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Three-dimensional conjugate gradient inversion of magnetotelluric sounding data

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Abstract

Based on the analysis of the conjugate gradient algorithm, we implement a threedimensional (3D) conjugate gradient inversion algorithm with magnetotelluric impedance data. During the inversion process, the 3D conjugate gradient inversion algorithm doesn’ t need to compute and store the Jacobian matrix but directly updates the model from the computation of the Jacobian matrix. Requiring only one forward and four pseudo-forward modeling applications per frequency to produce the model update at each iteration, this algorithm efficiently reduces the computation of the inversion. From a trial inversion with synthetic magnetotelluric data, the validity and stability of the 3D conjugate gradient inversion algorithm is verified.

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References

  • Avdeev, D. B., and Avdeeva, A. D., 2006, A rigorous three-dimensional magnetotelluric inversion: Progress in Electromagnetics Research, 62, 41–48.

    Article  Google Scholar 

  • DeGroot-Hedlin, C, and Constable, S., 1990, Occam’s inversion to generate smooth, two-dimensional models from magnetotelluric data: Geophysics, 55(12), 1613–1624.

    Article  Google Scholar 

  • Hu, Z. Z., and Hu, X. Y., 2005, Review of three dimensional magnetotelluric inversion methods: Progress in Geophysics, 20(1), 214–220.

    Google Scholar 

  • Hu, Z. Z., Hu, X. Y., and He, Z. X., 2006, Pseudo-threedimensional magnetotelluric inversion using nonlinear conjugate gradients: Chinese Journal of Geophysics, 49(4), 1226–1234.

    Google Scholar 

  • Jupp, D. L. B., and Vozoff, K., 1977, Two-dimensional magnetotelluric inversion: Geophys. J. Roy. Astr. Soc., 50, 333–352.

    Google Scholar 

  • Madden, T. R., and Mackie, R. L., 1989, Three-dimensional magnetotelluric modeling and inversion: Proc. IEEE, 77, 318–333.

    Article  Google Scholar 

  • Mackie, R. L. and Madden, T. R., 1993, Three-dimensional magnetotelluric inversion using conjugate gradients: Geophys. J. Int., 115, 215–229.

    Article  Google Scholar 

  • Newman, G. A., and Alumbaugh, D. L., 2000, Threedimensional magnetotelluric inversion using non-linear conjugate gradients: Geophys. J. Int., 140, 410–424.

    Article  Google Scholar 

  • Newman, G. A., and Boggs, P. T., 2004, Solution accelerators for large scale 3D electromagnetic inverse problems: 74th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 680–683.

  • Rodi, W., and Mackie, R. L., 2001, Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion: Geophysics, 66, 174–187.

    Article  Google Scholar 

  • Spichak V., and Popova., 2000, Artificial neural network inversion of magnetotelluric data in terms of threedimensional earth macroparameters: Geophys. J. Int., 142, 15–26.

    Article  Google Scholar 

  • Smith, J. T., and Booker, J. R., 1991, Rapid inversion of two- and three-dimensional magnetotelluric data: J. Geophys. Res., 96, 3905–3922.

    Article  Google Scholar 

  • Siripunvaraporn, W., Egbert, G., Lenbury, Y., and Uyeshima, M., 2005, Three-dimensional magnetotelluric inversion: data-space method: Physics of The Earth and Planetary Interiors, 150(1–3), 3–14.

    Article  Google Scholar 

  • Tan, H. D., Yu, Q. F., Booker, J., Wei, W., 2003a, Magnetotelluric three-dimensional modeling using the staggered-grid finite difference method: Chinese Journal of Geophysics, 46(5), 705–711.

    Google Scholar 

  • Tan, H. D., Yu, Q. F., Booker, J., Wei, W., 2003b, Three-dimensional rapid relaxation inversion for the magnetotelluric method: Chinese Journal of Geophysics, 46(6), 850–855.

    Google Scholar 

  • Tan, H. D., Wei, W., Deng, M., and Jin, S., 2004, General use formula in MT tensor impedance: Oil Geophysical Prospecting, 39(1), 114–116.

    Google Scholar 

  • Tikhonov, A. N., and Arsenin, V. Y., 1977, Solutions of illposed problems: V. H. Winston and Sons. Wu, X. P., and Xu, G. M., 2000, Study on 3-d resistivity inversion using conjugate gradient method: Chinese Journal of Geophysics, 43(3), 420–427.

    Google Scholar 

  • Zhdanov, M. S., Fang, S., and Hursan, G., 2000, Electromagnetic inversion using quasi-linear approximation: Geophysics, 65(5), 1501–1513.

    Article  Google Scholar 

  • Zhdanov, M., and Tolstaya, E., 2004, Minimum support nonlinear parametrization in the solution of a 3D magnetotelluric inverse problem: Inverse Problems, 20(3), 937–952.

    Article  Google Scholar 

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This work is jointly sponsored by National Natural Science Foundation of China (Grant Nos. 40774029, 40674037, and 40374024), the National Hi-tech Research and Development Program of China (863 Program) (No. 2007AA09Z310) and the Program for New Century Excellent Talents in University (NCET).

Lin Changhong graduated from the School of Geophysics and Information Technology of China University of Geosciences (Beijing) with a Bachelor degree in 2001. Currently he is studying for his PhD at China University of Geosciences (Beijing).

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Lin, C., Tan, H. & Tong, T. Three-dimensional conjugate gradient inversion of magnetotelluric sounding data. Appl. Geophys. 5, 314–321 (2008). https://doi.org/10.1007/s11770-008-0043-1

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  • DOI: https://doi.org/10.1007/s11770-008-0043-1

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