Eigendecomposition of TDR waveforms: a novel method to determine water content and pore fluid concentration of sandy soils

In this study, an incident pulse signal of several harmonics (i.e., multiples of the fundamental frequency) was used as a source in the time domain reflectometry (TDR) probing technique. Reflected signals were captured by an oscilloscope and their characteristics were determined via eigendecomposition. Autoregressive modeling and singular value decomposition were used to calculate the eigenvalues and the most significant ones were identified based on power spectrum. A multivariate statistical analysis was performed for the two most dominant eigenvalues, which are dependent on water content and salt concentrations, and regression equations were obtained. To determine the water content and salt concentrations in terms of the first and second eigenvalues, a modified Powell hybrid algorithm was used to solve the obtained system of nonlinear equations. Actual and predicted results are in agreement indicating that the developed method is very successful in predicting water content and salt concentrations. Furthermore, on comparing the eigendecomposition method with Fourier spectral analysis, one can observe that the former is superior in predicting water content and salt concentrations.     

Theoretical relationship between SSA and MESA with both application

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奇异值分解方法在季降水预测中的应用

用奇异值分解方法对冬季北太平洋海表温度与广东省４－６月降水量之间的关系进行了计算，得出奇异向量分布型。对前６对奇异向量进行了分析，并用历史资料进行了反查检验，用１９９４年和１９９５年的海温型进行了广东的降水趋势预测     

Nonlinear analysis of the three-dimensional datum transformation [conformal group ℂ7(3)]

 The weighted Procrustes algorithm is presented as a very effective tool for solving the three-dimensional datum transformation problem. In particular, the weighted Procrustes algorithm does not require any initial datum parameters for linearization or any iteration procedure. As a closed-form algorithm it only requires the values of Cartesian coordinates in both systems of reference. Where there is some prior information about the variance–covariance matrix of the two sets of Cartesian coordinates, also called pseudo-observations, the weighted Procrustes algorithm is able to incorporate such a quality property of the input data by means of a proper choice of weight matrix. Such a choice is based on a properly designed criterion matrix which is discussed in detail. Thanks to the weighted Procrustes algorithm, the problem of incorporating the stochasticity measures of both systems of coordinates involved in the seven parameter datum transformation problem [conformal group ℂ₇(3)] which is free of linearization and any iterative procedure can be considered to be solved. Illustrative examples are given. Received: 7 January 2002 / Accepted: 9 September 2002 Correspondence to: E. W. Grafarend     

Relationship between land cover and monsoon interannual variations in east Asia

Asian monsoon have multiple forms of variations such as seasonal variation, intra-seasonal variation, interannual variation, etc. The interannual variations have not only yearly variations but also variations among several years. In general, the yearly variations are described with winter temperature and summer precipitation, and the variations among several years are reflected by circulation of ENSO events. In this study, at first, we analyze the relationship between land cover and interannual monsoon variations represented by precipitation changes using Singular Value Decomposition method based on the time series precipitation data and 8km NOAA AVHRR NDVI data covering 1982 to 1993 in east Asia. Furthermore, after confirmation and reclassification of ENSO events which are recognized as the strong signal of several year monsoon variation, using the same time series NDVI data during 1982 to 1993 in east Asia, we make a Principle Component Analysis and analyzed the correlation of the 7th component eigenvectors and Southern Oscillation Index (SOI) that indicates the characteristic of ENSO events, and summed up the temporal-spatial distribution features of east Asian land cover’s inter-annual variations that are being driven by changes of ENSO events.     

东亚土地覆盖动态与季风气侯年际变化的关系

以东亚地区 １９８２～１９８９年时间序列降水资料及 ＡＶＨＲＲ ８ ｋｍ ＮＤＶＩ数据为基本数据源，应用地理信息系统技术，分别研究了东亚地区夏季（５－９月）降水及土地覆盖的年际变化，并揭示了研究时间段内各自的变化规律。进一步用奇异值分解（ＳＶＤ）模型方法分析了以降水变化为表征的东亚地区气候年际变化与土地覆盖年际变化之间的关系。     

一类奇异孤波解及其在高原低涡结构分析中的应用

文中利用相平面分析法 ,由非绝热大气运动方程组导出了与非线性重力内波有关的 Kd V方程 ,然后用直接积分法得到两类有意义的孤立波解 ,重点分析了一类具有间断点的奇异孤立波解的特征 ,初步建立了此波解与一类青藏高原暖性低涡的联系 ,讨论了高原加热和层结稳定度对高原低涡生成和移动的影响 ,并且从理论上论证了高原低涡具有与热带气旋类低涡( Tropical cyclone- like vortices)类似的涡眼和暖心结构     

东南沿海地区降水与全球海温变化的关系

为了解近50年来东南沿海地区降水与海温变化的关系,对该地区降水与全球海表温度进行了奇异值分解（SVD）。结果表明：印度洋、南海及赤道东太平洋地区是对东南沿海地区降水有影响的关键区域。东南沿海地区秋冬季的降水总体上来说对前期海温变化的响应不敏感,而东南沿海地区夏季降水受前期海温的影响较为明显,尤其是上年夏季北印度洋、南海地区海温的变化对当年降水有明显影响。因此,在预测东南沿海地区夏季降水时应该重点考虑上年夏季北印度洋及南海地区海温的变化情况。     

Singular value decomposition as a denoising tool for airborne time domain electromagnetic data

Airborne time domain electromagnetic (TDEM) surveys are increasingly carried out in anthropized areas as part of environmental studies. In such areas, noise arises mainly from either natural sources, such as spherics, or cultural sources, such as couplings with man-made installations. This results in various distortions on the measured decays, which make the EM noise spectrum complex and may lead to erroneous inversion and subsequent misinterpretations. Thresholding and stacking standard techniques, commonly used to filter TDEM data, are less efficient in such environment, requiring a time-consuming and subjective manual editing. The aim of this study was therefore to propose an alternative fast and efficient user-assisted filtering approach. This was achieved using the singular value decomposition (SVD). The SVD method uses the principal component analysis to extract into components the dominant shapes from a series of raw input curves. EM decays can then be reconstructed with particular components only. To do so, we had to adapt and implement the SVD, firstly, to separate clearly and so identify easily the components containing the geological signal, and then to denoise properly TDEM data.The reconstructed decays were used to detect noisy gates on their corresponding measured decays. This denoising step allowed rejecting efficiently mainly spikes and oscillations. Then, we focused on couplings with man-made installations, which may result in artifacts on the inverted models. An analysis of the map of weights of the selected “noisy components” highlighted high correlations with man-made installations localized by the flight video. We had therefore a tool to cull most likely decays biased by capacitive coupling noises. Finally, rejection of decays affected by galvanic coupling noises was also possible locating them through the analysis of specific SVD components. This SVD procedure was applied on airborne TDEM data surveyed by SkyTEM Aps. over an anthropized area, on behalf of the French geological survey (BRGM), near Courtenay in Région Centre, France. The established denoising procedure provides accurate denoising tools and makes, at least, the manual cleaning less time consuming and less subjective.     

Weakly nonlinear analysis of the α effect

We address mathematical issues raised by the so-called α?effect of dynamo theory, which is a dynamo mechanism arising in conducting flows with small scale fluctuations. Analytical results on the α?effect concern the linear induction equation, and are usually claimed to hold for the whole magnetohydrodynamics (MHD) system, as long as the amplitude of the perturbations is small. We discuss the justification of that claim, in the case of periodic fluctuations of the fields. We show a nonlinear instability result on the MHD system, that predicts dynamo action for a large class of high frequency periodic flows, up to the fully nonlinear regime.