Tidal evolution and hydrostatic equilibrium of phobos

Summary A dynamical model of Phobos has been set up: its boundary surface is defined by the 2nd degree Stokes zonal and sectorial parameters, the mass and angular velocity of rotation of the body (assumed homogeneous), plus the constant part of the tidal potential due to Mars which is relatively very large. The tidal evolution has been outlined, based on the condition that, at a certain epoch, the sum of the tidal and centrifugal forces on the surface of Phobos should be equal to the gravitation of opposite sign. The problem of hydrostatic equilibrium of Phobos is discussed.

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基于GRACE卫星重力数据确定地球重力场模型WHU-GM-05

基于卫星轨道运动的能量积分方程,可导出利用卫星跟踪卫星数据求解地球重力场的实用公式.本文在Jekeli给出的公式基础上导出了基于能量守恒方程利用两颗低-低卫星跟踪的扰动位差求解重力位系数的严密关系式.基于两颗GRACE卫星的观测数据,采用本文导出的严密能量积分方法求解得到120阶的GRACE地球重力场模型,命名为WHU-GM-05;将WHU-GM-05模型与国际上同类重力场模型EIGEN-GRACE系列和GGM02S分别在阶方差和大地水准面高等方面作了比较,并与美国和中国的部分地区GPS水准观测值进行了精度分析.结果表明基于本文推导的严密双星能量守恒方程得到的WHU-GM-05重力场模型精度与国际上同类重力场模型的精度相当.     

A synthetic Earth gravity model based on a topographic-isostatic model

The Earth??s gravity field is related to the topographic potential in medium and higher degrees, which is isostatically compensated. Hence, the topographic-isostatic (TI) data are indispensable for extending an available Earth Gravitational Model (EGM) to higher degrees. Here we use TI harmonic coefficients to construct a Synthetic Earth Gravitational Model (SEGM) to extend the EGMs to higher degrees. To achieve a high-quality SEGM, a global geopotential model (EGM96) is used to describe the low degrees, whereas the medium and high degrees are obtained from the TI or topographic potential. This study differes from others in that it uses a new gravimetric-isostatic model for determining the TI potential. We test different alternatives based on TI or only topographic data to determine the SEGM. Although the topography is isostatically compensated only to about degree 40?C60, our study shows that using a compensation model improves the SEGM in comparison with using only topographic data for higher degree harmonics. This is because the TI data better adjust the applied Butterworth filter, which bridges the known EGM and the new high-degree potential field than the topographic data alone.     

弹道扰动引力无奇异性计算模型的建立

利用地球重力场模型来计算飞行器轨道扰动引力,当飞行器飞越两极及其附近地区时,由于Legendre函数的一阶导数以及分母上所含余纬的正弦函数,将导致扰动引力的计算出现无穷大.本文推导了Legendre函数一阶导数以及球谐函数m (P)mn(cosθ)/sinθ无奇异性的计算公式,建立了飞行器轨道扰动引力各分量无奇异性的详细计算模型,并通过数值试验分析了扰动引力各分量在两极地区的变化趋势,从而彻底解决了利用地球重力场模型计算两极地区飞行器轨道扰动引力时存在的奇异性问题.     

The geoid-to-quasigeoid difference using an arbitrary gravity reduction model

Recently it was proved that the classical formula for computing the geoid to quasigeoid separation (GQS) by the Bouguer gravity anomaly needs a topographic correction. Here we generalize the modelling of the GQS not only to Bouguer types of anomalies, but also to arbitrary reductions of topographic gravity. Of particular interest for practical applications should be isostatic and Helmert types of reductions, which provide smaller and smoother components, more suitable for interpolation and calculation, than the Bouguer reduction.     

Island sheltering of surface gravity waves: model and experiment

A field experiment is used to evaluate a numerical model of the sheltering of gravity waves by islands offshore of the Southern California region. The sheltering model considered here includes only the effects of island blocking and wave refraction over the island bathymetry. Wave frequency and directional spectra measured in the deep ocean (unsheltered region west of the islands) were used as input to the sheltering model and compared with coastal observations. An airborne L-band synthetic aperture radar was used to image the directional properties of the waves in the deep ocean. In addition to the unsmoothed spectra, a unimodal directional spectrum model obtained from fits to the radar spectra was also employed to suppress the high noise level of this system. Coastal measurements were made in about 10 m depth at Torrey Pines Beach with a high resolution array of pressure sensors. The model predictions and data at Torrey Pines Beach agree well in a limited frequency range (0.082 to 0.114 Hz) where the unimodal deep ocean model is appropriate. The prediction that unimodal northern swell in the deep ocean results in a bimodal directional spectrum at Torrey Pines Beach is quantitatively verified. The northern peak of the bimodal spectra is due to waves coming through the window between San Clemente and San Miguel-Santa Rosa Islands. The southerly peak is due to wave refraction over Cortez and Tanner Banks. For lower frequency waves, the effects of strong refraction in the island vicinity are shown qualitatively. Refraction can theoretically supply up to approximately 10% of the deep ocean energy that is otherwise blocked at this site. The modifications of the island shadows due to wave refraction become theoretically negligible for wave frequencies 0.11Hz. Also, local wave generation effects, which are not included in this sheltering model, are shown to be occasionally important for waves with frequencies 0.12Hz.     

