位场垂向高阶导数的Tikhonov正则化迭代法

doi:10.13278/j.cnki.jjuese.20170246

吉林大学学报(地球科学版) ›› 2018, Vol. 48 ›› Issue (2): 394-401.doi: 10.13278/j.cnki.jjuese.20170246

• 地球物理数据处理与解释技术 • 上一篇下一篇

位场垂向高阶导数的Tikhonov正则化迭代法

杜威, 许家姝, 吴燕冈, 郝梦成

吉林大学地球探测科学与技术学院, 长春 130026

收稿日期:2017-09-21 出版日期:2018-03-26 发布日期:2018-03-26
通讯作者: 许家姝(1982-),女,工程师,主要从事重磁数据处理解释方面的研究,E-mail:xujiashuxjs@jlu.edu.cn E-mail:xujiashuxjs@jlu.edu.cn
作者简介:杜威(1990-),女,博士研究生,主要从事重磁数据处理解释方面的研究,E-mail:duwei0505@yeah.net
基金资助:
国家自然科学基金项目（40930314）

Tikhonov Regularization Iteration Method for High-Order Vertical Derivatives of Potential Field

Du Wei, Xu Jiashu, Wu Yangang, Hao Mengcheng

College of GeoExploration Science and Technology, Jilin University, Changchun 130026, China

Received:2017-09-21 Online:2018-03-26 Published:2018-03-26
Supported by:
Supported by National Natural Science Foundation of China (40930314)

摘要/Abstract

摘要： 在位场数据处理中，垂向导数具有重要的物理意义。其在一定程度上可以划分不同深度和大小异常源产生的叠加异常，且导数的阶次越高，这种分辨能力就越强，但通常认为高阶导数的换算是不稳定的。本文在Tikhonov正则化求位场垂向高阶导数的基础上，结合迭代法进行逐次逼近，提出了位场高阶导数的Tikhonov正则化迭代法，并且得到Tikhonov正则化迭代法的递推公式。通过对该方法的滤波特性分析可以看出，该方法计算的位场垂向高阶导数具有一定的稳定性及保幅性。模型试验和实际数据的处理表明，该方法计算结果较常规FFT求导法有更高的稳定性和实用价值。

关键词: Tikhonov正则化, 迭代法, 位场, 垂向导数

Abstract: In potential field data processing, high-order vertical derivative has important physical significance. It can divide superimposed anomalies generated by sources with different depth and size. With the order increase of the derivative, the resolution becomes higher, however the calculation of the higher order derivative is unstable. In this study we proposed the Tikhonov regularization iteration method for high-order vertical derivatives based on the combination of Tikhonov regularization method and iteration method,and obtained the recursive formula of Tikhonov regularization iterative method. Through analyzing the filter characteristics of the method, we can see that the method has certain stability and amplitude preservation in the calculation of high-order vertical derivative. The results of the model test and the real data show that the stability and practical value of the method are higher than that of the routine FFT method.

Key words: Tikhonov regularization, iteration method, potential field, vertical derivative

中图分类号:

P631.1

杜威, 许家姝, 吴燕冈, 郝梦成. 位场垂向高阶导数的Tikhonov正则化迭代法[J]. 吉林大学学报(地球科学版), 2018, 48(2): 394-401.

Du Wei, Xu Jiashu, Wu Yangang, Hao Mengcheng. Tikhonov Regularization Iteration Method for High-Order Vertical Derivatives of Potential Field[J]. Journal of Jilin University(Earth Science Edition), 2018, 48(2): 394-401.

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位场垂向高阶导数的Tikhonov正则化迭代法

Tikhonov Regularization Iteration Method for High-Order Vertical Derivatives of Potential Field

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