基于拉格朗日中值定理的航空重力异常向下延拓方法研究  

Downward Continuation of Airborne Gravity Anomaly based on Lagrange Mean-Value Theorem

作　　者：胡起 徐新禹[1] 赵永奇[1] 丁子凡 HU Qi;XU Xinyu;ZHAO Yongqi;DING Zifan(School of Geodesy and Geomatics,Wuhan University,129 Luoyu Road,Wuhan 430079,China)

机构地区：[1]武汉大学测绘学院,武汉市珞喻路129号,430079

出　　处：《大地测量与地球动力学》2021年第1期95-100,共6页Journal of Geodesy and Geodynamics

基　　金：高分辨率对地观测系统重大专项;国家自然科学基金(41774020)。

摘　　要：基于拉格朗日中值定理,改进使用重力异常垂直梯度进行重力异常向下延拓的方法,通过重力异常向上延拓后差分以及线性外推,得到更加准确的应用于向下延拓的垂直梯度近似值。首先介绍利用拉格朗日中值定理计算重力异常垂直梯度并进行向下延拓的基本原理,给出进行航空重力向下延拓的基本步骤;然后基于EGM2008全球重力场模型说明重力异常垂直梯度在0~10000 m的空间范围内在垂向上与高度呈强线性关系,证明进行垂直线性外推的合理性;最后使用EGM2008模型的模拟重力异常在台湾地区进行实验,向下延拓精度达到2.34 mGal,验证方法的可行性与有效性,同时将台湾地区5156 m高度面上的实测航空重力数据向下延拓到地面的3360个地面重力观测点,精度达到10.13 mGal。This paper improves the methods of downward continuation of gravity anomaly based on the Lagrange mean-value theorem.We apply the difference between upward continuation and linear extrapolation to obtain the precise vertical gradients of gravity anomaly used in the downward continuation.We first introduce the principles and the procedures of the proposed methods.Based on EGM2008 global gravity model,we validate the strong linear distribution pattern of gravity vertical gradients between 0 m and 10000 m in Taiwan Region and justify the linear extrapolation of these gradients.We conduct the simulated downward continuation experiment in Taiwan Region and the accuracy reaches 2.34 mGal.Finally,we downward continue the airborne gravity anomaly at 5155 m in Taiwan to the 3360 land gravity points and the accuracy reaches 10.13 mGal.

关 键 词：航空重力 向下延拓 垂直梯度 中值定理 

分 类 号：P223[天文地球—大地测量学与测量工程]