Global geopotential models are widely used in the remove-compute-restore technique for local gravity field modeling. In this paper, a method for regional improvement of global geopotential models using GPS/Leveling data is presented. The part of the spherical harmonic expansion degrees that can be subject to the regional improvement is determined depending on the spatial resolution of the GPS/Leveling data and the size of the study region. In this method, a global geopotential model is required as the original model. Using the GPS/Leveling data corrected for the systematic errors, the geoid surface is obtained at the GPS/Leveling points. By expanding the gravity potential of the geoid surface into the spherical harmonics, a mathematical model is made to estimate the spherical harmonic coefficients of the regionally improved geopotential model. To stabilize the mathematical model, pseudo data of the gravitational potential type produced by the original model on the entire Earth’s surface are added to the GPS/Leveling data. The relative weight of the two types of the data, i.e., the GPS/Leveling data and the pseudo data, is selected based on fitting the original model to the GPS/Leveling data. As numerical tests, the regionally improved geopotential model of the USA from degree 8 to 779 and the regionally improved geopotential model of Iran from degree 12 to 339 are developed. To develop both regionally improved geopotential models, the EGM2008 model up to degree 2160 is selected as the original model. The assessments at the GPS/Leveling checkpoints show that the regionally improved geopotential model of the USA has a 23% improvement and the regionally improved geopotential model of Iran has an 8% improvement with respect to the original model. The numerical tests confirm the efficiency of the proposed method for the regional improvement of global geopotential models using the GPS/Leveling data.

中文翻译：

---

使用GPS /水准仪数据对全球地势模型进行区域改进

全局地势模型被广泛用于局部重力场建模的删除计算恢复技术中。本文提出了一种利用GPS /水准仪数据进行全球地势模型区域改进的方法。根据GPS /水准仪数据的空间分辨率和研究区域的大小，确定可以进行区域改进的部分球谐展开度。在这种方法中，需要一个全局地理势模型作为原始模型。使用针对系统误差校正的GPS /水准仪数据，可在GPS /水准仪点获得大地水准面。通过将大地水准面的重力势扩展为球谐函数，可以建立一个数学模型来估计区域改进的地势模型的球谐系数。为了稳定数学模型，将原始模型在整个地球表面上产生的重力势能类型的伪数据添加到GPS /水准仪数据中。基于将原始模型拟合到GPS /水准仪数据来选择两种数据类型的相对权重，即GPS /水准仪数据和伪数据。作为数值测试，开发了美国从8度到779度的区域改进的地势模型和伊朗从12度到339度的区域改进的地势模型。为了开发两个区域改进的地势模型，原始模型选择了2160年以前的EGM2008模型。GPS /水准检查站的评估表明，相对于原始模型，美国的区域改进后的地势模型改善了23％，伊朗的区域改进后的地势模型改善了8％。数值测试证实了使用GPS /水准仪数据对全球地理潜力模型进行区域改进的方法的有效性。