半航空瞬变电磁L1范数自适应正则化反演

doi:10.11720/wtyht.2021.1586

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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 words： L1-norm adaptive regularization inversion semi-airborne transient electromagnetic iterative re-weighted least squares OpenMP parallel

Received: 28 December 2020 Published: 15 December 2021

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	Ke HE
	Ming GUO
	Zhang-Rong HU
	Guo-Cai YI
	Shi-Xing WANG

Cite this article:

Ke HE,Ming GUO,Zhang-Rong HU, et al. Semi-airborne transient electromagnetic inversion based on L1-norm adaptive regularization[J]. Geophysical and Geochemical Exploration, 2021, 45(5): 1338-1346.

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https://www.wutanyuhuatan.com/EN/10.11720/wtyht.2021.1586 OR https://www.wutanyuhuatan.com/EN/Y2021/V45/I5/1338

[1]	王绪本, 张赛民, 高嵩, 等. 无人机半航空瞬变电磁探测技术及其应用[C]// 2019年中国地球科学联合学术年会, 2019.
[1]	Wang X B, Zhang S M, Gao S, et al. Semi-airborne transient electromagnetic detection technology and its application[C]// 2019 Chinese Joint Annual Conference on Earth Sciences, 2019.
[2]	张澎, 余小东, 许洋, 等. 半航空时间域电磁数据一维自适应正则化反演[J]. 物探化探计算技术, 2017, 39(1):1-8.
[2]	Zhang P, Yu X D, Xu Y, et al. An adaptive regularized inversion of 1D semi-airborne time-domain electromagnetic data[J]. Computing Techniques for Geophysical and Geochemical exploration, 2017, 39(1):1-8.
[3]	Smith R S, Peter A A, McGowan P D. A comparison of data from airborne,semi-airborne,and ground[J]. Geophysics, 2001, 66(5):1379-1385.
[4]	刘富波, 李巨涛, 刘丽华, 等. 无人机平台半航空瞬变电磁勘探系统及其应用[J]. 地球物理学进展, 2017, 32(5):2222-2229.
[4]	Liu F B, Li J T, Liu L H, et al. Development and application of a new semi-airborne transient electromagnetic system with UAV platform[J]. Progress in Geophysics, 2017, 32(5):2222-2229.
[5]	杨聪, 毛立峰, 毛鑫鑫, 等. 半航空瞬变电磁自适应正则化-阻尼最小二乘算法研究[J]. 地质与勘探, 2020, 56(1):137-146.
[5]	Yang C, Mao L F, Mao X X, et al. Study on semi-aerospace transient electromagnetic adaptive regularization-damped least squares algorithm[J]. Geology and Exploration, 2020, 56(1):137-146.
[6]	李锋平, 杨海燕, 邓居智, 等. TEM正演响应计算的几种频-时域转换方法对比[J]. 物探与化探, 2016, 40(4):743-749.
[6]	Li F P, Yang H Y, Deng J Z, et al. Comparison of several frequency-time transformation methods for TEM forward modeling[J]. Geophysical and Geochemical Exploration, 2016, 40(4):743-749.
[7]	王鹏飞, 王书明, 安永宁. 不规则回线瞬变电磁法一维烟圈反演研究[J]. 地球物理学进展, 2019, 34(3):1113-1120.
[7]	Wang P F, Wang S M, An Y N. One-dimensional smoke ring inversion of irregular loop source transient electromagnetic method[J]. Progress in Geophysics, 2019, 34(3):1113-1120.
[8]	李刚, 潘和平, 王智, 等. 回线源瞬变电磁法一维反演算法[J]. 煤田地质与勘探, 2017, 45(5):161-166.
[8]	Li G, Pan H P, Wang Z, et al. One-dimensional inversion algorithm of loop-line source transient electromagnetic method[J]. Coal Geology and Exploration, 2017, 45(5):161-166.
[9]	Huang H, Palacky G J. Damped leas-squares inversion of time-domain airborne em data based on singular value decomposition[J]. Geophysical Prospecting, 1991, 39(6):827-844.
