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Parameterized inversion of frequency sounding data in horizontally stratified transverse isotropic medium

Zhou Jian-Mei Wang Hong-Nian Yao Jing-Jin Yang Shou-Wen Ma Yin-Zhi

Parameterized inversion of frequency sounding data in horizontally stratified transverse isotropic medium

Zhou Jian-Mei, Wang Hong-Nian, Yao Jing-Jin, Yang Shou-Wen, Ma Yin-Zhi
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  • In this paper, we advance a fast iterative inversion algorithm of frequency electromagnetic sounding data to simultaneously reconstruct the horizontal and the vertical conductivities and interface each bed in the horizontally stratified transversely isotropic (TI) medium. First, applying the analytic expression of the electromagnetic dyadic Green's functions in the TI medium, we realize the forward modeling of the frequency sounding via the fast algorithm of Sommerfeld integral. Then using the perturbation principles and Fourier inversion transform, we establish an efficient computation of Frchet derivatives of the frequency sounding data with respective to all the model parameters. And we use the least square criterion, the normalization and singular value decomposition to iteratively recovery all model parameters. Finally, numerical results validate the inversion algorithms and their antinoise ability.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 40874058) and the Fundamental Scientific Research Foundation of Jilin University, China (Grant Nos. 200903318, 201001006).
    [1]

    Liu G X 2003 Principles and Methods of Electrical Prospecting (Beijing: Geological Publishing House) p173 (in Chinese) [刘国兴 2003 电法勘探原理与方法 (北京: 地质出版社) 第173页]

    [2]

    Li D Q, Wang G J, Di Q Y, Wang M Y, Wang R 2008 Chin. J. Geophys. 51 1234 (in Chinese) [李帝铨, 王光杰, 底青云, 王妙月, 王若 2008 地球物理学报 51 1234]

    [3]

    Routh P S, Oldenburg D W 1999 Geophysics 64 1689

    [4]

    Constable S C, Parker R L, Constable C G 1987 Geophysics 52 289

    [5]

    Wu X P, Xu G M 1998 Chin. J. Geophys. 41 547 (in Chinese) [吴小平, 徐果明 1998 地球物理学报 41 547]

    [6]

    Wu X P, Xu G M 2000 Chin. J. Geophys. 43 420 (in Chinese) [吴小平, 徐果明 2000 地球物理学报 43 420]

    [7]

    Lu X Y, Martyn U, John B 1999 Geophys. J. Int. 138 381

    [8]

    Moran J H, Gianzero S 1979 Geophysics 44 1266

    [9]

    Chen G B, Wang H N, Yao J J, Han Z Y, Yang S W 2009 Acta Phys. Sin. 58 1608 (in Chinese) [陈桂波, 汪宏年, 姚敬金, 韩子夜, 杨守文 2009 物理学报 58 1608]

    [10]

    Chen G B, Wang H N, Yao J J, Han Z Y 2009 Acta Phys. Sin. 58 3848 (in Chinese) [陈桂波, 汪宏年, 姚敬金, 韩子夜 2009 物理学报 58 3848]

    [11]

    Wannamaker P E 2005 Surv. Geophys. 26 733

    [12]

    Ramananjaona C, MacGregor L, Andréis D 2011 Geophys. Prospect. 59 341

    [13]

    Li X B, Oskooi B, Pedersen L B 2000 Geophysics 65 452

    [14]

    Yin C C 2003 Geophysics 68 138

    [15]

    Pek J, Santos F A M 2006 Phys. Earth Planet. Int. 158 139

    [16]

    Michalski K A, Mosig J R 1997 IEEE Trans. Antennas Propag. 45 508

    [17]

    Wang H N, So P, Yang S W, Hoefer W J R, Du H L 2008 IEEE Trans. Geosci. Remote Sens. 46 1134

    [18]

    Luke Y L 1962 Integrals of Bessel Functions (New York: McGraw-Hill Book Company) p88

    [19]

    Wang H N, Tao H G, Yao J J, Chen G B 2008 IEEE Trans. Geosci. Remote Sens. 46 1525

    [20]

