We revisit the derivation of the linear relationships connecting the variations of the Earth’s length-of-day (more specifically its mass term ΔLOD_mass), 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 ΔLOD_mass 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 ΔLOD_mass from the observed ΔLOD, and the extent of the core’s participation in the angular momentum exchanges across the core-mantle boundary.

我们重新审视连接地球日长（更具体地说是其质量项 ΔLOD_质量）、极扁率 (Δ J ₂ ) 和由地球物理质量引起的总转动惯量 (Δ T ) 变化的线性关系的推导运输。这三个积分量被表示为扰动的内积，或者以欧拉描述中的密度变化的形式，或者以拉格朗日描述中的变形的形式，以及由不同的物理原理产生的相关基函数。我们讨论有关T是否守恒或 Δ T = 0 的质量传递过程的各种情况。当且仅当 Δ T = 0 时，ΔLOD_质量和 Δ J ₂彼此成正比，因此可以相互转换。后一种做法长期以来很常见，尽管经常被认为是理所当然的，在文献中特别是在地表地球物理流体中的质量传输以及等待基于物理的 GIA 模型进行数值评估的冰川均衡调整 (GIA) 方面。我们指出了容易被误解的微妙之处和警告，即 ΔLOD_质量与观测到的 ΔLOD 的区别，以及核心参与跨核心-地幔边界角动量交换的程度。