Wavelet Characteristics of Hydrological and Dissolved Oxygen Time Series in a Lowland River

In this study, we investigated the temporal variability of dissolved oxygen and water temperature in conjunction with water level fluctuations and river discharge in the Narew lowland river reach. For this purpose, high resolution hydrologic and water quality time series have been used. Spectral analyses of time series using continuous wavelet transform scheme have been applied in order to identify characteristic scales, its duration, and localisation in time. The results of wavelet analysis have shown a great number of periodicities in time series at the inter-annual time scale when compared to the classical Fourier analysis. Additionally, wavelet coherence revealed the complex nature of the relationship between dissolved oxygen and hydrological variables dependent on the scale and localisation in time. Hence, the results presented in this paper may provide an alternative representation to a frequency analysis of time series.     

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.     

Localized cultural denoising of high-resolution aeromagnetic data

We show how a denoising technique based on the wavelet transform can be used to deal with localized noise related to DC electrified railway lines. This method, which performs localized and sharp filtering of cultural noise, was applied to high‐resolution aeromagnetic data acquired in the Phlegrean volcanic area, southern Italy, in 1999 and 2001. The helicopter‐borne survey was aimed at giving new detailed insights into the distribution of the magnetization of the area and, therefore, into the volcanological characteristics of the region. The surveyed area is characterized by the presence of towns, buildings and DC electrified railway lines whose magnetic effects influenced the measurements and were responsible for some of the measured anomalies. This cultural noise has, therefore, to be minimized as much as possible in order to allow the data to be interpreted accurately. Due to the excellent space‐scale localization properties of the discrete wavelet transform, the cultural disturbance was removed very precisely, leaving the field in the adjacent areas unchanged.     

Rainfall data simulation by hidden Markov model and discrete wavelet transformation

In many regions, monthly (or bimonthly) rainfall data can be considered as deterministic while daily rainfall data may be treated as random. As a result, deterministic models may not sufficiently fit the daily data because of the strong stochastic nature, while stochastic models may also not reliably fit into daily rainfall time series because of the deterministic nature at the large scale (i.e. coarse scale). Although there are different approaches for simulating daily rainfall, mixing of deterministic and stochastic models (towards possible representation of both deterministic and stochastic properties) has not hitherto been proposed. An attempt is made in this study to simulate daily rainfall data by utilizing discrete wavelet transformation and hidden Markov model. We use a deterministic model to obtain large-scale data, and a stochastic model to simulate the wavelet tree coefficients. The simulated daily rainfall is obtained by inverse transformation. We then compare the accumulated simulated and accumulated observed data from the Chao Phraya Basin in Thailand. Because of the stochastic nature at the small scale, the simulated daily rainfall on a point to point comparison show deviations with the observed data. However the accumulated simulated data do show some level of agreement with the observed data.     

Translation-invariant wavelet denoising of full-tensor gravity –gradiometer data

Denoising of full-tensor gravity-gradiometer data involves detailed information from field sources, especially the data mixed with high-frequency random noise. We present a denoising method based on the translation-invariant wavelet with mixed thresholding and adaptive threshold to remove the random noise and retain the data details. The novel mixed thresholding approach is devised to filter the random noise based on the energy distribution of the wavelet coefficients corresponding to the signal and random noise. The translationinvariant wavelet suppresses pseudo-Gibbs phenomena, and the mixed thresholding better separates the wavelet coefficients than traditional thresholding. Adaptive Bayesian threshold is used to process the wavelet coefficients according to the specific characteristics of the wavelet coefficients at each decomposition scale. A two-dimensional discrete wavelet transform is used to denoise gridded data for better computational efficiency. The results of denoising model and real data suggest that compared with Gaussian regional filter, the proposed method suppresses the white Gaussian noise and preserves the high-frequency information in gravity-gradiometer data. Satisfactory denoising is achieved with the translation-invariant wavelet.     

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.     

