The thermal expansion effects of GNSS stations are influenced by not only temperature variations, but also bedrock depths and types. Unfortunately, the current studies treat the subsurface GNSS monument and their nearby bedrock as a whole, without taking into account the inconsistencies among bedrock depths and types, while the existing full-spectrum finite element method (FEM) cannot be easily extended to consider the bedrock information. To solve this problem, we propose a refined full-spectrum temperature-induced subsurface thermal expansion model (FSH_BDT) that considers both seasonal and non-seasonal temperature variations as well as bedrock information based on the half-space harmonic model. Results show that the full-spectrum half-space harmonic model (FSH), which considers only seasonal and non-seasonal temperature variations, can obtain comparable results to the FEM and even outperform the FEM for inland stations. In addition, the depth and type of bedrock have significant effects on the annual amplitude and phase of thermal expansion-induced vertical displacement. In particular, we find that the station displacement increases by more than 1 mm and the annual phase delays by up to 10° for high-latitude and deeper bedrock stations when bedrock depths are taken into account. The FSH_BDT improves the correlation coefficient between GNSS height and mass load displacements by up to 42.3% compared to the FEM and explains up to 8.2% of the nonlinear variation in the GNSS height time series. Our work confirms the advantage of rigorous subsurface thermal expansion modeling to correct the nonlinear variations of global GNSS stations, which might provide a potential opportunity to improve the terrestrial reference frame toward the goal of 1 mm accuracy.

GNSS 站的热膨胀效应不仅受到温度变化的影响，还受到基岩深度和类型的影响。不幸的是，目前的研究将地下GNSS纪念碑及其附近的基岩视为一个整体，没有考虑基岩深度和类型之间的不一致，而现有的全谱有限元方法（FEM）不能轻易扩展到考虑基岩。信息。为了解决这个问题，我们提出了一种改进的全谱温度诱发的地下热膨胀模型（FSH _BDT），该模型考虑了季节性和非季节性温度变化以及基于半空间谐波模型的基岩信息。结果表明，仅考虑季节性和非季节性温度变化的全谱半空间谐波模型（FSH）可以获得与有限元法相当的结果，甚至优于内陆站的有限元法。此外，基岩深度和类型对热膨胀引起的垂直位移的年振幅和相位也有显着影响。特别是，我们发现，当考虑基岩深度时，高纬度和较深基岩台站的台站位移增加超过1毫米，年相位延迟高达10°。与 FEM 相比， FSH _BDT将 GNSS 高度和质量载荷位移之间的相关系数提高了高达 42.3%，并解释了 GNSS 高度时间序列中高达 8.2% 的非线性变化。我们的工作证实了严格的地下热膨胀建模在纠正全球 GNSS 站非线性变化方面的优势，这可能为改进地面参考系以实现 1 毫米精度的目标提供潜在机会。