Wavelet analysis of the annual discharge records of the world’s largest rivers

The determination of the temporal variability of water resources is of high importance with respect to long-term water policy. This contribution provides a wavelet-based global analysis of 55 large river discharge fluctuations located on the five continents.     

Stochastic modeling of solute transport in 3-D heterogeneous porous media with random source condition

During probabilistic analysis of flow and transport in porous media, the uncertainty due to spatial heterogeneity of governing parameters are often taken into account. The randomness in the source conditions also play a major role on the stochastic behavior in distribution of the dependent variable. The present paper is focused on studying the effect of both uncertainty in the governing system parameters as well as the input source conditions. Under such circumstances, a method is proposed which combines with stochastic finite element method (SFEM) and is illustrated for probabilistic analysis of concentration distribution in a 3-D heterogeneous porous media under the influence of random source condition. In the first step SFEM used for probabilistic solution due to spatial heterogeneity of governing parameters for a unit source pulse. Further, the results from the unit source pulse case have been used for the analysis of multiple pulse case using the numerical convolution when the source condition is a random process. The source condition is modeled as a discrete release of random amount of masses at fixed intervals of time. The mean and standard deviation of concentration is compared for the deterministic and the stochastic system scenarios as well as for different values of system parameters. The effect of uncertainty of source condition is also demonstrated in terms of mean and standard deviation of concentration at various locations in the domain.     

Effect of permeability variations on solute transport in highly heterogeneous porous media

The effect of aquifer heterogeneity on flow and solute transport in two-dimensional isotropic porous media was analyzed using the Monte Carlo method. The two-dimensional logarithmic permeability (ln K) was assumed to be a non-stationary random field with its increments being a truncated fractional Lévy motion (fLm). The permeability fields were generated using the modified successive random additions (SRA) algorithm code SRA3DC [http://www.iamg.org/CGEditor/index.htm]. The velocity and concentration fields were computed respectively for two-dimensional flow and transport with a pulse input using the finite difference codes of MODFLOW 2000 and MT3DMS. Two fLm control parameters, namely the width parameter (C) and the Lévy index (α), were varied systematically to examine their effect on the resulting permeability, flow velocity and concentration fields. We also computed the first- and second-spatial moments, the dilution index, as well as the breakthrough curves at different control planes with the corresponding concentration fields. In addition, the derived breakthrough curves were fitted using the continuous time random walk (CTRW) and the traditional advection-dispersion equation (ADE). Results indicated that larger C and smaller α both led to more heterogeneous permeability and velocity fields. The Lévy-stable distribution of increments in ln K resulted in a Lévy-stable distribution of increments in logarithm of the velocity (ln v). Both larger C and smaller α created sharper leading edges and wider tailing edges of solute plumes. Furthermore, a relatively larger amount of solute still remained in the domain after a relatively longer time transport for smaller α values. The dilution indices were smaller than unity and increased as C increased and α decreased. The solute plume and its second-spatial moments increased as C increased and α decreased, while the first-spatial moments of the solute plume were independent of C and α values. The longitudinal macrodispersivity was scale-dependent and increased as a power law function of time. Increasing C and decreasing α both resulted in an increase in longitudinal macrodispersivity. The transport in such highly heterogeneous media was slightly non-Gaussian with its derived breakthrough curves being slightly better fitted by the CTRW than the ADE, especially in the early arrivals and late-time tails.     

小波分析及其在我国地球物理学研究中的应用进展

小波分析在当前数学领域、物理领域和地质领域中,是一个发展迅速的分析工具,它同时具有理论上的深刻性和应用的广泛性.由于小波具有时频分析的重要特性,已经在地球物理的相关问题研究中显示其独特的作用.本文较全面的介绍了小波分析理论基础、发展历史,及其在我国地球物理学研究中的应用进展,并在此基础上对地球物理领域小波分析所存在的问题以及应用前景作了进一步的分析.     

Wavelet analysis of lightning return stroke

In this investigation, time series consisting of electric field waveforms of 15 positive return strokes and 10 negative return strokes were analyzed. The data came from a summer thunderstorm in March in a range of about 200 km around São José dos Campos, São Paulo. The electric field recording system consisted of a flat plate antenna with a decay time constant of 260 μs and a sample rate of 800,000 samples per second. The bandwidth observed was up to 100 kHz and the recording system was synchronized with GPS time and located at São José dos Campos. Wavelet analysis of the electric field waveforms was done in order to investigate the behavior of the return stroke spectrum in time. The return stroke was suggested to be divided into two portions: initial stage and overshoot (for far return stroke) and initial stage and ramp (for close return stroke). The return stroke power spectrum was observed to be distributed in a frequency range with the peak value also distributed in a fraction of this range. Power peaks for ramps are stronger than power peaks for initial stage and overshoot. Finally, it was observed how powerful the wavelet is in the analysis of lightning.     

