Daubechies小波有限元求解GPR波动方程

基于可分离小波理论,由一维Daubechies尺度函数的张量积构造二维Daubechies小波基,并将它作为GPR波动方程求解的插值函数,导出了二维Daubechies小波有限元GPR方程离散格式;通过引入转换矩阵,实现小波系数空间与雷达场值之间转换.引入自由度凝聚技术,有效解决了小波有限元求解中小波单元内部自由度过多的问题,节约了计算量并方便与传统有限元法耦合.然后,详细阐述了Daubechies小波有限元联系系数计算方法,有效解决了小波有限元求解偏微分方程的难点与核心问题.最后,以两个典型GPR模型为例,对比了Daubechies小波有限元与传统有限元的雷达正演剖面图与单道波形图,结果表明:在相同的剖分方式及节点数目条件下,Daubechies小波有限元的紧支性与正交性一定程度上提高了求解效率,它与有限元法求解结果能较好地吻合,验证了Daubechies小波有限元算法的正确性.     

小波分析在前郭水化观测资料处理中的应用

本文从小波变换原理入手,选取正交小波（Daubechies小波）对前郭井近10年水化观测资料进行分析,结果表明小波分析可以很好的抑制数据的干扰,将原始信息中高频信息和低频信息分辨出来。运用小波变换对观测资料进行处理后,映震效果明显优于原始资料,一些趋势变化和短临变化更直观,异常信息更加丰富,更有利于利用前兆数据进行地震预测。     

Interaction between magnetic clouds and the heliospheric current sheet at 1 AU as it is observed by one single observation point

The effect of Magnetic Clouds (MCs) on the Heliospheric Current Sheet (HCS) local structure is yet an open question. Although it is widely accepted that a magnetic cloud has an important effect on the HCS shape, their structural relation, either the MC is part of the HCS or not, is not completely solved. Moreover, the problem grows up when trying to investigate three dimensional structures using one single observation point. We propose an approach to the MC–HCS study using magnetic models for the MC and local HCS structures, which are able of determining their relative orientation from one single spacecraft data. Three events have been selected in which an MC passage was observed close to HCS crossings. The results confirm the strong effect of MC passage on the HCS local orientation and they seem to be consistent with MCs propagating out of the HCS at 1 AU.     

Variation analysis of precipitation during past 286 years in Beijing area,China, using non‐parametric test and wavelet analysis

Non‐parametric methods including Mann–Kendall (M–K) test, continuous wavelet transform (CWT) and discrete wavelet transform analysis are applied in this paper to detect the trend and periodic trait of precipitation data series in Beijing area where the data set spans nearly 300 years from 1724 to 2009. First, the trend of precipitation variables is elaborated by the M–K test (Sequential M–K test). The results show that there is an increasing trend (the value of this trend is 1.98) at the 5%‐significance level and there are not turning points in the whole data series. Then, CWT and wavelet variance are used to check for significant periodic characteristics of data series. In the plots of wavelet transform coefficients and figure of wavelet variance, some periodic events affect the trend of the annual total precipitation series in Beijing area. 85‐year, 35‐year and 21‐year periodic events are found to be the main periodic series of long‐term precipitation data, and they are all statistically significant. Moreover, the results of non‐parametric M–K test are exhibited on seven different combinations of discrete wavelet components. D5 (32‐year periodicity) periodic component is the effective and significant component on data. It is coincident with the result (35‐year periodic event as one part of main periodicity) by using CWT analysis. Moreover, approximation mode shows potential trend of the whole data set because it is the residuals as all periodicities are removed from data series. Thus, the mode A + D5 is responsible for producing a real basic structure of the trend founded on the data. Copyright © 2012 John Wiley & Sons, Ltd.     

