利用CHAMP卫星几何法轨道恢复地球重力场模型

介绍了利用CHAMP几何法轨道恢复地球重力场模型的基本原理和算法,提出了基于牛顿数值微分公式并辅助移去-恢复方法计算卫星速度的算法.利用现有重力场模型标定CHAMP加速度计数据的差分算法,采用Technical University of Munich（TUM）提供的CHAMP几何法轨道,计算出了三组50×50地球重力场模型.与GRIM5_C1、EIGEN_1S和EIGEN_2模型的比较表明,无论位系数差值阶方差或大地水准面差值,恢复出的模型与EIGEN_2模型都最接近.利用北极实测重力数据对上述模型进行了检验,结果显示,本文得到的三组模型均优于GRIM5_C1模型,且与EIGEN_1S、EIGEN_2模型精度相当.     

顾及非线性改正的动力学方法反演GRACE时变重力场模型

本文利用解的叠加原理求解了轨道扰动微分方程组,构建了扰动位系数与轨道和星间距变率的观测方程,并分别引入非线性改正项.通过惯性坐标系与运动坐标系的转换求解状态转移方程组,分析了观测方程的低频误差特征,导出了目前常用的消除剩余星间距变率低频误差的五参数或七参数经验公式.此外,根据非惯性力模型误差是分段标定的特点,提出利用三次样条函数来处理低频误差,通过模拟计算表明三次样条函数处理低频误差略优于七参数.最后,处理实际的GRAEC Level-1b数据,解算了2006年1月至2009年12月期间的月时变重力场模型UCAS_Grace01,通过在不同区域进行比较可以得出本文计算的时变重力场模型与国际官方机构精度基本是一致的结论.

     

大磁暴期间TIEGCM模式和CHAMP卫星热层大气密度扰动特性的统计研究

本文统计分析了2001—2005年的39次大磁暴事件(Dst-100nT)期间TIEGCM模式和CHAMP卫星大气密度数据.研究结果表明,模式结果与实测数据具有较好的一致性,但仍存在一定的偏差.大气密度及增量与SYM-H指数相关性较好,并且随纬度、光照条件和地磁活动水平变化.模式低估了磁暴期间大气密度的增幅,特别是在地磁活动水平较强时模式与实测的偏差较大.模式的偏差在高纬地区高于低纬地区,日侧高于夜侧.Dst指数越低,偏差越大,而当Dst指数低于-150nT以后,绝对偏差和相对偏差变化不明显.     

基于B-spline和正则化算法的低轨卫星轨道平滑

本文提出了一个利用纯几何轨道和力模型的新算法来计算精确且相对平滑的卫星轨道. 该法将一个纯几何轨道表达为一个B-spline的线性组合,线性组合的系数可以由最小二乘法估计获得. 力模型通过计算加速度来附加约束. 为了平衡几何轨道的点位误差和加速度的不精确,一个基于“广义交互确认（GCV,generalized cross-validation）”的正则化算法运用其中. 由于B-spline的本地控制性,该方法的计算效率相当高. 本文的数值分析表明了该法的有效性. 模拟计算的结论是：带加速度约束较不带加速度约束的平滑效果好. 力模型越精确,平滑的轨道就越精确. 三个月的CHAMP实测轨道数据处理结果表明,平滑后的轨道改进了重力场模型.     

基于卫星轨道扰动理论的重力反演算法

为了更充分利用低轨重力卫星的高精度观测数据,根据卫星轨道的扰动理论,导出了应用卫星轨道与星间距离观测值联合反演地球重力场模型的算法.该算法的实质是将牛顿运动方程在卫星轨道处进行展开,转化为第二类Volterra积分方程,并采用基于移动窗口的9次多项式内插公式进行数值求解.给出了该算法的观测方程,用QR分解法消去局部参数矩阵,最后采用预条件共轭梯度法求解法方程.利用GRACE卫星2008-01-01~2008-08-01时间段内的轨道及星间距离观测数据,解算了120阶次的地球重力场模型SWJTU-GRACE01S,该模型在120阶处的阶方差为1.58×10-8,大地水准面差距累计误差为22.29 cm,与美国GPS水准网比较的标准差为0.793 m,结果表明:SWJTU-GRACE01S模型精度介于EIGEN-GRACE01S与EIGEN-GRACE02S模型之间,从而验证了该算法的有效性.     

