多维分形奇异功率谱分析与应用

地球物理信号中普遍含有噪声，消除噪声是地球物理信号处理中的关键技术之一.奇异功率谱分析（SSA）是在状态空间（又称相空间）中研究（系统）动力学、非线性科学与混沌现象的方法.本文在状态空间中通过SSA分解，研究、应用地球物理序列的尺度不变性进行多维分形滤波：通过在状态空间的SSA分解，构造了经验正交函数系（EOF）；在EOF子空间中定义了两种尺度与测度后，发现了两种测度与尺度皆在多个尺度范围内存在尺度不变性；利用这种尺度~测度的尺度不变性，设计、实现了多维分形奇异功率谱(MSSA)滤波模型；处理解释了大洋钻探（ODP）1143A孔岩芯自然反射性（NGR）资料；Fourier功率谱分析结果证明，MSSA能有效地压制噪声，提取有用信号.研究得出，嵌入维数对MSSA基本无影响（小于1/1000），多维分形滤波器（MSSA）能有效压制噪声或提取有用信号.     

GIS环境下对地球物理地球化学资料奇异性的各向异性估算及其在矿床勘探中的应用

地球物理、地球化学或遥感图像等资料的奇异性(singularity)反应了其内在的空间自相似、自仿射分形以及多维分形特性.奇异性可以应用在值估计(插值)与重建(提高分辨率)、矿产储量计算与勘探构造特征提取和环境评价中.目前,不存在时奇异值的各向异性的估计算法与应用.然而,在矿物勘探中对地球物理、地球化学与遥感资料处理解释时,各向异性是常见的现象.实践证明,矿产往往赋存在这些各项异性的次级构造与主构造的交会处.GIS是综舍各种地质、地球物理、地球化学与遥感等资料的有效工具.本文给出GIS环境下,各向异性奇异值以及有关的参数估计方法.用加拿大Nova Scotia省南半部的地球物理、地球化学资料进行了试算,计算结果与已知的地质、矿产分布模式有极好的相关性.这说明,各向异性奇异性参数在矿物勘探中有极大的应用前景.     

GIS环境下地球物理信号的奇异值分解、多维分形特征与应用

将布格异常作为二维实矩阵对其进行了奇异值分解。用其左特征向量矩阵与右特征向量矩阵的立积构造了一个二维完备(特征空间)正交基。布格异常投影到该正交基上的系数是布格异常矩阵的特征值(奇异值的平方)。奇异值代表了布格异常在其特征空间的一种功率密度。对比了密度分布面数、密度分布面数的变化率、密度分布面数的积分能量后，定义了奇异值谱半径量度下的能量测度。能量测度与能量谱半径符合(简单分形)指数或(多维分形)分段指数变化。利用教优分段方法得到这些分段点，利用这些分段点在特征空间中对地球物理场进行了重建、滤波。编制了与GIS结合的程序。用该方法分析和处理加拿大Nova Scotin的地球物理资料，并将结果与巳知的地质、金矿点进行了对比。结果表明，可以很好地提取地球物理场中的背景、异常场，该结果与岩性、构造、巳知矿点关联，可进行矿产资源评价和靶区预测。该方法还可用于各种地球物理信号的分离、图像处理、图像压缩等。作者开发的结合GIS的应用程序，使得这些分析能快速完成。     

龙马溪页岩弹性各向异性与矿物分布之间的关系探讨

岩石弹性各向异性特征是普遍存在的,但导致岩石弹性各向异性的原因复杂且仍然存在一定争议.本研究以龙马溪页岩为例,试图建立页岩弹性各向异性和矿物分布之间关系.研究使用无损超声波探测获取岩石弹性各向异性参数,并使用背散射技术获取岩石矿物分布特征.研究通过引进变异系数来描述矿物或孔裂隙在不同方向的差异性,并通过2个正交方向的变异系数建立微观异质性指标,用于表征微观尺度上矿物或孔裂隙在不同方向的差异程度.微观背散射图像显示,龙马溪组页岩主要由石英和伊利石构成,且这两种矿物和孔裂隙在X和Y面上都有定向排列特征.相应地,它们的变异系数在X面和Y面上均表现出随角度增大而降低的特征;而在Z面,石英、伊利石和孔裂隙变异系数变化不明显,这与Z面上矿物和孔裂隙无明显方向性的特点一致.无损超声波探测结果显示,波速在X和Y面上随角度增加而减小,这与主要矿物和孔裂隙变异系数变化趋势相同;而在Z面,波速变化不大,与主要矿物和孔裂隙变异系数变化不明显的特征一致.以上观测结果说明,宏观波速与矿物的微观变异系数明显相关,暗示岩石弹性各向异性与矿物分布直接相关.

