Spectral Estimation in Space and Time Domain by Nonstationary Minimum Variance Spectral Estimator

A multidimensional version of the nonstationary minimum variance spectral estimator has been developed. The numerical results have shown that this method has more resolution power than the conventional nonstationary spectral estimation methods based on periodograms. The application of the spectral estimation method to an irregularly sampled multidimensional nonstationary rainfall mode is also investigated. The other advantage of this spectral estimation method is that it does not require window selection.     

Spectral Estimation of Irregularly Sampled Nonstationary Multidimensional Processes by Time-Varying Periodogram

A multidimensional version of the time varying periodogram has been developed. The estimation method based on the multidimensional time-varying periodogram has been applied to a nonstationary multidimensional storm model. This work proposes that the multidimensional time varying periodogram is capable of estimating nonstationary spectral density functions in space and time.     

Multidimensional Nonstationary Maximum Entropy Spectral Analysis by Using Neural Net

A multidimensional version of the nonstationary maximum entropy spectral estimation method has been developed. By applying the neural net technique, the estimated maximum entropy spectral density function has more resolution power than the conventional nonstationary periodogram spectral density function. The application of spectral density functions to simulate multidimensional nonstationary random fields is also investigated.     

基于离散Gabor变换迭代时变滤波实现地震信号去噪

基于离散Gabor变换时变滤波对宽带和非平稳信号估计具有强大的能力,迭代时变滤波不仅计算上有效,而且能得到较好的信噪比。鉴于迭代时变滤波方法的特点和地震信号的非平稳性,我们提出了基于离散Gabor变换迭代时变滤波方法实现地震信号的去噪,并根据实际地震信号的带限性及其频带分布规律,提出了简单的掩模函数求取方法。经大量的理论模型和实际资料计算表明该方法是有一定效果的。      

复杂地震波场的自适应流预测插值方法

地震数据本质上是非平稳的,如何解决复杂非平稳地震波场的数据缺失问题是地震勘探数据处理的重要环节之一。预测滤波器在地震数据处理和分析中具有重要的作用,该技术可以有效地解决地震数据缺失问题,但传统的平稳预测滤波方法无法很好地适应地震数据的非平稳特征;因此,开发高效的复杂地震波场自适应预测插值方法具有重要的工业价值。本文将预测滤波器加入"流处理"的概念,滤波器系数随着地震数据的变化同时更新,此计算过程仅需矢量点积运算,能够提高计算效率并降低内存空间;并以此为基础开发基于流预测滤波的地震数据插值方法。利用多次波的动力学信息,通过互相关技术构建虚拟一次波,有效地解决了缺失数据位置滤波系数估计不准的问题,为插值过程提供了更为合理的滤波器估计,更好地解决了非平稳地震数据的重建问题。对Sigsbee 2B模型和实际数据的测试结果表明,该方法可以合理地针对复杂地震信息完成缺失数据的重建。     

Criteria to Compare Estimation Methods of Regionalized Compositions

The additive logratio (alr) transformation has been used in several case studies to predict regionalized compositions using standard geostatistical estimation methods such as ordinary kriging and ordinary cokriging. It is a simple method that allows application to transformed data all the body of knowledge available for geostatistical analysis of coregionalizations without a constant sum constraint. To compare the performance of methods, it is customary to use a univariate crossvalidation approach based on the leaving-one-out technique to evaluate the performance for each attribute separately. For multivariate observations this approach is difficult to interpret in terms of overall performance. Therefore, we propose using appropriate distances in real space and in the simplex, to improve the crossvalidation approach and, going a step forward, to adapt the concept of stress from multidimensional scaling to obtain a global measure of performance for each method. The Lyons West oil field of Kansas is used to illustrate the impactof using different distances in the performance of ordinary kriging versus ordinary cokriging.     

Prediction of weather parameters on a very short time scale by an Auto Regressive process for aviation flight planning

Forecasting weather parameters such as temperature and pressure with a reasonable degree of accuracy three hours ahead of the scheduled departure of an aircraft helps economic and efficient planning of aircraft operations. However, these two parameters exhibit a high degree of persistency and have nonstationary mean and variance at sub-periods (i.e. at 0000, 0300, 0600,…, 2100UTC). Hence these series have been standardised (to have mean 0 and variance 1) and thereafter seasonal differenced (lag 8) to achieve almost near stationarity. An attempt has been made to fit the standardised and seasonal differenced series of Chennai (a coastal station) and Trichy (an inland station) airport into an Auto Regressive (AR) process. The model coefficients have been estimated based on adaptive filter algorithm which uses the method of convergence by the steepest descent. The models were tested with an independent data set and diagnostic checks were made on the residual error series. An independent estimation of fractal dimension has also been made in this study to conform the number parameters used in the AR processes. The models contemplated in this study are parsimonious and can be used to forecast surface temperature and pressure.     

