviour of this filter makes it very robust in the presence of random and coherent noise, in addition to its computational simplicity and its ability to automatically identify noise in data. We have modified the strategy of trilateral filtering by adapting the rank-ordered absolute differences formula in order to extract the signal component. We have successfully used this filter for the removal of surface waves and random spiky noise from synthetic and field data. Results are very encouraging and show the superiority of this filter compared with other filters, particularly when used recursively.     

Functional data clustering using K-means and random projection with applications to climatological data

In this paper, an efficient pattern recognition method for functional data is introduced. The proposed method works based on reproducing kernel Hilbert space (RKHS), random projection and K-means algorithm. First, the infinite dimensional data are projected onto RKHS, then they are projected iteratively onto some spaces with increasing dimension via random projection. K-means algorithm is applied to the projected data, and its solution is used to start K-means on the projected data in the next spaces. We implement the proposed algorithm on some simulated and climatological datasets and compare the obtained results with those achieved by K-means clustering using a single random projection and classical K-means. The proposed algorithm presents better results based on mean square distance (MSD) and Rand index as we have expected. Furthermore, a new kernel based on a wavelet function is used that gives a suitable reconstruction of curves, and the results are satisfactory.     

Preliminary streamflow data analyses prior to water resources planning study / Analyses préliminaires des données de débit en vue d'une étude de planification des ressources en eau

Abstract

The analysis and use of hydrological data for decision making in water resources planning and management can only be meaningful if the data possess the appropriate characteristics. In general, it is customary that data being analysed are consistent, free of trend and constituting a stochastic process whose random component is described by an appropriate probability distribution hypothesis. This paper describes, using hypothetical numerical examples where possible, some of the commonly used tests for establishing the presence or otherwise of these attributes in hydrological data series. The tests were then applied to actual streamflow data records from seven sites, in Iran and England, which formed the basis of an extensive water resources planning study carried out recently. In general, the data from all seven sites possessed the right attributes, which made their use in the wider water resources planning study straightforward.     

二维叠后地震数据的平稳随机介质参数估计

随机介质参数估计是随机介质理论应用于地震勘探的关键.本文提出了一种从二维叠后地震数据中估计平稳随机介质参数的方法.文中阐述了二维叠后地震数据与随机介质波阻抗模型的关系,以及随机介质自相关函数参数的估计原理和方法,并结合实例详细介绍了应用功率谱法进行随机介质参数估计的具体步骤;通过多个二维理论模型的估计试验,验证了方法的可行性和正确性;还对实际地震数据进行了随机介质参数的估计试验,结果表明,随机介质参数可以为三角洲沉积相的进一步划分提供参考,反映了该方法有较好的应用前景.相比前人的研究,本文所提出的随机介质参数估计方法是一种真正的二维算法,特别是能给出自相关角度θ的估计,这种基于功率谱的估计方法具有直观且高效率的优点,但也存在着误差较大的问题,需要进一步的改进和完善.     

Return period of bivariate distributed extreme hydrological events

 Extreme hydrological events are inevitable and stochastic in nature. Characterized by multiple properties, the multivariate distribution is a better approach to represent this complex phenomenon than the univariate frequency analysis. However, it requires considerably more data and more sophisticated mathematical analysis. Therefore, a bivariate distribution is the most common method for modeling these extreme events. The return periods for a bivariate distribution can be defined using either separate single random variables or two joint random variables. In the latter case, the return periods can be defined using one random variable equaling or exceeding a certain magnitude and/or another random variable equaling or exceeding another magnitude or the conditional return periods of one random variable given another random variable equaling or exceeding a certain magnitude. In this study, the bivariate extreme value distribution with the Gumbel marginal distributions is used to model extreme flood events characterized by flood volume and flood peak. The proposed methodology is applied to the recorded daily streamflow from Ichu of the Pachang River located in Southern Taiwan. The results show a good agreement between the theoretical models and observed flood data. The author wishes to thank the two anonymous reviewers for their constructive comments that improving the quality of this work.