Continuation of normal doubly symmetric orbits in conservative reversible systems

In this paper we introduce the concept of a quasi-submersive mapping between two finite-dimensional spaces, we obtain the main properties of such mappings, and we introduce “normality conditions” under which a particular class of so-called “constrained mappings” are quasi-submersive at their zeros. Our main application is concerned with the continuation properties of normal doubly symmetric orbits in time-reversible systems with one or more first integrals. As examples we study the continuation of the figure-eight and the supereight choreographies in the N-body problem.     

analyzing the variation characteristics of stress field in hetao seismic belt using focal mechanism data

Based on analysis of background of geological tectonic movement and strong earthquake activity, we first obtained the focal mechanism solutions using amplitude ratio and CAP method, then determined the characteristic of average stress field of the study area by inversion of the stress field. On this basis, we selected the source mechanism consistency parameter as the inspection index to obtain the latest changes of stress field in Hetao seismic zone based on its temporal and spatial analysis. Two methods were used in the stress field inversion for comparison and analysis, which are average stress axis tensor and LSIB(Linear stress inversion bootstrap, LSIB). According to the geological tectonic movement and focal mechanism solutions of M_S≥4.0 earthquakes from 1970, we judge that the stress field evolution process of Hetao seismic belt is controlled jointly by vertical difference movement and horizontal shear movement, resulting in that the normal fault and strike-slip fault mechanisms are dominating.Taking into account the station layout of the study area, and in order to ensure the accuracy of calculation, we calculated 224 earthquakes focal mechanism solutions by using amplitude ratio and CAP method, including 164 earthquakes with 2.8≤M_L<3.5, 42 earthquakes with 3.5≤M_L<4.0, and 18 earthquakes with M_L≥4.0; The statistical results on type of focal mechanisms show that, there are 142 strike-slip earthquakes(63.4%), 50 normal fault earthquakes(22.3%)and 32 thrust fault earthquakes(14.3%). In this study period(from 2001 to 2012), most earthquakes had a strike-slip mechanism in Hetao seismic belt, this is one of the inherent characteristics of the stress field.The result of average stress axis tensor and LSIB shows that, the azimuth of maximum compressional stress is 47°～52°, direction is NE-SW; The azimuth of minimum compressional stress is 313°～322°, direction is NW-SE; This indicates that, the stress field characteristics of Hetao seismic belt and its sub-block are not completely consistent. Linhe Basin exhibits coordinated stress field characteristics with Hetao seismic belt, but Hubao Basin exhibits regional differences, direction of compressive stress has clockwise deflection in Baotou area, and the compressive stress direction is NEE. This heteropical character of stress field is also confirmed by horizontal projection distribution of stress axis of historical strong earthquakes and recent moderate and small earthquakes. Since 2003, the temporal sequence curve of consistency parameter of Hetao seismic belt had a downward trend, this change was caused by focal mechanism consistency parameter of Linhe to Wuhai area, which indicates that this structural position is possible to be a priority area for stress accumulation and accelerated release in future.     

Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: One-dimensional soil thaw with conduction and advection

Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.     

2012年4月15日福建仙游M_L 4.1地震震源机制解及震源深度

从2010年8月4日至2013年4月24日在福建仙游共发生记录到地震667次,其中最大地震为2012年4月15日发生的ML4.1级地震。本文利用矩张量反演方法 ,反演得到2012年4月15日ML4.1、2012年11月25日ML3.8地震的震源机制解。这两次地震的震源机制解都为走滑断层,断层走向为北西向,主压应力轴方向为近南北向。分别利用波形拟合和sPL深度震相方法确定2012年4月15日ML4.1地震的震源深度,认为该次地震的震源深度在8~9 km。     

Constraining the focal mechanism of the Lushan earthquake with observations of the Earth’s free oscillations

The amplitudes of the Earth's free oscillations have a close relationship to earthquake focal mechanisms. Focal mechanisms of large earthquakes can be well analyzed and constrained with observations of long period free oscillations. Although the 2013 Lushan earthquake was only moderately sized, observable spherical normal modes were excited and clearly observed by a superconductive gravimeter and a broadband seismometer. We compare observed free oscillations with synthetic normal modes corresponding to four different focal mechanisms for the Lushan earthquake. The results show that source parameters can be analyzed and constrained by spherical normal modes in a 2.3–5 mHz frequency band. The scalar seismic moment M0 has a major influence on the amplitudes of free oscillations; additionally, the strike, dip, rake and depth of the hypocenter have minor influences. We found that the synthetic modes corresponding to the focal mechanism determined by the Global Centroid Moment Tensor show agreement to the observed modes, suggesting that earthquake magnitudes predicted in this way can readily reflect the total energy released by the earthquake. The scalar seismic moment obtained by far-field body wave inversion is significantly underestimated. Focal mechanism solutions can be improved by joint inversion of far- and near-field data.     

