Martian Topography: Scaling, Craters, and High-Order Statistics

The high-order structure functions of Mars topography reveal three specific ranges of scales: (1) scaling range at small scales where the structure functions exhibit scaling behavior; (2) transition range where the structure functions continue to grow but do not reveal scaling; and (3) saturation range at large scales where the structure functions saturate. The scaling and saturation ranges are explored in detail in respect to scaling and intermittency. Analysis of the Mars Orbiter Laser Altimeter (MOLA) data and computer simulations suggest that there are two potential contributors to the small-scale scaling: (i) scale-invariant surface formation; and (ii) effects of discrete morphological forms such as craters. The crater effect also provides an explanation for the large-scale intermittency revealed using the normalized structure functions within the saturation range, which cannot be explained by the ‘scale-invariant’ concept. Overall, the obtained results suggest that the “crater” contribution to the structure function behavior often dominates over the effect of the scale-invariant surface formation.     

On the dependence of the saturated hydraulic conductivity upon the effective porosity through a power law model at different scales

We study the scale dependence of the saturated hydraulic conductivity K_s through the effective porosity n_e by means of a newly developed power‐law model (PLM) which allows to use simultaneously measurements at different scales. The model is expressed as product between a single PLM (capturing the impact of the dominating scale) and a characteristic function κ^? accounting for the correction because of the other scale(s). The simple (closed form) expression of the κ^?‐function enables one to easily identify the scales which are relevant for K_s. The proposed model is then applied to a set of real data taken at the experimental site of Montalto Uffugo (Italy), and we show that in this case two (i.e. laboratory and field) scales appear to be the main ones. The implications toward an important application (solute transport) in Hydrology are finally discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Scaling procedures for heterogeneous unconfined aquifers

Complex flows in heterogeneous confined and unconfined aquifers is a phenomenon that continues to present difficulties in flow mapping and modelling in the field, laboratory, and through numerical simulations. It is often the case with complicated phenomena that transformative scaling and reduction of the problem through symmetry is of great efficacy in the formation of predictive models in both the laboratory and computational settings. A detailed a study of the application of a broad class of Lie scaling transformations on a set of equations representing the groundwater flows in heterogeneous confined and unconfined aquifers has produced a set of scaling relationships between the spatial variables, hydrologic variables, and parameters. The set of scaling transformations preserve the structure of the equations in the sense that the scaling transformations leave the initial‐boundary value system representing the invariant groundwater flows. This theoretical approach elucidates not only the scaling relationships but also the properties that hydrologic variables and parameters must satisfy in order for calling to be possible. Validation of the theory developed is carried out through a series of four numerical simulations using the USGS modflow ‐2005 software package. The results of these experiments demonstrate that the derived scaling transformations can effectively form predictive models of large‐scale phenomena at small scales with negligible error in many cases. Comments on the limitations of the approach and directions for future research are made in the closing sections. Copyright © 2016 John Wiley & Sons, Ltd.     

关于水文地质水井钻探工程中新型自动解垢过滤器的分析研究

水文地质钻探、水井钻探是探矿工程的重要组成部分。随着水资源需求量的增加和生态环境保护要求的提高,水文地质和水井钻探工程显得更为重要。在其成井过程中,常见过滤器腐蚀结垢,直接影响井眼进水量和抽水效果,甚至导致过滤器和井眼报废。俄罗斯南方国立技术大学Третьяк А.Я.教授等人发明了自动解垢过滤器,解决了过滤器腐蚀结垢问题。     

免共振沉桩过程对地表振动影响的FLAC3D数值模拟

为研究免共振沉桩过程对地表振动影响,采用密度放大法以消除模型桩弹性模量过大对计算效率的影响,在有限差分软件FLAC^3D中建立了相应的连续振动沉桩模型,并和文献中的现场测试结果进行了比较,分析了激振力幅值和振动频率这两个施工参数对地表振动响应的影响。结果表明：密度放大法可有效提高数值模拟的计算效率,模拟沉桩7.0倍桩径（4.9 m）所需计算时间约为12.0 h,数值结果较好地模拟了现场测试中免共振沉桩的地表振动影响;激振力幅值和振动频率均主要对近场（水平距离为5.0倍桩径范围内）的地表振动有明显影响;临界沉桩深度与地表振动影响峰值相对应,该深度随水平距离先增大后趋于稳定;激振力幅值对临界沉桩深度的改变不明显,振动频率对远场临界沉桩深度则有较明显影响。     