Solar connections of geoeffective magnetic structures

Coronal mass ejections (CMEs) and high-speed solar wind streams (HSS) are two solar phenomena that produce large-scale structures in the interplanetary (IP) medium. CMEs evolve into interplanetary CMEs (ICMEs) and the HSS result in corotating interaction regions (CIRs) when they interact with preceding slow solar wind. This paper summarizes the properties of these structures and describes their geoeffectiveness. The primary focus is on the intense storms of solar cycle 23 because this is the first solar cycle during which simultaneous, extensive, and uniform data on solar, IP, and geospace phenomena exist. After presenting illustrative examples of coronal holes and CMEs, I discuss the internal structure of ICMEs, in particular the magnetic clouds (MCs). I then discuss how the magnetic field and speed correlate in the sheath and cloud portions of ICMEs. CME speed measured near the Sun also has significant correlations with the speed and magnetic field strengths measured at 1 AU. The dependence of storm intensity on MC, sheath, and CME properties is discussed pointing to the close connection between solar and IP phenomena. I compare the delay time between MC arrival at 1 AU and the peak time of storms for the cloud and sheath portions and show that the internal structure of MCs leads to the variations in the observed delay times. Finally, we examine the variation of solar-source latitudes of IP structures as a function of the solar cycle and find that they have to be very close to the disk center.     

时程信号的Hilbert-Huang变换与小波分析/

在简要介绍时程信号的小波分析和Hilbert-Huang变换(HHT)理论的基础上，通过地震波和其它时程信号实例，对比分析了小波变换和HHT变换结果. 比较显示:HHT变换和小波变换均能用于对非平稳的信号进行分析，并能捕捉到信号变化的主要特征；与受所选母波影响较大的小波分析不同，HHT变换得到的固有模态函数是直接从原始时程数据中分离出来的，它更能反映原始数据的固有特性；小波分析得到的谱的能量在频率范围内分布较广，而HHT变换的Hilbert谱的大部分能量都集中在一定的时间和频率范围内，能清晰地刻画信号能量随时间、频率的分布. 因此，Hilbert-Huang变换不仅是对非平稳信号进行分析的有效方法，而且也是检测时程信号局部特征的有用工具.      

流体饱和多孔隙介质二维弹性波方程正演模拟的小波有限元法

本文将小波有限元法引入到流体饱和多孔隙介质二维波动方程的正演模拟中,以二维Daubechies小波的尺度函数代替多项式函数作为插值函数,构造二维张量积小波单元.引入一类特征函数解决了Daubechies小波没有显式解析表达式所带来的基函数积分值计算问题,并推导出计算分数节点上Daubechies小波函数值的递推公式,从而构造出由小波系数空间到波场位移空间的快速小波变换.数值模拟结果表明该方法是有效的.     

Geoeffectiveness of solar wind interplanetary magnetic structures

We address the geoeffectiveness of three interplanetary structures in the interplanetary space: magnetic clouds (MCs), interplanetary shocks (IPSs), and corotating interaction regions (CIRs). The geoeffectiveness is evaluated using the geomagnetic indices Kp, AE, and Dst. We find that MCs are more geoeffective than IPSs, or CIRs. The average values of magnetic indices are significantly enhanced during disturbed periods associated with MCs, IPSs and CIRs, compared to the whole interval. The highest effect is noted for MC disturbed periods.Results obtained for the three data sets are used to derive a theoretical (continuous) probability distribution function (PDF) by fitting the histograms representing the percentage of events against the intervals of magnetic index. PDFs allow estimation of the probability of a given level of geomagnetic activity to be reached after the detection, by in situ solar wind observations, of a given interplanetary structure approaching the Earth.     

磁暴主相多阶发展行星际起因的初步分析

本文利用1998～2006年与磁云有关的80起中强磁暴(Dst*≤-50 nT),对其主相期间不同发展阶数磁暴的行星际起因进行了统计分析.重点研究了鞘区磁场单独作用、磁云本体单独作用、鞘区与磁云共同作用以及其他复杂行星际结构在磁暴主相多阶发展中的相对重要性,并对导致磁暴主相增加一阶的行星际起因做了初步分析.统计结果表明...     

