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
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.
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.
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.
doi: 10.1190/1.1487084
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.
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.
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.
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.
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.
doi: 10.1111/gpr.1991.39.issue-6
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.
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.
doi: 10.1190/1.1442303
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.
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.
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.
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.
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.
doi: 10.1093/gji/ggx274
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.
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.
doi: 10.1190/1.1441501
[24]
Portniaguine O, Zhdanov M S. Focusing geophysical inversion images[J]. Geophysics, 1999, 64(3):874-887.
doi: 10.1190/1.1444596
[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.
doi: 10.1190/1.1778236
[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.
doi: 10.3969/j.issn.0001-5733.2010.03.017
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.
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.
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.
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.
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.