[10]	杨云见, 何展翔, 赵晓明. 接地长导线源瞬变电磁法全区视电阻率定义探讨[J]. 物探装备, 2010, 20(2):117-120.
[10]	Yang Y J, He Z X, Zhao X M. Research on the defining all time apparent resistivity of the TEM method excitated with grounding long line current source[J]. Equipment for Geophysical Prospecting, 2010, 20(2):117-120.
[11]	唐荣江, 王绪本, 甘露. 一种利用特征值性质的MT 阻尼最小二乘反演[J]. 石油物探, 2017, 56(6):898-904.
[11]	Tang R J, Wang X B, Gan L. A damped least square inversion for MT utilizing eigenvalue property[J]. Geophysical Prospecting for Petroleum, 2017, 56(6):898-904.
[12]	Constable S C, Parker R L, Constable C G. Occam’s inversion:Apractical algorithm for generating smooth models from electromagnetic sounding data[J]. Geophysics, 1987, 52(3):289-300.
[13]	徐玉聪, 赵宁, 秦策, 等. 大定源瞬变电磁一维自适应正则化反演[J]. 地质与勘探, 2015, 51(2):360-365.
[13]	Xu Y C, Zhao N, Qin C, et al. One-dimensional adaptive regularization inversion of transient electromagnetic sounding with a large fixed source[J]. Geology and Exploration, 2015, 51(2):360-365.
[14]	翁爱华. Occam 反演及其在瞬变电磁测深中的应用[J]. 地质与勘探, 2007, 43(5):74-76.
[14]	Weng A H. Occam inversion and its application to transient electromagnetic method[J]. Geology and Exploration, 2007, 43(5):74-76.
[15]	毛立峰, 王绪本, 李文杰. 飞行高度同时反演的固定翼航空瞬变电磁一维反演[J]. 地球物理学报, 2011, 54(8):2136-2147.
[15]	Mao L F, Wang X B, Li W J. Research on 1D inversion method of fix-wing airborne transient electromagnetic record with flight altitude inversion simultaneously[J]. Chinese Journal of Geophysics, 2011, 54(8):2136-2147.
[16]	覃庆炎, 王绪本, 毛立峰. 导电导磁层状介质上的固定翼航空瞬变电磁响应[J]. 地球物理学进展, 2011, 26(5):1796-1801.
[16]	Qin Q Y, Wang X B, Mao L F. The fixed-wing airborne transient electromagnetic response of a magnetic conductive layered medium[J]. Progress in Geophysics, 2011, 26(5):1796-1801.
[17]	刘俊峰, 邓居智, 陈辉, 等. 一种用于Occam反演中搜索拉格朗日乘子的方法[J]. 工程地球物理学报, 2013, 10(3):344-350.
[17]	Liu J F, Deng J Z, Chen H, et al. A method used for searching Lagrange multiplier in Occam inversion[J]. Chinese Journal of Engineering Geophysics, 2013, 10(3):344-350.
[18]	陈小斌, 赵国泽, 汤吉, 等. 大地电磁自适应正则化反演算法[J]. 地球物理学报, 2005, 48(4):937-946.
[18]	Chen X B, Zhao G Z, Tang J, et al. An adaptive regularized inversion algorithm for magnetotelluric data[J]. Chinese Journal of Geophysics, 2005, 48(4):937-946.
[19]	Gholami A, Gheymasi H M. Regularization of geophysical ill-posed problems by iteratively re-weighted and refined least squares[J]. Computational Geosciences, 2016(20):19-33.
[20]	Vatankhah S, Renaut R A, Ardestani V E. 3-D Projected L1 inversion of gravity data using truncated unbiased predictive risk estimator for regularization parameter estimation[J]. Geophysical Journal International, 2017, 210(3):1872-1887.
[21]	苏扬, 殷长春, 刘云鹤, 等. 基于广义模型约束的时间域航空电磁反演研究[J]. 地球物理学报, 2019, 62(2):743-751.
[21]	Su Y, Yin C C, Liu Y H, et al. Inversions of time-domain airborne EM based on generalized model constraints[J]. Chinese Journal of Geophysics, 2019, 62(2):743-751.
[22]	阮帅, 汤吉, 陈小斌, 等. 三维大地电磁自适应L1范数正则化反演[J]. 地球物理学报, 2020, 63(10):3896-3911.