普朗斑岩型铜矿床成矿元素多重分形特征及其矿化强度指示

成矿元素品位的变化受控于长期地质作用过程,具有较强的非线性特征,定量刻画其变化特征有助于深入理解成矿过程,并为找矿预测提供理论依据。运用多重分形去趋势移动均值（MFDMA） 法,分析云南普朗斑岩型铜矿床4号勘探线钻孔Cu元素品位的多重分形特征及其对矿化强度的指示意义。结果显示：所有钻孔Cu元素品位具有多重分形特征,且不同矿化等级的元素分布存在局部奇异性差异,多重分形强度随矿化强度等级减弱而增加;这些特征指示在钾硅化带—带内侧强矿化钻孔的高品位相对聚集,而带外侧角岩化—青磐岩化带的高品位相对分散;通过数据随机重排技术推测Cu品位多重分形结构奇异性差异是由其分布概率密度和长相关性共同作用引起,后者的作用贡献大于前者。     

Multifractal behaviour of long‐term karstic discharge fluctuations

Karstic watersheds are highly complex hydrogeological systems that are characterized by a multiscale behaviour corresponding to the different pathways of water in these systems. The main issue of karstic spring discharge fluctuations consists in the presence and the identification of characteristic time scales in the discharge time series. To identify and characterize these dynamics, we acquired, for many years at the outlet of two karstic watersheds in South of France, discharge data at 3‐mn, 30‐mn and daily sampling rate. These hydrological records constitute to our knowledge the longest uninterrupted discharge time series available at these sampling rates. The analysis of the hydrological records at different levels of detail leads to a natural scale analysis of these time series in a multifractal framework. From a universal class of multifractal models based on cascade multiplicative processes, the time series first highlights two cut‐off scales around 1 and 16 h that correspond to distinct responses of the aquifer drainage system. Then we provide estimates of the multifractal parameters α and C₁ and the moment of divergence q_D corresponding to the behaviour of karstic systems. These results constitute the first estimates of the multifractal characteristics of karstic spingflows based on 10 years of high‐resolution discharge time series and should lead to several improvements in rainfall‐karstic springflow simulation models. Copyright © 2012 John Wiley & Sons, Ltd.     

Uncertainty,entropy, scaling and hydrological stochastics. 1. Marginal distributional properties of hydrological processes and state scaling / Incertitude,entropie, effet d'échelle et propriétés stochastiques hydrologiques. 1. Propriétés distributionnelles marginales des processus hydrologiques et échelle d'état

Abstract

The well-established physical and mathematical principle of maximum entropy (ME), is used to explain the distributional and autocorrelation properties of hydrological processes, including the scaling behaviour both in state and in time. In this context, maximum entropy is interpreted as maximum uncertainty. The conditions used for the maximization of entropy are as simple as possible, i.e. that hydrological processes are non-negative with specified coefficients of variation (CV) and lag one autocorrelation. In this first part of the study, the marginal distributional properties of hydrological variables and the state scaling behaviour are investigated. Application of the ME principle under these very simple conditions results in the truncated normal distribution for small values of CV and in a nonexponential type (Pareto) distribution for high values of CV. In addition, the normal and the exponential distributions appear as limiting cases of these two distributions. Testing of these theoretical results with numerous hydrological data sets on several scales validates the applicability of the ME principle, thus emphasizing the dominance of uncertainty in hydrological processes. Both theoretical and empirical results show that the state scaling is only an approximation for the high return periods, which is merely valid when processes have high variation on small time scales. In other cases the normal distributional behaviour, which does not have state scaling properties, is a more appropriate approximation. Interestingly however, as discussed in the second part of the study, the normal distribution combined with positive autocorrelation of a process, results in time scaling behaviour due to the ME principle.