• ISSN 2097-1893
    • CN 10-1855/P

    半无限空间表面热负荷产生的形变和重力场变化

    Deformation and gravity changes induced by surface heat sources in a thermoelastic half-space

    • 摘要: 对多种已知机制引起的重力场变化进行高精度理论建模,是利用重力学研究地球表层与内部动力学过程的重要前提. 地球及外天体表面的温度场在太阳辐射或岩浆喷发等因素作用下,常表现为周期性或突变性的温度波动. 这些温度扰动不仅会导致介质发生形变,同时也会引起空间重力场的变化. 本文基于热弹性半无限空间模型,通过微分方程的解析求解,系统推导了表面点状与圆盘状热源在周期性及阶跃温度扰动下,产生的形变场与重力场变化的解析表达式. 结果表明,热弹性效应导致的表面重力变化表现为重力测量仪器随表层形变产生的自由空气重力梯度效应,内部体应变引起的密度变化效应与表层位移的布格层效应在一阶近似下互相抵消. 最后,本文给出了两个典型算例,简要分析了其产生的形变与重力效应:一是月表周期温度波动,估算其产生的变形在亚毫米级,重力变化小于1 μGal;二是尼拉贡戈火山永久性熔岩湖的突发温度扰动,假定岩浆湖400 m半径、温度升高40 K,其中心处稳态热弹性垂直位移约10 cm、重力变化约30 μGal.

       

      Abstract: High-precision theoretical modelling of gravity field variations induced by multiple known mechanisms is a prerequisite for studying dynamic processes of the Earth's surface and interior through gravimetry. Temperature fields on the Earth and other celestial bodies, driven by factors such as solar radiation and magmatic eruptions, often exhibit periodic or step-like fluctuations. These thermal perturbations not only generate deformation fields but also disturb the gravity field. In this study, we employ a thermoelastic half-space model and solve the governing partial differential equations analytically to derive explicit expressions for the deformation and gravity changes induced by surface point and disk-shaped heat sources under periodic and step-like temperature fluctuations. The results demonstrate that gravity variations at the surface caused by thermoelastic effects are manifested solely as the free-air gradient due to the movement of gravimetric instruments with surface deformation, while the contributions from internal strain and Bouguer-layer surface displacement cancel each other at the first order. Finally, two representative examples are presented to illustrate the magnitude of thermoelastic deformation and its gravitational effects: (1) for periodic temperature fluctuations on the lunar surface, the resulting surface uplift is estimated to be at the sub-millimeter level, with gravity changes smaller than 1 μGal; (2) for a sudden temperature disturbance in the permanent lava lake of Mount Nyiragongo, assuming a magma lake with a radius of 400 m and a temperature increase of 40 K, the predicted stable thermoelastic vertical displacement at the center is about 10 cm and the associated gravity change is about 30 μGal.

       

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