用小波变换研究赤道西太平洋温度细结构

使用小波变换分析了赤道西太平洋暖池区的CTD资料的温度序列,表明垂向温度细结构具有自相似特征,有可能使用分数维模型来描述.计算了温度序列的奇异性指数及其概率分布,发现此分布具有近似普适的形式.非零概率的负指数意味着温度剖面可能存在奇异点.对经小波变换后的序列的周期性统计表明周期△和尺度α遵从幂律标度△～αβ,β≈1.这提示着细结构背后可能存在简单的二分串级机制.小波变换的振幅反映了温度脉动的强弱.据此可以确定脉动能量的垂向分布和能谱密度,和传统方法的比较表明小波能谱较为光滑,有利于精确测定谱斜率.     

Wavelet analysis for processing of ocean surface wave records

Wavelet analysis is a relatively new technique and in the recent years enormous interest in application of wavelets has been observed. This modern technique is particularly suitable for non-stationary processes as in contrast to the Fourier transform, (FT), the wavelet transform (WT) allows exceptional localization, both in time and frequency domains. The wavelet transform has been successfully implemented in signal and image processing, ordinary and partial differential equation theory, numerical analysis, communication theory and other fields. On the other hand, the application of the WT to ocean engineering and oceanography is rare. In this paper the WTs capability to give a full time–frequency representation of the wave signals is demonstrated. The processing of the time series of the non-stationary deep water waves, waves breaking at the tropical coral reefs and mechanically generated waves in the wave flume demonstrates the ability of the wavelet transform technique to detect a complex variability of these signals in the time–frequency domain. Various spectral representations resulting from the wavelet transform are discussed and their application for wave signals is shown.     

基于现场实测的渤海风速特性研究

风荷载是影响海洋结构物设计和安全服役最为显著的环境因素之一。利用在役海洋平台监测系统对渤海风速场展开长期监测,获得了长期的风速信息。对极值风速进行分析,利用极值Ⅰ、Ⅱ、Ⅲ型分布对风速极值的概率密度进行拟合。基于极值Ⅰ型概率分布,获得了渤海海域重现期为5 a、10 a、30 a和50 a的最大风速值。对年最大风速的脉动风分量、湍流强度、阵风因子进行了分析。考虑高频分量的影响,利用小波变换,得到了脉动风速的近似分量和细节分量,计算了实测风速的纵向和横向的空间积分尺度。对比经验脉动风谱与实测脉动风谱,证明了Davenport风速谱能够较好地拟合渤海现场风速场。     

Wave grouping characteristics in nearshore Great Lakes

The recently advanced approach of wavelet transform is applied to the analysis of wave data measured in the nearshore areas of the Great Lakes. The conventional spectrum analysis of wave time series in the frequency domain can be readily generalized to the frequency and time domain using the wavelet transform. The traditional Fourier transform approach has not been able to directly assess the time localized nature of wave groups. With the application of wavelet transformation, the relatively unexplored wave grouping characteristics come to light as the predominant feature of wave processes.     

由模拟波面分析双峰谱型海浪的统计特征

采用目前国际上最新的随机波分析方法,由协方差矩阵的循环嵌套技术,对美国国家浮标44008站2002年6月一典型的双峰海浪谱资料进行谱分析.以实测平均谱为靶谱,对随机波面进行模拟.得到模拟波面估计谱与实测谱极为相近,谱峰及谱峰频率都基本一致.说明利用模拟波面研究海浪具有代表性,它可以反映实测海浪的特征.利用实测海浪谱密度,统计波特征量的周期概率分布,得到理论周期概率密度与估计周期概率密度分布相符较好,且与模拟波面的波周期分布也较好的一致.利用Longuet-Higgins(1983)模型计算了波高-周期联合概率密度分布.得到变换高斯过程计算的波高与周期联合分布与实测情况基本相同,更好地描述了波高-周期联合概率密度分布.     