    Wang H N 2011 IEEE Trans. Geosci. Remote Sens. 49 4483

  • [1]

    Liu G X 2003 Principles and Methods of Electrical Prospecting (Beijing: Geological Publishing House) p173 (in Chinese) [刘国兴 2003 电法勘探原理与方法 (北京: 地质出版社) 第173页]

    [2]

    Li D Q, Wang G J, Di Q Y, Wang M Y, Wang R 2008 Chin. J. Geophys. 51 1234 (in Chinese) [李帝铨, 王光杰, 底青云, 王妙月, 王若 2008 地球物理学报 51 1234]

    [3]

    Routh P S, Oldenburg D W 1999 Geophysics 64 1689

    [4]

    Constable S C, Parker R L, Constable C G 1987 Geophysics 52 289

    [5]

    Wu X P, Xu G M 1998 Chin. J. Geophys. 41 547 (in Chinese) [吴小平, 徐果明 1998 地球物理学报 41 547]

    [6]

    Wu X P, Xu G M 2000 Chin. J. Geophys. 43 420 (in Chinese) [吴小平, 徐果明 2000 地球物理学报 43 420]

    [7]

    Lu X Y, Martyn U, John B 1999 Geophys. J. Int. 138 381

    [8]

    Moran J H, Gianzero S 1979 Geophysics 44 1266

    [9]

    Chen G B, Wang H N, Yao J J, Han Z Y, Yang S W 2009 Acta Phys. Sin. 58 1608 (in Chinese) [陈桂波, 汪宏年, 姚敬金, 韩子夜, 杨守文 2009 物理学报 58 1608]

    [10]

    Chen G B, Wang H N, Yao J J, Han Z Y 2009 Acta Phys. Sin. 58 3848 (in Chinese) [陈桂波, 汪宏年, 姚敬金, 韩子夜 2009 物理学报 58 3848]

    [11]

    Wannamaker P E 2005 Surv. Geophys. 26 733

    [12]

    Ramananjaona C, MacGregor L, Andréis D 2011 Geophys. Prospect. 59 341

    [13]

    Li X B, Oskooi B, Pedersen L B 2000 Geophysics 65 452

    [14]

    Yin C C 2003 Geophysics 68 138

    [15]

    Pek J, Santos F A M 2006 Phys. Earth Planet. Int. 158 139

    [16]

    Michalski K A, Mosig J R 1997 IEEE Trans. Antennas Propag. 45 508

    [17]

    Wang H N, So P, Yang S W, Hoefer W J R, Du H L 2008 IEEE Trans. Geosci. Remote Sens. 46 1134

    [18]

    Luke Y L 1962 Integrals of Bessel Functions (New York: McGraw-Hill Book Company) p88

    [19]

    Wang H N, Tao H G, Yao J J, Chen G B 2008 IEEE Trans. Geosci. Remote Sens. 46 1525

    [20]

    Wang H N 2011 IEEE Trans. Geosci. Remote Sens. 49 4483

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  • Received Date:  27 April 2011
  • Accepted Date:  28 April 2012
  • Published Online:  20 April 2012

Parameterized inversion of frequency sounding data in horizontally stratified transverse isotropic medium

  • 1. College of Physics, Jilin University, Changchun 130012, China;
  • 2. China Railway Resources Mineral Exploration Company, Beijing 100039, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 40874058) and the Fundamental Scientific Research Foundation of Jilin University, China (Grant Nos. 200903318, 201001006).

Abstract: In this paper, we advance a fast iterative inversion algorithm of frequency electromagnetic sounding data to simultaneously reconstruct the horizontal and the vertical conductivities and interface each bed in the horizontally stratified transversely isotropic (TI) medium. First, applying the analytic expression of the electromagnetic dyadic Green's functions in the TI medium, we realize the forward modeling of the frequency sounding via the fast algorithm of Sommerfeld integral. Then using the perturbation principles and Fourier inversion transform, we establish an efficient computation of Frchet derivatives of the frequency sounding data with respective to all the model parameters. And we use the least square criterion, the normalization and singular value decomposition to iteratively recovery all model parameters. Finally, numerical results validate the inversion algorithms and their antinoise ability.

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