沈阳及其附近地区小震复合震源机制解

在收集了沈阳及其附近地区 (12 1°30′～ 12 4°30′E ,4 1°～ 4 3°N)已有地震震源机制解成果的基础上 ,利用MAPSIS系统提供的P波初动求解方法 ,求解了 1974年 12月～ 2 0 0 1年 12月期间 ,该区域小震复合震源机制解 (平均解 )。结果表明 ,研究区主压应力轴P轴集中分布在NEE SWW方向 ,主张应力轴T轴集中分布在NNW SSE方向 ,这与本地区区域应力场的方向一致。     

CONSTRAINING THE FOCAL MECHANISM OF THE 2015 NEPAL EARTHQUAKE WITH OBSERVATIONS OF THE CONTINUOUS GRAVITY STATIONS

On 25 April 2015, a magnitude M_S8.1 interplate thrust earthquake ruptured a densely instrumented region of Nepal. After earthquake, the focal mechanism solutions of Nepal earthquake were provided by well-respected international earthquake research institutions based on different data and methods, which were different. We compared free oscillations observed by 18 spring gravimeters of continuous gravity stations with synthetic normal modes corresponding to 3 different focal mechanisms for the Nepal earthquake, and the focal mechanisms solutions of Nepal earthquake were analyzed and constrained by spherical normal modes in a 2 to 5mHz frequency band. Based on the optimal focal mechanism, the accurate magnitude was searched. The results show that the focal mechanism of Nepal earthquake can be estimated by spherical modes in the 2 to 5mHz frequency band. The synthetic modes corresponding to the focal mechanism determined by the GCMT Moment Tensor Solution showed agreement to the observed modes, the average of misfit factors F was 0.03, and the average of scaling factors was 1.04, which was closest to 1, suggesting that earthquake magnitudes predicted in this way can reflect the total energy released by the earthquake. Based on the focal mechanism solutions provided by GCMT, keeping the strike, dip, slip, depth constant, adjusting the scalar moment, the real scalar moment was searched. When the average of scaling factors was 1, the average of misfit factors F was only 0.03. After calculation, the scalar moment of Nepal earthquake was 8.09×10²⁰ Nm, and the corresponding magnitude was M_W7.91.     

中心裂纹巴西圆盘压缩载荷下T应力研究

为了研究中心裂纹巴西圆盘试件在压缩载荷作用下T应力的解析计算方法,通过权函数法推导出集中载荷作用下T应力的显式表达式,进而得到分布载荷作用下的T应力表达式。与边界配位法进行对比,所得公式优点在于任意相对裂纹长度和任意加载角下的T应力值都能较容易的精确得到。进一步分析表明,分布载荷与集中载荷作用下T应力的偏差随着载荷分布角的增加而增加。集中载荷作用下,相对裂纹长度固定时,T应力随着加载角的增大而增大。中心裂纹巴西圆盘纯I型与纯II型断裂试验时,大多数情况下的T应力都为负值。T应力值对中心裂纹巴西圆盘测定断裂韧度试验有影响,想要通过使T应力为0来消除这种影响是很难达到目的的。     

基于3D-FSM的预紧力端锚数值模拟及其多核并行化研究

在对传统锚杆荷载传递机制分析的基础上,提出了一种考虑托板、锚杆与岩体相互作用的数值模拟方法：通过Kelvin基本解计算出锚杆集中力对围岩的影响,同时就锚杆自由段与相应岩体两端点的位移差相等建立位移方程,结合先前开发的3D-FSM数值模拟系统中的表面受力平衡方程进行联立求解,利用所得结果可以计算域内任意点的应力及位移变化,形成完整的预紧力端锚边界元数值模拟系统。通过与Flac3D系统模拟对比,验证了该系统的可靠性。为提高运算效率,对该系统进行基于OpenMP的多核并行化改进,给出了改进的基本思路和加速比对比图。由于边界元本身具有建模简单、计算区域大、计算精度高等优点,因此,这种模拟方法有很大的应用价值。     

利用连续重力观测约束2014智利Iquique地震的震源机制解

2014年4月1日,智利北部Iquique地区近海发生MW8.1地震,地震发生之后,国际上一些著名的地震科研机构和学者采用不同的数据和方法计算得到此次地震的震源机制解,但这些结果存在较大差异.地球长周期自由振荡的振幅主要依赖于地震矩的大小及地震断层的破裂方式,可以很好地约束地震震源机制.因此,本文根据2014年Iquique地震现有的6个不同震源机制解模拟计算了该地震激发的自由振荡信号,并与全国连续重力台网中16个弹簧重力仪的观测结果进行比对,基于1.5~5.3mHz的球型简正模分析和约束了Iquique地震的震源机制解.研究发现,基于美国地质调查局WPhase Moment Tensor Solution反演的震源机制解的自由振荡模拟值与实际观测符合最好,其相应的震级能较好反映Iquique地震释放的总能量,而利用海啸数据反演的标量地震矩偏小,联合远场和近场长周期观测数据反演可显著改善震源机制解.另外,还基于格尔木重力台站的模拟值与观测值定量分析了不同震源机制解参数对自由振荡振幅的影响.结果表明地震的标量地震矩M0对自由振荡振幅的影响最大,而断层走向、倾角、滑动方向角和震源深度对自由振荡的振幅影响相对较小.