Denoising of seismic data via multi-scale ridgelet transform

Noise has traditionally been suppressed or eliminated in seismic data sets by the use of Fourier filters and, to a lesser degree, nonlinear statistical filters. Although these methods are quite useful under specific conditions, they may produce undesirable effects for the low signal to noise ratio data. In this paper, a new method, multi-scale ridgelet transform, is used in the light of the theory of ridgelet transform. We employ wavelet transform to do sub-band decomposition for the signals and then use non-linear thresholding in ridgelet domain for every block. In other words, it is based on the idea of partition, at sufficiently fine scale, a curving singularity looks straight, and so ridgelet transform can work well in such cases. Applications on both synthetic data and actual seismic data from Sichuan basin, South China, show that the new method eliminates the noise portion of the signal more efficiently and retains a greater amount of geologic data than other methods, the quality and consecutiveness of seismic event are improved obviously as well as the quality of section is improved.     

非稳态地震记录时变子波估计

地震子波估计是地震资料处理和解释中的一个关键问题,子波估计的可靠性会直接影响反褶积和反演的准确度.现有的子波估计方法分为确定型和统计型两种类型,本文通过结合这两类方法,利用确定型的谱分析法和统计型的偏度最大化方法,分别提取时变子波的振幅和相位信息,得到估计的时变子波.这种方法不需要对子波进行任何时不变或相位等的假设,具有对时变相位的估计能力.进而利用估计时变子波进行非稳态反褶积,提高地震记录的保真度,为精细储层预测和描述提供高质量的剖面.理论模型试算验证了方法的可行性,通过实际地震资料的处理应用,表明该方法能有效地提取出子波时变信息.     

基于小波包和峰度赤池信息量准则的P波震相自动识别方法

基于小波包变换和峰度赤池信息量准则(AIC), 提出了一种新的自动识别P波震相的综合方法, 即小波包-峰度AIC方法． 首先对由加权长短时窗平均比(STA/LTA)法粗略确定的P波到时前后3 s的记录进行小波包三尺度的分解与重构, 分别计算每个尺度重构信号的峰度AIC曲线并将其叠加, 叠加曲线的最小值则为P波震相到时; 然后对原始地震记录进行有限冲激响应自适应滤波以提高信噪比和识别精度; 最后将小波包-峰度AIC方法应用到合成理论地震图及实际地震记录的P波初至自动识别中. 结果表明: 初至清晰度对识别精度的影响比信噪比对其影响更大; 与单独使用加权STA/LTA方法和峰度AIC法相比, 小波包-峰度AIC法具有更强的抗噪能力, 识别精度更高; 当初至清晰时, 小波包-峰度AIC法自动识别与人工识别的P波到时平均绝对差值为(0.077±0.075) s．      

A critical analysis of the cumulative rainfall departure concept

Evaluation of trends in time-series, such as precipitation or ground water levels, is an essential element in many hydrologic evaluations, including water resource studies and planning efforts. The cumulative rainfall departure (CRD) from normal rainfall is a concept sometimes utilized to evaluate the temporal correlation of rainfall with surface water or ground water levels. Permutations of the concept have been used to estimate recharge or aquifer storativity, and in attempts to explain declining ground water levels. The cumulative departure concept has hydrologic meaning in the short term, as a generalized evaluation of either meager or abundant rainfall, and when utilized in connection with a detailed water budget analysis can be used in a predictive fashion. However, the concept can be misapplied if extended over lengthy periods. Misapplication occurs because of several factors including the separation of the mean and median in nonnormal distributions, how the choice of beginning and end points of the data can affect the results, the lack of consideration that above-average rainfall can reset the hydrologic system without mathematically eliminating the accumulated deficit, and the lack of support for the necessary inference that rainfall events and hydrologic levels widely separated in time are linked. Standard statistical techniques are available to reliably determine trends and can provide rigorous statistical measures of the significance of conclusions. Misuse of the CRD concept can lead to erroneous and unsupported conclusions regarding hydrologic relationships and can potentially result in misguided water resource decision-making.     

基于稀疏表达的OBS去噪方法

海底地震仪（OBS）采集数据的去噪处理是开展OBS震相分析及后续处理反演的基础.本文结合曲波（Curvelet）变换及压缩感知提出一种稀疏化表达的OBS去噪方法,并通过与小波变化对比等探讨去噪效果.曲波变换具有抛物尺度及识别线性异常的优点,可以稀疏地表示OBS数据,再结合压缩感知思想对稀疏表达OBS数据进行去噪处理和重构.通过对变换后的系数进行基于L₁范数的冷却阈值迭代滤波,获得最优的变换系数,本文指出基于曲波变换的冷却阈值迭代法能够很好地对OBS数据去噪.对比小波和曲波两种变换在相同迭代次数下对理论模型数据进行去噪处理,表明曲波变换得到的结果信噪比更高.利用本文方法对渤海地区采集的OBS数据进行去噪处理获得了更加清晰连续的震相,噪声压制效果更明显,为震相拾取及后续速度模型反演奠定了良好的基础.     

