发表机构
Federal Research Center for Information and Computational Technologies（联邦信息与计算技术研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过反向构造精确大气模型，揭示了3.7–4.4 mHz声学共振的机制，提出Darboux-Crum和Rosen-Morse势能解释观测频谱，并验证了特定事件中的基模振荡。
AI 中文摘要
大型爆炸性喷发和地震激发约3.7和4.4 mHz的大气振荡，这些振荡与固体地球耦合。对于流体静力学理想气体大气中的垂直传播线性声学-重力波，走时公式给出一个具有势函数$Q(\ au)$的Klein-Gordon方程。我们建立了三个主要结果。首先，对于每个允许正零能解势函数，相应的大气剖面通过求积显式构造；这扩展了已知的恒定$Q$的无反射剖面。其次，Darboux-Crum势给出一个平滑大气，在11至100 km之间再现美国标准大气，误差在3 K以内，并且在其截止频率以上对垂直波完全透明；它不支持4.4 mHz附近的阻尼泛音，其截止频率以下的地面约束模式被完美捕获。因此，观测到的频谱需要一个有限厚度的截止屏障，连接低层大气和热层。第三，Rosen-Morse屏障给出一个精确可解的大气，具有闭式超几何共振条件。其在3.76和4.37 mHz处的共振，泄漏品质因子分别为173和20，解释了两个振荡的不同阻尼：基模位于中间层截止屏障顶部以下，通过隧穿泄漏，而泛音位于其上方。针对特定事件大气的全波计算再现了所报告的3.7–3.8 mHz基模振荡，在七个事件中，有六个事件中识别出这种模式。
英文摘要
Large explosive eruptions and earthquakes excite atmospheric oscillations near 3.7 and 4.4\,mHz that couple to the solid Earth. For vertically propagating linear acoustic--gravity waves in a hydrostatic ideal-gas atmosphere, the travel-time formulation gives a Klein--Gordon equation with a potential $Q(τ)$. We establish three main results. First, for every potential admitting a positive zero-energy solution, the corresponding atmospheric profiles are constructed explicitly by quadrature; this extends the known reflectionless profiles of constant $Q$. Second, Darboux--Crum potentials give a smooth atmosphere that reproduces the U.S. Standard Atmosphere between 11 and 100\,km to within 3\,K and is exactly transparent to vertical waves above its cut-off; it supports no damped overtone near 4.4\,mHz, and its ground-confined mode below the cut-off is perfectly trapped. The observed spectrum therefore requires a cut-off barrier of finite thickness connecting the lower atmosphere to the thermosphere. Third, a Rosen--Morse barrier gives an exactly solvable atmosphere with a closed-form hypergeometric resonance condition. Its resonances at 3.76 and 4.37\,mHz, with leakage quality factors 173 and 20, explain the different damping of the two oscillations: the fundamental lies below the top of the mesospheric cut-off barrier and leaks by tunnelling, whereas the overtone lies above it. Full-wave computations for event-specific atmospheres reproduce the reported 3.7--3.8\,mHz fundamental oscillation in all six events, of seven considered, in which such a mode was identified.
