The paper deals with geoid modeling using the least-squares modification of the Stokes' and Hotine's formulae using gridded and non-gridded terrestrial gravity data over the Auvergne test area (France). Differently from the conventional way of using gridded gravity data, this study utilizes non-gridded data as the input to the geoid modeling and compare the differences between the computational approaches in terms of the geoid model accuracies. For this purpose, the calculated gravimetric geoid models are validated at high-accuracy GNSS/leveling benchmarks provided in the test dataset. The geoid models computed using the grid gravity data yielded 3.8 cm and 4.0 cm accuracies before fitting for Hotine's and Stokes' methods, whilst the evaluation of the geoid models with non-gridded data yielded 6.6 cm and 5.7 cm, respectively. The numerical comparisons of the different geoid models are presented and discussed in detail.

该论文使用奥弗涅测试区（法国）上的网格和非网格地面重力数据，使用 Stokes 和 Hotine 公式的最小二乘修正处理大地水准面建模。不同于传统的使用网格化重力数据的方法，本研究利用非网格化数据作为大地水准面建模的输入，并在大地水准面模型精度方面比较了计算方法之间的差异。为此，计算出的重力大地水准面模型在测试数据集中提供的高精度 GNSS/水准基准上进行验证。在拟合 Hotine 和 Stokes 方法之前，使用网格重力数据计算的大地水准面模型的精度分别为 3.8 厘米和 4.0 厘米，而使用非网格数据评估大地水准面模型的精度分别为 6.6 厘米和 5.7 厘米。