Numerical Investigation of the Galactic Problem by Computing Families of Periodic Solutions

The galactic dynamical system expressed by a third-order axisymmetric polynomial potential is investigated numerically by computing periodic solutions. We define as Sthe compact set of initial conditions generating bounded motions, and as S ^p , with S ^p ? S, the countable set of all initial conditions generating periodic solutions. Then, we consider the subsets S _s ^p and S _a ^p of S ^p , where S _s ^p ∪ S _a ^p = S ^p , S _s ^p S _a ^p = Ø, the first of which corresponds to symmetric periodic solutions, and the second to asymmetric solutions. Then, we approximate the set S _s ^p , leaving treatment of the set S _a ^p of asymmetric solutions for a future publication. The set S _s ^p is known to be dense in S (‘Last Geometric Theorem of Poincar;’, Birkhoff, 1913). Using a computer programme capable to locate all elements of the set S _s ^p that generate symmetric periodic solutions that re-enter after intersecting the axis of symmetry from 1 to ntimes. The results of the approximation of S _s ^p in the total domain and in the sample sub-domains of zooming, we present in graphical form as family curves in the (x, C) plane. The solutions located with the largest periods re-enter after 440 galaxy revolutions while the families calculated fully (initial conditions, period, energy, stability co-efficient) include solutions that re-enter after 340 galaxy revolutions. To advance further the approximation of the set S _s ^p thus obtained, we applied the same procedure inside eight sub-domains of the domain Sinto which we ‘zoomed’ through selection of finer search steps and double maximum periods. The family curves thus calculated presented in the (x, C) plane do not intersect anywhere in some sub-domains and their pattern resembles that of laminar flow. In other sub-domains, however, we found family curves from which branching families emanate. The concepts of completeand non-completeapproximation of S _s ^p in sub-domains of laminar and sub-domains with branching family curves, respectively, is introduced. Also, the concept of basic family of order1, 2, ..., n, are defined. The morphology of individual periodic solutions of all families is investigated, and the types of envelopes found are described. The approximate set S _s ^p was also checked by computing Poincar; sections for energy values corresponding to the mean energy range of the eight sub-domains of zooming mentioned above. These sections show that most parts of the compact domain in Sgenerating non-periodic but bounded solutions correspond to with well-shaped tori that intersect the x-axis, a fact that implies that dominant to exclusive type of periodic solutions are the symmetric ones with two normal crossings of this axis. The presence of non-symmetric periodic solutions as well as of chaotic regions is encountered. All calculations reported here were performed using the variable step R-K 8th-order direct integration and setting the allowable energy variation Δ C= |C _start? C _end| < 10^?13. The output, consisting of many thousands of families and their properties (initial conditions, morphology, stability, etc.), is stored in a directory entitled ‘Atlas of the Symmetric Periodic Solution of the Galactic Motion Problem’.     

Discovery of Potassium-Bearing Cuttings from the Well Yangta 4 in the Kuqa Depression and Seam Division

正The world petroleum exploration suggests that,about70%of the world’s potash resources were discovered during oil and gas exploration(Zheng et al.,2007).The Kuqa depression in the Tarim basin is abundant with petroleum exploration data,and     

On the recent global mean sea level changes: Trend extraction and El Niño's impact

The spatial sampling offered by TOPEX and Jason series of satellite radar altimeters and its continuity during the last twenty years are major assets to provide an improved vision of the global mean sea level (GMSL). The objective of this paper is to examine the recent GMSL variations (1993–2012) and to investigate the correlation between the GMSL and ENSO (El Niño-southern oscillation) episodes. For this purpose, a mean sea level anomalies time series, obtained from TOPEX, Jason-1 and Jason-2 measurements, is used to determine the trend of GMSL changes by using a simplified form of an unobserved components model (namely UCM). Then, to investigate the impact of the ENSO phenomenon on the GMSL changes, we considered the sea surface temperature anomalies (SSTA) index over the Niño3 region (5N–5S 150W–90W). Cross wavelet transform and wavelet coherence analysis are performed to expose common power between the GMSL changes and the SSTA index and their relative phase in the time–frequency space. The results indicate that there are in the estimated GMSL's trend a number of fluctuations over short periods that are least partly related to the El Niño/La Niña episodes. Cross wavelet transform and wavelet coherence analysis indicate that a significant correlation between GMSL and ENSO occurred during 1997–1998, 2006–2007, 2009–2010 El Niño events and 2007–2008 and 2010–2011 La Niña ones. All these areas show in-phase relationship, suggesting that GMSL and SSTA index vary synchronously.     

