For decades, the residual terrain model (RTM) concept (Forsberg and Tscherning in J Geophys Res Solid Earth 86(B9):7843–7854, https://doi.org/10.1029/JB086iB09p07843, 1981) has been widely used in regional quasigeoid modeling. In the commonly used remove-compute-restore (RCR) framework, RTM provides a topographic reduction commensurate with the spectral resolution of global geopotential models. This is usually achieved by utilizing a long-wavelength (smooth) topography model known as reference topography. For computation points in valleys this neccessitates a harmonic correction (HC) which has been treated in several publications, but mainly with focus on gravity. The HC for the height anomaly only recently attracted more attention, and so far its relevance has yet to be shown also empirically in a regional case study. In this paper, the residual spherical-harmonic topographic potential (RSHTP) approach is introduced as a new technique and compared with the classic RTM. Both techniques are applied to a test region in the central European Alps including validation of the quasigeoid solutions against ground-truthing data. Hence, the practical feasibility and benefits for quasigeoid computations with the RCR technique are demonstrated. Most notably, the RSHTP avoids explicit HC in the first place, and spectral consistency of the residual topographic potential with global geopotential models is inherently achieved. Although one could conclude that thereby the problem of the HC is finally solved, there remain practical reasons for the classic RTM reduction with HC. In this regard, both intra-method comparison and ground-truthing with GNSS/leveling data confirms that the classic RTM (Forsberg and Tscherning 1981; Forsberg in A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modeling. Report 355, Department of Geodetic Sciences and Surveying, Ohio State University, Columbus, Ohio, USA, https://earthsciences.osu.edu/sites/earthsciences.osu.edu/files/report-355.pdf, 1984) provides reasonable results also for a high-resolution (degree 2160) RTM, yet neglecting the HC for the height anomaly leads to a systematic bias in deep valleys of up to 10–20 cm.

几十年来，残差地形模型（RTM）概念（Forsberg 和 Tscherning in J Geophys Res Solid Earth 86(B9):7843–7854, https://doi.org/10.1029/JB086iB09p07843, 1981）已广泛应用于区域准大地水准面建模。在常用的移除-计算-恢复 (RCR) 框架中，RTM 提供了与全球位势模型的光谱分辨率相称的地形缩减。这通常是通过利用称为参考地形的长波长（平滑）地形模型来实现的。对于山谷中的计算点，这需要谐波校正（HC），该校正已在多个出版物中进行过处理，但主要集中在重力上。高度异常的 HC 最近才引起更多关注，到目前为止，其相关性尚未在区域案例研究中得到实证证明。本文引入了残余球谐地形势（RSHTP）方法作为一种新技术，并与经典的 RTM 进行了比较。这两种技术都应用于中欧阿尔卑斯山的测试区域，包括根据地面实况数据验证准大地水准面解决方案。因此，证明了使用 RCR 技术进行准大地水准面计算的实际可行性和优势。最值得注意的是，RSHTP 首先避免了显式 HC，并且本质上实现了残余地形势与全球位势模型的光谱一致性。尽管可以得出这样的结论：HC 的问题最终得到解决，但用 HC 进行经典的 RTM 还原仍然存在实际原因。 在这方面，方法内比较和 GNSS/水准测量数据的地面实况都证实了经典的 RTM（Forsberg 和 Tscherning 1981；Forsberg 的《重力场建模中的地形减少、密度异常和地球物理反演方法的研究》）。报告 355 ，大地测量科学与测量系，俄亥俄州立大学，哥伦布，俄亥俄州，美国，https://earthsciences.osu.edu/sites/earthsciences.osu.edu/files/report-355.pdf，1984）也提供了合理的结果对于高分辨率（2160 度）RTM，但忽略高度异常的 HC 会导致高达 10-20 厘米的深谷中的系统偏差。