Relationships Among Variations in the Earth’s Length-of-Day, Polar Oblateness, and Total Moment of Inertia: A Tutorial Review

IF 4.9 2区 地球科学 Q1 GEOCHEMISTRY & GEOPHYSICS Surveys in Geophysics Pub Date : 2024-10-07 DOI:10.1007/s10712-024-09858-4
Benjamin F. Chao
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Abstract

We revisit the derivation of the linear relationships connecting the variations of the Earth’s length-of-day (more specifically its mass term ΔLODmass), polar oblateness (ΔJ2), and total moment of inertia (ΔT) caused by geophysical mass transports. The three integral quantities are expressed as inner products of the perturbation, either in the form of density change in the Eulerian description or deformation in the Lagrangian description, with pertinent base functions arising from distinct physical principles. We discuss various cases of mass transport processes regarding whether or not T is conserved, or ΔT = 0. When and only when ΔT = 0, the ΔLODmass and ΔJ2 become proportional to each other and hence mutually convertible. This latter practice has long been common, albeit often taken for granted, in the literature notably with respect to the mass transports in surface geophysical fluids and by the glacial isostatic adjustment (GIA) that awaits numerical assessments per physics-based GIA models. We point to subtleties and caveats that tend to be misrepresented, namely, the distinction of ΔLODmass from the observed ΔLOD, and the extent of the core’s participation in the angular momentum exchanges across the core-mantle boundary.

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地球日长、极地扁平和总惯性矩变化之间的关系:教程回顾
我们重新探讨了地球物理质量迁移引起的地球日长(更具体地说是其质量项ΔLODmass)、极地扁平(ΔJ2)和总惯性矩(ΔT)变化之间的线性关系的推导。这三个积分量以扰动的内积表示,在欧拉描述中以密度变化的形式表示,在拉格朗日描述中以变形的形式表示,相关的基函数产生于不同的物理原理。我们讨论了质量输运过程中有关 T 是否守恒或 ΔT = 0 的各种情况。只有当 ΔT = 0 时,ΔLODmass 和 ΔJ2 才会成正比,从而可以相互转换。后一种做法在文献中早已司空见惯,尽管常常被认为是理所当然的,特别是在地表地球物理流体的质量传输和冰川等静力调整(GIA)方面。我们指出了容易被误解的微妙之处和注意事项,即ΔLODmass 与观测到的ΔLOD 的区别,以及地核在地核-地幔边界角动量交换中的参与程度。
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来源期刊
Surveys in Geophysics
Surveys in Geophysics 地学-地球化学与地球物理
CiteScore
10.00
自引率
10.90%
发文量
64
审稿时长
4.5 months
期刊介绍: Surveys in Geophysics publishes refereed review articles on the physical, chemical and biological processes occurring within the Earth, on its surface, in its atmosphere and in the near-Earth space environment, including relations with other bodies in the solar system. Observations, their interpretation, theory and modelling are covered in papers dealing with any of the Earth and space sciences.
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