     

分形噪声、多维分形滤波及地球物理测井曲线处理应用

白噪声、布郎运动以及其它满足在双对数坐标中呈一直线和信号具分形结构、自相似性或尺度无关性。地球物理信号通常表现为多个这种信号的叠加,表面为多维分形特征,研究、模拟在双对数坐标中成一直线的信号以及如何将多维分形中多个这种信号剖分出来,对于理解相应的地质、地球物理成因机制有重要意义。通过对两口井的地球物理测井曲线处理,可以初步看出,在选定的物理测井曲线中,其具多维分形特征,不同的沉积过程相互叠架在原始测井曲线中,用滤波方法分析分解信号,可以了解不同沉积作用特征并进一步分析可能的环境变化控制机制。开发的图形界面程序使得这一过程极为容易。     

大陆岩石圈流变与地震波速各向异性

岩石的流变决定了地球各时空尺度的变形,是理解大陆岩石圈构造演化的关键.岩石流变学的研究主要通过高温高压流变学实验和天然变形岩石的多尺度观测来实现,目前已经积累了大量的数据.本文总结了岩石圈不同深度主要造岩矿物,包括橄榄石、斜方辉石、单斜辉石、角闪石、斜长石、石英和云母的流变机制、组构类型以及地震学性质;介绍了岩石圈地幔橄榄岩、榴辉岩、基性麻粒岩、斜长角闪岩和长英质岩石的高温高压实验和天然变形观测进展,包括流变学强度和行为、地震波速和各向异性等;以青藏高原为例,讨论了岩石流变学研究在解译地震波速各向异性的定量化约束作用.将矿物变形组构与地震波各向异性相结合,有望在岩石圈流变学机制和结构的研究中取得重要突破.     

国家数字地震台网台站地动噪声功率谱分析

介绍了国家数字地震台站仪器的配置,通过对37个新建数字地震台站自2002年8月至2003年7月台基噪声功率谱的计算和分析,把37个国家数字地震台站的台基分为3类。为了得到台站地动噪声的变化情况,我们已经把计算地动噪声功率谱作为国家数字地震台网资料分析处理的一项日常工作进行。     

地球物理信号能量(密度)多维分形及应用

地球物理信号代表的地质地球物理过程在多种尺度上和尺度之间表现为自相似性（self-affinity)或尺度无关性（Scale Invariant)，称为地球物理信号的分形性质，多个分形地球物理信号叠加在一起表现为多维分形特征，研究多维分形地球物理信号的能量或能量密度特征，可以进行时间或空间地球物理信号的校正、奇异性研究分析，或进行不同地球物理动力学过程的分解，本文描述了地球物理时间（空间）信号的多维分形过程和功率谱密度（能量密度）与波数以及重磁场能谱密度及面积（能量）与能谱密度的多维分形关系，并用地球物理测井与重磁资料作了试算。     

灾变破坏幂律奇异性前兆提取的奇异积分变换方法

1 研究背景 幂律奇异性是材料灾变破坏及地震发生时的一个典型前兆特征(Voight,1989;Xue et al,2018).在灾变破坏发生时,系统的响应函数R = du/dU发散到无穷大,表现出临界幂律奇异性(Xue et al,2018).其中,u是系统响应量,U是系统的加载控制量.响应函数R的临界幂律奇异性是灾变破坏能量准则的体现,对大理岩、花岗岩试样进行的准静态单轴压缩实验表明,响应函数幂律奇异性指数分布在-1/2到-1之间.利用灾变破坏点处响应函数的幂律奇异性以及幂指数的分布范围,可以建立对于灾变破坏时间的实时预测方法(Voight,1988;Xue et al,2018),但噪声对灾变破坏预测却会产生较大影响.因此,准确地从包含噪声的时间序列中提取幂律前兆并确定其幂指数,对于灾变预测至关重要.本文即是针对包含噪声的信号,提出一种提取幂律奇异性前兆的方法.     

