重力场向下延拓的三阶Adams-Bashforth公式法

doi:10.13278/j.cnki.jjuese.201705301

吉林大学学报(地球科学版) ›› 2017, Vol. 47 ›› Issue (5): 1533-1542.doi: 10.13278/j.cnki.jjuese.201705301

重力场向下延拓的三阶Adams-Bashforth公式法

张冲¹, 黄大年¹, 秦朋波², 吴国超³, 方刚⁴

1. 吉林大学地球探测科学与技术学院, 长春 130026;
2. 国防科学技术大学机电工程与自动化学院, 长沙 410000;
3. 浙江大学地球科学学院, 杭州 310000;
4. 武警黄金部队第二支队, 呼和浩特 010000

收稿日期:2016-12-22 出版日期:2017-09-26 发布日期:2017-09-26
作者简介:张冲(1989),男,博士研究生,主要从事重磁场数据处理与解释研究,E-mail:zhangchong12@mails.jlu.edu.cn
基金资助:
国家深部探测技术与实验研究专项项目SinoPrbe-09-01（201311192）；国家高技术研究发展计划（"863"计划）项目（2014AA06A613）

Third-Order Adams-Bashforth Formula Method for Downward Continuation of Gravity Field

Zhang Chong¹, Huang Danian¹, Qin Pengbo², Wu Guochao³, Fang Gang⁴

1. College of GeoExploration Science and Technology, Jilin University, Changchun 130026, China;
2. College of Mechatronic Engineering and Automation, National University of Defense Technology, Changsha 410000, China;
3. School of Earth Sciences, Zhejiang University, Hangzhou 310000, China;
4. Second Gold detachment, The Chinese Armed Police Force, Hohhot 010000, China

Received:2016-12-22 Online:2017-09-26 Published:2017-09-26
Supported by:
Supported by Deep Exploration in China of SinoProbe-09-01 (201311192) and National High-Tech R&D Program ("863" Program)of China(2014AA06A613)

摘要/Abstract

摘要： 重力场向上延拓是稳定且收敛的过程，而向下延拓是不稳定且发散的过程。为此，本文提出一种重力场向下延拓新方法。首先，对重力场及其垂向一阶导数向上延拓，得到不同高度的重力场垂向导数；然后，基于求解微分方程的三阶Adams-Bashforth多步法，推导出稳定的向下延拓公式；最后，为验证本文方法，将其分别应用于模型数据和实际数据。理论模型试验及误差曲线表明，相对于经典下延方法——傅里叶变换下延法和积分迭代下延法，新方法三阶Adams-Bashforth公式法下延过程稳定，边界效应不明显，下延深度可达5倍点距，下延结果与真实值的相对误差更小，结果更准确。将本文方法应用于加拿大某区实测航空重力数据，得到有效且准确的下延结果，能够识别和圈定一些细小异常特征。

关键词: 重力场下延, 垂向导数, Adams-Bashforth公式

Abstract: Upward continuation of gravity field is considered to be a stable and convergence process, but downward continuation is not. This paper presents a new method of downward continuation of gravity field. Firstly, the gravity field and its vertical first-order derivatives are continued upward to different height. Secondly, the authors derive with the stable downward continuation based on multistep method of Adams-Bashforth formula of third-order of the differential equation. Finally, the method is applied to the synthetic model data and the real data. Compared with the classical downward continuation methods which are the Fourier transform method and integral-iteration method, the synthetic results show that the new method, which is Adams-Bashforth formula of third-order, is more stable, less edge effect, the depth of downward continuation is 5 intervals, the relative error of the downward result and the real value is smaller, and the result is more accurate. The method is applied to the measured airborne gravity data in Canada, and the results obtained are valid and accurate. Small sources are identified and delineated.

Key words: gravity downward continuation, vertical derivative, Adams-Bashforth formula

中图分类号:

P631.1

张冲, 黄大年, 秦朋波, 吴国超, 方刚. 重力场向下延拓的三阶Adams-Bashforth公式法[J]. 吉林大学学报(地球科学版), 2017, 47(5): 1533-1542.

Zhang Chong, Huang Danian, Qin Pengbo, Wu Guochao, Fang Gang. Third-Order Adams-Bashforth Formula Method for Downward Continuation of Gravity Field[J]. Journal of Jilin University(Earth Science Edition), 2017, 47(5): 1533-1542.

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重力场向下延拓的三阶Adams-Bashforth公式法

Third-Order Adams-Bashforth Formula Method for Downward Continuation of Gravity Field

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