The harmonic correction (HC) is one of the key quantities when using residual terrain modelling (RTM) for high-frequency gravity field modelling. In the RTM technique, high-frequency topographic gravitational signals are obtained through removing gravitational effects of a long-wavelength reference surface, e.g., MERIT2160. There might be points located below the reference surface. In such cases, the RTM gravity field is calculated in the non-harmonic condition, HC is therefore required. Over past decades, though various methods have been proposed to handle the HC issue for the RTM technique, most of them were focused on the HC for RTM gravity anomaly rather than for other gravity functionals, such as RTM geoid height. In practice, the HC for RTM geoid height was generally assumed to be negligible, but a detailed quantification was missing for present-day RTM computations. This might cause large errors in the regional geoid determination over rugged areas. In this study, we derive HC expressions for the RTM geoid height in the framework of the classical condensation method. The HC terms are derived under four different assumptions separately: residual masses approximated by an unlimited Bouguer plate, residual masses approximated by a limited Bouguer plate which overcomes the mass inconsistency effect, residual masses approximated by a Bouguer shell which overcomes the effect of planar approximation, and residual masses approximated by a limited Bouguer shell which overcomes the errors induced by both planar approximation and mass-inconsistency. The errors due to various approximations in HC terms are investigated through comparison among various terms. Besides, HC terms are computed using an expansion up to degree and order 2159. Our results show that HC for RTM geoid height is less 1 mm and could be ignored over \(\sim 99\)% of continental areas, but be of great significance for regional geoid determination over mountain areas, e.g., more than 10 cm effect over very rugged areas. The validation through comparison with terrestrial measurements and a baseline solution of the RTM technique proves that the HC terms provided in this study can improve the accuracy of RTM geoid heights and are expected to be useful for applications of the RTM technique in regional and global gravity field modelling.

谐波校正（HC）是使用残余地形建模（RTM）进行高频重力场建模时的关键量之一。在RTM技术中，高频地形引力信号是通过去除长波参考面的引力效应得到的，例如MERIT2160。可能有一些点位于参考表面下方。在这种情况下，RTM 重力场是在非谐波条件下计算的，因此需要 HC。在过去的几十年里，尽管已经提出了各种方法来处理 RTM 技术的 HC 问题，但大多数都集中在 RTM 重力异常的 HC 上，而不是其他重力泛函，例如 RTM 大地水准面高度。在实践中，通常假设 RTM 大地水准面高度的 HC 可以忽略不计，但是目前的 RTM 计算缺少详细的量化。这可能会在崎岖地区的区域大地水准面确定中造成很大的误差。在这项研究中，我们在经典凝聚法的框架下推导出了 RTM 大地水准面高度的 HC 表达式。HC 项分别在四种不同的假设下推导出来：由无限布格板近似的残余质量，由克服质量不一致性效应的有限布格板近似的残余质量，由克服平面近似效应的布格壳近似的残余质量，和残余质量由有限的布格壳近似，克服了平面近似和质量不一致引起的误差。通过各种项之间的比较，研究了由于HC项的各种近似导致的误差。此外，HC 项是使用高达 2159 度和阶数的展开计算的。我们的结果表明，RTM 大地水准面高度的 HC 小于 1 毫米，可以忽略不计\(\sim 99\) % 的大陆地区，但对于山区的区域大地水准面测定具有重要意义，例如，在非常崎岖的地区超过 10 厘米的影响。通过与地面测量和 RTM 技术基线解的比较验证，证明本研究提供的 HC 项可以提高 RTM 大地水准面高度的准确性，有望对 RTM 技术在区域和全球重力场中的应用有所帮助造型。