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物探与化探  2021, Vol. 45 Issue (5): 1338-1346    DOI: 10.11720/wtyht.2021.1586
  方法研究·信息处理·仪器研制 本期目录 | 过刊浏览 | 高级检索 |
半航空瞬变电磁L1范数自适应正则化反演
何可1,2(), 郭明2, 胡章荣1, 易国财2, 王仕兴2
1.西华师范大学 教育信息技术中心,四川 南充 637002
2.成都理工大学 地球物理学院,四川 成都 610059
Semi-airborne transient electromagnetic inversion based on L1-norm adaptive regularization
HE Ke1,2(), GUO Ming2, HU Zhang-Rong1, YI Guo-Cai2, WANG Shi-Xing2
1. Education Information Technology Center, West China Normal University, Nanchong 637002, China
2. College of Geophysics, Chengdu University of Technology, Chengdu 610059,China
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摘要 

长导线源半航空瞬变电磁正则化反演正则项通常采用L2范数,其拟合结果较光滑,不能有效刻画层界面信息。针对层状介质陡变模型实现正则项为L1范数的反演算法,采用迭代重加权最小二乘法将原问题转化为L2正则化子问题求解,解决L1范数存在不可导问题;采用OpenMP技术对雅可比矩阵并行计算,提高了反演速度;对自适应正则化因子分段迭代法的调整策略进行分析并改进,改进后的自适应正则化因子调整策略更适合半航空瞬变电磁L1正则反演算法。最后对电阻率进行反演并与Occam反演结果作比较,结果表明L1正则反演充分迭代后能够突出符合真实模型的电性界面,反演电阻率与模型真实值更接近。

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何可
郭明
胡章荣
易国财
王仕兴
关键词 L1范数自适应正则化反演半航空瞬变电磁迭代重加权最小二乘OpenMP并行    
Abstract

The regularization term for semi-airborne transient electromagnetic regularization of long-line source usually adopts L2 norm, and the fitting result is relatively smooth, which cannot effectively describe the layer interface information. Aiming at the stratified medium steep change model to realize the inversion algorithm whose regular term is the L1 norm, the authors transform the original problem into the L2 regularization sub-problem by the iterative re-weighted least squares method to solve the problem of non-differentiation in the L1 norm; OpenMP technology is used to solve the problem. The parallel calculation of the Jacobian matrix improves the inversion speed; the adjustment strategy of the adaptive regularization factor segmentation iteration method is analyzed and improved. The improved adaptive regularization factor adjustment strategy is more suitable for semi-airborne transient electromagnetic inversion algorithm of L1-norm regularization. Finally, the resistivity is inverted and compared with the Occam inversion results. The results show that the inversion of L1-norm regularization can highlight the electrical interface conforming to the real model after sufficient iterations, and the inversion resistivity is closer to the true value of the model.

Key wordsL1-norm    adaptive regularization inversion    semi-airborne transient electromagnetic    iterative re-weighted least squares    OpenMP parallel
收稿日期: 2020-12-28      出版日期: 2021-12-15
:  P631  
基金资助:国家自然科学基金项目“稳定条件突破CFL限制的显式有限差分法模拟地形模型的三维半航空瞬变电磁响应”(41974158)
作者简介: 何可(1988-),男,在读博士,从事半航空瞬变电磁法正反演研究工作。Email: hk812760098@163.com
引用本文:   
何可, 郭明, 胡章荣, 易国财, 王仕兴. 半航空瞬变电磁L1范数自适应正则化反演[J]. 物探与化探, 2021, 45(5): 1338-1346.
HE Ke, GUO Ming, HU Zhang-Rong, YI Guo-Cai, WANG Shi-Xing. Semi-airborne transient electromagnetic inversion based on L1-norm adaptive regularization. Geophysical and Geochemical Exploration, 2021, 45(5): 1338-1346.
链接本文:  
https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2021.1586      或      https://www.wutanyuhuatan.com/CN/Y2021/V45/I5/1338
Fig.1  数据拟合项与模型约束项等值线
Fig.2  OpenMP运算并行策略
迭代次数
5 15 30 60
串行计算时间/s 69 203 407 807
并行计算时间/s 15 44 91 194
Table 1  串并行计算时间对比
Fig.3  H形模型反演结果
Fig.4  K形模型反演结果
Fig.5  HK形模型反演结果
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