引用本文: 邓凯亮, 黄谟涛, 吴太旗, 王伟平, 欧阳永忠, 陈欣, 熊雄, 刘敏, 王许. 利用高阶径向导数带限模型进行重力向下延拓计算[J]. 武汉大学学报 ( 信息科学版).
DENG Kailiang, HUANG Motao, WU Taiqi, WANG Weiping, OUYANG Yongzhong, CHEN Xin, XIONG Xiong, LIU Min, WANG Xu. Downward Continuation of Gravity Using the Band-Limited Models for High-Order Radial Derivatives of Gravity Anomaly[J]. Geomatics and Information Science of Wuhan University.
 Citation: DENG Kailiang, HUANG Motao, WU Taiqi, WANG Weiping, OUYANG Yongzhong, CHEN Xin, XIONG Xiong, LIU Min, WANG Xu. Downward Continuation of Gravity Using the Band-Limited Models for High-Order Radial Derivatives of Gravity Anomaly[J]. Geomatics and Information Science of Wuhan University.

## Downward Continuation of Gravity Using the Band-Limited Models for High-Order Radial Derivatives of Gravity Anomaly

• 摘要: 泰勒（Taylor）级数展开是实施位场向下延拓解算的主要方法之一。该方法的有效性主要取决于位场延拓参量各阶垂向（或径向）偏导数的求取精度及其可靠性。为了避免使用封闭解析核函数在球边界面出现奇异性带来的不确定性问题，本文依据各类重力观测经滤波处理后均表现为一类有限频谱带宽信号的特点，提出将地球外部重力异常Poisson积分式的核函数表示为球谐级数展开式，并将其截断为与重力观测值频谱范围相一致的带限求和式，进而通过直接求导方法，推导得到一组与带限核函数相对应的重力异常高阶径向导数带限计算公式，同时对该组公式进行了实用性改化，最后将其应用于重力异常向下延拓泰勒级数展开式计算。使用超高阶地球位模型EGM2008并设计两个阶段的数值计算检验方案，分别对重力异常高阶径向偏导数带限模型及其Taylor级数展开向下延拓模型的计算精度进行了检核评估，表明新模型具有良好的可靠性和有效性，在解算稳定性和计算精度两个方面都优于其他同类模型。

Abstract: Taylor series expansion is often used in the downward continuation of potential field, and its performance depends on the accuracy and reliability of the vertical or radial partial derivatives (VPDs or RPDs) of potential field parameters. In order to avoid the singularity on spherical boundary and the uncertainty to the computational results by using the closed analytic kernel function to solve the partial derivative, considering the fact that all kinds of gravity observations behave as a type of limited spectrum bandwidth signal after being filtered, this research proposes to express the kernel function of the Poisson integral for the external gravity anomaly by a spherical harmonic series expansion, which is then truncated into a band-limited summation that has the same spectrum range as the gravity observation. After that, we derive a set of band-limited formulas to calculate the high-order RPDs, which are modified and applied to the downward continuation of the gravity anomaly by Taylor series expansion. The formulas are validated using the ultra-high-degree geopotential model EGM2008 by a two-stage procedure. The numerical tests of the band-limited formulas and the Taylor series expansion downward continuation model show that the proposed band-limited formulas have good reliability and validity, and are superior to other models in terms of stability and accuracy.

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