Estimation of periodicities in hydrologic data

Periodicites in hydrologic data are frequently estimated and studied. In some cases the periodic components are subtracted from the data to obtain the stochastic components. In other cases the physical reasons for the occurrence of these periodicities are investigated. Apart from the annual cycle in the hydrologic data, periods corresponding to the 11 year sunspot cycle, the Hale cycle and others have been detected.The conclusions from most of these studies depend on the reliability and robustness of the methods used to detect these periodicities. Several spectral analysis methods have been proposed to investigate periodicities in time series data. Several of these have been compared to each other. The methods by Siddiqui and Wang and by Damsleth and Spjotvoll, which are stepwise procedures of spectrum estimation, have not been evaluated.Two of the methods of spectral analysis proposed by Siddiqui and Wang and by Damsleth and Spjotvoll are investigated in this study by using generated and observed data. Siddiqui and Wang's method is found to be superior to the Damsleth and Spjotvoll's method.     

A physically constrained wavelet-aided statistical model for multi-decadal groundwater dynamics predictions

A physically constrained wavelet-aided statistical model (PCWASM) is presented to analyse and predict monthly groundwater dynamics on multi-decadal or longer time scales. The approach retains the simplicity of regression modelling but is constrained by temporal scales of processes responsible for groundwater level variation, including aquifer recharge and pumping. The methodology integrates statistical correlations enhanced with wavelet analysis into established principles of groundwater hydraulics including convolution, superposition and the Cooper–Jacob solution. The systematic approach includes (1) identification of hydrologic trends and correlations using cross-correlation and multi-time scale wavelet analyses; (2) integrating temperature-based evapotranspiration and groundwater pumping stresses and (3) assessing model prediction performances using fixed-block k-fold cross-validation and split calibration-validation methods. The approach is applied at three hydrogeologicaly distinct sites in North Florida in the United States using over 40 years of monthly groundwater levels. The systematic approach identifies two patterns of cross-correlations between groundwater levels and historical rainfall, indicating low-frequency variabilities are critical for long-term predictions. The models performed well for predicting monthly groundwater levels from 7 to 22 years with less than 2.1 ft (0.7 m) errors. Further evaluation by the moving-block bootstrap regression indicates the PCWASM can be a reliable tool for long-term groundwater level predictions. This study provides a parsimonious approach to predict multi-decadal groundwater dynamics with the ability to discern impacts of pumping and climate change on aquifer levels. The PCWASM is computationally efficient and can be implemented using publicly available datasets. Thus, it should provide a versatile tool for managers and researchers for predicting multi-decadal monthly groundwater levels under changing climatic and pumping impacts over a long time period.     

小波多分辨率分析时变系统参数识别算法的鲁棒性研究

针对多自由度时变系统参数识别问题,基于Daubechies小波多分辨率展开的时变参数辨识方法分析影响参数识别鲁棒性的各个因素。通过数值分析针对突变、线性慢变以及谐波快变的时变参数进行识别,研究结果表明:当基函数dbN一定时,在预先确立的分解尺度范围内,识别精度随分解尺度的增加而增加;待识别参数的频率特性对分解尺度的选择有很大影响,快时变参数比慢时变参数对分解尺度更为敏感;基函数dbN并不是影响识别精度的主要因素;在分解尺度相同的情况下,可以通过提高采样频率增加快时变参数识别精度。     

地震数据去噪中的小波方法

地震资料去噪是地震数据处理中是必不可少的步骤,随着地震勘探的进步和勘探目的层加深,对地震资料的信噪比和分辨率提出了越来越高的要求.小波分析作为一个新兴的数学方法在地震资料去噪中也有巨大的潜力.本文从小波去噪的特点出发,介绍了小波分频和小波域阈值去噪的特点,并详细总结了地震资料去噪中的小波方法,主要有面波的压制和随机噪声的衰减.最后简要叙述了地震资料小波去噪的一些问题和发展.     