Quasi indicatrix approach for distortion visualization and analysis for map projections

Tissot’s indicatrix or ellipse of distortion is a diagram that is the projection of an infinitesimal circle on the original surface. It is normally an ellipse of which elongation depends on the amount of distortion caused by map projection. It provides a medium for analyzing existing projections and developing new ones. The ellipse can be scaled and depicted on the map for visualization purposes. This paper presents an alternative approach, in which the projection of a finite small circle on the sphere is used. Its projection is normally an ellipse that can be very close to Tissot’s indicatrix, and is called quasi indicatrix, here. Its parameters can be derived from the forward projection equations without using partial derivatives. Therefore, it is a useful and practical approach from a programmer’s point of view. The quasi indicatrix approach is also numerically tested on Aitoff–Hammer projection with a set of points. The indicatrix parameters obtained by using this approach deviate 0.5% from the ground truths at most, being the average less than 0.2%.     

4350–3130 Ma detrital zircons in the Southern Cross Granite‐Greenstone Terrane,Western Australia: Implications for the early evolution of the Yilgarn Craton

SHRIMP U–Pb zircon analysis indicates that detrital zircons from extensive quartzite units in the Southern Cross Granite‐Greenstone Terrane of the central Yilgarn Craton have ages ranging from ca 4350 Ma to ca 3130 Ma. Regional mapping studies indicate that the quartzites lie at the stratigraphic base of the exposed succession. The detrital zircon age profiles of the Southern Cross Granite‐Greenstone Terrane quartzites are remarkably similar to those of quartzites in the Narryer and South West Terranes, in the northwest and southwest of the Yilgarn Craton respectively, and are significantly older than any igneous rocks that have been dated anywhere in the Yilgarn Craton other than the Narryer Terrane. Similar detrital‐zircon‐bearing quartzites have not been identified in the Murchison Granite‐Greenstone Terrane. These age profiles suggest that the quartzites have a common depositional history. Granites in the central Yilgarn Craton are mainly younger than ca 2750 Ma and contain rare xenocrystic zircons older than 3100 Ma. If the central and western Yilgarn quartzites were all deposited at approximately the same time, the lack of preserved continental crust in the Southern Cross and Murchison Granite‐Greenstone Terranes, and the South West Terrane, that is older than 3100 Ma, suggests that pre‐3100 Ma Narryer‐like continental crust may have been rifted or extensively reworked during deposition of greenstone successions between ca 3000 and ca 2700 Ma. If not, then a ca 4350 Ma detrital zircon in the Southern Cross Granite‐Greenstone Terrane indicates more widespread, very old, continental crust than has previously been identified.     

层状黏弹性介质中Rayleigh波频散曲线“交叉”现象分析

Rayleigh波勘探方法在探测近地表横波速度、动力学特征等环境与工程地球物理领域获得了广泛应用.这种方法以弹性层状介质理论为基础,然而实际介质具有黏弹性,研究面波在层状黏弹性介质中的传播特征,将为近地表面波勘探提供有益帮助.在某些弹性层状介质模型中,例如存在低速夹层和强波阻抗差异地层模型,Rayleigh波相邻两条频散曲线彼此会非常靠近,产生看似彼此"交叉"的现象,即"osculation"现象,但对于黏弹性介质中的这种现象并没有进行相关的研究.本文利用Muller法计算层状黏弹性介质Rayleigh波频散方程,基于层状介质模型中Rayleigh波频散和衰减曲线连续的性质,结合本征位移曲线特征,分析二层黏弹性介质模型中Rayleigh波频散曲线"交叉"现象以及"交叉"点附近的波动特性.结果表明:与弹性介质相比,黏弹性介质中Rayleigh波的波动特性存在明显差异,随着介质对地震波的损耗越来越强,将导致Rayleigh波频散曲线发生"交叉"现象.     

