复杂形体重力场、梯度及磁场计算方法

骆遥; 姚长利

复杂形体重力场、梯度及磁场计算方法

骆遥^{1, 2, 3,},
姚长利^{1, 2}

1.
地质过程与矿产资源国家重点实验室和地下信息探测技术与仪器教育部重点实验室, 北京 100083
2.
中国地质大学地球物理与信息技术学院, 北京 100083
3.
中国科学院地质与地球物理研究所, 北京 100029

基金项目:

国家自然科学基金项目 40374039

新世纪优秀人才支持计划项目 NCET-04-0726

北京市重点学科“地球探测与信息技术” XK104910598

详细信息

作者简介:
骆遥(1982-), 男, 现为中国科学院地质与地球物理研究所硕士研究生.E-mail: luoyao@mail.iggcas.ac.cn

中图分类号: P631
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- 被引次数: 0
出版历程
- 收稿日期: 2007-04-12
- 刊出日期: 2007-07-25

Forward Method for Gravity, Gravity Gradient and Magnetic Anomalies of Complex Body

LUO Yao^{1, 2, 3
,},
YAO Zhang-li^{1, 2}

1.
State Key Laboratory of Geological Processes and Mineral Resources; Geo-detection Laboratory of the Ministry of Education, Beijing 100083, China
2.
School of Geophysics and Information Technology, China University of Geosciences, Beijing 100083, China
3.
Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China

摘要

摘要: 在改进均匀多面体重力场正演公式基础上, 利用二阶张量的坐标变换实现对多面体重力场梯度的求解, 推导了新的多面体重力梯度和磁场的正演公式, 给出了新的统一的均匀多面体重力场、梯度及磁场正演表达式形式, 并用理论模型进行了检验.同时, 应用新的多面体重力场梯度正演公式推导出新的长方体重力场垂直梯度理论表达式.本文给出的均匀多面体重力场、梯度及磁场正演表达式形式统一, 重磁场联合正演中可相互利用其计算过程中的结果, 避免重复计算以提高正演计算效率.
- 多面体 /
- 重磁场 /
- 梯度张量 /
- 正演 /
- 坐标变换
Abstract: Based on the improved analytical expression for computing the gravity anomalies due to a homogeneous polyhedral body composed of polygonal facets, and by applying the forward theory with the coordinate transformation of vector and tensor, we deduced the analytical expressions for both gravity gradient tensor and magnetic anomalies due to a polygon, and obtained new analytical expressions for computing vertical gradient of gravity anomalies and vertical component of magnetic anomalies due to a polyhedral body. And we also explicitly developed the complete and unified expressions for calculating gravity anomalies, gravity gradient and magnetic anomalies due to the homogeneous polyhedra. Furthermore, we deduced new analytical expressions for computing the vertical gradient of gravity anomalies due to a finite rectangular prism by applying the new obtained expressions for gravity gradient tensor due to a polyhedral target body. Comparison with forward calculation of models testified the correctness of these new expressions. It will reduce forward time of gravimagnetic anomaly and improve computational efficiency by applying our unified expressions for joint forward of gravimagnetic anomalies due to homogeneous polyhedral bodies.
- polyhedral body /
- gravitational field and magnetic field /
- gravity gradient tensor /
- forward calculation /
- coordinate transformation

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图 1 任意水平多边形示意图

Fig. 1. The sketch map of an arbitrary polygon surface

下载: 全尺寸图片幻灯片

图 2 新老坐标系关系示意图

Fig. 2. The sketch map of coordinate systems

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图 3 长方体模型示意图

Fig. 3. The sketch map of cuboid and its geometry

下载: 全尺寸图片幻灯片

图 4 多面体重力场U_Z (a) 及其梯度U_ZZ (b) 和ΔT场(c) 等值线图

图中实线为正值, 虚线为负值; 模型计算参数I=60°, A=30°, 网格间距5 m×5 m, 等值线单位分别10^-6m·s^-2, 10^-6s^-2, nT.

Fig. 4. The gravity U_Z (a), gravity gradient U_ZZ (b) and ΔT (c) contour map

下载: 全尺寸图片幻灯片

表 1 组合四面体模型顶点坐标

Table 1. Vertices of homogeneous polyhedral bodies

参考文献(13)

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