天体运行的介质层壳与离散轨道引论

采用介质层壳弯曲的唯象方法,在规整三维空间中给出了能量曲率方程及物体间的能量引力形式表述,其引力方程的二个条件解分别与Newton引力理论及Einstein引力理论的有关结果相近．讨论了目前分维微积分在函数方面的局限性,给出了相似扩展方程,随后通过讨论天体运行轨道的基线扩展特征,给出了天体运行的离散轨道方程,并以太阳系行星及部分卫星为例,给出了这些天体运行离散轨道方程的具体表述形式。     

宇宙分维构造及其数学基础

探讨了宇宙分维构造的形式,给出了分维微积分及分形测度的数学基础,包括分维导数及分维微积分的表述形式、分维微分方程的规整空间积分解、分形测度的分维微积分定义及自相似分形的测度计算方程．作为诠释,探讨了原子核内中子与质子的趋势关系方程,以及其周期解和原子序数极限值。     

天体运行轨道的一般性Binet方程形式

通过讨论已有质速关系的方程形式,给出质速关系的等效极坐标方程及其Binet方程,进而给出质速关系及质能关系的几个较为具体的方程形式,包括超光速运动形式.随后应用质能关系探讨介质层壳弯曲方法中能量曲率方程解的一般形式,给出天体运行轨道的一般性Binet方程,给出了行星近日点进动、光线弯曲的解析分析.     

模糊分维及其在地震研究中的某些应用

在模糊集理论与分形理论的基础上,引进了模糊分维的概念;给出了模湖容量维D₀与模糊关联维D₂的定义与确定方法;讨论了模糊分维与常用的分维（清晰分维）的关系.给出了模糊分维在地震研究中的应用结果: 1.根据模糊容量维D₀随时间的上升趋势变化,可以划分出大地震活动的高潮期;由模糊容量维D₀与模糊关联维D₂随时间变化的曲线,可以分析识别大地震前的中长期前兆异常. 2.根据模糊容量维D₀随空间和时间的变化,可以划分出未来大震所在的地区,并可发现大震前数年D₀呈现增大或减小的趋势. 3.根据前兆数据的模糊时间分维D₀随时间的变化,可以发现大地震的短期前兆异常.     

断层分形几何学在判定强震危险区中的应用前景初探

本文利用box—Counting法讨论了新疆各主要断裂带的几何分形,得出了各断裂带的分维值。结合区域构造及地震活动性特点,分析讨论了断层分形几何学在判定强震危险区方面的应用前景。结果表明,相应于较大的断层分维数,则对应于较强的地震活动水平;相应于较小的断层分维值,则对应于较弱的地震活动水平。一方面,断裂分维值较高的断裂带,其构造也较复杂。因而,断层分维有可能作为判定活动断裂带地震活动水平的一种特征物理量。     

CHAMP型卫星定轨顾及非线性改正的轨道扰动方程

本文针对CHAMP型卫星建立了顾及非线性改正的轨道扰动方程定轨理论与方法.首先从卫星运动的二阶微分方程出发,引入了正常引力位以及相应的参考轨道,然后分别推导了线性化轨道扰动方程与顾及非线性改正的轨道扰动方程,同时说明了建立的线性化轨道扰动方程与目前处理CHAMP卫星数据的动力学定轨方法是等价的.其次分别对线性化轨道扰动方程与顾及非线性改正的轨道扰动方程的精度进行了估计,在卫星定位精度为3cm与非惯性力测量精度为3×10~(-10)m·s~(-2)的前提下证明了下列结论:当参考轨道与实际轨道之间的距离ρ≤4.7m时线性化轨道扰动方程的精度能达到非惯性力的测量精度以及当ρ≤4.14×10~3m时顾及非线性改正的轨道扰动方程能达到非惯性力的测量精度.由此便可得出结论:相对于线性化轨道扰动方程,顾及非线性改正的轨道扰动方程具有更高的精度,且适合在更长的时间弧段上建立关于引力场位系数的法方程组,特别是针对CHAMP卫星计划进行的模拟计算也完全验证了该结论.最后利用叠加原理,给出了顾及非线性改正的轨道扰动方程的求解方法.此外,还针对GRACE卫星计划利用顾及非线性改正的轨道扰动方程进行了恢复引力场的模拟计算,结果表明:分段建立位系数的法方程组时子弧段分别取值2h、1d、6 d对恢复引力场的结果几乎不产生影响,这表明在处理GRACE数据时能够以6d的弧长来建立法方程组.     