MAXIMUM LIKELIHOOD ESTIMATION OF SEISMIC REFLECTION COEFFICIENTS*

A seismic trace is modeled as a moving average (MA) process both in signal and noise: a signal wavelet convolved with a reflection coefficient series plus colored random noise. Seismic reflection coefficients can be estimated from seismic traces using suitable estimation algorithms if the input wavelet is known and vice versa. The maximum likelihood (ML) algorithm is used to estimate the system order and the reflection coefficients. The system order is related to the arrival time of the latest signal in a complex seismic reflection event. The least-squares (LS) method does not provide such information. The ML algorithm makes assumptions only about the Gaussian nature of the noise. It is better suited for seismic applications since the LS method inherits the white noise assumption. The Gauss-Newton (G-N) and Newton-Raphson (N-R) optimization algorithms are used to obtain the ML and the LS estimates. Reflection coefficient estimations are affected by the choice of sampling rate of seismic data. Theoretically, the optimum choice in system identification is the Nyquist rate. Experience with synthetic data confirms the theory. In practice, good estimates of reflection coefficients are possible only up to certain pulse separations (or, equivalently, orders). This is mostly due to numerical problems with the optimization algorithms used and partly due to the limited bandwidth of seismic signals. Good estimates from data simulated using three airgun array pulses recorded with 6–128 Hz filter setting are possible up to about 40.0 ms pulse separations. Successful estimations from pinchout and thin layer simulations and well controlled offshore “bright-spots” are given.     

基于连续小波变换的大地电磁信号谱估计方法

在基于连续小波变换的大地电磁信号谱估计方法中 ,通过引入整体平均、小波系数收缩和显著性检验等统计技术 ,以提高谱估计的精度 .文中同时讨论了连续小波变换中各种参数的选取问题 ,给出了Morlet小波函数中尺度与傅里叶频率之间转换的经验公式 ,并给出了谱估计的具体算法 .结果表明 ,本文方法可有效压制较强的白噪声和局部相关噪声 .与FFT谱估计方法相比 ,该方法大大降低了对信号记录长度的要求 ,因而对大地电磁信号的处理有实际意义 .     

Estimation of periodicities in hydrologic data

Periodicites in hydrologic data are frequently estimated and studied. In some cases the periodic components are subtracted from the data to obtain the stochastic components. In other cases the physical reasons for the occurrence of these periodicities are investigated. Apart from the annual cycle in the hydrologic data, periods corresponding to the 11 year sunspot cycle, the Hale cycle and others have been detected.The conclusions from most of these studies depend on the reliability and robustness of the methods used to detect these periodicities. Several spectral analysis methods have been proposed to investigate periodicities in time series data. Several of these have been compared to each other. The methods by Siddiqui and Wang and by Damsleth and Spjotvoll, which are stepwise procedures of spectrum estimation, have not been evaluated.     

Analyses on normal background characteristics about deformation observation data on the basis of wavelet transform method

Introduction Fourier transform that summed up a series discomposed sin functions of signal has been one of the widely used methods in the field of signal process all along. While for time information be-ing thrown away by this transform, it is difficult for us to judge when a special signal occurs on the way. Though short time Fourier transform (STFT) was developed later, which can probe local features of signals, it can not reveal what is really there because uniform window functions de-fin…     

Intra-seasonal variability and wavelet characteristics of lake evaporation in comparison with hydro-meteorological data at Lake Keban (Turkey)

ABSTRACT

This study focuses on the variability of lake evaporation and also the periodic relationships among hydro-meteorological variables. The monthly hydro-meteorological data of Lake Keban were investigated by wavelet transforms. The results show that the main periodicity is on an annual scale. This periodicity is weaker for precipitation and wind speed but higher for evaporation, temperature, runoff and relative humidity. In addition to this, the continuous wavelet figures show some weak periodicities on the almost 10-year scale level but they are not continuous over time. Also, strong events on a short-term monthly scale are seen for evaporation, precipitation and runoff in 1988. This event in 1988 may be explained by the 1988 La Niña event, which was one of the strongest on record. Also, the periodicities on the 2–8-month scales in the precipitation data can be interpreted as being connected with the strong El Niño events of 1982 and 1992.

Editor D. Koutsoyiannis; Associate editor A. Carsteanu