基于Bspline和正则化算法的低轨卫星轨道平滑

本文提出了一个利用纯几何轨道和力模型的新算法来计算精确且相对平滑的卫星轨道. 该法将一个纯几何轨道表达为一个Bspline的线性组合，线性组合的系数可以由最小二乘法估计获得. 力模型通过计算加速度来附加约束. 为了平衡几何轨道的点位误差和加速度的不精确，一个基于“广义交互确认（GCV，generalized crossvalidation）”的正则化算法运用其中. 由于Bspline的本地控制性，该方法的计算效率相当高. 本文的数值分析表明了该法的有效性. 模拟计算的结论是：带加速度约束较不带加速度约束的平滑效果好. 力模型越精确，平滑的轨道就越精确. 三个月的CHAMP实测轨道数据处理结果表明，平滑后的轨道改进了重力场模型.     

2003年11月超强磁暴热层大气密度扰动及其与焦耳加热和环电流指数的关系——CHAMP卫星观测

本文利用CHAMP卫星加速度仪测量数据,计算和分析2003年11月20～21日大磁暴期间大气质量密度扰动的全球分布特征;研究暴时变化与极区大尺度对流引起的全球焦耳加热总功率及环电流指数SYM-H之间的关系.结果表明,磁暴期间400 km高度上热层大气质量密度大幅度上升, NRLMSISE-00模式预测值与此相比有很大差别;暴时大气密度的增大存在昼/夜半球不对称性：白天强于夜晚,且白天随纬度的分布呈现出比较复杂的图像,在赤道附近和南半球中低纬区（10°N ～50°S）大气密度增大较强,并呈双峰分布,两个峰分别位于0°和45°S,另外在极区也出现大气密度扰动的局部极大,而在夜晚,大气密度变化南北半球比较对称,在赤道低纬区大气密度增大较强;互相关分析表明,中低纬区大气密度变化滞后于全球焦耳加热总功率3～7 h,滞后于环电流指数（SYM-H）0～3 h,与二者存在很强的相关,表明极区焦耳加热和赤道环电流过程对暴时热层大气密度扰动有重要影响.     

卫星精密定轨与重力场建模的同解法

现代卫星跟踪卫星重力测量技术显著改善了地球重力场模型的中长波段信号,并拓展了重力场模型在相关科学研究中的应用.同解法作为卫星重力观测数据的主要处理手段之一,国内一直没有实质突破.本文从基本模型和关键技术的分析出发,剖析了同解法的特点,特别是在建立同解法与几何法(运动学)定轨、一般动力学方法关系的基础上,给出了一种同解法的实现路线.在已有的精细数据预处理和并行计算研究基础上,结合GRACE卫星的实测飞行数据,在国内首次获得了真实卫星任务数据条件下的同解法结果,并进行了动力法轨道的外部质量检核、卫星非保守力分析、重力场模型的GPS水准检验等.利用卫星激光测距数据检验,卫星精密轨道的径向精度优于2cm,同时建立了质量可靠的卫星重力场模型,充分展示了同解法的优点.数值结果及其分析表明,本文所提的同解法实施方案合理可行,已经掌握了实现同解法的关键技术,获得了从仿真研究到实际飞行数据处理的新进展.最后,本文对同解法今后的发展思路,以及如何进一步挖掘同解法的潜力,提出了见解和今后的工作方向.     

基于轨道扰动引力谱分析的方法确定低低观测重力卫星反演重力场的空间分辨率

基于低低卫-卫跟踪重力卫星的轨道特性,从垂直和水平两个方向计算了重力卫星高空扰动引力,并根据其谱特性及星载加速度的测量噪声水平分析了重力卫星能反演重力场的阶数.利用EGM96重力场模型分别计算了400 km、450 km和500 km 轨道高度处重力卫星受到的扰动引力谱及扰动引力谱的平均量级,分析其垂直特性表明:在三个轨道高度处能分别能反演150、140和130阶的重力场模型.利用两颗同轨重力卫星相距220 km的特性,计算了400 km、450 km和500 km 轨道高度处纬度相差2°的两颗卫星纬向扰动引力差,即扰动引力水平分量,分析其谱特性,表明:重力卫星能反演至117阶的地球重力场模型.     