What drives high flow events in the Swiss Alps? Recent developments in wavelet spectral analysis and their application to hydrology

Extreme hydrological events are often triggered by exceptional co-variations of the relevant hydrometeorological processes and in particular by exceptional co-oscillations at various temporal scales. Wavelet and cross wavelet spectral analysis offers promising time-scale resolved analysis methods to detect and analyze such exceptional co-oscillations. This paper presents the state-of-the-art methods of wavelet spectral analysis, discusses related subtleties, potential pitfalls and recently developed solutions to overcome them and shows how wavelet spectral analysis, if combined to a rigorous significance test, can lead to reliable new insights into hydrometeorological processes for real-world applications. The presented methods are applied to detect potentially flood triggering situations in a high Alpine catchment for which a recent re-estimation of design floods encountered significant problems simulating the observed high flows. For this case study, wavelet spectral analysis of precipitation, temperature and discharge offers a powerful tool to help detecting potentially flood producing meteorological situations and to distinguish between different types of floods with respect to the prevailing critical hydrometeorological conditions. This opens very new perspectives for the analysis of model performances focusing on the occurrence and non-occurrence of different types of high flow events. Based on the obtained results, the paper summarizes important recommendations for future applications of wavelet spectral analysis in hydrology.     

3D multi-fractal analysis of porous media using 3D digital images: considerations for heterogeneity evaluation

Pore structure heterogeneity is a critical parameter controlling mechanical, electrical and flow transport behaviour of rock. Multi-fractal analysis method was used for a heterogeneity comparison of three-dimensional rock samples with different lithology. Six real digital samples, containing three sandstones and three carbonates, were used. Based on the mercury injection capillary pressure test on these samples, we found that the carbonate samples are more heterogeneous than sandstones, but primary results of multi-fractal behaviours for all samples were similar. We show that if multi-fractal is used to evaluate and compare heterogeneity of different samples, one needs to follow some considerations such as (1) all samples must have the same size in pixel, (2) samples volume must be bigger than representative volume element, (3) multi-fractal dimensions should be firstly normalized to a determined porosity value and (4) multi-fractal results should be interpreted based on resolution of the imaging tool (effects of fine scale sub-resolution pores are missed). Results revealed that using normalized fractal dimensions, the real samples were divided to less and high heterogeneous groups. Moreover, the study of scale effect also showed that porous structures of these samples are scale invariant in a wide range of scales (from one to eight times bigger).     

Coupling multiscale finite element method for consolidation analysis of heterogeneous saturated porous media

The multiscale finite element method is developed for solving the coupling problems of consolidation of heterogeneous saturated porous media under external loading conditions. Two sets of multiscale base functions are constructed, respectively, for the pressure field of fluid flow and the displacement field of solid skeleton. The coupling problems are then solved with a multiscale numerical procedure in space and time domain. The heterogeneities induced by permeabilities and mechanical parameters of the saturated porous media are both taken into account. Numerical experiments are carried out for different cases in comparison with the standard finite element method. The numerical results show that the coupling multiscale finite element method can be successfully used for solving the complicated coupling problems. It reduces greatly the computing effort in both memory and time for transient problems.     

Coupling upscaling finite element method for consolidation analysis of heterogeneous saturated porous media

The coupling upscaling finite element method is developed for solving the coupling problems of deformation and consolidation of heterogeneous saturated porous media under external loading conditions. The method couples two kinds of fully developed methodologies together, i.e., the numerical techniques developed for calculating the apparent and effective physical properties of the heterogeneous media and the upscaling techniques developed for simulating the fluid flow and mass transport properties in heterogeneous porous media. Equivalent permeability tensors and equivalent elastic modulus tensors are calculated for every coarse grid block in the coarse-scale model of the heterogeneous saturated porous media. Moreover, an oversampling technique is introduced to improve the calculation accuracy of the equivalent elastic modulus tensors. A numerical integration process is performed over the fine mesh within every coarse grid element to capture the small scale information induced by non-uniform scalar field properties such as density, compressibility, etc. Numerical experiments are carried out to examine the accuracy of the developed method. It shows that the numerical results obtained by the coupling upscaling finite element method on the coarse-scale models fit fairly well with the reference solutions obtained by traditional finite element method on the fine-scale models. Moreover, this method gets more accurate coarse-scale results than the previously developed coupling multiscale finite element method for solving this kind of coupling problems though it cannot recover the fine-scale solutions. At the same time, the method developed reduces dramatically the computing effort in both CPU time and memory for solving the transient problems, and therefore more large and computational-demanding coupling problems can be solved by computers.     