非平稳条件下北京市最大月降水量频率特征分析

为探究气候变化下极端降水的频率变化特征,基于北京市22个雨量站实测月降水量数据,以时间为协变量构建平稳和非平稳GEV模型,对北京市最大月降水量序列(极值降水序列)进行模拟和频率分析,并采用Bootstrap方法对频率分析结果的不确定性进行评价.结果表明:所有极值降水序列的最优概率分布模型均为非平稳GEV模型,该模型能够...     

Analysis of Time of Occurrence of Earthquakes: A Functional Data Approach

There is no single method available for estimating the seismic risk in a given area, and as a result most studies are based on some statistical model. If we denote by Z the random variable that measures the maximum magnitude of earthquakes per unit time, the seismic risk of a value m is the probability that this value will be exceeded in the next time units, that is, R(m)=P(Z>m). Several approximations can be made by adjusting different theoretical distributions to the function R, assuming different distributions for the magnitude of earthquakes. A related method used to treat this problem is to consider the difference between the times of occurrence of consecutive earthquakes, or inter-event times. The hazard function, or failure rate function, of this variable measures the instantaneous risk of occurrence of a new earthquake, supposing that the last earthquake happened at time 0. In this paper, we will consider the estimation of the variable that measures the inter-event time and apply nonparametric techniques; that is, we do not consider any theoretical distribution. Moreover, because the stochastic process associated with this variable can sometimes be non-stationary, we condition each time by the previous ones. We then work with a multidimensional estimation, and consider each multidimensional variable as a functional datum. Functional data analysis deals with data consisting of curves or multidimensional variables. Nonparametric estimation can be applied to functional data, to describe the behavior of seismic zones and their associated instantaneous risk. The applications of estimation techniques are shown by applying them to two different regions and data catalogues: California and southern Spain.     

Disjunctive kriging, universal kriging, or no kriging: Small sample results with simulated fields

This paper provides a comparison between linear (universal) and nonlinear (disjunctive) kriging estimators when they are computed from small samples chosen randomly on simulated stationary and nonstationary fields. Point estimation results are reported. In all cases considered, kriging estimators were found better than a local mean estimator, with universal kriging either better than or as good as disjunctive kriging. The latter, which is suited to handle stationary fields, did not provide more accurate estimates because the use of small samples led to inconsistencies in the assumed bivariate model. Universal kriging was particularly better with nonstationary fields.     

Three-Dimensional Numerical Method of Moments for Linear Equilibrium-Adsorbing Solute Transport in Physically and Chemically Nonstationary Formations

A Lagrangian perturbation method is applied to develop a method of moments for reactive solute flux through a three-dimensional, nonstationary flow field. The flow nonstationarity may stem from medium nonstationarity, finite domain boundaries, and/or fluid pumping and injecting. The reactive solute flux is described as a space–time process where time refers to the solute flux breakthrough in a control plane at some distance downstream of the solute source and space refers to the transverse displacement distribution at the control plane. The analytically derived moments equations for solute transport in a nonstationary flow field are too complicated to solve analytically; therefore, a numerical finite difference method is implemented to obtain the solutions. This approach combines the stochastic model with the flexibility of the numerical method to boundary and initial conditions. The approach provides a tool to apply stochastic theory to reactive solute transport in complex subsurface environments. Several case studies have been conducted to investigate the influence of the physical and chemical heterogeneity of a medium on the reactive solute flux prediction in nonstationary flow field. It is found that both physical and chemical heterogeneity significantly affect solute transport behavior in a nonstationary flow field. The developed method is also applied to an environmental project for predicting solute flux in the saturated zone below the Yucca Mountain Project area, demonstrating the applicability of the method in practical environmental projects.     

考虑局部趋势的非一致性水文频率分析方法

变化环境下水文序列常表现出非一致性,导致基于独立同分布假设的频率分析方法受到严峻挑战,故亟需研究适用于非一致性水文序列的频率分析方法。针对具有趋势变异的水文序列,提出了一种考虑局部趋势的非一致性水文频率分析方法:以具有局部与整体趋势识别能力的滑动窗口趋势分析法诊断序列;构造时变概率分布模型组,采用融合了贝叶斯理论的广义极大似然法估计模型参数;优选模型并按照等可靠度原则推求设计值及置信区间。应用该方法对甘肃石羊河流域红崖山水库站年径流量序列开展了实例研究,结果表明从设计值及95%置信区间角度看,所提方法与现行的一致性频率分析方法及考虑整体趋势的时变分布方法相比存在一定的差异,揭示了在准确识别序列局部或整体趋势成分的基础上,开展非一致性水文频率分析有助于合理估计设计值。     