论风浪的局域结构──Ⅰ.风浪的局域结构与局域小波能谱

基于小波变换,引入了能刻画风浪局域结构的局域小波能谱。论述了风浪的整体结构与局域结构。指出了在不同时间尺度上,风浪具有不同的局域化特征。提出了风场演化过程中整体的共振在线性相互作用是否存在的质疑。     

Low dimensional chaos in the AT and GC skew profiles of DNA sequences

This paper investigates the existence of low-dimensional deterministic chaos in the AT and GC skew profiles of DNA sequences. It has taken DNA sequences from eight organisms as samples. The skew profiles are analysed using continuous wavelet transform and then nonlinear time series methods. The invariant measures of correlation dimension and the largest Lyapunov exponent are calculated. It is demonstrated that the AT and GC skew profiles of these DNA sequences all exhibit low dimensional chaotic behaviour. It suggests that chaotic properties may be ubiquitous in the DNA sequences of all organisms.     

The influence of long tides on ecosystem dynamics in the Barents Sea

The Barents Sea ecosystem has been associated with large biomass fluctuations. If there is a hidden deterministic process behind the Barents Sea ecosystem, we may forecast the biomass in order to control it. This presentation concludes, for the first time, investigations of a long data series from North Atlantic water and the Barents Sea ecosystem. The analysis is based on a wavelet spectrum analysis from the data series of annual mean Atlantic sea level, North Atlantic water temperature, the Kola section water temperature, and species from the Barents Sea ecosystem.The investigation has identified dominant fluctuations correlated with the 9.3-yr phase tide, the 18.6-yr amplitude tide, and a 74-yr superharmonic cycle in the North Atlantic water, Barents Sea water, and Arctic data series. The correlation between the tidal cycles and dominant Barents Sea ecosystem cycles is estimated to be R=0.6 or better. The long-term mean fluctuations correlate with the 74-yr superharmonic cycle. The wavelets analysis shows that the long-term 74-yr cycle may introduce a phase reversal in the identified 18-yr periods of temperature and salinity. The present analysis suggests that forced vertical and horizontal nodal tides influence the ocean's thermohaline circulation, and that they behave as a coupled non-linear oscillation system.The Barents Sea ecosystem analysis shows that the biomass life cycle and the long-term fluctuations correlate better than R=0.5 to the lunar nodal tide spectrum. Barents Sea capelin has a life cycle related to a third harmonic of the 9.3-yr tide. The life cycles of shrimp, cod, herring, and haddock are related to a third harmonic of the 18.6-yr tide. Biomass growth was synchronized to the lunar nodal tide. The biomass growth of zooplankton and shrimp correlates with the current aspect of lunar nodal tidal inflow to the Barents Sea. The long-term biomass fluctuation of cod and herring is correlated with a cycle period of about 3×18.6=55.8 yr. This analysis suggests that we may understand the Barents Sea ecosystem dynamic as a free-coupled oscillating system to the forced lunar nodal tides. This free-coupled oscillating system has a resonance related to the oscillating long tides and the third harmonic and superharmonic cycles.     

Fluctuations of peak energy and peak frequency of local wavelet energy spectrum for wind waves

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Case study of the transformation of swells propagating into Sendai Bay

A high-resolution two-dimensional map of swell wavelength and propagating direction was retrieved from a phased array type L-band synthetic aperture radar scene observed on 24 September 2006 over Sendai Bay in the Tohoku region of Japan. Features of the wavelength map were compared with a wavelength map calculated from in situ measurements of the swell period using infinitesimal amplitude surface wave theory. The maps corresponded well in most areas, although large differences appeared in the near-shore area (area I) and an area of complicated bottom topography (area II). Because the spatial resolution of swell parameters was too coarse to investigate the surface waves in area I, wavelet transform (WT) was applied along a swell ray to improve the spatial resolution. In the resulting WT wavelength map, the large difference in area I disappeared. For area II, perturbation theory was introduced for surface waves propagating obliquely on a gentle slope. The large wavelength difference in area II was well explained by the second-order solution of perturbation theory.     