太阳黑子相对数最强周期的小波分析

利用小波变换,分析了1749年以来每个太阳活动周太阳黑子相对数的最强周期以及第1～22太阳活动周的最强周期. 分析结果表明,在第5和第6个太阳活动周,太阳黑子相对数最强的周期分别为64.67年和69.31年;在第13～15太阳活动周,太阳黑子相对数的最强周期分别为98.02年,105.06年和105.06年. 在第1～22太阳活动周中,太阳黑子相对数最强的周期是128个月,约10.67年,其他太阳活动周的最强周期介于9.29～11.43年之间. 本文最后给出了128个月周期的幅度随时间的变化.     

Towards realistic flow modelling. Creation and evaluation of two-dimensional simulated porous media: An image analysis approach

This work is part of an attempt to quantify the relationship between the permeability tensor (K) and the micro-structure of natural porous media. A brief account is first provided of popular theories used to relate the micro-structure toK. Reasons for the lack of predictive power and restricted generality of current models are discussed. An alternative is an empirically based implicit model whereinK is expressed as a consequence of a few pore-types arising from the dynamics of depositional processes. The analytical form of that implicit model arises from evidence of universal association between pore-type and throat size in sandstones and carbonates. An explicit model, relying on the local change of scale technique is then addressed. That explicit model allows, from knowledge of the three-dimensional micro-geometry to calculateK explicitly without having recourse to any constitutive assumptions. The predictive and general character of the explicit model is underlined. The relevance of the change of scale technique is recalled to be contingent on the availability of rock-like three-dimensional synthetic media. A random stationary ergodic process is developed, that allows us to generate three-dimensional synthetic media from a two-dimensional autocorrelation functionr( _x , _y ) and associated probability density function measured on a single binary image. The focus of this work is to ensure the rock-like character of those synthetic media. This is done first through a direct approach:n two-dimensional synthetic media, derived from single set ( ,r( _x , _y )) yieldn permeability tensorsK _i-1,n ⁱ (calculated by the local change of scale) of the same order. This is a necessary condition to ensure thatr( _x , _y ) and carry all structural information relevant toK. The limits of this direct approach, in terms of required Central Process Unit time and Memory is underlined, raising the need for an alternative. This is done by comparing the pore-type content of a sandstone sample andn synthetic media derived fromr( _x , _y ) and measured on that sandstone-sample. Achievement of a good match ensures that the synthetic media comprise the fundamental structural level of all natural sandstones, that is a domainal structure of well-packed clusters of grains bounded by loose-packed pores.     

Probabilistic sensitivity and modeling of two-dimensional transport in porous media

A reliability approach is used to develop a probabilistic model of two-dimensional non-reactive and reactive contaminant transport in porous media. The reliability approach provides two important quantitative results: an estimate of the probability that contaminant concentration is exceeded at some location and time, and measures of the sensitivity of the probabilistic outcome to likely changes in the uncertain variables. The method requires that each uncertain variable be assigned at least a mean and variance; in this work we also incorporate and investigate the influence of marginal probability distributions. Uncertain variables includex andy components of average groundwater flow velocity,x andy components of dispersivity, diffusion coefficient, distribution coefficient, porosity and bulk density. The objective is to examine the relative importance of each uncertain variable, the marginal distribution assigned to each variable, and possible correlation between the variables. Results utilizing a two-dimensional analytical solution indicate that the probabilistic outcome is generally very sensitive to likely changes in the uncertain flow velocity. Uncertainty associated with dispersivity and diffusion coefficient is often not a significant issue with respect to the probabilistic analysis; therefore, dispersivity and diffusion coefficient can often be treated for practical analysis as deterministic constants. The probabilistic outcome is sensitive to the uncertainty of the reaction terms for early times in the flow event. At later times, when source contaminants are released at constant rate throughout the study period, the probabilistic outcome may not be sensitive to changes in the reaction terms. These results, although limited at present by assumptions and conceptual restrictions inherent to the closed-form analytical solution, provide insight into the critical issues to consider in a probabilistic analysis of contaminant transport. Such information concerning the most important uncertain parameters can be used to guide field and laboratory investigations.     

Probabilistic sensitivity and modeling of two-dimensional transport in porous media