沂沭断裂带重复地震识别及断裂深部活动速率的估算

利用山东及邻区数字地震台网2001- 2012 年的地震观测报告及波形资料分析了沂沭断裂带及周缘地区的地震活动并利用识别出的重复地震估算了断层深部滑动速率。重新定位后的地震图像清晰展示了沂沭断裂带南北两段及东西两侧地震活动的显著差异,在研究时段内,60%以上的地震发生在沂沭带东侧的两条断裂上,震源深度分布与研究区的深部构造吻合。根据波形意义上相似地震(cc≥0.8)的定义,识别出了沂沭断裂带及其周缘相似地震共50例,组成相似地震对和多重相似地震对共19组,相似地震对的复发间隔较为随机,从数小时到数百天不等。通过对相似地震对震源位置- -致性的强约束后,基于1组重复地震估算出安丘-莒县断裂在地表以下5.9km处的滑动速率估计值为2.19mm/a,与GPS和地质等浅表观测的滑动速率值基本一致。     

直达Ps与接收函数Ps联合分析地壳各向异性

本文尝试直接利用地震图记录中的Ps转换波,而非传统的接收函数方法,检测地壳介质的各向异性.虽然远震记录中的P波对Ps转换波会有干扰,但P波与Ps转换波具有不同的偏振特性,最小能量法可以将Ps转换波的各向异性参数检测出来,对时间窗的选择也很强壮.本文利用IC台网（New China Digital Seismograph Network,中国新数字地震台网）中的KMI,ENH,LSA,BJT,XAN,WMQ六个台站接收的宽频远震记录进行了测试,并且对比了接收函数方法的结果.研究表明,利用最小能量法直接测量与利用旋转相关法测量接收函数中Ps转换波的结果基本一致.两种方法测量所得的快波偏振方向与地壳运动方向,最大水平主压应力方向,震源机制解压缩轴方向,最大主压应变率方向以及已有的各向异性研究结果基本一致.     

土岩复合地层中CRD隧道施工的变形监测与风险控制

以典型城市土岩复合地层中的某地铁CRD（交叉中隔壁法）隧道为依托,通过分析洞内、外变形监测数据,总结变形规律,对该隧道风险进行有效控制。研究结果表明：洞内、外变形量的60%以上是由上2层导洞开挖引起的;隧道开挖引起的地表沉降槽特征较为明显,地表最大沉降点位于隧道中心线上方偏左;隧道掌子面开挖的横向影响明显,范围约为60m。洞内变形监测的分析指标以拱顶沉降为主,水平收敛为辅;拱顶下沉曲线分段组成,总体呈台阶状下降。综合变形监测分析和施工经验认为：施工中应着重控制上2层导洞初期支护结构的及时闭合;相邻导洞掌子面间距控制在15~20m;台阶长度控制在5m以内,及时封闭仰拱,闭合成环,可有效地控制洞内、外变形和保证初期支护结构稳定性。     

南沙永暑礁近海面风的特征分析

选用南沙永暑礁1989年1月到2009年12月的水文气象月报表资料,运用概率统计的方法将风向和风速记录资料进行分析,定义了永暑礁的4个风期,通过风向风速的年内变化分析得出永暑礁盛行风风向在年内变化成顺时针向右偏移;无论是东北季风期,还是西南季风期,盛行风平均风速都大于非盛行风。东北季风期主导风向顺时针偏移时风力减小,西南季风期主导风向顺时针偏移时,到南南西风时最大,在西南风时略有减弱,呈现波状发展趋势。通过引入风速不稳定指数概念,发现永暑礁西南季风期风速变化突然,更不稳定。