Multifractal Distribution of Eigenvalues and Eigenvectors from 2D Multiplicative Cascade Multifractal Fields

Two-dimensional fields (maps) generated by isotropic and anisotropic multiplicative cascade multifractal processes are common in many fields including oceans, atmosphere, the climate and solid earth geophysics. Modeling the anisotropic scaling property and heterogeneity of these types of fields are essential for understanding the underlying processes. The paper explicitly derives the eigenvalues and eigenvectors from these types of fields and proves that the eigenvalues and eigenvectors are described by non-conservative multifractal distributions. This results in a new multifractal model implemented in eigen domain to characterize 2D fields not only with respect to overall heterogeneity and singularity as characterized by the ordinary multifractal model applied to the field itself, but also with respect to orientational heterogeneity of the field. It may also result in a new way to characterize the distribution of extreme large eigenvalues involved in other studies such as principal component analysis. A newly defined operator and its properties as derived in this paper may be useful for studying other types of multifractal cascade processes.     

Preservation of rainfall properties in stochastic disaggregation by a simple random cascade model

We analyse properties of a simple discrete multiplicative random cascade model for rainfall disaggregation in urban hydrology. Two types of cascade models (canonical and microcanonical) are applied to the stochastic fine graining of rainfall observations into high resolution data. In particular, we analyse the disaggregation of 1280-min into 10-min data for a 20-year record period (Zurich raingauge, 1979–1998). Differences between the models and parameter estimation techniques are explored on simulated data with a special focus on three important properties of observed rainfall: distribution, intermittency, and extremes. The canonical models are overall better at preserving the distribution of rainfall at the 10-min scale. It is demonstrated that the growth of intermittency across scales is preserved well with all studied models. The ability of the models to reproduce rainfall extremes is a fundamental requirement in disaggregation. The studied models preserved annual rainfall maxima satisfactorily for short durations; however, the performance deteriorated for longer durations. The canonical models performed substantially better in capturing the variability in rainfall. The results are encouraging considering the parsimonious nature of the models and simple parameter estimation.     

Discrete multifractals

The concept of multifractal modeling has been used intensively in various fields of science for characterizing measures with self- similarity. It has been shown that multifractal modeling provides powerful tools for characterizing patterns in the spatial distribution of geological quantities and objects. Existing multifractal models were proposed for the purpose of handling spatially intertwined fractals with continuous fractal spectrum f(α) (or continuous codimension function C(γ)). In this paper, these conventional multifractals are termed “continuous multifractals” whereas multifractals with discrete fractal dimensions are termed “discrete multifractals.” The properties of discrete multifractals are investigated. It is shown by various artificial examples and a case study of stratigraphy of Ocean Drilling Program (ODP) site 645 that spatially intertwined fractals/multifractals indeed can have discrete fractal dimensions. Histogram-and moment-based techniques are proposed for discrete multifractal modeling and illustrated using the artificial examples. The new concept of discrete multifractals and associated multifractal modeling yields not only techniques for characterizing multifractals with discrete fractal dimensions but it also provides insight into the relationships between fractals, bifractals, and multifractals.     

DSSRM级联分割的SAR图像变化检测

SRM(Statistical Region Merging)分割算法具有快速、稳定和抗噪强的优点,基于此,本文提出一种基于DSSRM(Dynamic Sorting Statistical Region Merging)级联分割的SAR图像变化检测方法。首先,针对SRM算法基于单特征静态排序导致的过分割问题,提出一种动态排序模式的DSSRM算法以减少差异图像分割错误,该算法建立基于合并区域的多特征马氏距离排序准则,在每次合并之后更新区域邻接矩阵并重新排序;然后,基于互信息最小化准则构造多通道差异数据集以提高算法对区域合并的约束能力;最后,提出一种级联分割变化检测框架,第1级利用SRM算法将差异图像映射到超像素空间,第2级采用DSSRM算法对超像素进行动态合并获得收敛的分割结果,第3级采用简化SRM方法进行三次合并获得最终的变化检测图。实验结果表明,该方法可以获得比SRM方法和目前流行方法更好的检测性能。     

梯级水电开发对大通河流域洪水过程的影响分析

应用大通河流域实测洪水资料和水利普查数据,定性和定量分析了梯级水电开发对流域洪水过程和洪水特征的影响,建立了梯级水电站数量与洪水涨落率、涨落频次的数学关系模型。结果表明:随着流域水电站数量的增多,洪水过程变化频繁,洪水涨落率增大,涨落频次增多;梯级水电开发使流域最大洪峰流量增大了19.7%~21.5%,最大洪峰传播时间减少了6.1%,而对次洪水总量的影响较小。研究水文过程受人类活动的影响规律,对加强流域水电站统一调度、水能水资源可持续利用和水生态文明建设具有十分重要的意义。     