地震记录的广义分维及其应用

根据分形理论,对不同信噪比地震记录的分维特征进行了分析,指出地震记录中噪声背景与信号部分具有不同的分维尺度,地震道时间序列的分维数值与计算时所用的测量尺度有关,因此,可利用广义分维的概念计算地震记录的分数维.地震记录广义分维大大提高了分形算法在计算机自动识别地震波震相时的抗噪声能力.最后用本文方法对实际地震记录进行了有效的初至波自动拾取.     

小波多尺度分解的振幅谱分维算法油气预测

本文结合小波变换理论和分形分维理论,利用小波变换的多尺度分解对地震资料进行分解,选取不同尺度的信息,计算其振幅谱分维数;根据含油气井的振幅谱确定能够反映油气异常信息的标度不变区,在该标度不变区内求分形维数,分维数值越大,说明含油气的可能性越大,据此预测储层的含油气性.实践表明,多尺度分形分维技术能够较准确地反映由地震波...     

多分形断层模型与地震序列研究

本文提出形成地震序列的多分形断层模型并利用分形分维理论讨论该模型及其序列。给出本模型的震级—频度关系、余震序列中强余震预报公式和多分维D_q—q关系式,探讨了利用多分维预报地震的有效性。     

玛纳斯地震前后地震活动信息熵及分维的动态变化

根据耗散结构理论及Mandelbort提出的分形几何学观点,研究了玛纳斯5.8级地震前后地震(M_s≥1.5)序列的时空分布特征、地震活动信息熵及分维的动态变化。发现玛纳斯5.8级地震前存在减熵和降维。认为,地震熵或分维可以定量描述地震时空分布变化过程,并量度变化过程从无序向有序的演化。     

GOCE satellite orbit in the aspect of selected gravitational perturbations

In this work, the GOCE satellite orbit is described in the aspect of perturbations in the Keplerian osculating elements. The perturbations come from the Earth and ocean tides, the gravitation of the Moon, the gravitation of the Sun, the gravitation of planets and Pluto, and the relativity effects. These perturbations are computed for the 30-day interval with a sampling of 2 min. To obtain the simulated orbit, the Cowell numerical integration method of 8th order is used. The first part of the work contains the root mean square (RMS) values of aforementioned perturbations due to the specified forces. The perturbations were compared taking into account their RMS characteristics.     

Lunar Laser Ranging: Glorious Past And A Bright Future

Lunar Laser Ranging (LLR), a part of the NASA Apollo program, has beenon-going for more than 30 years. It provides the grist for a multi-disciplinarydata analysis mill. Results exist for solid Earth sciences, geodesy and geodynamics,solar system ephemerides, terrestrial and celestial reference frames, lunar physics,general relativity and gravitational theory. Combined with other data, it treatsprecession of the Earth's spin axis, lunar induced nutation, polar motion/Earthrotation, Earth orbit obliquity to the ecliptic, intersection of the celestial equatorwith the ecliptic, luni-solar solid body tides, lunar tidal deceleration, lunar physicaland free librations, structure of the moon and energy dissipation in the lunar interior.LLR provides input to lunar surface cartography and surveying, Earth station and lunar retroreflector location and motion, mass of the Earth-moon system, lunar and terrestrial gravity harmonics and Love numbers, relativistic geodesic precession, and the equivalence principle of general relativity. With the passive nature of the reflectors and steady improvement in observing equipment and data analysis, LLR continues to provide state-of-the-art results. Gains are steady as the data-base expands. After more than 30 years, LLR remains the only active Apollo experiment. It is important to recognize examples of efficient and cost effective progress of research. LLR is just such an example.     