A global experimental model for gravity tides of the Earth

The long-term, continuous and high-quality tidal gravity data, recorded with the superconducting gravimeters (SGs) at 19 stations in the Global Geodynamics Project (GGP), were simultaneously used to investigate the global pattern of the tidal gravity variations. The atmospheric effects were removed from the gravity observations by using the simultaneous pressure records at the stations. A total of six global co-tidal models were employed to remove the loading effects of oceanic tides. The resonance parameters of the Earth's free core nutation (FCN), as well as the spheroidal constant components in the gravimetric factors of waves O₁ and M₂, were accurately retrieved. As a result, a global experimental model for gravity tides (GEMGT) was developed, considering the nearly diurnal resonance and the latitude-dependence of the gravimetric amplitude factors. The final results indicate that the mean discrepancy of the four main tidal waves (i.e. O₁, K₁, M₂ and S₂) between the GEMGT and SG observations is less than 0.2% on average. The GEMGT is in good agreement with the theoretical models based on the inelastic non-hydrostatic equilibrium Earth models [Dehant, V., Defraigne, P., Wahr, J., 1999. Tides for a convective Earth. J. Geophys. Res. 104, 1035–1058; Mathews, P.M., 2001. Love numbers and gravimetric factor for diurnal tides. J. Geodetic Soc. Jpn. 46 (4), 231–236] with a mean discrepancy less than 0.15%. However, the GEMGT is in closer accordance with the theoretical model given by Mathews [Mathews, P.M., 2001. Love numbers and gravimetric factor for diurnal tides. J. Geodetic Soc. Jpn. 46 (4), 231–236] for the diurnal tides while it is in closer agreement with one obtained by Dehant et al. [Dehant, V., Defraigne, P., Wahr, J., 1999. Tides for a convective Earth. J. Geophys. Res. 104, 1035–1058] for the semi-diurnal tides.     

Boundary element reservoir model for seismic analysis of gravity dams

The boundary element method has been successfully applied in the past to the analysis of hydrodynamic forces in two- and three-dimensional finite water reservoirs subjected to seismic ground motions. In extending the method to an infinite reservoir, the loss of energy due to pressure waves moving away towards infinity must be taken into account. In addition, for both finite and infinite reservoirs, energy is lost owing to partial absorption of the waves incident on a flexible bottom consisting of alluvial deposits. This paper presents the results of more recent research on the application of the boundary element method to the analysis of 2D reservoir vibration. Two different formulations are used: a constant boundary element formulation and a linear boundary element formulation. Special boundary conditions to treat infinite radiation and foundation damping have been incorporated in both formulations. Numerical results have been obtained for each of the two alternative formulations and compared against each other as well as with classical solutions and results obtained by other researchers.     

A nonhydrostatic unstructured-mesh soundproof model for simulation of internal gravity waves

A semi-implicit edge-based unstructured-mesh model is developed that integrates nonhydrostatic soundproof equations, inclusive of anelastic and pseudo-incompressible systems of partial differential equations. The model builds on nonoscillatory forward-in-time MPDATA approach using finite-volume discretization and unstructured meshes with arbitrarily shaped cells. Implicit treatment of gravity waves benefits both accuracy and stability of the model. The unstructured-mesh solutions are compared to equivalent structured-grid results for intricate, multiscale internal-wave phenomenon of a non-Boussinesq amplification and breaking of deep stratospheric gravity waves. The departures of the anelastic and pseudoincompressible results are quantified in reference to a recent asymptotic theory [Achatz et al. 2010, J. Fluid Mech., 663, 120–147)].     

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.     

双层界面重磁联合反演方法研究

Based on the synchronous joint gravity and magnetic inversion of single interface by Pilkington and the need of revealing Cenozoic and crystalline basement thickness in the new round of oil-gas exploration, we propose a joint gravity and magnetic inversion methodfor two-layer models by concentrating on the relationship between the change of thicknessI and position of the middle layer and anomaly and discuss the effects of the key parameters. Model tests and application to field data show the validity of this method.     