水电开发对大渡河瀑布沟以下河段的水温影响

为探究水电开发对大渡河水温过程的影响,采用原型观测和数学模型相结合的方法,对比分析了瀑布沟电站开发前后下游河道的水温时空变化特性。研究成果表明,与天然情况相比,现阶段瀑布沟下游沿程水温出现了明显的均化效应和延迟效应以及春夏季低温水、秋冬季高温水现象,最大降温2.4℃出现在4月的龚嘴尾水断面,最大升温3.3℃出现在12月的瀑布沟尾水断面;瀑布沟下游小型水库均未出现水温分层现象,但形成的蓄水体对沿程升温有一定的弱化,沿程增温率由天然状态的0.8℃/100 km降至现阶段的0.5℃/100 km;采用考虑了机械能转化的数学模型能较好地模拟瀑布沟下游河道的水温过程,率定得到的"机械能-内能"转化率为55%。     

甘肃省区域重力场特征

张新虎等人在区域成矿地质背景研究过程中,根据甘肃省区域地球物理新成果,对地球物理特征进行梳理。本文认为甘肃省处于中国西北地区五大板块交汇地带,地质历史漫长,地质构造复杂,在各单元间的相互作用和影响,形成了一幅复杂的应变图像。甘肃省的地球物理场特征也极为复杂。文章介绍了区域重力调查工作概况,分析了区域地层岩性的密度特征,随地层层序从新到老密度值呈递增趋势。在古生界—太古界间岩层密度接近或略高于地壳表层平均密度2.67×10~3 kg/m~3。不同期构造层之间形成密度层及密度界面,较明显的是新生界与中生界之间、中生界与古生界之间。岩体密度随岩石由酸性到基性、超基性岩密度变大;酸性花岗岩和同质火山岩熔岩较地层平均密度偏小;区域布格重力异常主要反映地壳深部信息的区域分量和浅部信息的局部分量,根据区域布格重力异常分布,划分出甘肃北山—秦岭东段重力异常带、阿克塞—张掖—永靖—舟曲弧形重力梯级带,对四顶黑山—红石山、玉门关—前红泉—旧寺墩、阿尔金山—祁连山—西秦岭、六盘山—陇山、天水—武山—临夏—尖扎、青川—阳平关、天水—武都重力梯级带特征进行了分析总结。甘肃省区域重力场特征是甘肃及邻区基础地质研究的主要组成部分,可为中大比例尺的成矿预测提供基础资料。本文试图对甘肃区域重力场特征进行系统总结,形成规律性认识供参考。     

梯级水库蓄水对三峡水库洪峰沙峰异步特性的影响

梯级水库蓄水后，三峡水库入库泥沙大幅度减少，同时三峡水库洪峰沙峰传播特性发生变化，有必要研究新水沙条件下三峡水库洪峰沙峰异步特性变化及其原因，为深入认识水库洪峰沙峰异步特性机理和精细化减淤调度方式提供理论基础。采用实测资料分析法和理论分析法，以2003—2018年三峡水库实测水文资料为基础，对梯级水库蓄水后三峡水库洪峰沙峰异步特性变化进行分析，初步探讨这些变化的主要原因。结果表明：梯级水库蓄水后，三峡水库洪峰沙峰异步现象加剧，表现为入库滞后沙峰比例增加最多、库区洪峰传播时间减少以及沙峰传播时间增加。造成该现象的原因是入库泥沙来源发生变化、入库洪峰流量减少以及入库泥沙颗粒粗化。     

Dynamic response analysis of nonlinear secondary oscillators to idealised seismic pulses

The paper deals with the seismic response analysis of nonlinear secondary oscillators. Bilinear, sliding and rocking single-degree-of-freedom dynamic systems are analysed as representative of a wide spectrum of secondary structures and nonstructural components. In the first stage, the equations governing their full dynamic interaction with linear multi-degree-of-freedom primary structures are formulated, and then conveniently simplified using primary-secondary two-degree-of-freedom systems and dimensionless coefficients. In the second stage, the cascade approximation is applied, whereby the feedback action of the secondary oscillator on the primary structure is neglected. Owing to the piecewise linearity of the secondary systems being considered, efficient semi-analytical and step-by-step numerical solutions are presented. The semi-analytical solutions allow the direct evaluation of the seismic response under pulse-type ground excitations and are also used to validate step-by-step numerical schemes, which in turn can be used for general-type seismic excitations. In the third stage, a set of decoupling criteria are proposed for the pulse-type base excitations, identifying the conditions under which a cascade analysis is admissible from an engineering standpoint. Finally, the influence and relative dependencies between the input parameters of the ground motion and the primary-secondary assembly are quantified on the response of the secondary systems through nonlinear floor response spectra, and general trends are identified and discussed.     

利用多任务级联网络解决6D Pose预测问题

针对基于单张RGB(red-green-blue)图像预测目标6D Pose的问题,设计了多任务级联结构的卷积神经网络(convolutional neural networks,CNN)和BBE(bounding box equation)算法实现快速高效的6D Pose预测.在LINE-MOD数据集上进行实验,并与...