发表机构
King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过局部微分映射构建物理到有效的传递矩阵，解释分层粘弹性内部对应的等效均质流变学参数，应用于月球模型，识别出内核刚度不可观测，并验证了简化流变模型的准确性。
AI 中文摘要
分层粘弹性内部结构决定了行星潮汐耗散的频率依赖性，但重复的分层Love数计算在长期轨道和自旋积分中代价高昂。等效均质流变学提供了相同响应的更廉价表示，但其有效参数本身并不能识别它们所代表的内部层。我们通过关于固定几何基线的分层到均质构造的微分，仅扰动选定的层刚度和粘度，开发了此类参数的局部解释。我们利用二阶Love数的极点-留数表示来构建物理到有效的传递矩阵。然后，我们使用其奇异值、分辨率矩阵和模态主导矩阵来确定哪些物理扰动在Love数响应中可见，以及它们如何在有效流变学坐标中显现。应用于五层月球模型时，完整的二阶响应对八个固态层流变参数中的七个敏感。唯一的近零方向是内核刚度，这与流体外核的屏蔽作用以及Love数对核弹性结构的弱依赖性一致。在LLR频率区间内，可见的物理方向较少。一阶近似下，弹性弹簧、孤立阻尼器和两个Voigt元件在该区间内再现了九极点响应。有限扰动证实切线预测在几个百分点以内，有效性半径受限于一对近简并的长时标模态。
英文摘要
Layered viscoelastic interiors control the frequency dependence of planetary tidal dissipation, but repeated layered Love-number calculations are expensive in long-term orbital and spin integrations. Equivalent homogeneous rheologies provide a cheaper representation of the same response, but their effective parameters do not by themselves identify the interior layers they represent. We develop a local interpretation of such parameters by differentiating the layered-to-homogeneous construction about a fixed-geometry baseline, perturbing only selected layer rigidities and viscosities. We use the pole-residue representation of the degree-two Love number to construct a physical-to-effective transfer matrix. We then use its singular values, resolution matrix, and mode-dominance matrix to determine which physical perturbations are visible in the Love-number response and how they appear in effective-rheology coordinates. Applied to a five-layer lunar model, the full degree-two response is sensitive to seven of eight solid-layer rheological parameters. The single near-null direction is the inner-core rigidity, consistent with shielding by the fluid outer core and with the weak dependence of Love numbers on core elastic structure. Over the LLR frequency interval, fewer physical directions are visible. To first order, the elastic spring, isolated dashpot, and two Voigt elements reproduce the nine-pole response over this interval. Finite perturbations confirm the tangent prediction to within a few percent, with the validity radius limited by a nearly degenerate pair of long-timescale modes.
Comments11 pages, 5 figures