[22]	Ruan S, Tang J, Chen X B, et al. Three-dimensional magnetotelluric inversion base on adaptive L1-norm Regularization[J]. Chinese J. Geophys., 2020, 63(10):3896-3911.
[23]	Last B J, Kubik K. Compact gravity inversion[J]. Geophysics, 1983, 48(6):713-721.
[24]	Portniaguine O, Zhdanov M S. Focusing geophysical inversion images[J]. Geophysics, 1999, 64(3):874-887.
[25]	Zhdanov , Ellis M S, Mukherjee R, et al. Three-dimensional regularized focusing inversion of gravity gradient tensor component data[J]. Geophysics, 2004, 69(4):925-937.
[26]	Zhang L L, Yu P, Wang J L, et al. A study on 2D magnetotelluric sharp boundary inversion[J]. Chinese Journal of Geophysics, 2010, 53(3):631-637.doi: 10.3969/j.issn.0001-5733.2010.03.017.
[27]	陈闫, 李桐林, 范翠松, 等. 重力梯度全张量数据三维共轭梯度聚焦反演[J]. 地球物理学进展, 2014, 29(3):1133-1142.
[27]	Chen Y, Li T L, Fan C S, et al. The 3D focusing inversion of full tensor gravity gradient data based on conjugate gradient[J]. Progress in Geophysics, 2014, 29(3):1133-1142.
[28]	秦朋波, 黄大年. 重力和重力梯度数据联合聚焦反演方法[J]. 地球物理学报, 2016, 59(6):2203-2224.
[28]	Qin P B, Huang D N. Integrated gravity and gravity gradient data focusing inversion[J]. Chinese Journal of Geophysics, 2016, 59(6):2203-2224.
[29]	米萨克·纳比吉安. 应用地球物理学中的电磁方法[M].赵经祥,王彦军,译. 北京: 地质出版社, 1992:226-231.
[29]	Misac N Nabighian. Electromagnetic methods in applied geophysics [M]. Translated by Zhao Jingxiang,Wang Yanjun. Beijing: Geological Publishing House, 1992:226-231.
[30]	Knight J H, Raich A P. Transient electromagnetic calculations using the Gaver-Stehfest inverse Laplace transform method[J]. Geophysics, 1982, 47(1):47-50.
[31]	张伟, 王绪本, 覃庆炎. 汉克尔变换的数值计算与精度的对比[J]. 物探与化探, 2010, 34(6):753-755.
[31]	Zhang W, Wang X B, Qin Q Y. Research and application on numberical integration of Hankel Transforms by digital filtering[J]. Geophysical and Geochemical Exploration, 2010, 34(6):753-755.
[32]	朴化荣, 殷长春. 利用G-S逆拉氏变换法计算瞬变测深正演问题[J]. 物探化探计算技术, 1987, 9(4):295-302.
[32]	Piao H R, Yin C C. Calculation of transient E.M sounding using the Gaver-Stehfest inverse Laplace transform method[J]. Computing Techniques for Geophysical and Geochemical Exploration, 1987, 9(4):295-302.
[33]	罗延钟, 昌彦君. G-S变换的快速算法[J]. 地球物理学报, 2000, 43(5):684-690.
[33]	Luo Y Z, Chang Y J. A rapid algorithm for G-S transform[J]. Chinese Journal of Geophysics, 2000, 43(5):684-690.
[34]	邓琰, 汤吉, 阮帅. 三维大地电磁自适应正则化有限内存拟牛顿反演[J]. 地球物理学报, 2019, 62(9):3601-3614.
[34]	Deng Y, Tang J, Ruan S. Adaptive regularized three-dimensional magnetotelluric inversion based on the LBFGS quasi-Newton method[J]. Chinese Journal of Geophysics, 2019, 62(9):3601-3614.
[35]	吴小平, 徐果明. 大地电磁数据的Occam反演改进[J]. 地球物理学报, 1998, 41(4):547-554.
[35]	Wu X P, Xu G M. Improvement of Occam’s inversion for MT data[J]. Chinese Journal of Geophysics, 1998, 41(4):547-554.
[36]	徐凤洲, 张健飞. 基于OpenMP的近场动力学模拟并行实现[J]. 河南理工大学学报:自然科学版, 2020, 39(5):130-138.
[36]	Xu F Z, Zhang J F. Parallel implementation of peridynamic simulation based on OpenMP[J]. Journal of Henan Polytechnic University:Natural Science, 2020, 39(5):130-138.