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.     

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。     

中国城市标度律及标度因子时空特征

城市标度律刻画了城市系统中城市要素与人口数量之间的规模缩放关系,但标度律在中国城市系统中的适用性和意义尚不明确。本文采用中国275个地级及以上城市数据,探究不同城市要素与人口规模的标度关系,并从时空维度探究标度因子的时空演化规律。结果表明：作为典型的快速城市化发展中国家,中国城市发展符合标度律,且呈现出与发达国家不同的特征：中国城市人口集聚带来的经济产出集聚效应显著,而土地利用、基础设施与公共服务的规模经济效应还有待增强。部分基础设施、生活设施要素与人口规模呈超线性或线性关系,与预期的次线性相悖,基础教育、医疗等要素的标度因子则远低于发达国家的次线性阈值,反映了公共资源向大城市聚集、不同规模城市发展不平衡等快速城镇化进程中城市系统的独特性。标度因子的区域分异反映城市发展协调程度差异,其中东北地区不同规模城市差异最为显著。主要城市要素标度因子随时间的变化表明,中国大城市的经济产出集聚效应在2009年最为显著,而后略有下降;中国大城市土地扩张总体上自2000年以来持续加速,2008年以后仍维持在较高水平,管控城市特别是大城市的外延式扩张、提高土地利用效率具有紧迫性。中国城市标度律研究有助于认知快速城市化地区城市系统特征和演化规律,为实现区域协调发展与落实新型城镇化发展战略提供支持。     

京津冀城市用地形态的双分形特征及其演化

区域城乡一体化的标志之一是城镇体系结构的一体化,这个过程可以从标度的角度进行描述和评价。分形是标度分析的重要方法,地理空间无尺度分布特征的典型参数是分维。论文以京津冀城镇体系为例,利用遥感图像的解译数据和人口普查数据开展分形分析、位序-规模分布分析和异速标度分析,用以解释1995—2013年间京津冀城镇体系演化的过程。结果表明,京津冀城镇体系及其演化的特征有：①京津冀空间结构和位序-规模分布都表现为自仿射双分形结构;②京津冀区域的城市人口-城区面积异速标度退化为假线性关系;③随着城镇体系的演化,自仿射的双分形结构逐步向自相似分形结构演化。由此得出结论：其一,京津冀城镇体系存在结构性的不协调因素。其空间结构和等级结构具有二元化特征,但演化方向却呈现内在结构一体化的显著趋势。其二,大城市用地不够集约。城市边缘区的无序扩张导致土地利用铺张浪费。地方政府和规划专家可以有意识地利用城镇体系演化的这种特征和趋势制定管理措施和优化规划方案。     

基于灯光数据的京津冀城市多标度异速分析

城镇体系的时空演化是一个复杂的动力学过程,具有无尺度性,其特征可以采用异速标度指数定量描述。论文以京津冀为例,基于1992—2013年夜间灯光数据的校正结果,提取城镇夜间灯光信息,采用多标度异速分析方法,分析京津冀城镇体系的相对发展特征及其空间分异格局。研究发现：①京津冀大城市的增长空间局限日益显著。虽然大城市如京津唐的绝对发展水平高,但接近环境承载量的极限,22 a间增长快速的是大城市交接地带的小城市(如三河、迁安、廊坊等)。②相对增长速度快的城市从东北到西南呈现带状分布——政府选择发展的“雄安新区”就在这个轴带上。由此可以得出两个结论：其一,京津冀城市演化的趋势相对均衡化,空间结构异质性逐步减弱,整个城镇体系的发展趋于相对平衡状态;其二,大、小城市“两极”贯通或许是增强城镇体系功能的有效途径。京津冀的空间格局优化不能仅仅考虑主要的、规模大的中心城市,而应该基于等级结构协调整个城镇网络体系。     

GRACE时变信号恢复方法对比分析

针对利用GRACE重力数据反演地表质量变化过程中产生的时变信号削弱和泄露现象,分别采用尺度因子法和迭代恢复法对信号进行恢复,并选用CSR Mascon产品从时间序列变化和空间分布两个角度对两种恢复方法的效果进行对比分析。结果表明:1)尺度因子法虽实现上较为简单,但其计算结果完全依赖于所选的先验模型,当所选模型的可靠性较差时,会影响到GRACE反演结果的可靠性。2)迭代恢复法的恢复过程仅受GRACE原始观测值的约束,能较好地恢复研究区域的长期趋势信号和周期信号,但在部分区域可能存在信号过量恢复的现象。建议采用迭代恢复法进行GRACE时变信号恢复。