地下水水位时间序列中的混沌特征

利用相空间重构技术、G -P算法以及Wolf提出的从单变量中提取Lyapunov指数的方法 ,分别计算了太原盆地 4组地下水水位时间序列的关联维数和Lyapunov指数。结果揭示在自然状态下 ,太原盆地某些孔隙潜水和孔隙承压水水位变化存在明显的混沌特征。这不仅为以后建立水位预测模型提供了理论依据 ,并且也为运用分形理论研究地质参数的时空变异性以及含水层结构的自相似性提供了进一步的支持。     

0-1测试方法的径流时间序列混沌特性应用

径流时间序列混沌特性识别的常用方法是基于相空间重构的关联维数法、最大Lyapunov指数法和Kolmogorov熵法。引入一种新的时间序列混沌特性识别方法:0-1混沌测试方法。该方法直接应用于时间序列不需要相空间重构,并且通过量化指标K_c是否接近于0或1来识别时间序列的混沌特性。以Logistic映射生成的序列、金沙江流域和美国Umpqua河多年日径流序列为研究对象,首先利用0-1混沌测试方法进行了混沌特性识别和判定;然后基于相空间重构,运用相空间重构、伪最近邻点法、关联维数方法、最大Lyapunov指数法和Kolmogorov熵5种非线性研究方法分析了这两列径流时间序列混沌特性。研究结果表明0-1混沌测试方法简单有效。以上方法交互验证了该两列径流时间序列存在低维混沌特性。     

对水文时间序列混沌特征参数估计问题的讨论

水文过程到底是不是低维混沌过程一直是个有争议的问题。相关文献在混沌特征参数估计中存在不少问题,包括:时延量估计的主观性很强,不同研究者的估计值差别很大;在关联维估计中,很多研究者有意无意地忽略了一个基本原则,即只有在关联维估计图上存在明确的标度区的情况下才能准确判断存在有限关联维;很多研究者在计算水文时间序列的关联维时仍采用原始的G-P计算公式,而没有采用Theiler提的修正公式,从而可能误将相点在时序上的相关性当做一种状态空间几何特征,造成关联维估计错误;国内相关研究中还普遍存在序列长度偏短的问题,对这些问题进行了讨论并给出了相应的结论。     

Fractal analysis of the roughness and size distribution of granular materials

The roughness, i.e. general shape and surface irregularity, of particulate soil is an important characteristic that affects the mass behavior of the soil. Characterization of roughness has typically been limited to visual comparison of particles to standard charts, although other more quantitative methods such as Fourier analysis have also been used. Particle size distribution is another important mass-behavioral characteristic of granular soils, and similar to roughness, is defined within limited boundaries. Fractal geometry can be applied to irregular or fragmented patterns such as roughness and grain size distribution to provide quantifying and unique numerical values. This paper presents an evaluation of the applicability of fractal dimensioning techniques to the quantification of both physical particle roughness and grain size distribution of granular soil. The divider and the area-perimeter fractal dimensioning techniques are used to quantify roughness of planar profiles of individual sand grains. The characterization of the size distribution of granular material using fractal geometry is evaluated through Korcak's fragmentation theory. As shown herein, both the divider and the area-perimeter fractal dimensioning techniques are useful in characterizing soil particle roughness, and the results confirm the importance of differentiating between textural and structural aspects of roughness. Fractal geometry can also be used to quantify the size distribution of granular soils with relatively well-graded size distributions.     

基于时间序列分形的济南岩溶大泉动态研究

为研究岩溶大泉动态变化的影响机制,以济南泉域为例,根据2003年关闭地下水供水水源地以来趵突泉及黑虎泉的泉水位、泉域内降水量、地下水开采及人工补源资料,采用分形理论中时间序列分形维数法,计算各要素数据序列分维值及稳定性指数,结果表明:旬尺度下泉水位分维值大于月尺度下泉水位分维值;奥陶系灰岩分布区雨量站降水量分维值较小,但奥陶系灰岩降水入渗补给条件好,因此与泉群的水位波动关系更为密切。各泉水位影响因素中,人工补源因素的稳定性最差,极易受外界因素干扰发生改变。利用灰色关联度验证分析表明降水量、人工开采量、人工补源量与趵突泉泉水位的关联度分别为0. 858、0. 647、0. 667,与黑虎泉泉水位的关联度分别为0. 859、0. 646、0. 668;关联度总体排序为:降水量>人工补源量>人工开采量,说明2003年以来影响泉水位动态的首要因素是大气降水并非人工开采,即泉水动态主控因素发生转变。在分析了泉域资源量的演化基础上,对各影响因素的分维值与泉水位动态分维值进行回归分析认为,为保持泉水持续喷涌奥陶系灰岩分布区更适宜作为泉水人工补源地带。研究结果为济南岩溶大泉的保护提供科学依据。     

Hydrodynamic characteristics of a typical karst spring system based on time series analysis in northern China

In order to study the hydrodynamic characteristics of the karst aquifers in northern China, time series analyses (correlation and spectral analysis in addition with hydrograph recession analysis) are applied on Baotu Spring and Heihu Spring in Jinan karst spring system, a typical karst spring system in northern China. Results show that the auto-correlation coefficient of spring water level reaches the value of 0.2 after 123 days and 117 days for Baotu Spring and Heihu Spring, respectively. The regulation time obtained from the simple spectral density function in the same period is 187 days and 175 days for Baotu Spring and Heihu Spring. The auto-correlation coefficient of spring water level reaches the value of 0.2 in 34–82 days, and regulation time ranges among 40–59 days for every single hydrological year. The delay time between precipitation and spring water level obtained from cross correlation function is around 56 days for the period of 2012–2019, and varies among 30–79 days for every single hydrological year. In addition, the spectral bands in cross amplitude functions and gain functions are small with 0.02, and the values in the coherence functions are small. All these behaviors illustrate that Jinan karst spring system has a strong memory effect, large storage capacity, noticeable regulation effect, and time series analysis is a useful tool for studying the hydrodynamic characteristics of karst spring system in northern China.© 2021 China Geology Editorial Office.     

