Caustics in seismology

Summary. Catastrophe optics provides insights into the structure of the caustics produced by seismic events. Two examples are given. The first is the caustic formed on the surface of the Earth between 10° and 30° from the event by P rays that have reached the transition zone of the mantle. This is organized by one or more approximately circular cusp lines; these are generally below the surface, but because of lateral (regional) variations, they are puckered. Where they intersect the surface they give rise to characteristic beak-to-beak and lips patterns. The second example is the caustic structure produced by refraction at the core–mantle boundary. There is a four-cusped figure at the antipodal point, and, in addition, it is suggested that the main 143° PKP caustic is actually cusped, the cusps being smeared out when radially symmetric earth models are used. The cusps arise from bumps on the core–mantle boundary. In general, the caustic, and its accompanying diffraction structure, associated with a bump can be understood as an unfolding of the parabolic umbilic catastrophe.     

南海中北部热带气旋强度突变的天气气候特征分析

本文对1960-2002年在南海中北部活动的热带气旋进行分析统计,发现有如下气候特征：南海中北部平均每年有6.7个热带气旋,有4.9个热带气旋强度发生突变,其中有3%的热带气旋只发生突然增强,72%的热带气旋只发生突然减弱,25%的热带气旋既发生突然增强又发生突然减弱过程.强度突然减弱发生在4-12月,主要集中在登陆和登陆后的陆地区域,分布较广;强度突然增强发生在4-11月,主要出现在珠江口以西至海南岛东部海面、东沙群岛和西沙群岛海面.     

中国地级及以上城市对外开放度时空分异格局

对外开放是推动中国经济改革与发展的重要机制和动力,是国家繁荣发展的必由之路。以中国343个地级及以上行政单元为研究对象,通过构建熵值-突变系统模型从3个维度测算对外开放度;运用探索性空间数据分析、三维插值拟合分析及重心迁移、空间变差函数等方法,分析中国地级单元对外开放度的时空分异格局及演化的内在机理。结果显示：（1）中国地级单元对外开放度表现出明显的行政指向性、空间地带性和开放区域性等多重分异特征。对外开放度整体呈现东部 > 中部 > 东北 > 西部,南方 > 北方的特征;直辖市、副省级城市、省会城市、经济特区及沿海开放城市整体对外开放水平较高,地级市间差异较大;10 a间,对外开放度总体差异逐渐减小。（2）对外开放度存在明显的空间依赖性,表现为"小分散大集聚"的空间俱乐部趋同特征;10 a间,开放型纹理分散程度趋于提升,闭塞型纹理集聚程度趋于收敛,高原型整体呈破碎化分布。（3）中国对外开放度格局变异的随机成分在逐渐减小,空间自组织性和连续性较为显著,东北-西南方向均质性最好,东南-西北方向空间差异明显。科学剖析地级单元对外开放度时空格局分异及演化机理,对制定合理的对外开放战略和促进外向型经济与区域经济双轨融合发展具有重要的意义。     

狭窄煤柱冲击地压的折迭突变模型

对简化的狭窄煤柱岩爆分析模型,通过功、能增量平衡关系的途径,导出狭窄煤柱岩爆的突变模式属折迭突变模型。该突变模型的平衡方程和平衡路径所展示的全部性态, 可对煤柱以岩爆形式破坏和渐进形式破坏过程中,包括系统稳定性在内的所有行为,作一一相对应的描述。并首次给出的岩梁弹性能变化（释放）率曲线包含了丰富的信息量,对理解岩梁-煤柱系统在各阶段的行为规律有着重要的作用。所给出的能量输入率 ,是系统失稳临界条件的提法和表达式中蕴涵了Cook刚度判据,故看作是Cook判据能量形式的动态推广。利用能量输入率可将极限状态下岩煤系统稳定性的定性认识提高到用定量形式描述,为岩煤系统稳定性的表述赋予新的形式。     

锚固体梁的弯曲突变失稳问题分析

现场经验及模型实验表明,煤巷锚杆支护中有时出现锚固体的弯曲突变失稳现象。通过力学模型解析,系统地研究了锚固体的弯曲突变失稳机理及平衡条件,并对锚固体的横向承载面积及水平推力进行了分析,发现锚固体梁在受载变形的不同阶段维持不同的自稳特征,保持不同的动态平衡。因此,研究锚固体突变失稳的发生和控制具有理论价值和工程意义。     

