An approximate method for joint sequential simulation of multiple spatial variables

Multivariate simulation is an important longstanding problem in geostatistics. Fitting a model of coregionalization to many variables is intractable and often not permitted; however, the matrix of collocated correlation coefficients is often well informed. Performing a matrix simulation with LU decomposition of the correlation matrix at each step of sequential simulation is implemented in some software. The target correlation matrix is not reproduced because of conditioning to local data and the particular variable ordering in the sequential/LU decomposition. A correction procedure is developed to calculate a modified correlation matrix that leads to reproduction of the target correlation matrix. The theoretical and practical aspects of this correction are developed.     

Extraction of information content from stochastic disaggregation and bias corrected downscaled precipitation variables for crop simulation

We applied a simple statistical downscaling procedure for transforming daily global climate model (GCM) rainfall to the scale of an agricultural experimental station in Katumani, Kenya. The transformation made was two-fold. First, we corrected the rainfall frequency bias of the climate model by truncating its daily rainfall cumulative distribution into the station’s distribution based on a prescribed observed wet-day threshold. Then, we corrected the climate model rainfall intensity bias by mapping its truncated rainfall distribution into the station’s truncated distribution. Further improvements were made to the bias corrected GCM rainfall by linking it with a stochastic disaggregation scheme to correct the time structure problem inherent with daily GCM rainfall. Results of the simple and hybridized GCM downscaled precipitation variables (total, probability of occurrence, intensity and dry spell length) were linked with a crop model for a more objective evaluation of their performance using a non-linear measure based on mutual information based on entropy. This study is useful for the identification of both suitable downscaling technique as well as the effective precipitation variables for forecasting crop yields using GCM’s outputs which can be useful for addressing food security problems beforehand in critical basins around the world.     

A stochastic conflict resolution model for water quality management in reservoir–river systems

In this paper, optimal operating rules for water quality management in reservoir–river systems are developed using a methodology combining a water quality simulation model and a stochastic GA-based conflict resolution technique. As different decision-makers and stakeholders are involved in the water quality management in reservoir–river systems, a new stochastic form of the Nash bargaining theory is used to resolve the existing conflict of interests related to water supply to different demands, allocated water quality and waste load allocation in downstream river. The expected value of the Nash product is considered as the objective function of the model which can incorporate the inherent uncertainty of reservoir inflow. A water quality simulation model is also developed to simulate the thermal stratification cycle in the reservoir, the quality of releases from different outlets as well as the temporal and spatial variation of the pollutants in the downstream river. In this study, a Varying Chromosome Length Genetic Algorithm (VLGA), which has computational advantages comparing to other alternative models, is used. VLGA provides a good initial solution for Simple Genetic Algorithms and comparing to Stochastic Dynamic Programming (SDP) reduces the number of state transitions checked in each stage. The proposed model, which is called Stochastic Varying Chromosome Length Genetic Algorithm with water Quality constraints (SVLGAQ), is applied to the Ghomrud Reservoir–River system in the central part of Iran. The results show, the proposed model for reservoir operation and waste load allocation can reduce the salinity of the allocated water demands as well as the salinity build-up in the reservoir.     

Integrated spatial sampling modeling of geospatial data

Sampling is to, by efficient selection of samples, acquire the accurate information about the population (the research object) at less cost. Spatial sampling is a kind of sampling toward geospatial objects or features with spatial correlation. The differences between effi-cient sampling and completely universal survey lie in quality, time and cost. Sampling provides a kind of economical, prompt and accurate survey[13]. Efficient spatial sampling can be regarded as the optimization of the sampl…     

Random partitioning and adaptive filters for multiple-point stochastic simulation

Multiple-point geostatistical simulation is used to simulate the spatial structures of geological phenomena. In contrast to conventional two-point variogram based geostatistical methods, the multiple-point approach is capable of simulating complex spatial patterns, shapes, and structures normally observed in geological media. A commonly used pattern based multiple-point geostatistical simulation algorithms is called FILTERSIM. In the conventional FILTERSIM algorithm, the patterns identified in training images are transformed into filter score space using fixed filters that are neither dependent on the training images nor on the characteristics of the patterns extracted from them. In this paper, we introduce two new methods, one for geostatistical simulation and another for conditioning the results. At first, new filters are designed using principal component analysis in such a way to include most structural information specific to the governing training images resulting in the selection of closer patterns in the filter score space. We then propose to combine adaptive filters with an overlap strategy along a raster path and an efficient conditioning method to develop an algorithm for reservoir simulation with high accuracy and continuity. We also combine image quilting with this algorithm to improve connectivity a lot. The proposed method, which we call random partitioning with adaptive filters simulation method, can be used both for continuous and discrete variables. The results of the proposed method show a significant improvement in recovering the expected shapes and structural continuity in the final simulated realizations as compared to those of conventional FILTERSIM algorithm and the algorithm is more than ten times faster than FILTERSIM because of using raster path and using small overlap specially when we use image quilting.     