基于时间序列分析法的岩溶泉水位预测

济南城区岩溶泉是当地主要的供水水源,查明泉水动态规律并科学合理的预测泉水位对于泉域岩溶水资源的开发利用和保护具有重要意义。本文首先应用时间序列分析法将趵突泉和黑虎泉自2012年5月2日至2018年10月31日的逐日水位数据分解为趋势项、周期项和随机项,分析其水位动态变化规律并建立水位预测模型,结果显示泉水位动态在该阶段无显著趋势性;但受降水的影响,泉水位动态变化呈现两个主要的周期,多年性变化（3.2年）和季节性变化;同时由于受到各种无规律干扰因素的影响,泉水位动态呈现随机波动的随机项。其次,利用2018年11月1日至2020年8月24日的逐日泉水位数据验证上述水位预测模型的预测精度,结果表明该模型运行合理,预测效果较好,具有一定的实用价值。最后利用该模型预测了2020年8月25日至2022年10月31日泉水位动态变化,为当地岩溶水资源开发和管理提供了依据。     

南洞地下河月径流时间序列的混沌特征及预测

利用基于相空间重构技术、混沌识别与预测理论对1993-2013年南洞地下河月径流时间序列的非线性特征进行了分析,由所获得的延迟时间和最佳嵌入维数实现了月径流时间序列的相空间重构,运用饱和关联维数法和小数据量法计算出南洞地下河月径流时间序列的饱和关联维数和最大Lyapunov指数,并运用Volterra模型对南洞地下河月径流时间序列进行了多步预测研究。研究结果表明,南洞地下河月径流时间序列相空间重构的延迟时间和最佳嵌入维数分别为τ=5、m=8,饱和关联维数D和最大Lyapunov指数λ分别为4.63、0.748 9,从定性和定量的角度证明了南洞地下河月径流时间序列具有弱混沌特征。Volterra自适应滤波模型的预测结果能较好地表征南洞地下河月径流的变化趋势和规律,对18个月内的短期预测精度较高,模拟效果较好。      

Estimation of the transfer function by autoregressive deconvolution techniques—An application to time series analysis

The transfer function of time-dependent models is classically inferred by the ordinary least squares (OLS) techniques. This OLS technique assumes independence of the residuals with time. However, in practical cases, this hypothesis is often not justified producing inefficient estimation of the transfer function. When the residuals constitute an autoregressive process, we propose to apply the Box-Jenkins' method to model the residuals, and to modify in a simple manner the primary convolution equation. Then, a multivariate regression technique is used to infer the transfer function of the new equation producing time-independent residuals. This three-step autoregressive deconvolution technique is particularly efficient for time series analysis. The reconstitution and the forecasting of real data are improved efficiently. Theoretically, the proposed method can be extended to the convolution equations for which the residuals follow a moving average or an autoregressive-moving average process, but the mathematical formulation is no longer direct and explicit. For this general case, we propose to approximate the moving average or the autoregressive-moving average process by an autoregressive process of sufficient order, and then the transfer function. Two case studies in hydrogeology will be used to illustrate the procedure.     

Structures,kinematic analysis,rheological parameters and temperature-pressure estimate of the Mesozoic Xingcheng-Taili ductile shear zone in the North China Craton

The NE to ENE trending Mesozoic Xingcheng-Taili ductile shear zone of the northeastern North China Craton was shaped by three phases of deformation. Deformation phase D₁ is characterized by a steep, generally E–W striking gneissosity. It was then overprinted by deformation phase D₂ with NE-sinistral shear with K-feldspar porphyroclasts forming a subhorizontal low-angle stretching lineation on a steep foliation. During deformation phase D₃, lateral motion accommodated by ENE sinistral strike-slip shear zones dominated. Associated fabrics developed at upper greenschist metamorphic facies conditions and show the deformation characteristics of middle- to shallow crustal levels. In some parts, the older structures have been in turn overprinted by late-stage sinistral D₃ shearing. Finite strain and kinematic vorticity in all deformed granitic rocks indicate a prolate ellipsoid (L-S tectonites) near plane strain. Simple shear-dominated general shear during D₃ deformation is probably of general significance. The quartz c-axis textures indicate prism-gliding with a dominant rhomb <a> slip and basal <a> slip system formed mainly at low-middle temperatures. Mineral deformation behavior, quartz c-axis textures, quartz grain size and the Kruhl thermometer demonstrate that the ductile shear zone developed under greenschist facies metamorphic conditions at deformation temperatures ranging from 400 to 500 °C. Dislocation creep is the main deformation mechanism at a shallow crustal level. Fractal analysis showed that the boundaries of recrystallized quartz grains had statistically self-similarities. Differential stresses deduced from dynamically recrystallized quartz grain size are at around 20–39 MPa, and strain rates in the order of 10⁻¹² to 10⁻¹⁴ s⁻¹. This indicates deformation of granitic rocks in the Xingcheng-Taili ductile shear zone at low strain rates, which is consistent with most other ductile shear zones. Hornblende-plagioclase thermometer and white mica barometer indicate metamorphic conditions of medium pressures at around ca. 3–5 kbar and temperatures of 400–500 °C within greenschist facies conditions. The main D₃ deformation of the ENE-trending sinistral strike-slip ductile shearing is related to the roll-back of the subducting Pacific plate beneath the North China Craton.