Elliptic-type motion in Fock's gravitational field

The elliptic-type motion in the gravitational field found by Fock as exact solution of Einstein's vacuum equations in the case of spherical symmetry (Solution called here Fock's gravitational field) is studied by means of a classic method based on the perturbation theory. Regarding the deviations of the orbit from a Kepleian orbit as perturbations, the first and second order variations of the Keplerian orbital elements over one nodal period as well as those of the nodal period itself are determined.     

Spacecraft potential control aboard Equator-S as a test for Cluster-II

The payload of Equator-S was complemented by the potential control device (PCD) to stabilise the electric potential of the spacecraft with respect to the ambient plasma. Low potentials are essential for accurate measurements of the thermal plasma. The design of PCD is inherited from instruments for Geotail and Cluster and utilises liquid metal ion sources generating a beam of indium ions at several keV. The set-up of the instrument and its interaction with the plasma instruments on board is presented. When the instrument was switched on during commissioning, unexpectedly high ignition and operating voltages of some ion emitters were observed. An extensive investigation was initiated and the results, which lead to an improved design for Cluster-II, are summarised. The cause of the abnormal behaviour could be linked to surface contamination of some emitters, which will be monitored and cured by on-board procedures in future. The mission operations on Equator-S were not at all affected, because of the high redundancy built into the instrument so that a sufficient number of perfectly operating emitters were available and were turned on routinely throughout the mission. Observations of the effect of spacecraft potential control on the plasma remained limited to just one event on January 8, 1998, which is analysed in detail. It is concluded that the ion beam lead to the predicted improvement of the particle measurements even outside the low density regions of the magnetosphere where the effect of spacecraft potential control would have been much more pronounced, and that the similar instruments for the four Cluster-II spacecraft to be launched in 2000 will be very important to ensure accurate plasma data from this mission.     

Linearized amplitude variation with offset and azimuth and anisotropic poroelasticity

The normal-to-shear weakness ratio is commonly used as a fracture fluid indicator, but it depends not only on the fluid types but also on the fracture intensity and internal architecture. Amplitude variation with offset and azimuth is commonly used to perform the fluid identification and fracture characterization in fractured porous rocks. We demonstrate a direct inversion approach to utilize the observable azimuthal data to estimate the decoupled fluid (fluid/porosity term) and fracture (normal and shear weaknesses) parameters instead of the calculation of normal-to-shear weakness ratio to help reduce the uncertainties in fracture characterization and fluid identification of a gas-saturated porous medium permeated by a single set of parallel vertical fractures. Based on the anisotropic poroelasticity and perturbation theory, we first derive a linearized amplitude versus offset and azimuth approximation using the scattering function to decouple the fluid indicator and fracture parameters. Incorporating Bayes formula and convolution theory, we propose a feasible direct inversion approach in a Bayesian framework to obtain the direct estimations of model parameters, in which Cauchy and Gaussian distribution are used for the a priori information of model parameters and the likelihood function, respectively. We finally use the non-linear iteratively reweighted least squares to solve the maximum a posteriori solutions of model parameters. The synthetic examples containing a moderate noise demonstrate the feasibility of the proposed approach, and the real data illustrates the stabilities of estimated fluid indicator and dry fracture parameters in gas-saturated fractured porous rocks.     

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.     

Upstream perturbation and floodplain formation effects on chute-cutoff-dominated meandering river pattern and dynamics

A sustained dynamic inflow perturbation and bar–floodplain conversion are considered crucial to dynamic meandering. Past experiments, one-dimensional modelling and linear theory have demonstrated that the initiation and persistence of dynamic meandering require a periodic transverse motion of the inflow. However, it remains unknown whether the period of the inflow perturbation affects self-formed meander dynamics. Here, we numerically study the effect of the inflow perturbation period on the development and meander dynamics of a chute-cutoff-dominated river, which requires two-dimensional modelling with vegetation forming floodplain on bars. We extended the morphodynamic model Nays2D with growth and mortality rules of vegetation to allow for meandering. We tested the effect of a transversely migrating inflow boundary by varying the perturbation period between runs over an order of magnitude around typical modelled meander periods. Following the cutoff cascade after initial meander formation from a straight channel, all runs with sufficient vegetation show series of growing meanders terminated by chute cutoffs. This generates an intricate channel belt topography with point bar complexes truncated by chutes, oxbow lakes, and scroll-bar-related vegetation age patterns. The sinuosity, braiding index and meander period, which emerge from the inherent biomorphological feedback loops, are unrelated to the inflow perturbation period, although the spin-up to dynamic equilibrium takes a longer time and distance for weak and absent inflow perturbations. This explains why, in previous experimental studies, dynamic meandering was only accomplished with a sustained upstream perturbation in flumes that were short relative to the meander wavelength. Our modelling of self-formed meander patterns is evidence that scroll-bar-dominated and chute-cutoff-dominated meanders develop from downstream convecting instabilities. This insight extends to many more fluvial, estuarine and coastal systems in morphological models and experiments, which require sustained dynamic perturbations to form complex patterns and develop natural dynamics. © 2019 The Authors. Earth Surface Processes and Landforms Published by John Wiley & Sons Ltd.     