A multivariate Bernstein copula model for permeability stochastic simulation

This paper introduces a general nonparametric method for joint stochastic simulation of petrophysical properties using the Bernstein copula. This method consists basically in generating stochastic simulations of a given petrophysical property (primary variable) modeling the underlying empirical dependence with other petrophysical properties (secondary variables) while reproducing the spatial dependence of the first one.This multivariate approach provides a very flexible tool to model the complex dependence relationships of petrophysical properties. It has several advantages over other traditional methods, since it is not restricted to the case of linear dependence among variables, it does not require the assumption of normality and/or existence of moments.In this paper this method is applied to simulate rock permeability using Vugular Porosity and Shear Wave Velocity (S-Waves) as covariates in a carbonate double-porosity formation at well log scale. Simulated permeability values show a high degree of accuracy compared to the actual values.     

A statistical framework of data fusion for spatial prediction of categorical variables

With rapid advances of geospatial technologies, the amount of spatial data has been increasing exponentially over the past few decades. Usually collected by diverse source providers, the available spatial data tend to be fragmented by a large variety of data heterogeneities, which highlights the need of sound methods capable of efficiently fusing the diverse and incompatible spatial information. Within the context of spatial prediction of categorical variables, this paper describes a statistical framework for integrating and drawing inferences from a collection of spatially correlated variables while accounting for data heterogeneities and complex spatial dependencies. In this framework, we discuss the spatial prediction of categorical variables in the paradigm of latent random fields, and represent each spatial variable via spatial covariance functions, which define two-point similarities or dependencies of spatially correlated variables. The representation of spatial covariance functions derived from different spatial variables is independent of heterogeneous characteristics and can be combined in a straightforward fashion. Therefore it provides a unified and flexible representation of heterogeneous spatial variables in spatial analysis while accounting for complex spatial dependencies. We show that in the spatial prediction of categorical variables, the sought-after class occurrence probability at a target location can be formulated as a multinomial logistic function of spatial covariances of spatial variables between the target and sampled locations. Group least absolute shrinkage and selection operator is adopted for parameter estimation, which prevents the model from over-fitting, and simultaneously selects an optimal subset of important information (variables). Synthetic and real case studies are provided to illustrate the introduced concepts, and showcase the advantages of the proposed statistical framework.     

硅藻群落结构的差异:比较样本采集过程与空间梯度

硅藻种群的分布与其所处的生境条件密切相关,但在实际过程中的一些人为因素,例如取样方法、样本的制备以及藻种鉴定都可能会干扰到种群结构的分析结果.因此很有必要探究这些人为因素是否会对真实的硅藻群落生态学研究产生误导性的判断,以免干扰硅藻生物水质评价的客观性.选取采样方法及样本制备为代表的人为因素对硅藻群落生态分析结果引入的误差大小进行评估.结果显示,子样本之间(同一样品重复制作的玻片样本)和样品之间(同一样点重复取样)群落结构差异大小分别是1.26%和1.97%,同一条河流的样点之间则为3.38%,而所选定的跨河流研究区域的样点间群落结构差异最大(42.03%).生态学的排序结果和数理统计分析表明,在硅藻群落结构分析中,现场取样方法和样本制备过程相对于不同生境条件所引起的变化,并不会带来较大的差异.因此在河流附生硅藻的群落生态学研究中,可基本不考虑取样方法等因子的干扰,而是侧重于环境因子对硅藻生态分布的影响.     

An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering

The ensemble Kalman filter (EnKF) is a commonly used real-time data assimilation algorithm in various disciplines. Here, the EnKF is applied, in a hydrogeological context, to condition log-conductivity realizations on log-conductivity and transient piezometric head data. In this case, the state vector is made up of log-conductivities and piezometric heads over a discretized aquifer domain, the forecast model is a groundwater flow numerical model, and the transient piezometric head data are sequentially assimilated to update the state vector. It is well known that all Kalman filters perform optimally for linear forecast models and a multiGaussian-distributed state vector. Of the different Kalman filters, the EnKF provides a robust solution to address non-linearities; however, it does not handle well non-Gaussian state-vector distributions. In the standard EnKF, as time passes and more state observations are assimilated, the distributions become closer to Gaussian, even if the initial ones are clearly non-Gaussian. A new method is proposed that transforms the original state vector into a new vector that is univariate Gaussian at all times. Back transforming the vector after the filtering ensures that the initial non-Gaussian univariate distributions of the state-vector components are preserved throughout. The proposed method is based in normal-score transforming each variable for all locations and all time steps. This new method, termed the normal-score ensemble Kalman filter (NS-EnKF), is demonstrated in a synthetic bimodal aquifer resembling a fluvial deposit, and it is compared to the standard EnKF. The proposed method performs better than the standard EnKF in all aspects analyzed (log-conductivity characterization and flow and transport predictions).     