Estimation of the time of magma chamber solidification beneath the Strel’tsovka caldera and its effect on the nonstationary temperature distribution in the upper crust,the eastern Transbaikal region,Russia

The hydrothermal Mo-U deposits of the Strel’tsovka ore field, unique in reserves, are localized in the Late Mesozoic caldera of the same name. The consideration of geochemical processes that controlled uranium transfer by ore-bearing fluids and its precipitation in orebodies has shown that a nonstationary temperature distribution could have exerted a substantial effect on ore formation. The temperature field in the Strel’tsovka caldera, which was caused by a shallow-seated magma chamber that existed beneath the caldera by the onset of the ore stage, was simulated by mathematical modeling. A one-dimensional nonstationary model of conductive heat transfer taking into account the latent heat of magmatic melt crystallization was used. The problem was solved with the finite difference method. It has been established that, at optimal parameters of the model, the magma chamber would have completely crystallized in 56 ka; the maximum estimate is 133 ka. Three million years after emplacement of the granitic intrusion, the related thermal anomaly in the upper crust should have disappeared. The results obtained indicate that granitic melt of this chamber could not have been a source of uranium-bearing solutions that formed deposits 5 Ma after the cessation of magmatic activity.     

Multiple-Point Simulation with an Existing Reservoir Model as Training Image

The multiple-point simulation (MPS) method has been increasingly used to describe the complex geologic features of petroleum reservoirs. The MPS method is based on multiple-point statistics from training images that represent geologic patterns of the reservoir heterogeneity. The traditional MPS algorithm, however, requires the training images to be stationary in space, although the spatial distribution of geologic patterns/features is usually nonstationary. Building geologically realistic but statistically stationary training images is somehow contradictory for reservoir modelers. In recent research on MPS, the concept of a training image has been widely extended. The MPS approach is no longer restricted by the size or the stationarity of training images; a training image can be a small geometrical element or a full-field reservoir model. In this paper, the different types of training images and their corresponding MPS algorithms are first reviewed. Then focus is placed on a case where a reservoir model exists, but needs to be conditioned to well data. The existing model can be built by process-based, object-based, or any other type of reservoir modeling approach. In general, the geologic patterns in a reservoir model are constrained by depositional environment, seismic data, or other trend maps. Thus, they are nonstationary, in the sense that they are location dependent. A new MPS algorithm is proposed that can use any existing model as training image and condition it to well data. In particular, this algorithm is a practical solution for conditioning geologic-process-based reservoir models to well data.     

An innovative micro-scale approach for vulnerability and flood risk assessment with the application to property-level protection adoptions

Economic damage assessment for flood risk estimation is established in many countries, but attentions have been focused on macro- or meso-scale approaches and less on micro-scale approaches. Whilst the macro- or meso-scale approaches of flood damage assessment are suitable for regional- or national-oriented studies, micro-scale approaches are more suitable for cost–benefit analysis of engineered protection measures. Furthermore, there remains lack of systematic and automated approaches to estimate economic flood damage for multiple flood scenarios for the purpose of flood risk assessment. Studies on flood risk have also been driven by the assumption of stationary characteristic of flood hazard, hence the stationary-oriented vulnerability assessment. This study proposes a novel approach to assess vulnerability and flood risk and accounts for adaptability of the approach to nonstationary conditions of flood hazard. The approach is innovative in which an automated concurrent estimation of economic flood damage for a range of flood events on the basis of a micro-scale flood risk assessment is made possible. It accounts for the heterogeneous distribution of residential buildings of a community exposed to flood hazard. The feasibility of the methodology was tested using real historical flow records and spatial information of Teddington, London. Vulnerability curves and residual risk associated with a number of alternative extents of property-level protection adoptions are estimated by the application of the proposed methodology. It is found that the methodology has the capacity to provide valuable information on vulnerability and flood risk that can be integrated in a practical decision-making process for a reliable cost–benefit analysis of flood risk reduction options.     