圆形硐室岩爆的折迭突变模型

均匀围压下圆形硐室岩爆是传统意义上的软化区内岩环经过塑性变形局部化阶段完成的。当处于极限状态的塑性变形集中区承载能力下降时, 岩环中相对完好部分以弹性方式卸载,当后者释放的弹性能超过前者塑性变形所耗散的能量时便发生岩爆。简捷地通过等效应力 和等效应变 关系建立突变模型对硐室岩爆进行了分析, 将状态变量 用软化区半径 来表示。分析表明: 岩爆发生条件与硐室岩体的升降模量比 和岩体裂隙发育程度 的乘积有关; 对于特定冲击倾性的岩体,存在对应的临界软化区深度 , 即软化区深度达到 时便发生岩爆;还给出硐室岩爆释放地震能等计算式,岩爆释放的地震能量级则与硐室软化区深入程度有关。     

岩盐溶腔顶板稳定性突变理论分析

采用固支大变形圆板突变模型研究了单井溶腔顶板的稳定性,得出了溶腔顶板岩层失稳的必要条件;并考虑了自重侧压力及水平构造应力的综合作用,用平直梁尖点突变模型研究了连通井顶板的失稳突跳,得出了连通井顶板失稳的充要条件。为溶腔稳定性控制和溶腔用于战略石油和天然气的储备打下理论基础。     

灰色灾变模型在蒋家沟泥石流年输沙量短期预测中的应用

根据蒋家沟泥石流年输沙量最近8年的实测资料,运用灰色系统理论的灾变预测方法建立了泥石流年输沙量的灾变预测模型,对未来可能出现的年输沙量超过200万立方米的灾变年份进行了预测,并引入等维新息模型,使短期灾变预测得以连续进行。     

近50a来北方农牧交错带气温变化趋势及突变分析

利用北方农牧交错带内及邻近的共46个气象站点1957—2007年的气温数据资料,运用Mann-Kendall非参数检验法、R/S分析法,对气温变化趋势及突变特征进行了分析。结果表明,近50a来北方农牧交错带年、季气温普遍升高,20世纪90年代以后气温上升趋势显著,达到了99%的信度水平,年平均气温增温速率约为0.32℃/10a,明显高于全国和全球的气温增长率,其中冬季增温尤为明显,对全年增温贡献率最大;Hurst指数分析表明,整个北方农牧交错带年、季气温在未来仍表现出上升趋势,冬季的增温持续性最强;北方农牧交错带年、季升温幅度在空间上表现出一定的区域差异性,其年平均气温在90年代初发生了升温突变。     

A tale of two planets: geomorphology applied to Mars' surface,fluvio‐deltaic processes and landforms

Deltas on planet Mars record past climate, but so far a wide range of hypotheses for their formation have been proposed. The objective of this paper is to understand martian fan deltas, their formative conditions, evolution and formative duration, and implications for the past climate. As an introduction to Mars, physiographic provinces are described and unambiguous proof is listed for the presence of flowing water in the past, such as certain minerals, groundwater, catastrophic outflow channels, alluvial fans and fan deltas, distributary networks and glaciers. The climate history of Mars differs from that of Earth by having had much drier conditions than on Earth, extreme intermittency and extreme events, most of them billions of years ago. Tens of fan deltas, unchannelized fan deltas and stepped fans have been found in impact crater and other lakes. The stepped fans were likely formed by backstepping under fast rising lake levels and have no known terrestrial equivalent. The fan deltas were formed once the lake overflowed. Alluvial fans are much more numerous and formed with less water. The delta studies illustrate how major challenges of martian morphology and reconstruction of past conditions can be taken up most effectively by combinations of the available high‐resolution images and digital elevation models, terrestrial analogues, laboratory experiments and physics‐based models gleaned from geomorphology. To resolve formative mechanisms and time scale of martian fans and deltas, morphological distinctions between dense debris flows and dilute fluvial flows must be identified for both source and sink areas. Furthermore, the properties of the martian surface material are very poorly constrained but can be explored by modelling various mass wasting, fluvial and glacial phenomena and hydrology, and by experimentation with slightly cohesive sediment. Finally, the highly debated role of groundwater sapping in valley and delta formation on Mars should be explored experimentally. Copyright © 2010 John Wiley & Sons, Ltd.