多道奇异谱分析压制强振幅窄带随机噪声研究

地震数据残留噪声往往不满足白噪假设,而是与地震数据频带一致的窄带非白噪随机噪声,传统的去噪方法难以进行彻底的压制,其残留的噪声会造成地质解释认识的多解性.文中就多道奇异谱分析降秩去噪、阻尼多道奇异谱分析降秩去噪、三维曲波变换去噪方法对此类强振幅噪声压制效果进行了研究,阻尼多道奇异谱分析去噪方法在降秩过程中通过对噪声进行...     

Multifractal modelling and spectrum analysis: Methods and applications to gamma ray spectrometer data from southwestern Nova Scotia, Canada

Multifractal theory was developed for handling scale invariant fields instead of geometry only[1―4]. From a multifractal point of view, some fractal models, ordinary physical processes and relevant probability distribution types can be considered as special cases of multifractal models which provides new insight into the interrelationships between systems and subjects. For example, the low order moment exponents τ (0), τ (1), τ (2) or τ ″(1) obtained by means of the moment method determi…     

Improvement of Nakamura technique by singular spectrum analysis

In this work we investigate the application of the Singular Spectrum Analysis to improve Nakamura Technique. The SSA has a wide and multidisciplinary range of applications; it allows a time series to be decomposed into different components, e.g. the signal itself, as well as various noise components, which can be subsequently removed from the data. Removal of the minor component of the data can lead to significant improvements in the identification of the system. In this paper the use of SSA Technique allows to optimize the signal to noise ratio before computing the classical Nakamura spectral ratios. A number of typical applications are also presented.     

Application of singular spectrum analysis to identify the degrading structure using deteriorating distributed element model

Reinforced concrete structure may exhibit significant inelastic hysteretic behavior when subject to strong earthquake excitation. To investigate such an inelastic behavior, in this study, a new system identification technique is applied by using the deteriorating distributed element (DDE) model to simulate the hysteretic behavior of a degrading structure. Through the advanced signal processing technique, the multiple singular spectrum analysis (SSA) and the nonlinear SSA, the recorded inelastic restoring force of a deteriorating structure can be decomposed into several independent additive components in its sequentially degrading order and with decreasing weight. With each decomposed hysteresis loop, the model parameters of the DDE model are identified. The evolutionary properties of the progressive stiffness degradation behavior of reinforced concrete structure can be observed from the identified model parameters. Finally, comparison on the physical properties of the identified DDE model with respect to the seismic response data of the deteriorating structure is also discussed. The result shows that the proposed identification technique can have a good estimation on the seismic behavior of the degrading structure. Copyright © 2012 John Wiley & Sons, Ltd.     

基于奇异谱分析的重磁位场分离方法

奇异谱分析是一种近年兴起的时间序列分析方法,它利用降秩原理实现信号分离.该方法将数据空间投影到不同特征的子空间中,并用奇异值来表征这些子空间的性质,最后通过截取奇异值实现数据的重构.重磁位场分离可以看成一种多信号叠加的分离问题.不同特征的重磁异常具有不同特征的奇异谱,这是奇异谱分析用于解决位场分离问题的应用基础.本文通过建立理论模型,分析重磁异常的奇异谱特征,得出适用于重磁位场分离的最优参数选择方法,并与传统方法进行比较.对比发现,无论是横向叠加模型、垂向叠加模型还是斜向叠加模型,奇异谱分析都具有很好的分离效果.最后,将奇异谱分析用于鄂东南某矿区的重力资料处理中,实现弱异常的识别和分离.

