联合卫星重力与地形位模型恢复重力异常方法的对比分析

Comparative Analysis of Methods for Recovering Gravity Anomalies by Combining Satellite Gravity and Topographic Potential Models

  • 摘要: 当前,全球陆地仍存在大量重力空白或稀疏区,超高阶重力场建模中常用的方法是采用地形数据对重力场进行加密与填充。考虑到卫星重力场和地形位模型各自信号频谱的互补性,深入分析对比联合卫星重力场和地形位模型恢复重力信号的3种方法(即位系数直接拼接法、位系数加权联合法与法方程联合法),利用GOSG02S等4个卫星重力场模型和dV_ELL_Earth2014_5480地形位模型在美国5个不同地形特征的区域开展了恢复重力异常的对比分析实验。结果表明,位系数直接拼接法在不同地形特征区域最优组合阶不同,高山区相比平原地区最优组合阶更大。位系数加权联合法中汉宁权整体表现优于经验法和方差权函数法,其最优过渡区随地形特征不同,联合模型在过渡区为230-300阶时与实测数据的差异最小。法方程联合法相比位系数直接拼接法的联合模型过渡区频谱更平滑,精度上总体更优。与实测数据相比,3种方法重力异常差异的标准差在平原区为8到9mGal,在高山区为15mGal;美国中北部区域差异的空间分布呈现明显的地质构造特征(中大陆的裂谷构造),可能是组合模型缺失了部分地下构造产生的信号。总体而言,法方程联合方法和位系数加权联合方法各有优劣,前者从法方程角度联合,难度大,但联合模型适用于全球任意区域,后者较为简单,但需要针对不同区域选择最优加权策略构建相应的最优模型,具有一定的经验性。

     

    Abstract: Objectives: Currently, extensive terrestrial areas remain either unmeasured or sparsely covered by gravity data, and a commonly used approach is to use topographic data to densify and fill in the gravity field. Considering the complementary spectral advantages of satellite gravity field models and topographic potential models, we compare and analyze three methods for recovering gravity anomalies by combining satellite gravity field model and topographic potential model.Methods: Four satellite gravity field models are combined with the dV_ELL_Earth2014_5480 topographic potential model to conduct comparative experiments in five regions of the United States with different terrain types. We analyze and compare three methods for recovering regional gravity anomalies: the potential coefficient direct splicing (DS) method, the potential coefficient weighted combination method, and the normal equation (NEQ) combination method, along with the parameter settings for each approach.Results: The optimal degree for the DS method varies in different regions, with higher optimal degrees in mountainous areas. The optimal transition zone for the weighted combination method also differs, with the models performing best when the transition zone is between degrees 230–300. Among the weight functions of the weighted combination method, the Hanning function demonstrates superior performance. Compared to the DS method, the NEQ method provides smoother spectral transitions and better accuracy. The standard deviations of gravity anomaly differences for the three methods are 8–9 mGal in plains and 15 mGal in mountainous areas. Discrepancies in north-central United States highlight the limitations of current models in detecting certain gravity signals.Conclusions: Overall, the NEQ method and the potential coefficient weighted combination method each have their strengths and weaknesses. The NEQ method is more complex as it requires combination of normal equations, but it is applicable to any region globally. The spectral domain weighted method is simpler but relies on selecting optimal weighting strategies for different regions, making it more empirical.

     

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