共查询到16条相似文献，搜索用时 125 毫秒
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根据体谐函数一阶、二阶水平导数（广义球函数）也是球面正交函数系的性质,详细推导了水平重力梯度边值问题的级数解.根据扰动位与重力场元的微分关系,导出了由水平重力梯度计算重力异常、垂线偏差的公式.完善了全张量重力梯度的有关应用. 相似文献
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针对球谐函数定积分计算中Legendre函数递推问题展开研究,分析了标准向前列推法、Belikov法、跨阶次法、X数法以及顾及麦克劳林级数展开式对球谐函数定积分计算的影响。利用Eigen6c-4地球重力场模型计算扰动引力梯度径向分量,分析不同方法之间的差异。实验表明,不考虑麦克劳林级数展开式时4种方法的相对精度在高纬度地区较差,但计算模型扰动引力径向分量的精度一致,结合麦克劳林级数式可提高高纬度地区定积分计算的相对精度,但会降低中低纬度地区定积分计算的精度,并且对高纬度地区扰动引力径向分量的影响极小,但会严重降低低纬度地区扰动引力梯度计算的精度。 相似文献
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基于势流理论和时域高阶边界元方法,建立了三维完全非线性数值波浪水槽模型.利用源造波法产生入射波浪,应用五阶斯托克斯波理论给定波浪速度;采用混合欧拉-拉格朗日方法追踪流体瞬时水面,将二阶泰勒级数展开法应用于更新下一时间步的波面和速度势;通过加速势的方法准确计算自由水面速度的法向导数和物面速度势的时间导数.对完全非线性波浪进行了模拟,得到了稳定的波形.当波浪非线性较小时,与四阶Runge- Kutta法(RK4)计算结果和五阶斯托克斯波理论解均吻合良好;随着波浪非线性的增大,计算结果误差逐渐增大.通过数值试验分析,在满足精度要求的基础上,本方法计算时间略大于四阶Runge- Kutta法的四分之一,大大减少了计算量. 相似文献
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在建立局部地区的地球重力场模型中,球冠谐分析是一种有效的方法。在球冠坐标系下建立重力场模型时,仅涉及到重力位的垂向分量,不必进行关于极角的微分运算,所以仅用单个正交基来建模,但若要在球冠坐标系下对重力场作进一步分析,如类似于平面处理的导数运算,来突出地质体的边界,要计算极角的微分,利用单个正交基表示则不易收敛,且误差较大。本文中作者采用两个正交基函数在球冠坐标系下对重力场建模,推导计算了径向导数和曲面导数模,并利用棱柱体正演模型进行检验,结果表明双基函数建模更适合曲面上的位场表示。最后计算了冲绳海槽地区卫星测高重力异常数据的曲面导数,径向导数清晰划分了东海陆架上大构造单元,曲面导数梯度带显示了东海陆架外缘隆起带,也指示了陆架盆地内的一些局部构造。这表明双基函数的球冠谐分析是一种有效的曲面位场建模方法。 相似文献
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建立了一个分离中、低频重力场的数学模型。根据南沙群岛地质构造的特征，选择4条具有代表性的重力测线N2，N9，N10和N11的自由空间重力异常，进行福里哀频谱值的计算并研究振幅谱值的分布规律，确定61.44km为4条重力测线的低频和中频重力场的临界值；设计分开低频和中频重力场的分离因子，分离出4条重力剖面的低频和中频重力异常；进而分析其低频和中频重力异常的特征。结果表明：N2和N11频谱值的分布带窄，低频重力场显著，中频重力场不显著；N9和N10的频谱值分布带宽，中频和低频重力场均显著。分析了它们和地质构造的关系。曾母盆地、南华盆地和南薇盆地的低频重力异常和沉积厚度成反关系，其余地区成正关系。 相似文献
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基于106个月的Grace（gravity recovery and climate experiment）月重力场模型（120阶次）,消除了月重力场的月、季度及年度变化,得到了稳态的地球重力场模型（Grace_sta）。在2～120阶次之间,Grace_sta与已有高阶重力场EGM2008及EGM96三个模型的阶方差是一致的。在2～100阶次之间,Grace_sta模型误差阶方差要小于EGM2008与EGM96误差阶方差。在全球范围内,Grace_sta重力场的大地水准面与EGM2008相应阶次的大地水准面标准差约为3cm,与EGM96模型大地水准面差异则高达52cm。结果表明,Grace_sta足可以取代EGM2008重力场模型2～100阶次的低阶部分,新得到的稳态重力场模型可为海面地形分析提供了可靠的参考场。 相似文献
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The constant and harmonic parts of the global ocean tide are modeled by up to nine major tidal constituents, namely, S2, M2,
N2, K1, P1, O1, Mf, Mm, and Ssa. Our computations start with the Fourier sine and cosine series expansion for the tidal constituents,
including the constant Mean Sea Level (MSL). Although the frequencies of the tidal constituents are considered known, the
coefficients of the sine and cosine functions are assumed to be unknown. Subsequently, the coefficients of the sine and cosine
functions, as well as the constant part of the Fourier expansion, were expanded into spherical harmonics up to degree and
order n, where n corresponds to the number of linearly independent spherical harmonic base functions needed to model the tidal constituents,
determined via independent columns of the Gram matrix. The unknown coefficients of the spherical harmonic expansions are computed
using sea level observations within cycles #1–#350 of the TOPEX/Poseidon satellite altimetry over 11 years of its mission.
A set of orthonormal base functions was generated for the marine areas covered by TOPEX/Poseidon observations from the spherical
