利用Abel-Poisson径向基函数模型化局部重力场

doi:10.11947/j.AGCS.2016.20150519

测绘学报 ›› 2016, Vol. 45 ›› Issue (9): 1019-1027.doi: 10.11947/j.AGCS.2016.20150519

利用Abel-Poisson径向基函数模型化局部重力场

马志伟^1,2, 陆洋^1,2, 涂弋^1,2, 朱传东^1,2, 郗慧^1,2

1. 中国科学院测量与地球物理研究所大地测量与地球动力学国家重点实验室, 湖北武汉 430077;
2. 中国科学院大学, 北京 100049

收稿日期:2015-10-14 修回日期:2016-06-27 出版日期:2016-09-20 发布日期:2016-09-29
作者简介:马志伟(1986-),男,博士生,主要从事多源重力数据融合研究工作.E-mail:jzmazhiwei@163.com
基金资助:
国家973计划（2013CB733301）；国家自然科学基金（41274025；41174064）

Regional Gravity Field Modeling with Abel-Poisson Radial Basis Functions

MA Zhiwei^1,2, LU Yang^1,2, TU Yi^1,2, ZHU Chuandong^1,2, XI Hui^1,2

1. State Key laboratory of Geodesy and Earth's Dynamics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China;
2. University of Chinese Academy of Sciences, Beijing 100049, China

Received:2015-10-14 Revised:2016-06-27 Online:2016-09-20 Published:2016-09-29
Supported by:
The National Basic Research Program of China (973)(No.2013CB733301);The National Natural Science Foundation of China (Nos.41274025;41174064)

摘要/Abstract

摘要： 多种类型高分辨率重力场数据的不断增加，使得在局部范围内精化重力场模型成为了可能。本文采用Abel-Poisson核将重力场量表示成有限个径向基函数线性求和的形式，对局部区域的多种重力场数据进行联合建模。为了提高运算速度，运用了基于自适应精化格网算法的最小均方根误差准则（RMS）来求解径向基函数平均带宽。以南海核心地区为例，联合两种不同类型、不同分辨率的重力场资料（大地水准面起伏6'×6'、重力异常2'×2'），构建了局部区域高分辨率的重力场模型。所建模型表示的重力场参量达到了2'×2'的分辨率，对原始的重力异常数据（2'×2'）拟合的符合程度达到±0.8×10^－5m/s²。结果表明，利用径向基函数方法进行局部重力场建模，避免了球谐函数建模收敛慢的问题，有效提高了模型表示重力场的分辨率。

关键词: 局部重力场建模, 重力异常, 径向基函数, 数据自适应, 最小均方根误差准则

Abstract: With the increasing number of various types of high-resolution gravity observations, earth gravity models can be regionally refined. We use Abel-Poisson kernel to represent the gravity as the linear summation of finite radial basis functions and combine the multiple gravity data to build a regional gravity model with high resolution. The minimum root mean square criterion based on the data adaptive algorithm is proposed to calculate the base function, which promote the speed of computation significantly. Taking the central South China Sea as an example, two different types of gravity data, namely geoid undulations with resolution of 6'×6' and gravity anomaly with resolution of 2'×2', are used to construct the high-resolution regional gravity model. The model has a resolution of 2'×2', and has a great agreement with original gravity anomaly, reaching to ±0.8×10^-5m/s².Our results show that using radial basis functions to construct the regional gravity field can avoid the problem of slow convergence of spherical harmonic functions, and can improve the resolution remarkably.

Key words: local gravity field modeling, gravity anomaly, radial basis function, data adaptive, root mean square error criterion

中图分类号:

P223

马志伟, 陆洋, 涂弋, 朱传东, 郗慧. 利用Abel-Poisson径向基函数模型化局部重力场[J]. 测绘学报, 2016, 45(9): 1019-1027.

MA Zhiwei, LU Yang, TU Yi, ZHU Chuandong, XI Hui. Regional Gravity Field Modeling with Abel-Poisson Radial Basis Functions[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(9): 1019-1027.

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利用Abel-Poisson径向基函数模型化局部重力场

Regional Gravity Field Modeling with Abel-Poisson Radial Basis Functions

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