考虑斜拉索刚度、垂度、阻尼的非线性运动方程研究

随着斜拉桥跨径的快速增长,斜拉索的长度也大大增加,斜拉索是斜拉桥的主要受力构件,其在外荷载作用下经常引发大幅振动,这样就降低了斜拉索的寿命或造成拉索的破坏,因此研究斜拉索的非线性运动方程对解决振动问题具有实际工程的意义。本文在考虑斜拉索非线性静平衡曲线、抗弯刚度、粘滞阻尼影响的斜拉索平面内非线性振动的基础上,建立了斜拉索非线性运动方程。采用Galerkin法解耦了斜拉索非线性运动方程,并运用Runge-Kutta法对其自由振动和周期强迫振动两种情形进行了求解,最后,通过对该索的理论计算数据与原型仿真数据的对比分析,可知上述非线性方程比传统的线性方程更精确。本文的研究为今后斜拉索的非线性分析及其振动控制奠定了一定的理论基础。     

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)     

Development of the instantaneous unit hydrograph using stochastic differential equations

Recognizing that simple watershed conceptual models such as the Nash cascade ofn equal linear reservoirs continue to be reasonable means to approximate the Instantaneous Unit Hydrograph (IUH), it is natural to accept that random errors generated by climatological variability of data used in fitting an imprecise conceptual model will produce an IUH which is random itself. It is desirable to define the random properties of the IUH in a watershed in order to have a more realistic hydrologic application of this important function. Since in this case the IUH results from a series of differential equations where one or more of the uncertain parameters is treated in stochastic terms, then the statistical properties of the IUH are best described by the solution of the corresponding Stochastic Differential Equations (SDE's). This article attempts to present a methodology to derive the IUH in a small watershed by combining a classical conceptual model with the theory of SDE's. The procedure is illustrated with the application to the Middle Thames River, Ontario, Canada, and the model is verified by the comparison of the simulated statistical measures of the IUH with the corresponding observed ones with good agreement.     

Development of the instantaneous unit hydrograph using stochastic differential equations

Recognizing that simple watershed conceptual models such as the Nash cascade ofn equal linear reservoirs continue to be reasonable means to approximate the Instantaneous Unit Hydrograph (IUH), it is natural to accept that random errors generated by climatological variability of data used in fitting an imprecise conceptual model will produce an IUH which is random itself. It is desirable to define the random properties of the IUH in a watershed in order to have a more realistic hydrologic application of this important function. Since in this case the IUH results from a series of differential equations where one or more of the uncertain parameters is treated in stochastic terms, then the statistical properties of the IUH are best described by the solution of the corresponding Stochastic Differential Equations (SDE's). This article attempts to present a methodology to derive the IUH in a small watershed by combining a classical conceptual model with the theory of SDE's. The procedure is illustrated with the application to the Middle Thames River, Ontario, Canada, and the model is verified by the comparison of the simulated statistical measures of the IUH with the corresponding observed ones with good agreement.     

A survey of numerical methods for stochastic differential equations

The development of numerical methods for stochastic differential equations has intensified over the past decade. The earliest methods were usually heuristic adaptations of deterministic methods, but were found to have limited accuracy regardless of the order of the original scheme. A stochastic counterpart of the Taylor formula now provides a framework for the systematic investigation of numerical methods for stochastic differential equations. It suggests numerical schemes, which involve multiple stochastic integrals, of higher order of convergence. We shall survey the literature on these and on the earlier schemes in this paper. Our discussion will focus on diffusion processes, but we shall also indicate the extensions needed to handle processes with jump components. In particular, we shall classify the schemes according to strong or weak convergence criteria, depending on whether the approximation of the sample paths or of the probability distribution is of main interest.     

A survey of numerical methods for stochastic differential equations

The development of numerical methods for stochastic differential equations has intensified over the past decade. The earliest methods were usually heuristic adaptations of deterministic methods, but were found to have limited accuracy regardless of the order of the original scheme. A stochastic counterpart of the Taylor formula now provides a framework for the systematic investigation of numerical methods for stochastic differential equations. It suggests numerical schemes, which involve multiple stochastic integrals, of higher order of convergence. We shall survey the literature on these and on the earlier schemes in this paper. Our discussion will focus on diffusion processes, but we shall also indicate the extensions needed to handle processes with jump components. In particular, we shall classify the schemes according to strong or weak convergence criteria, depending on whether the approximation of the sample paths or of the probability distribution is of main interest.     

