SUMMARY We propose a parametric approach to the topographic (TOP) coupling between the mantle and outer core for refinement of the latest triaxial three-layered Earth rotation theory. Based on three models of the core–mantle boundary (CMB) topography, we obtain the axial components of the TOP torque as −2.08 × 1019, −2.72 × 1018 and −1.97 × 1017 N m, respectively. Under the frame of the triaxial three-layered Earth rotation theory, we solve the corresponding periods of free core nutation as −(329.83 ± 28.12), −(457.54 ± ∼) and −(428.23 ± 1.09) mean solar days (d), respectively. The other three normal modes, namely, Chandler wobble, inner core wobble and free inner core nutation, are almost not affected by the TOP coupling of the CMB, their period values being 433.24, 2718.69 and 934.02 d, respectively. Calculations show that the TOP torque is highly sensitive to the adopted model of the topography, which is known to be robust. Taking into account the normal modes of the triaxial three-layered Earth rotation, the results of the CMB topography obtained by seismic tomography can be constrained in the future to a certain extent. In this study, considering the TOP coupling with the appropriate topography model, the estimates for the dynamic ellipticity ef of the fluid core lie between 0.0026340 and 0.0026430, values that are 3.56 % higher than the hydrostatic equilibrium value.

中文翻译：

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核幔地形耦合：一种参数化方法及其对三轴三层地球自转公式的影响

总结 我们提出了一种参数化方法来处理地幔和外核之间的地形（TOP）耦合，以完善最新的三轴三层地球自转理论。基于核幔边界（CMB）地形的三个模型，我们获得了TOP扭矩的轴向分量分别为-2.08×1019、-2.72×1018和-1.97×1017 N·m。在三轴三层地球自转理论的框架下，我们将自由核心章动的相应周期求解为-（329.83±28.12），-（457.54±∼）和-（428.23±1.09）平均太阳日（d），分别。其他三种正常模式，即钱德勒摆动、内核摆动和自由内核章动，几乎不受CMB TOP耦合的影响，它们的周期值分别为433.24、2718.69和934.02 d。计算表明，TOP 扭矩对所采用的地形模型高度敏感，众所周知，地形模型是稳健的。考虑到三轴三层地球自转的正常模式，未来地震层析成像获得的CMB地形结果可以在一定程度上受到约束。在这项研究中，考虑到与适当地形模型的 TOP 耦合，流体核心的动态椭圆率 ef 的估计值介于 0.0026340 和 0.0026430 之间，比流体静力平衡值高 3.56%。地震层析成像得到的 CMB 地形结果在未来会受到一定的约束。在这项研究中，考虑到与适当地形模型的 TOP 耦合，流体核心的动态椭圆率 ef 的估计值介于 0.0026340 和 0.0026430 之间，比流体静力平衡值高 3.56%。地震层析成像得到的 CMB 地形结果在未来会受到一定的约束。在这项研究中，考虑到与适当地形模型的 TOP 耦合，流体核心的动态椭圆率 ef 的估计值介于 0.0026340 和 0.0026430 之间，比流体静力平衡值高 3.56%。