Analysis of explosions and seismic phenomena based on electromagnetic cracking of piezoelectric and piezomagnetic plates

Electromagnetic emission caused by fracturing of piezoelectric and piezomagnetic crystals in plates and its application for remote sensing of explosions and natural seismic and volcanic phenomena were studied theoretically. The difference of emission from piezoelectric and piezomagnetic plates in cases of explosions versus seismic and volcanic phenomena enables use of this analysis method for phenomenon identification. The analysis herein is based on a model of a plate of finite size with a uniformly moving crack. It has been demonstrated that time-dependent mechanical stresses, which exist in the vicinity of the crack apex, are sources of an alternating electromagnetic field. The nonstationary mechanical stresses in the vicinity of the moving crack cause nonstationary polarization currents, which include both potential and vortical components in the case of a piezoelectric crystal but only the vortical component in the case of a piezomagnetic crystal. In both cases, it is possible to observe the nonstationary magnetic dipole which is the source of the excited magnetic field in the near zone. Such a dipole is created due to the motion of the crack apex and depends on the specific crystalline symmetry. Comparison of the two types of crystal (piezoelectric and piezomagnetic) shows that emission from the piezomagnetic crystal is more effective. A very important result is that it is possible to observe the difference between seismic and volcanic versus industrial phenomena through analysis of the unloading wave, which is absent in the case of industrial phenomena. This opens the possibility to identify the type of disaster and take the correct decision.     

用连续小波变换分析探地雷达回波信号

脉冲探地雷达回波信号是典型的非平稳、非线性信号.本文通过连续小波变换,对地下圆柱目标实测结果进行分析,得到了目标冲击响应的典型波形特征.分析结果证明,这种方法可以有效地用于目标检测,时延估计等脉冲探地雷达信号处理中的关键问题     

An assessment of multidimensional flood vulnerability at the provincial scale in China based on the DEA method

China suffers frequent and severe floods. A lot of studies have been done in the field of flood disaster, including flood vulnerability assessment. This paper develops assessment models of multidimensional flood vulnerability based on the data envelopment analysis method and identifies multidimensional flood vulnerability??population, death, agriculture and economy??at the provincial scale in China using flood damage data and socioeconomic statistical data from 2001 to 2010. Based on the characteristics of multidimensional flood vulnerability of each province, some suggestions for flood prevention and mitigation are suggested. The assessment models of multidimensional flood vulnerability are simple and can be used for vulnerability analysis of natural disaster at regional or national levels. The assessment of multidimensional flood vulnerability can provide multifaceted information that contributes to a deeper understanding of the flood vulnerability and provides a scientific base for the policy making and implementation of flood prevention and mitigation designs.     

Moving averages for Gaussian simulation in two and three dimensions

The square-root method provides a simple and computationally inexpensive way to generate multidimensional Gaussian random fields. It is applied by factoring the multidimensional covariance operator analytically, then sampling the factorization at discrete points to compute an array of weighted averages that can be convolved with an array of random normal deviates to generate a correlated random field. In many respects this is similar to the LUdecomposition method and to the one-dimensional method of moving averages. However it has been assumed that the method of moving averages could not be used in higher dimensions, whereas direct application of the matrix decomposition approach is too expensive to be practical on large grids. In this paper, I show that it is possible to calculate the square root of many two- and three dimensional covariance operators analytically so that the method of moving averages can be applied directly to the problem of multidimensional simulation. A few numerical examples of nonconditional simulation on a 256×256 grid that show the simplicity of the method are included. The method is fast and can be applied easily to nested and anisotropic variograms.     

Digital simulation of multivariate two- and three-dimensional stochastic processes with a spectral turning bands method

The space domain version of the turning bands method can simulate multidimensional stochastic processes (random fields) having particular forms of covariance functions. To alleviate this limitation a spectral representation of the turning bands method in the two-dimensional case has shown that the spectral approach allows simulation of isotropic two-dimensional processes having any covariance or spectral density function. The present paper extends the spectral turning bands method (STBM) even further for simulation of much more general classes of multidimensional stochastic processes. Particular extensions include: (i) simulation of three-dimensional processes using STBM, (ii) simulation of anisotropic two- or three-dimensional stochastic processes, (iii) simulation of multivariate stochastic processes, and (iv) simulation of spatial averaged (integrated) processes. The turning bands method transforms the multidimensional simulation problem into a sum of a series of one-dimensional simulations. Explicit and simple expressions relating the cross-spectral density functions of the one-dimensional processes to the cross-spectral density function of the multidimensional process are derived. Using such expressions the one-dimensional processes can be simulated using a simple one-dimensional spectral method. Examples illustrating that the spectral turning bands method preserves the theoretical statistics are presented. The spectral turning bands method is inexpensive in terms of computer time compared to other multidimensional simulation methods. In fact, the cost of the turning bands method grows as the square root or the cubic root of the number of points simulated in the discretized random field, in the two- or three-dimensional case, respectively, whereas the cost of other multidimensional methods grows linearly with the number of simulated points. The spectral turning bands method currently is being used in hydrologic applications. This method is also applicable to other fields where multidimensional simulations are needed, e.g., mining, oil reservoir modeling, geophysics, remote sensing, etc.