harmonics using a Gram-Schmidt orthogonalization process. These were used for modeling the dominant tidal constituents. The
computed models based on orthonormal base functions for the nine tidal constituents and the constant part of the Fourier expansion,
were tested numerically for their validity and accuracy, proving centimeter accuracy. 相似文献
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The multiscale method is used to obtain asymptotic expansions up to the quantities of the third order for the elevations of the surface of the basin and the velocity potential of motion of liquid particles in the wave disturbances formed in the process of nonlinear interaction of periodic running waves of the first and second harmonics in a homogeneous ideal incompressible liquid of constant finite depth covered with broken ice. The dependences of the amplitude-phase structure of disturbances on the ice thickness, depth of the basin, and the parameters of interacting harmonics are investigated. We estimate the error of evaluation of the characteristics of the formed vertical displacement of the surface of the basin and nonlinear mass transfer introduced by neglecting the curvature of the wave profile in the expression for the velocity potential in deducing the kinematic and dynamic surface boundary conditions for nonlinear approximations. 相似文献
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Higher Harmonics Induced by Waves Propagating over A Submerged Obstacle in the Presence of Uniform Current 总被引：1，自引：0，他引：1
To investigate higher harmonics induced by a submerged obstacle in the presence of uniform current, a 2D fully nonlinear numerical wave flume（NWF） is developed by use of a time-domain higher-order boundary element method（HOBEM） based on potential flow theory. A four-point method is developed to decompose higher bound and free harmonic waves propagating upstream and downstream around the obstacle. The model predictions are in good agreement with the experimental data for free harmonics induced by a submerged horizontal cylinder in the absence of currents. This serves as a benchmark to reveal the current effects on higher harmonic waves. The peak value of non-dimensional second free harmonic amplitude is shifted upstream for the opposing current relative to that for zero current with the variation of current-free incident wave amplitude, and it is vice versa for the following current. The second-order analysis shows a resonant behavior which is related to the ratio of the cylinder diameter to the second bound mode wavelength over the cylinder. The second-order resonant position slightly downshifted for the opposing current and upshifted for the following current. 相似文献
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K. E. Steele 《Ocean Engineering》1999,26(12):483
A discrete wave displacement time-series record is usually analyzed by a Discrete Fourier Transform (DFT), which represents the record as the sum of a finite number of harmonic sinusoids. When the dominant sinusoid of the record is not one of these harmonics, DFT “leakage” produces a distorted picture of the dominant wave, particularly for records not much longer than the largest period in the record. This paper proposes a non-Fourier method for determining the dominant wave period that is applicable even when the record is short relative to the largest period present in the record. 相似文献