Equipment–structure interaction considering the effect of torsion and base isolation

This paper attempts to study the response of equipment items attached to torsional buildings supported by elastic bearings under earthquake excitations. To account for the effect of torsion and translation, each storey of the building is modelled with two degrees of freedom, one for translation and the other for torsion. The equipment is assumed to be so light that it affects slightly the vibration modes of the primary structure to which it is attached. Modal synthesis results obtained by the perturbation technique together with the CQC procedure are compared with those from a complete eigenvalue analysis. Using the present semi-analytical approach, the key parameters that govern the equipment and structure responses can be easily identified. In the numerical studies, it is confirmed that the response of the equipment and the building to which it is mounted, can be effectively reduced through installation of the base isolators. The optimal point for mounting the equipment is the one where the equipment remains undisplaced during vibration of the tuned mode. © 1998 John Wiley & Sons, Ltd.     

A non-iterative and non-singular perturbation solution for transforming Cartesian to geodetic coordinates

The Cartesian-to-Geodetic coordinate transformation is re-cast as a minimization algorithm for the height of the Satellite above the reference Earth surface. Optimal necessary conditions are obtained that fix the satellite ground track vector components in the Earth surface. The introduction of an artificial perturbation variable yields a rapidly converging second order power series solution. The initial starting guess for the solution provides 3–4 digits of precision. Convergence of the perturbation series expansion is accelerated by replacing the series solution with a Padé approximation. For satellites with heights < 30,000 km the second-order expansions yields ~mm satellite geodetic height errors and ~10⁻¹² rad errors for the geodetic latitude. No quartic or cubic solutions are required: the algorithm is both non-iterative and non-singular. Only two square root and two arc-tan calculations are required for the entire transformation. The proposed algorithm has been measured to be ~41% faster than the celebrated Bowring method. Several numerical examples are provided to demonstrate the effectiveness of the new algorithm.     

伽师强震群区上地壳三维速度层析成像——人工爆破和天然地震的联合反演

伽师震区位于天山褶皱、帕米尔构造弧与塔里木块体三个构造单元的交接地带,近年来该区发生了一系列的强震活动.为进一步获得该震区详细的地壳速度结构,本文利用人工爆破和天然地震资料联合反演的方法,对1997年新疆伽师震区布设的三维人工地震透射台阵和流动地震台网的资料进行处理,重建了台阵下方上地壳三维速度扰动图像,并结合地震活动分布,对伽师强震群的地震成因作出进一步分析.结果表明研究区上地壳速度结构在纵向和横向上具有明显的非均匀性,随着深度的逐渐加深,震区下方以萨如锡为中心的低速异常体逐步被高速异常体所替代.自12 km深度开始,在与强震群震中相应的位置上,明显出现沿北北西向的高P波速度异常体,在其周围为相对低速分布,呈现出低速条带环绕高速条带的分布格局,V_P/V_S在相同的位置上也表现为高值分布.这种结构上的差异可能与伽师强震群发生有密切关系.16 km深度的P波速度层析图表明,伽师强震群发生在地壳相对高速扰动区内或是高速扰动向低速扰动过渡的边缘,壳内高速体的存在为强震的孕育和发生提供了重要基础.     

初始误差对双环流变异可预报性的影响

使用球坐标下1.5 层约化重力浅水模式模拟海洋风生双环流, 结果显示双环流射流存在拉伸模态和收缩模态间的年际变化。以双环流从拉伸模态向收缩模态的转变过程为背景场, 利用条件非线性最优扰动(CNOP)方法, 考察初始误差对双环流变异可预报性的影响, 得到两类初始误差: 全局CNOP型和局部CNOP(LCNOP)型, 两类初始误差对双环流变异的影响几乎相反。通过考察误差发展, 发现在射流从拉伸模态向收缩模态转变过程中, CNOP 型初始误差使射流弯曲程度变大, 并在预报时刻导致涡脱落; 而LCNOP 型初始误差则使射流弯曲程度变小。相比LCNOP, CNOP 型初始误差引起更大预报误差, 导致双环流变异的预报技巧下降更多。两类误差得到较大发展的区域可能存在正压不稳定, 使误差能够不断从背景场吸收能量进而得到快速发展。给出了两类使双环流变异预报技巧下降最大的初始误差, 在实际的数值预报中减少这两种类型的误差, 将有助于提高双环流变异的预报技巧。     

递归型多业务宽带GEO卫星网络跨层流量控制算法研究

提出了一种递归型多业务跨层流量控制算法。该算法首先将多业务输入的流量控制问题抽象为具有输入端速率控制机制的缓冲区门限优化问题,建立多输入递归型SFM单节点模型MRSFM;确定了反映用户应用层QoS丢包和延时性能要求的系统代价函数,建立了用于跨层流量控制优化模型。在跨层优化模型的基础上,以建立的MRSFM模型为基础,运用IPA方法推导了代价函数相对于优化参数(缓冲区门限)的IPA导数,并利用SA理论进行优化。仿真实验验证了宽带GEO卫星网络跨层流量控制算法的正确性。