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复杂地区局部重力场带限SRBF二次逼近法

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本文利用基于带限球面径向基函数(SRBF)的重力场二次累积逼近法,对地形复杂地区重力场模型的构建进行了较为详细的数值分析和验证工作.首先,利用带限SRBF将卫星重力场模型(GGM)数据与航空重力数据进行融合,构建了研究地区的初始重力场模型(基于SRBF的重力场第一次逼近).与仅依赖于航空数据得到的重力场模型相比,初始重力场模型与GPS/水准数据之间的大地水准面差异标准差(STD)在研究区域降低了约0.022 m,表明了融合GGM和航空重力数据进行初始重力场建模的有效性.然后,在移去参考重力场模型、初始重力场模型和残余地形模型效应的基础上,利用残余地面和航空重力数据进行了基于带限SRBF的重力场第二次逼近.与传统的基于SRBF的一次逼近方法相比,二次SRBF逼近方法所得模型在研究区域的大地水准面差异STD和RMS值分别降低了0.036m和0.024m,显示了带限SRBF二次累积逼近方法的优越性.此外,研究区域地形属于复杂的山区,可以为复杂地区重力场模型的构建提供一定参考.
Band-limited SRBF quadratic approximation method for local gravity fields in complex regions
Utilizing the SRBF-based two-step cumulative approximation method, this study conducted a detailed numerical analysis and validation for the construction of a local gravity field model in complex areas. First, data from the global gravity field model were combined with airborne gravity data to construct the initial SRBF-based gravity field model for the study area (the first gravity field approximation based on band-limited SRBFs).When compared to the airborne-only gravity field model, the standard deviation of geoid height discrepancies between the initial gravity field model and GPS/leveling data decreased by approximately 0.022m. This suggests the effectiveness of merging GGM and airborne gravity data for initial modeling. Subse-quently, after removing the effects of the reference gravity field model, the initial gravity field model and the residual terrain model from the terrestrial and airborne gravity data, a secondary SRBF-based modeling process was conducted (the second gravity field approximation based on band-limited SRBFs). Compared to the one-step SRBF model, the two-step approach yiel-ded reductions of 0.036m and 0.024m in terms of STD and RMS, respectively, highlighting the superiority of the SRBF-based two-step cumulative approximation method. Moreover, the study area features a complex mountainous terrain, which can serve as a reference for constructing gravity field model in similar complex regions.

band-limited spherical radial basis functiontwo-step cumulative approximation method for local gravity fieldGGM gravity dataairborne gravity dataterrestrial gravity data

马志伟、边少锋、徐如一、陈永冰

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河南财经政法大学工程管理与房地产学院,河南郑州 450046

海军工程大学电气工程学院,湖北武汉 430033

河南财经政法大学金融学院,河南郑州 450046

带限径向基函数 局部重力场二次累积逼近法 卫星重力数据 航空重力数据 地面重力数据

国家自然科学基金国家自然科学基金

4210408742074010

2024

10.11947/j.AGCS.2024.20230132

测绘学报
中国测绘学会

测绘学报

CSTPCD北大核心
影响因子：1.602
ISSN：1001-1595
年,卷(期)：2024.53(5)
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