地球表层物质非均匀分布对地球动力学扁率的贡献

The Contribution of the Upper Crust to Global Dynamic Flattening

全球动力学扁率(H)是研究地球自转与岁差的一个重要物理量.由对岁差的观测有H_(obs)= 0.0032737≈1/305.5.该文依据内部场理论重新计算了流体静平衡态下的地球内部几何扁率剖面,结果与Denis(1989)的结果相吻合.该文还推导了三阶扁率精度下H的计算式,并计算出PREM地球模型的H理论值为H_(PREM)=1/308.5,这与其他人的结果一样,与观测值之间存在1%的差别.为了研究这个差别的来源,该文将PREM模型中均一的上地壳层与海洋层替换为ECCO、GTOPO30和ETOPO5等真实的地球表层数据,结果表明替换后得到的H更加偏离观测值.此结果说明来自于地幔及更深处质量异常引起的正面影响可能要比先前预期的高,并为地壳均衡理论提供了间接的证据.

Global dynamic flattening （H） is an important parameter in the study of the Earth rotation. Precession observations give Hobs = 0.0032737 ≈ 1/305.5. The geometrical flattening （f） profile of the Earth interior is recalculated from potential theory in hydrostatic equilibrium （HSE） state, and the results coincide with that of Denis（1989）. In this paper, H expression hasbeen derived to third-order accuracy, and the value of H obtained from PREM earth model is 1/308.5. This coincides with other similar works, in all of which there is a difference about 1% between them and the observed value. In order to study where the difference come from, the homogenous uppest crust and oceanic layers in PREM are replaced by some real surface layers data, such as oceanic layer （ECCO model） , topography data （GTOPO30 model）, crust data （CRUST2.0 model） and mixed data （ETOPO5 model）. According to the depth range of each model, three Earth models have been constructed with real surface data from PREM, ECCO, GTOPO30 and so on. Our attention is focused on the effect from non-uniform distribution of mass in the real surface layer, while the effect from the change of the gravitational field inside the Earth is ignored in our calculation. So, it is simply assumed that tile shapes of the equipotential and equidensity surfaces in our new constructed models are as the same as in PREM. From results of the dynamic flattening of each model, the mass of surface layers is less than 0.1% of tile whole Earth, but the real surface layers can reduce the global dynamic flattening from 1/308.53 to 1/318.14 （about 3%）. It is really a large effect and related to the fact that dynamic flattening is associated with not only how much the mass is but also how the mass distributed. The surface layers is the outermost layer of the Earth and plays an important role. If the surface layers are replaced from the surface to 5.615 kilometers under tile mean sea level （ECCO）, H deviates from that of PREM. When the surface layers are replaced deeper till 10.376 kilometers under the mean sea level （ETOPO5）, H deviates more. But when go further till 70.137 kilometers under the mean sea level, the value of H is being enlarged and deviates less than that of above two models. The isostasy theory maybe can explain why this happened. There are several compensation models in isostasy theory. All of them thinks that the mass above the geoid will be counteracted by the loss of mass under geoid with some kinds. There is a compensation level in most compensation models. The compensation level is under geoid and the depth of it; is assumed fi＇om 30 kilometers to 100 kilometers for different models. When it is replaced that the volume from surface to 5.615 kilometers depth, there is no mass loss under the geoid to counteract the mass above the geoid, so the real lands distribution makes H deviate from HpREM. When it goes further to 10.376 kilometers depth, there is still no mass loss under the geoid, because the depth we replaced is not reach the depth of compensation level, things become more serious. But when it reachs 70.137 kilometers depth, mass loss under the geoid and counteracting effect appear, and it drags back H from 1/320.22 to 1/310.70. Although the theory of isostasy can explain the difference among three models, there is still a difference between the calculated value and the observed value.