用最小二乘配置法构建局部重力场模型

基于非均匀分布的陆地重力观测数据,重构局部重力场模型是区域重力资料处理与解释的重要环节。本文对比了多种局部重力场建模方法,并以EGM2008模型提供的自由空气重力异常模型重采样数据进行测试,综合比较了不同噪声条件下不同建模方法的实际效果。结果表明:在不同噪声水平下,优选出适合重力位场问题的协方差函数后,最小二乘配置法的建模效果优于其它方法。      

基于CHAMP短弧长动力学轨道的地球重力场模型

讨论了基于CHAMP卫星动力学轨道数据以及加速度计数据推求地球重力场模型的动力学法,推导了将加速度计观测数据的尺度和偏差以及卫星初始状态向量与地球重力场位系数一起求解的数学模型. 采用CHAMP卫星120天的动力学轨道数据和加速度数据解算出50阶次的地球重力场模型TJCHAMP01S,并利用各种方法对该模型进行了检核,结果表明：TJCHAMP01S模型精度优于相同阶次的EGM96和EIGEN_1S模型.     

A gradational density model for gravity anomalies over oceanic ridges

The long-wavelength gravity anomalies observed over oceanic ridges have been interpreted in terms of horizontal slabs with lateral variation of density. The location of such a slab in the earth's interior is estimated to be between the depths of 350 and 430 km, which defines the boundaries of the upper phase-transition zone of the mantle. A total density contrast, between the end planes of the horizontal slab, of 0.3 g/cm³ appears to be satisfactory for the interpretation. This remarkable coincidence in depth and density contrast associated with the pyroxene-garnet transformation process is considered to suggest that this process may possibly be: (1) taking place laterally; and (2) generating the gradational density contact which is reflected in the gravity anomalies. In turn, the mechanism for this lateral phase transformation may ultimately be attributable to the convection currents in the asthenosphere.     

用传输函数构建的大气重力波传播理论模式

本文根据考虑大气热传导和黏滞的重力波复色散关系,采用传输函数的概念,基于重力波的线性理论,构建了用于研究对流层内重力波激发源与电离层响应之间的传输函数数值模式.在相空间中讨论了传输函数振幅的分布特性,并以地面单位脉冲源为例,分析了从地面到300 km高空的响应,得到了物理量的时空分布特征.结果表明：（1）对内重力波的传播而言,大气相当于一个滤波器,只有波动周期在15～30 min,水平波长在200～450 km之间的重力波扰动才最容易到达300 km电离层高度;（2）电离层的响应主要在与地面的激发源之间相隔较远的水平距离上发生;（3）黏滞和热传导系数在低层对上传重力波的影响较小,随着高度的增加它们对重力波的影响越来越大;（4）在低层计算的波动频率与Row理论的计算结果比较一致,然而到了高层却相差较大.     

On the colocation iterative solution model and algorithm for gravity anomaly

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应用全张量重力梯度数据优化密度和速度模型

重力梯度全张量数据具有高灵敏度反映探测目标局部微弱变化的特点,可以对单一地震数据在建立速度模型过程中的不确定性,尤其是各向异性速度模型建立过程中的精细结构进行补充修正.本文主要研究重震两类数据与各自所反映的物理模型关系以及密度模型与速度模型之间的相互联系和制约关系,从而建立重力全张量数据与地震速度模型间的信息互补关系和模型参数间的解析表达式.在此基础上,提出多参数加权正反演算法流程,逐层异常分离技术和约束条件下迭代反演模型修正方法,并实现模块编程和验证.实验数据和结果表明,重力全张量数据和地震数据多参数融合能够明显提高地震速度建模精度,减小模型解释的不确定性.     

GRAPES全球非静力大气模式的正规模分析

为分析数值模式动力学框架中不同波动的特性及对数值天气预报模式计算稳定性的影响,文章对GRAPES（Global/Regional Assimilation and PrEdiction System）全球非静力大气模式进行了正规模分析.首先,建立了静止大气状态下模式的线性化系统,并在适当的边界条件下将线性化系统分解成具有垂直与水平结构方程的本征值、本征函数耦合问题.然后在等温大气条件下,利用耦合问题的数值结果分析得出：GRAPES非静力模式除了有几乎和对应的静力模式一致的向东、向西传播的重力惯性波及向西传播的Rossby波外,还有一个向东、向西传播的声惯性波;特别是,只有当纵横比较大时,非静力模式对重力惯性波才会有显著影响.     

重力坝抗震安全评价中有限元梁杆体系新模型的适用性

传统的材料力学法静动力分析一直是我国重力坝规范规定的重力坝抗震安全评价的基本依据。但为了简化传统经典的重力坝材料力学法模型在动力分析中的复杂度,近年来,随着有限元分析技术的日益推广,许多重力坝有限元梁杆体系新模型在工程界开始得到应用,部分替代了传统材料力学法模型的作用,并在考虑多向地震耦合问题方面体现了一定的优势。从材料力学法的基本定义出发,提出了一种合理的坝面载荷处理模式,并从模态、抗侧力刚度、坝顶位移、内力结果等方面建立适用度指标,对这些有限元新模型进行细致对比,建议了一种最优的有限元梁杆模型,由该模型得到的结果与传统材料力学法的结果吻合,因此可供工程借鉴。