Long-term trend analysis using discrete wavelet components of annual precipitations measurements in Marmara region (Turkey)

The purpose of this study is to determine the possible trends in annual total precipitation series by using the non-parametric methods such as the wavelet analysis and Mann-Kendall test. The wavelet trend (W-T) analysis is for the first time presented in this study. Using discrete wavelet components of measurement series, we aimed to find which periodicities are mainly responsible for trend of the measurement series. We found that some periodic events clearly affect the trend of precipitation series. 16-yearly periodic component is the effective component on Bal?kesir annual precipitation data and is responsible for producing a real trend founded on the data. Also, global wavelet spectra and continuous wavelet transform were used for analysis to precipitation time series in order to clarify time-scale characteristics of the measured series. The effects of regional differences on W-T analysis are checked by using records of measurement stations located in different climatic areas. The data set spans from 1929 to 1993 and includes precipitation records from meteorological stations of Turkey. The trend analysis on DW components of the precipitation time series (W-T model) clearly explains the trend structure of data.     

基于第二代小波自适应网格的二维声波方程波传模拟

本文利用第二代小波多尺度分解和快速变换的特点,构造自适应计算网格.对初始计算网格上的数值解进行第二代小波变换,得到数值解对应的小波系数空间.小波系数的大小表示相邻网格上数值变化率,小波系数大的区域网格点上的数值解变化梯度大.当小波系数大于等于预设的阈值时,在小波系数对应的网格点周围插入新的计算网格点,通过阈值可以实现网格的细化,得到多尺度下层层嵌套的细化自适应网格;由有限差分法得到相应网格点的空间导数.比较数值算例得到的波场快照和计算时间,验证了该方法的有效性.     

Stream flow forecasting using neuro‐wavelet technique

This paper proposes the application of a neuro‐wavelet technique for modelling monthly stream flows. The neuro‐wavelet model is improved by combining two methods, discrete wavelet transform and multi‐layer perceptron, for one‐month‐ahead stream flow forecasting and results are compared with those of the single multi‐layer perceptron (MLP), multi‐linear regression (MLR) and auto‐regressive (AR) models. Monthly flow data from two stations, Gerdelli Station on Canakdere River and Isakoy Station on Goksudere River, in the Eastern Black Sea region of Turkey are used in the study. The comparison results revealed that the suggested model could increase the forecast accuracy and perform better than the MLP, MLR and AR models. Copyright © 2008 John Wiley & Sons, Ltd.     

Interplanetary origins of November 2004 superstorms

The sun was very active in the declining phase of solar cycle 23. Large sunspot active regions gave origin to multiple flare and coronal mass ejection (CME) activity in the interval 2003–2005. On November 2004, the active region AR 10696 was the origin of dozens of flares and many CMEs. Some events of this solar activity region resulted in two large geomagnetic storms, or superstorms (Dst??250 nT) on November 8, peak Dst=?373 nT, and on November 10, peak Dst=?289 nT. It is the purpose of this article to identify the interplanetary origins of these two superstorms. The southward-directed interplanetary magnetic fields (IMF Bs) that caused the two superstorms were related to a magnetic cloud (MC) field for the first superstorm, and a combination of sheath and MC fields for the second superstorm. However, this simple, classic picture is complicated by the presence of multiple shocks and waves. Six fast-forward shocks and, at least, two reverse waves were observed in the period of the two superstorms. A detailed analysis of these complex interplanetary features is performed in this work.     

四川地区地震前跨断层数据异常分析

概述四川7.0级以上大震前观测场地的异常情况。在核实2个大震震前异常的基础上,将传统异常判别方法进行汇总。总结近年来针对跨断层监测数据进行分析进而识别异常的方法:原始数据反映的断层活动速率异常以及转折异常。在此基础上,引入小波分析的方法对大震前的异常进行判别。对小波分解得到的两个趋势项进行分析,发现了大震与小波分解项异常的对应性。最后,基于对原始数据和小波分解项的分析,提出利用跨断层数据分析大震前兆的参考意见,为以后的震前异常研究工作提供了基础。     

On-line estimation of unit hydrographs using the wavelet-based LMS algorithm / Estimation en ligne des hydrogrammes unitaires grâce à l'algorithme des moindres carrés moyens à base d'ondelettes