A reliability approach is used to develop a probabilistic model of two-dimensional non-reactive and reactive contaminant transport in porous media. The reliability approach provides two important quantitative results: an estimate of the probability that contaminant concentration is exceeded at some location and time, and measures of the sensitivity of the probabilistic outcome to likely changes in the uncertain variables. The method requires that each uncertain variable be assigned at least a mean and variance; in this work we also incorporate and investigate the influence of marginal probability distributions. Uncertain variables includex andy components of average groundwater flow velocity,x andy components of dispersivity, diffusion coefficient, distribution coefficient, porosity and bulk density. The objective is to examine the relative importance of each uncertain variable, the marginal distribution assigned to each variable, and possible correlation between the variables. Results utilizing a two-dimensional analytical solution indicate that the probabilistic outcome is generally very sensitive to likely changes in the uncertain flow velocity. Uncertainty associated with dispersivity and diffusion coefficient is often not a significant issue with respect to the probabilistic analysis; therefore, dispersivity and diffusion coefficient can often be treated for practical analysis as deterministic constants. The probabilistic outcome is sensitive to the uncertainty of the reaction terms for early times in the flow event. At later times, when source contaminants are released at constant rate throughout the study period, the probabilistic outcome may not be sensitive to changes in the reaction terms. These results, although limited at present by assumptions and conceptual restrictions inherent to the closed-form analytical solution, provide insight into the critical issues to consider in a probabilistic analysis of contaminant transport. Such information concerning the most important uncertain parameters can be used to guide field and laboratory investigations.     

From the pore scale to the lab scale: 3-D lab experiment and numerical simulation of drainage in heterogeneous porous media

A well-controlled 3-D experiment with pre-defined block heterogeneities is conducted, where neutron tomography is used to map 3-D water distribution after two successive drainage steps. The material and hydraulic properties of the two sands are first measured in the laboratory with multistep outflow experiments. Additionally, the pore structure of the sands is acquired by means of image analysis of synchrotron tomography data and the structure is used for pore-scale simulation of one- and two-phase flow with Lattice-Boltzmann methods. This gives us another set of material and hydraulic parameters of the sands. The two sets of hydraulic properties (from the lab scale and from the pore scale) are then used in numerical simulations of the 3-D experiment.     

小波及小波包消噪方法在山西北部水准数据处理中的应用

文中简要介绍小波及小波包去噪的基本原理,并对代县台短水准观测数据的小波及小波包阈值去噪曲线进行对比分析。采用Matlab小波包消噪方法对山西北部水准历史资料进行处理,发现小波包消噪后的曲线既可以保留多的有效信号,又可使曲线形态更有利于异常特征分析。同时,将处理后得到的小波包消噪曲线结合长趋势观测曲线对主要震例进行分析,结果显示,周边4级以上地震前,异常对应明显,地震一般发生在水准消噪曲线低值异常时。     

斜坡演化前兆异常识别的小波分析

崩滑灾害预测是一个世界性的难题,滑坡和地震一样,都属于非线性系统的失稳,地震前兆信息的识别与提取,并以此作为地震发生时间及震级预报的主要依据,岩石监测数据中很难用肉眼和传统的方法观察出岩石破裂斜坡演化的异常特征,小波分析作为信号处理的强有力数学工具,以其优秀的时频分析能力已经被应用到斜坡演化前兆异常识别中来.小波分析方法识别岩石应力应变和斜坡演化监测信号的前兆异常,得到工程中理想的处理效果,说明小波分析方法对岩石应力应变和斜坡演化监测信号的前兆异常提取是可行的、有效的.     

南京地磁台地铁干扰特征分析与抑制处理

地铁运行时产生的漏电流而形成的附加磁场会对附近的地磁观测造成严重干扰。通过对地铁供电系统的模拟分析得出了地铁干扰的一些基本特征。选取了2008年5月1日到30日南京地磁台受地铁干扰的日变数据和泉州参考地磁台日变数据,利用Welch功率谱估计法进行功率谱对比分析,发现地铁干扰主要对地磁场的Z分量、D分量的功率谱的高频部分造成影响,并且影响的频带范围几乎一致,主要集中在0．004-0．03Hz范围,而对H分量的影响比较微弱。在此基础上,通过小波变换对受干扰数据的Z分量和D分量进行干扰抑制处理,处理结果表明该方法能够有效抑制地铁造成的地磁场干扰。因此本文研究也提供了地磁台站干扰抑制的一种方法。     

Wavelet analysis and interpretation of gravity data in Sichuan-Yunnan region, China

Introduction Sichuan-Yunnan region, located in the east margin of Qinghai-Xizang (Tibetean) Plateau, is a transitional zone between the rapidly upheaving Tibetean Plateau and relatively steady Yangtze Platform. Under the pressure exerted by the northward movement of Indian Plate, Sichuan-Yunnan region has been undergone strong deformation and regmagenesis, becoming one of the regions with the most intensive seismicity in the world. The research on the tectonics and seismicity there is alw…     

山西地区中强地震数字记录特征分析

对山西地区4次Ms≥4.0地震震中距20-80 km的近台PG、SG波列进行频谱分析,结果显示,不同震相的频谱特征存在较大差异,优势频段不一.并对山西大同Ms4.6、阳曲Ms4.6地震波列进行小波多分辨分解,结果显示,PG、SG波均表现为多组波列,且差异较大,可能与两次地震的破裂机制、所处构造部位不同有关.