Displacements due to surface temperature variation on a uniform elastic sphere with its centre of mass stationary
Displacements due to surface temperature variation on a uniform elastic sphere with its centre of mass stationary
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质心静止的均匀弹性球体上由于表面温度变化而产生的位移
DOI：
10.1093/gji/ggt335
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发表时间：
2014-01-01
影响因子：
2.8
通讯作者：
Hager, Bradford H.
中科院分区：
文献类型：
--
作者：
Fang, Ming;Dong, Danan;Hager, Bradford H.
总结我们调查的位移场引起的温度变化的球形热边界层的表面加热下的地球一样的条件下，通过推导的解析解的约束下，其质量中心保持静止的空间均匀的弹性球。类似的应变解决方案，我们的位移解决方案包括两个独特的模式的频谱：一个指数模式的热体力和幂律模式（等效）热表面载荷。结果表明，该解中的热体力的指数模式与经典半空间解中的热体力的指数模式相同，而幂律模式对球解中的热载荷的影响与半空间解中的指数模式不同。热表面载荷被发现，通过解析和numericalanalysis，同样重要的数量级的热体力在整个谐波频谱的表面产生的径向位移。横向位移主要来自于表面热载荷的幂律模式。根据美国航天局对全球陆地表面温度（海洋被掩盖）的空间观测进行的数值模拟显示，全球位移场的年度变化具有独特的模式，符合气候和地理环境。预测的全球尺度地表热变形幅度为毫米级，最大径向位移为0.2mm，最大横向位移为0.1mm。比较分析表明，径向位移场是渐近成比例的表面温度分布，这证明了使用的半空间的解决方案作为一个很好的近似建模的全球径向位移。拼接半空间解所得到的横向位移不能反映球面上的横向变化，不足以模拟和综合整体横向位移。
SUMMARY We investigate the displacement field induced by temperature variation within a spherical thermal boundary layer under an Earth-like condition of surface heating by deriving analytical solutions on a uniform elastic sphere under the constraint that its centre of mass remains stationary in space. Similar to strain solutions, our displacement solution consists of spectra of two distinctive modes: an exponential mode relating to the thermal body force and a powerlaw mode relating to the (equivalent) thermal surface loading. The exponential modes of the thermalbodyforceinoursolutionturnouttobeidenticaltothatinaclassichalf-spacesolution, whiletheeffectofthermalloadingbythepower-lawmodesinoursphericalsolutionisdifferent from the exponential modes of thermal loading in the half-space solution. The thermal surface loadingisfound,byanalyticalandnumericalanalyses,equallyimportantinorderofmagnitude as the thermal body force in producing the radial displacement at the surface throughout the entire harmonic spectrum. The transverse displacement arises mainly from the power-law modes of thermal surface loading. Numerical simulations, based on NASA’s space-borne observation of the global land surface temperature (ocean is masked out), have shown unique patterns in the annual variation of the global displacement field that fits the climatological and geographical settings. The predicted amplitude of the thermally induced surface deformation in global scale is at the millimetre level with the largest ∼2mm for radial displacement and ∼1mm for transverse displacement. Comparative analysis shows that the radial displacement field is asymptotically proportional to the surface temperature distribution, which justifies the use of the half-space solution as a good approximation for modelling the global radial displacement. The transverse displacement obtained by patched half-space solution fails to capture the long-range transverse variations on a spherical surface, and thus, is inadequate for modelling and synthesizing the global transverse displacement.