Abstract

This study applies the discrete wavelet transform (DWT) to decompose the unit hydrograph, thereby generating parsimonious reparameterizations of the unit hydrograph. A model compression method is then employed to significantly compress the unit hydrograph requiring that fewer coefficients be estimated. Moreover, a wavelet-based linearly constrained least mean squares (WLCLMS) algorithm is also used to estimate on-line the wavelet coefficients of the unit hydrograph. The updated wavelet coefficients of the unit hydrograph, convoluted with effective rainfall input in the wavelet domain, allow for accurate prediction of one-step-ahead runoff in the time domain. The proposed approach allows the unit hydrographs to vary in time and accurately predicts runoff from a basin in Taiwan, thus making it highly promising for flood forecasting.     

基于广义高斯分布的地震盲反褶积方法研究

Bussgang算法是针对褶积盲源分离问题提出的,本文将其用于地震盲反褶积处理.由于广义高斯概率密度函数具有逼近任意概率密度函数的能力,从反射系数序列的统计特征出发,引入广义高斯分布来体现反射系数序列超高斯分布特征.依据反射系数序列的统计特征和Bussgang算法原理,建立以Kullback-Leibler距离为非高斯性度量的目标函数,并导出算法中涉及到的无记忆非线性函数,最终实现了地震盲反褶积.模型试算和实际资料处理结果表明,该方法能较好地适应非最小相位系统,能够同时实现地震子波和反射系数估计,有效地提高地震资料分辨率.     

高速铁路路基动土压力测试信号的小波分析

阐述了小波分析的基本原理与方法,选用Daubechies小波对某高速铁路路基土压力的现场振动测试信号进行分析处理。由此对高速列车荷载作用下,路基动土压力产生的机理及其土压力的构成进行较深入的研究。     

利用多分辨率小波网络进行地震资料反演

在讨论小波网络理论方法的基础上,研究了利用地震纪录小波多尺度分解属性资料进行虚井声波时差反演的技术方法。分析了利用地震信号进行小波分解和网络学习、训练的理论方法。研究中发现:对于相邻的地震道,较小一段的相似性比整个地震道的相似性要好。据此,利用小波时-频分析技术方法,可以把相邻道的信息外推到其它地震道上。通过以上综合研究及对实际资料进行反演计算、分析,认为小波网络与人工神经网络相比其网络结构要容易选定,并且收敛速度快。同时,利用地震资料分段时-频分析的相似性较好和小波网络学习、训练及记忆能力较强的特点,可以较好地把井旁道的高、低频信息转换到相邻道上。这样在提高分辨率的同时,又增加了反演结果的真实可靠性     

自适应多尺度第二代小波配点法探地雷达数值模拟

基于第二代小波变换的提升方案构造了插值小波,将雷达波场函数进行了二维小波变换,得到所有尺度上与计算网格相联系的小波系数和尺度系数.对所有尺度上的小波系数进行分析,根据解的局部性与小波系数阈值的控制,实现网格压缩和配点的自适应调节.保留大于给定阈值的小波系数及对应网格点,令小于给定阈值的小波系数为零,并舍弃其对应网格点.达到光滑区域采用较少的计算网格点,在奇异性较大的区域采用较多的计算网格点的目的.通过对自适应网格进行邻域校正、重构检查等附加修正,推导了场值更新的显式时间迭代方案.最后,以均匀、阶梯与复杂三个典型GPR模型为例,与常规数值计算结果对比表明：自适应小波配点法（AWCM）利用第二代小波的多尺度分解和快速变换的特点,可以使计算网格随着时间步适应解的移动和变化,允许计算资源更有效地使用,具有高压缩率,达到跟踪奇异性的目的,特别适合于探地雷达正演中波传问题的模拟.     

利用小波变换分析朝鲜核爆波形特征

基于小波变换方法,对2009-2017年黑龙江省牡丹江地震台（MDJ）记录的5次朝鲜核爆信号进行Daubechies小波8层多尺度分解,通过对比分析近似和细节部分信息,发现核爆信号进行小波分解后,在不同层存在相同特征,且有别于地震信号分解后在相应各层的特征。可见,利用该方法可有效识别朝鲜核爆。