An energy-based envelope function for the stochastic simulation of earthquake accelerograms

An energy-based envelope function is developed for use in the stochastic simulation of earthquake ground motion. The envelope function is directly related to the Arias intensity of the ground motion as well to the manner in which this Arias intensity is built-up over time. It is shown that this build-up, represented by a Husid plot, can be very well modelled using a simple lognormal distribution. The proposed envelope makes use of parameters that are commonly available in seismic design situations, either following a deterministic scenario-type analysis or following a more comprehensive probabilistic seismic hazard analysis (PSHA), either in terms of Arias intensity or the more common spectral acceleration. The shape parameters of the envelope function are estimated following the calculation of the analytic envelopes for a large number of records from PEER Next Generation of Attenuation (NGA) database. The envelope may also be used to predict the distribution of peak ground acceleration values corresponding to an earthquake scenario. The distribution thus obtained is remarkably consistent with those of the recent NGA models.     

Principle and application of high density spatial sampling in seismic migration

To avoid spatial aliasing problems in broad band high resolution seismic sections, I present a high density migration processing solution. I first analyze the spatial aliasing definition for stack and migration seismic sections and point out the differences between the two. We recognize that migration sections more often show spatial aliasing than stacked sections. Second, from wave propagation theory, I know that migration output is a new spatial sampling process and seismic prestack time migration can provide the high density sampling to prevent spatial aliasing on high resolution migration sections. Using a 2D seismic forward modeling analysis, I have found that seismic spatial aliasing noise can be eliminated by high density spatial sampling in prestack migration. In a 3D seismic data study for Daqing Oilfield in the Songliao Basin, I have also found that seismic sections obtained by high-density spatial sampling (10 × 10 m) in prestack migration have less spatial aliasing noise than those obtained by conventional low density spatial sampling (20 × 40 m) in prestack migration.     

Investigation on the stochastic simulation of strong ground motions for Bucharest area

This short article evaluates the stochastic method of ground motion simulation for Bucharest area using both the single-corner frequency model and recently introduced double-corner frequency models. A dedicated Q model is derived using ground motions obtained during the largest Vrancea earthquakes from the past 30 years. The simulated ground motions are tested against the observed data from the Vrancea earthquakes of August 1986 and May 1990. Moreover, the observed data are also compared against simulations obtained using the Q model derived by Oth et al. (2008). Finally, the results of the simulations show that the derived Q model is better suited for larger magnitude events, while the Q model of Oth et al. (2008) provides better results for smaller earthquakes.     

太湖水体遥感反演参数的空间异质性

空间异质性的存在,会导致水质参数遥感反演中的尺度效应,影响反演精度,因此通过分析水质参数空间异质性,对于选择适当分辨率的遥感影像,提高反演精度具有重要意义.通过2008年10月在太湖布置的3个样方,利用GIS地统计学原理和分形维数的方法,对水质遥感反演中的三要素浓度,包括叶绿素a(Chl.a)、总悬浮物(TSM)和溶解有机碳(DOC)的空间异质性及其可能产生的尺度效应进行了研究.结果表明:太湖水体的三要素浓度在不同样方单元中变异系数相差较大,存在着明显的尺度效应;三个样方内Chl.a变异函数曲线斜率在变程范围内变化都较为剧烈,分形维数较高,说明太湖水体Chl.a受到某种起主导作用的生态过程的影响和控制;Chl.a和TSM的空间结构比例都在90%左右,有较强的空间相关性,表明其空间异质性的产生主要是由于结构性因素引起的,随机性因素作用微弱;DOC空间结构比例较小,说明随机性因素对其空间异质性的产生起了主导作用.三个样方中Chl.a的变程分别为147.3m、129.3m和115.0m,TSM的变程分别为1131.7m、130.6m、149.1m,因此在遥感反演中可选择TM影像,选择5×5窗口,以150m×150m作为基本单元;而DOC的变程分别为34.3m、38.5m、26.4m,表明其自相关距离较小,建议直接选择分辨率为30m的TM影像,使实际测量值与遥感影像最小单元相对应,消除反演过程中的尺度效应带来的误差.该研究也表明,MODIS的像元尺寸(250、500、1000m)明显偏大,在太湖水体三要素反演过程中,由于空间异质性引起的尺度效应,会造成一定的误差.     