APOD mission status and preliminary results

On September 20 th, 2015, twenty satellites were successfully deployed into a near-polar circular orbit at 520 km altitude by the Chinese CZ-6 test rocket, which was launched from the Tai Yuan Satellite Launch Center. Among these satellites, a set of 4 Cube Sats conform the atmospheric density detection and precise orbit determination(APOD) mission, which is projected for atmospheric density estimation from in-situ detection and precise orbit products. The APOD satellites are manufactured by China Spacesat Co. Ltd. and the payload instruments include an atmospheric density detector(ADD), a dual-frequency dualmode global navigation satellite system(GNSS) receiver(GPS and Beidou), a satellite laser ranging(SLR) reflector, and an S/Xband very long baseline interferometry(VLBI) beacon. In this paper, we compare the GNSS precise orbit products with colocated SLR observations, and the 3 D orbit accuracy shows better than 10 cm RMS. These results reveal the great potential of the onboard micro-electro-mechanical system(MEMS) GNSS receiver. After calibrating ADD density estimates with precise orbit products, the accuracy of our density products can reach about 10% with respect to the background density. Density estimates from APOD are of a great importance for scientific studies on upper atmosphere variations and useful for model data assimilation.     

Zero initial partial derivatives of satellite orbits with respect to force parameters violate the physics of motion of celestial bodies

Satellite orbits have been routinely used to produce models of the Earth’s gravity field. In connection with such productions, the partial derivatives of a satellite orbit with respect to the force parameters to be determined, namely, the unknown harmonic coefficients of the gravitational model, have been first computed by setting the initial values of partial derivatives to zero. In this note, we first design some simple mathematical examples to show that setting the initial values of partial derivatives to zero is generally erroneous mathematically. We then prove that it is prohibited physically. In other words, setting the initial values of partial derivatives to zero violates the physics of motion of celestial bodies. Supported by a Grant-in-Aid for Scientific Research (Grant No. B19340129)     

基于星载GPS的HY-2卫星高精度精密定轨模拟研究(英文)

HY-2卫星是我国第一颗测高卫星,其径向定轨精度要求厘米量级,搭载了星载GPS接收机。目前HY-2还处于测试阶段,没有公布观测数据。为了确定基于星载GPS的HY-2精密定轨流程及其定轨精度,本文模拟了HY-2卫星星载GPS观测数据,结果表明HY-2星载GPS天线每个历元至少观测7颗GPS卫星。给出了基于星载GPS的精密定轨流程,分别采用简化动力学方法和动态几何法进行了精密定轨实验。对于相位1mm和3mm随机误差的相位观测数据,简化动力学法和动态几何法定轨都能够实现厘米量级的径向精密定轨,几何法定轨精度略低于简化动力定轨。地球重力场模型是影响HY-2卫星精密定轨的重要因素,本文对不同阶次的重力场模型EIGEN2、EGM96、TEG4和GEMT3进行了简化动力学定轨实验,高于50阶次的重力场模型都能够实现厘米级径向精密定轨,主要原因在于大量的高精度星载GPS观测数据和重力场模型精度的提高。     

On precise orbit determination of HY-2 with space geodetic techniques

As the first radar altimetric satellite of China, HY-2 requires the precise orbit determination with a higher accuracy than that of other satellites. In order to achieve the designed radial orbit with the accuracy better than 10 cm for HY-2, the methods of precise orbit determination for HY-2 with the centimeter-level accuracy based on space geodetic techniques (DORIS, SLR, and satellite-borne GPS) are studied in this paper. Perturbations on HY-2 orbit are analyzed, in particular those due to the non-spherical gravitation of the earth, ocean tide, solid earth tide, solar and earth radiation, and atmospheric drag. Space geodetic data of HY-2 are simulated with the designed HY-2 orbit parameters based on the orbit dynamics theory to optimize the approaches and strategies of precise orbit determination of HY-2 with the dynamic and reduced-dynamic methods, respectively. Different methods based on different techniques are analyzed and compared. The experiment results show that the nonspherical perturbation modeled by GGM02C causes a maximum perturbation, and errors caused by the imperfect modeling of atmospheric drag have an increasing trend on T direction, but errors are relatively stable on the other two directions; besides, the methods with three space geodetic techniques achieve the radial orbit with the precision better than 10 cm.