Modeling of nutation and precession: New nutation series for nonrigid Earth and insights into the Earth's interior
Modeling of nutation and precession: New nutation series for nonrigid Earth and insights into the Earth's interior
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DOI：
10.1029/2001jb000390
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发表时间：
2002-04-10
影响因子：
3.9
通讯作者：
Buffett, BA
中科院分区：
文献类型：
--
作者：
Mathews, PM;Herring, TA;Buffett, BA
[1]章动和摆动理论的分析公式揭示了支配地球对天体引力（潮汐）作用力的章动-摆动反应的基本地球参数的组合，并使人们能够通过将理论表达式与现有高精度数据进行最小二乘拟合来估计其中几个参数。本文介绍的理论框架的要点，我们使用的基本地球参数的最小二乘估计的过程，通过理论拟合章动，岁差数据来自一个最新的很长的基线干涉测量数据集，估计的结果和地球物理解释，章动序列构造使用的参数估计值。这里所用的理论公式与以前的不同之处在于，在理论动力学方程的基本结构中加入了滞弹性和海潮效应，并加入了地幔和固体内核与流体外核的电磁耦合，尽管这种普遍化的代价是使某些系统参数变得复杂和与频率有关;它也是更完整的，因为它考虑了这些方程中的非线性项，包括由纬向和扇形潮汐产生的随时间变化的变形的影响，这在传统的非刚性地球理论中被忽略了。从我们的拟合中获得的地球物理结果包括对地球的动态椭圆率e（e = 0.0032845479，最后一位数的不确定性为12）、流体核的动态椭圆率e（f）（比其流体静力平衡值高3.8%，而不是迄今为止的5%）和两个复杂的电磁耦合常数的估计。当磁场配置被限制在某些简单类时，我们基于对这些耦合常数的估计，对核幔边界和内核边界处的RMS径向磁场的最佳估计分别为6.9和72高斯。如果内核边界处的流体密度或固体内核的椭圆率低于初步参考地球模型，则内核边界处所需的场强可能较低。我们对向前自由核心章动模式的共振频率的估计（不确定性接近10%）构成了对与该模式相关的共振的第一次可靠检测;发现的周期类似于1025天，是忽略电磁耦合的两倍。（在本书中，“日”指的是周期，代表“平均太阳日”。“）通过直接求解每个强迫频率的线性化动力学方程（对所有估计的地球参数采用我们的最佳拟合值），并加入线性化方程中未包括的非线性项和其他效应的贡献，构造了一个新的章动序列（MHB 2000）。这一系列给出了一个相当好的适合章动数据比任何早期的系列地球物理理论的基础上。特别是逆行18.6年章动和年章动的异相振幅的残差，长期以来一直保持在0.5毫秒弧（mas）左右，现在主要由于电磁耦合所起的作用，已经降低到观测估计的不确定性水平。剩下的最大差异是在反相18.6年章动中，类似于72微秒弧（μ A）。章动振幅的频率依赖性不能通过共振公式精确地表示，也不能将共振频率本身解释为自由模式的本征频率，因为存在复杂且依赖于频率的系统参数。尽管如此，我们已经构建了一个新的共振公式，它精确地再现了几乎所有章动频率的章动序列;对于剩下的几个频率，给出了一个列表，列出了为了再现直接解的精确结果而应用的修正。
[1] The analytical formulation of the theories of nutation and wobble reveals the combinations of basic Earth parameters that govern the nutation-wobble response of the Earth to gravitational (tidal) forcing by heavenly bodies and makes it possible to estimate several of them through a least squares fit of the theoretical expressions to the high-precision data now available. This paper presents the essentials of the theoretical framework, the procedure that we used for least squares estimation of basic Earth parameters through a fit of theory to nutation-precession data derived from an up-to-date very long baseline interferometry data set, the results of the estimation and their geophysical interpretation, and the nutation series constructed using the estimated values of the parameters. The theoretical formulation used here differs from earlier ones in the incorporation of anelasticity and ocean tide effects into the basic structure of the dynamical equations of the theory and in the inclusion of electromagnetic couplings of the mantle and the solid inner core to the fluid outer core, though this generalization comes at the cost of making some of the system parameters complex and frequency dependent; it is also more complete, as it takes account of nonlinear terms in these equations, including effects of the time-dependent deformations produced by zonal and sectorial tides, which had been traditionally neglected in nonrigid Earth theories. Among the geophysical results obtained from our fit are estimates for the dynamic ellipticity e of the Earth (e = 0.0032845479 with an uncertainty of 12 in the last digit), for the dynamical ellipticity e(f) of the fluid core (3.8% higher than its hydrostatic equilibrium value, rather than similar to5% as hitherto), and for the two complex electromagnetic coupling constants. Our best estimates for the RMS radial magnetic fields at the core mantle boundary and at the inner core boundary, based on the estimates for these coupling constants, are similar to6.9 and 72 gauss, respectively, when the magnetic field configurations are restricted to certain simple classes. The field strength needed at the inner core boundary could be lower if the density of the core fluid at this boundary or the ellipticity of the solid inner core were lower than that for the Preliminary Reference Earth Model. Our estimate for the resonance frequency of the prograde free core nutation mode, with an uncertainty of similar to10%, constitutes the first firm detection of the resonance associated with this mode; the period found is similar to1025 days, double that with electromagnetic couplings ignored. (Throughout this work, "days," referring to periods, stands for "mean solar days.") A new nutation series (MHB2000) is constructed by direct solution of the linearized dynamical equations (with our best fit values adopted for all the estimated Earth parameters) for each forcing frequency, and adding on the contributions from the nonlinear terms and other effects not included in the linearized equations. This series gives a considerably better fit to the nutation data than any of the earlier series based on geophysical theory. In particular, the residuals in the out of phase amplitudes of the retrograde 18.6 year and annual nutations, which had long remained at similar to0.5 milliseconds of arc (mas), are now reduced to the level of the uncertainties in the observational estimates, thanks mainly to the role played by the electromagnetic couplings.The largest remaining discrepancy is that in the out of phase prograde 18.6 year nutation, of similar to72 microseconds of arc (muas). The frequency dependence of the nutation amplitudes cannot be exactly represented through a resonance formula, nor may the resonance frequencies themselves be interpreted as the eigenfrequencies of free modes because of the presence of complex and frequency-dependent system parameters. Nevertheless, we have constructed a new resonance formula which reproduces our nutation series accurately for almost all nutation frequencies; for the few remaining frequencies, a listing is given of the corrections to be applied in order to reproduce the exact results of the direct solution.