用于结构计算仿真的神经网络样本点选择方法研究

本文对影响结构计算仿真神经网络精度的训练样本选择方法进行了分析。以卫星天线模型(ANTENNA)和飞机模型(GARTEUR)为对象,以样本数量和网络模型的均方误差为指标,对多种样本选择方法进行了比较。结果表明,均匀设计方法可以用较少的训练样本,保证神经网络模型较高的精度,是结构计算仿真中神经网络训练样本的最优选取方法。     

Uncertainty analysis of flood inundation modelling using GLUE with surrogate models in stochastic sampling

A generalized likelihood uncertainty estimation (GLUE) method incorporating moving least squares (MLS) with entropy for stochastic sampling (denoted as GLUE‐MLS‐E) was proposed for uncertainty analysis of flood inundation modelling. The MLS with entropy (MLS‐E) was established according to the pairs of parameters/likelihoods generated from a limited number of direct model executions. It was then applied to approximate the model evaluation to facilitate the target sample acceptance of GLUE during the Monte‐Carlo‐based stochastic simulation process. The results from a case study showed that the proposed GLUE‐MLS‐E method had a comparable performance as GLUE in terms of posterior parameter estimation and predicted confidence intervals; however, it could significantly reduce the computational cost. A comparison to other surrogate models, including MLS, quadratic response surface and artificial neural networks (ANN), revealed that the MLS‐E outperformed others in light of both the predicted confidence interval and the most likely value of water depths. ANN was shown to be a viable alternative, which performed slightly poorer than MLS‐E. The proposed surrogate method in stochastic sampling is of practical significance in computationally expensive problems like flood risk analysis, real‐time forecasting, and simulation‐based engineering design, and has a general applicability in many other numerical simulation fields that requires extensive efforts in uncertainty assessment. Copyright © 2014 John Wiley & Sons, Ltd.     

Simple stochastic simulation of time irreversible and reversible processes

ABSTRACT

As time irreversibility of streamflow is marked for time scales up to several days, while common stochastic generation methods are good only for time-symmetric processes, the need for new methods to handle irreversibility, particularly in flood simulations, has been recently highlighted. From an investigation of the historical evolution of existing stochastic generation methods, which is a useful step before proposing new methods, the strengths and weaknesses of current approaches are located. Following this investigation, a generic solution to the stochastic generation problem is proposed. This is an analytical exact method based on an asymmetric moving-average scheme, capable of handling time irreversibility in addition to preserving the second-order stochastic structure, as well as higher-order marginal statistics, of a process. The method is studied theoretically in its general setting, as well as in its most interesting special cases, and is successfully applied to streamflow generation at an hourly scale.     

轨道不平顺随机过程的数值模拟

轨道不平顺是列车-轨道系统的动力响应的主要影响因素,不平顺样本是列车-轨道系统动力分析模型中不可缺少的参数.根据随机理论原理推导了轨道不平顺谱的空间、时间域的相互转化关系,得到了时域功率谱的表达式.分析了目前广泛应用几种轨道不平顺随机过程的模拟方法的原理及作法,通过对功率谱快速数值算法的分析给出了一种新三角级数模拟方法,该方法与逆傅氏变换法具有等效性,同时也论证了逆傅氏变换方法样本是高斯过程.最后通过实际算例的分析论证了新三角级数法与傅氏逆变换法在简便、合理等方面的优点.     

基于随机地震反演的Russell流体因子直接估算方法

本文研究了一种基于随机地震反演的Russell流体因子直接估算方法,该方法是一种基于蒙特卡罗的非线性反演,能够有效地融合测井资料中的高频信息,提高反演结果的分辨率.本文应用贝叶斯理论框架,首先通过测井数据计算井位置处的Russell流体因子,利用序贯高斯模拟方法(sequential Gaussian simulation, SGS)得到流体因子的先验信息;然后构建似然函数;最后利用Metropolis抽样算法对后验概率密度进行抽样,得到反演的Russell流体因子.其中对每道数据进行序贯高斯模拟时,采用一种新的逐点模拟方式,具有较高的计算速度.数值试验表明:反演结果与理论模型和实际测井数据吻合较好,具有较高的分辨率,对于判识储层含流体特征具有较好的指示作用.     

考虑降雨空间变化的随机产汇流模型

引入两个负指数型差值函数,估计降雨量的概率分布,以此描述流域降雨空间变异性问题.将降雨量空间统计分布与垂向混合产流模型耦合进行产流量计算,即对地表径流,采用超渗产流模式,根据降雨与土壤下渗能力的联合分布推求其空间分布;对地面以下径流,采用蓄满产流模式,以地表渗入量的均值作为输入,进行简化处理以提高其实用性;最终推导出总产流量概率分布函数计算公式.将流域概化成一个线性水库,并根据随机微分方程理论,推导任一计算时段洪水流量的概率分布,从而构建了一个完整的随机产汇流模型.以淮河支流黄泥庄流域为例进行应用研究,结果表明,该模型可提供洪水过程的概率预报,可用于防洪风险分析,若以概率分布的期望值作为确定性预报,亦具有较高精度.