台湾龟山岛东南部海域白色热泉特征分析

海底热液活动及其周边环境的调查研究是海洋科学领域的热点之一。海底热液喷口环境的物理化学参数,尤其是浅水型热液,会受到潮汐变化的影响。台湾龟山岛靠近冲绳海槽南端分布有多处浅水型热液喷口(30m)。2010年5月,浙江大学、杭州电子科技大学和台湾中山大学对该海域实施了联合考察,利用电化学传感器获得了低温热液喷口(24.834 14°N,121.961 91°E)连续87h的温度和pH现场观测数据。基于Morlet复小波变换方法,分析了浅水型热液喷口的温度和pH现场观测时间序列的变化周期,并通过与当地潮汐记录数据作比较,获得了其与潮汐信号之间的潜在关系,证实了潮汐变化是海底白色热泉喷口物理化学参数现场观测最主要的影响因素。温度和pH现场观测数据经Morlet复小波变换后的小波系数分别存在规律的12.9h和12.5h变化周期,并且温度的小波系数在准半日周期尺度与潮汐高度呈负相关变化,相关系数为-0.89;pH的小波系数情况相反,相关系数为0.76。     

风浪局域小波谱峰的涨落

将湍流研究中已得到有效应用的局域小波能谱概念引入到风浪研究.分析了实验室不同风速下风浪的局域小波能谱.结果表明,局域小波谱峰值存在着显着的涨落,涨落的方差随风速的增加而增大.这不仅体现了风浪的局域结构,还意味着通常风浪谱的应用中除了要考虑平均意义下的频谱峰值外,还必须考虑局域小波谱峰值的涨落方差.     

Wavelet and artificial neural network analyses of tide forecasting and supplement of tides around Taiwan and South China Sea

In multi-resolution analysis (MRA) by wavelet function Daubechies (db), we decompose the signal in two parts, the low and high-frequency contents. We remove the high-frequency content and reconstruct a new “de-noise” signal by using inverse wavelet transform. The calculation of tidal constituent phase-lags was made to determine the input and output data patterns used in building network structure of Artificial Neuron-Network (ANN) model. The “de-noise” signal was, then, used as the input data to improve the forecasting accuracy of the ANN model. The wavelet spectrum, conventional energy spectrum (fast Fourier transform, FFT), and harmonic analysis were used to analyze the characteristics of tidal data.Using only a very short-period data as a training data set in Artificial Neuron-Network Back-Propagate (ANN-BP) model, the developed ANN+Wavelet model can accurately predict or supply the missing tide data for a long period (1–5 years). The results also show that the concept of tidal constituent phase-lags can improve ANN model of tidal forecasting and data supplement. The addition of the wavelet analysis to ANN method can prominently improve the prediction quality.     

Autocovariance function and power spectrum of the vertical temperature gradient in the thermocline

The nature of the autocovariance function and power spectrum of time series of spike-array type is discussed. As the spacing of spikes is not easily seen directly in power spectrum, prudence should be exercised in interpreting the gradient spectrum of oceanic fine-structure. We calculated the autocovariance function and lag joint probability density of the record of the vertical profile of the vertical temperature gradient measured in the San Diego Trough. The results obtained support the results of the bispectral analysis in the previous paper (Nagata, 1978) that the predominant length scale of about 5 m has two meanings: spacing of the spikes and wavelength of a sinusoidal wave. The results seem to show the existence of nernal waves having a vertical wavelength the same as the spacing of the spikes or the thickness of the homogeneous layer in the oceanic fine-structure.     