     

Multifractal analysis as a tool for validating a rainfall model

A multifractal analysis was carried out in order to validate the simulation of hourly rainfall records of a local climate model for the Iberian Peninsula. Observed and simulated hourly rainfall data from four locations in Andalusia (southern Spain) were used to carry out the study. In order to detect the influence of the length of the data series on the results, two different sizes were used for the real data: 4 years, and 20 years. The results show that algebraic tails are required to fit the probability distribution of extreme rain event sizes, and rain and dry event durations for both kinds of rainfall data. Similar results are found for the extreme rain event sizes and dry event durations fits when the real and synthetic data are considered. Nevertheless, some differences appear in the cases of rain event durations. The detection of the presence of a first‐order multifractal phase transition associated with a critical moment in the empirical moment scaling exponent function and the results of the extreme rain event sizes fits, reveal that real rainfall is a self‐organized criticality (SOC) process. That behaviour is less evident in the simulated rainfall series. The same ‘synoptic maximum’ value was found for each place with both types of rainfall data. A time clustering analysis was carried out applying the count‐based periodogram and the Fano factor methods. Some periodicities have been detected in the periodograms, especially for the longest real rainfall data series. Copyright © 2007 John Wiley & Sons, Ltd.     

Multifractal analysis of earthquakes

Multifractal properties of the epicenter and hypocenter distribution and also of the energy distribution of earthquakes are studied for California, Japan, and Greece. The calculatedD _q-q curves (the generalized dimension) indicate that the earthquake process is multifractal or heterogeneous in the fractal dimension. Japanese earthquakes are the most heterogeneous and Californian earthquakes are the least. Since the earthquake process is multifractal, a single value of the so-called fractal dimension is not sufficient to characterize the earthquake process. Studies of multifractal models of earthquakes are recommended. Temporal changes of theD _q-q curve are also obtained for Californian and Japanese earthquakes. TheD _q-q curve shows two distinctly different types in each region; the gentle type and the steep type. The steeptype corresponds to a strongly heterogeneous multifractal, which appears during seismically active periods when large earthquakes occur.D _q for smallq or negativeq is considerably more sensitive to the change in fractal structure of earthquakes thanD _q forq2. We recommend use ofD _q at smallq to detect the seismicity change in a local area.     

基于奇异谱分析的静态相对重力观测重力固体潮提取

针对相对重力测量数据中存在的重力固体潮信号,本文提出将奇异谱分析方法（Singular Spectrum Analysis,SSA）应用到相对重力测量数据处理中,在不需要测站坐标等先验信息的条件下从相对重力数据中提取重力固体潮,提供了一种获取重力固体潮的新思路.采用模拟的相对重力数据进行实验,利用SSA方法和小波变换方法分别从模拟信号中提取重力固体潮并进行结果对比,SSA获取的重力固体潮与理论值残差RMS为0.3 μGal,小波方法获取的残差RMS为1.6 μGal.利用CG-5相对重力仪实测数据进行实验,提出一种利用SSA外推时间序列来削弱边界效应的新思路,实验结果显示采用这种方法后重力固体潮值与理论值残差序列的RMS和STD均有所减小.通过实验发现削弱边界效应后SSA提取的重力固体潮与采用Tamura潮波表计算的重力固体潮理论值残差RMS值为2.2 μGal.利用SSA提取的零点漂移值与最小二乘拟合得到的结果基本一致,十天内的差值小于0.4 μGal/d.

     

Site response analysis of Vartholomio W-Greece from singular spectrum analysis of microtremor and weak motion data

Twenty six sites were instrumented in the city of Vartholomio following the December 2, 2002 Ms 6.0 earthquake. Thirty weak events from the aftershock sequence as well as microtremors were used to identify amplifications due to geological site effects. Horizontal-to-vertical spectral ratios (HVSR—Nakamura estimates) and weak events ratios were calculated and the singular spectrum analysis (SSA) method was used. The results showed that the effects of SSA on the stability of the frequency peak and amplitude distribution of HVSR for both weak motion and microtremors. The data analysis confirms the role of near surface geology in causing locally significant variations of the predominant frequencies and amplitudes of ground shaking as already inferred from the distribution of damages. The site response spectra exhibited significant peaks within the range of 1.5–2.6 Hz and the amplification factor did not exceed 6.5. Finally the parts of the HVSR ratios from ～0.2 up to 10 Hz were used, in order to create an automatic optimal zonation of the study area using a genetic algorithm. This procedure resulted in the division of the city into 2 main zones.