A review on stochastic differential equations for applications in hydrology

Fundamentals of the theory of stochastic calculus and stochastic differential equations (SDE's) which are finding increasing application in water resources engineering are reviewed. The basics of probability theory, mean square calculus and the Wiener, white Gaussian and compound Poisson processes are given in preparation for a discussion of the general Itô SDE with drift, diffusion and jump discontinuity terms driven by Gaussian white noise and compound Poissionian impulses. Also discussed are stochastic integration and the derivation of moment equations via the Itô differential rule. The lierature of SDE's is reviewed with an emphasis on the more accessible sources.     

内编队重力场测量系统轨道参数与载荷指标设计方法

内编队系统通过构造内卫星纯引力轨道完成高精度重力场测量,实现了不依赖于加速度计的重力卫星实施新途径.针对内编队系统轨道参数和载荷指标设计任务,从定性的角度分析了轨道高度、轨道倾角、偏心率等轨道参数的选择原则,以及外卫星定轨精度、内外卫星相对状态测量精度、内卫星非引力干扰抑制精度、系统采样率等载荷指标对内编队重力场测量性能的影响,并建立了这些参数之间的匹配关系.为获取内编队系统轨道参数和载荷指标的定量设计结果,给出了内编队重力场测量数据模拟和反演计算方法.结合轨道参数和载荷指标对重力场测量性能的影响及其匹配关系,提出了由解析推导和数值计算相结合的方法,获取重力场最高反演阶数、大地水准面精度、重力异常精度等重力场测量性能与轨道参数、载荷指标之间的解析关系,并给出了该解析关系的具体数学形式.与解析法、半解析法相比,该公式由解析推导和大量数值计算得到,因而考虑的影响因素更加全面,计算结果更加合理,可用于快速准确设计内编队系统轨道参数和载荷指标.     

The appraisal of surface orbital vibrators with buried geophone array for permanent reservoir monitoring

Time-lapse seismic is one of the main methods for monitoring changes in reservoir conditions caused by production or injection of fluids. One approach to time-lapse seismic is through permanent reservoir monitoring, whereby seismic sources and/or receivers are permanently deployed. Permanent reservoir monitoring can offer a more cost-effective and environmentally friendly solution than traditional campaign-based surveys that rely on temporarily deployed equipment while facilitating more frequent measurements. At the CO2CRC Otway Project, surface orbital vibrators were coupled to a buried geophone array to form a permanent reservoir monitoring system. These are fixed position seismic sources that provide both P and S waves using induction motor-driven eccentric masses. After an initial injection of CO₂ in February 2016, five months of continuous seismic data were acquired, and reflection imaging was used to assess the system performance. Analysis of the data showed the effects of weather variations on the near-surface conditions and the sweep signatures of surface orbital vibrators. Data processing flows of the continuous data was adapted from Vibroseis four-dimensional data processing flows. Ground roll proved a significant challenge to data processing. In addition, variations in the surface wave pattern were linked to major rainfall events. For the appraisal of surface orbital vibrators in imaging, a Vibroseis four-dimensional monitor survey data with similar geometry was also processed. Surface orbital vibrators are observed to be reliable sources with a potential to provide a repeatable signal, especially if the ground roll should fall outside the target window of interest. To guide future permanent reservoir monitoring applications, a repeatability analysis was performed for the various key data processing steps.     

High-order finite volume WENO schemes for the shallow water equations with dry states

The shallow water equations are used to model flows in rivers and coastal areas, and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. These equations have still water steady state solutions in which the flux gradients are balanced by the source term. It is desirable to develop numerical methods which preserve exactly these steady state solutions. Another main difficulty usually arising from the simulation of dam breaks and flood waves flows is the appearance of dry areas where no water is present. If no special attention is paid, standard numerical methods may fail near dry/wet front and produce non-physical negative water height. A high-order accurate finite volume weighted essentially non-oscillatory (WENO) scheme is proposed in this paper to address these difficulties and to provide an efficient and robust method for solving the shallow water equations. A simple, easy-to-implement positivity-preserving limiter is introduced. One- and two-dimensional numerical examples are provided to verify the positivity-preserving property, well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions.     

有限弹性变形地壳中的地震波

地壳由半无限大的基岩上一层厚度为H^-的表土层组成，入射地震波为垂直的SH波，产生水平地面运动。当浅源大地震发生时，在极震区以外行波传播产生地面运动将使地壳介质有非线性的有限弹性变形。用小参数摄动法使非线性控制方程为线性化的小参数各阶控制方程，得出头两阶线性控制方程的解析解。