Hilbert变换在海浪波高与周期联合分布函数中的应用

Longuet-Higgins(1983)[1]导出了波高与周期的联合分布函数,此分布函数虽然与实际数据符合良好,但存在很大的缺陷,如:由此分布函数得出的波高分布为形式较为复杂的非Rayleigh分布,很难应用于工程计算中。孙孚(1988a)[2]应用射线理论导出了一种波高与周期联合分布,虽然弥补了Longuet-Higgins的一些缺陷,但推导过程过于复杂。本文在窄谱假定下通过应用Hilbert变换方法得出新的分布函数并与前两者比较,表明Hilbert变换的方法不但简便,而且完全克服Longuet-Higgins的不足,可以方便的应用于工程计算中。本文也为Hilbert变换的方法在工程中的应用提供了理论依据。     

Application of Wavelet Algorithm to Spectral Analysis of Oceanic Waves and Offshore Structure Responses

Fourier transform (FT) is a commonly used method in spectral analysis of ocean wave and offshore structure responses,but it is not suitable for records of short length.In this paper another method,wavelet transform (WT),is applied to analyze the data of short length.The Morlet wavelet is employed to calculate the spectral density functions for wave records and simulated Floating Production Storage and Offloading (FPSO) vessels' responses.Computed wave data include simulated wave data based on JONSWAP spectr...     

Detection of fluvial sand systems using seismic attributes and continuous wavelet transform spectral decomposition: case study from the Gulf of Thailand

Fluvial sands host excellent oil and gas reservoirs in various fields throughout the world. However, the lateral heterogeneity of reservoir properties within these reservoirs can be significant and determining the distribution of good reservoirs is a challenge. This study attempts to predict sand distribution within fluvial depositional systems by applying the Continuous Wavelet Transformation technique of spectral decomposition along with full spectrum seismic attributes, to a 3D seismic data set in the Pattani Basin, Gulf of Thailand. Full spectrum seismic attributes such as root mean square and coherency help to effectively map fluvial systems down to certain depth below which imaging is difficult in the intervals of interest in this study. However, continuous wavelet transform used in conjunction with other attributes by applying visualization techniques of transparency and RGB can be used at greater depths to extract from 3D seismic data useful information of fluvial depositional elements. This workflow may help to identify different reservoir compartments within the fluvial systems of the Gulf of Thailand.     

Characterization of bedform morphology generated under combined flows and currents using wavelet analysis

The wavelet transform (WT) has been successfully implemented in many fields such as signal and image processing, communication theory, optics, numerical analysis, and fluid mechanics. However, the application of WT to describe bedform morphology in coastal areas, oceans, and rivers is rare. The present study demonstrates the capability of WT analysis to fully represent the space–frequency characteristics of signals describing bed topography generated in marine and river environments. In this study WT is used to examine the morphological characteristics of bedforms generated in two separate laboratory facilities: a wave tank and a meandering channel. In the wave tank a set of ripples superimposed upon large wave ripples were generated; while in the meandering channel, 2D and 3D migrating ripples and dunes were observed. The WT proved to be a useful tool in detecting the complex variability of the generated bedform structures. The size distribution of the bottom features such as ripples, large wave ripples and sandbars were first examined along a 2D bed profile. Later analysis studied the variability of features in the transverse direction by using the power Hovmöller. Experiments in the wave tank were conducted for a mobility number of ψ=(10, 28), and a Reynolds wave number of R_ew=(17,500, 83,500) which correspond to waves alone (WA) and to combined flow (CF) scenarios, respectively. Experiments in the meandering channel were conducted under a morphological regime that produced mainly migrating sandbars.     

二维EMD 方法在微尺度波斜率波数谱提取中的应用

进行海面微尺度波频率分析时,为消除重力波影响,引入二维 EMD(经验模态分解)方法滤除造成频率混叠的长重力波,然后进行傅立叶变换,得到海面微尺度波谱,进一步处理得到斜率波数谱。斜率波数谱提取结果表明：采用二维EMD方法可以有效滤除图像中混叠的长波信息,在此基础上进行微尺度斜率波谱计算的结果与国外已有结果基本一致。文中还将二维 EMD 方法与小波方法的处理结果进行了比对,结果表明在滤除长波的影响时,二维EMD方法具有其较明显的优势。