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Volume 56 Supplement 2

Special Issue: Special section for IUGG workshop: Lithospheric Structure of a Supercontinent:Gondwana

Three-dimensional inversion of static-shifted magnetotelluric data

Earth, Planets and Space volume 56, pages 239–248 (2004)Cite this article

Abstract

A practical method for inverting static-shifted magnetotelluric (MT) data to produce a 3-D resistivity model is presented. Static-shift parameters are incorporated into an iterative, linearized inversion method, with a constraint added on the assumption that static shifts are due to a zero-mean, Gaussian process. A staggered finite-difference scheme is used to evaluate both the forward problem and the ‘pseudo-forward’ problem needed to construct the full sensitivity matrix. The linear system of equations is efficiently solved by alternating the incomplete Cholesky biconjugate gradient (ICBCG) solver with the static divergence correction procedure. Even with this efficiency in the forward modeling, generating the full sensitivity matrix at every iteration is still impractical on modern PCs. To reduce the computer time to a reasonable level, an efficient procedure for updating the sensitivities is implemented: (1) in the first few iterations, the sensitivities for the starting homogeneous half-space are used, (2) the full sensitivity matrix is computed only once (e.g. at the third iteration), and (3) for the subsequent iterations it is updated using Broyden’s algorithm. The synthetic and real data examples show that the method is robust in the presence of static shifts and can be used for 3-D problems of realistic size.

References

  • deGroot-Hedlin, C., Removal of static shift in two dimensions by regularized inversion, Geophysics, 56, 2102–2106, 1991.

    Article  Google Scholar 

  • Farquharson, C. G. and D. W. Oldenburg, Approximate sensitivities for the electromagnetic inverse problem, Geophys. J. Int., 126, 235–252, 1996.

    Article  Google Scholar 

  • Jones, A. G., Static shift of magnetotelluric data and its removal in a sedimentary basin environment, Geophysics, 53, 967–978, 1988.

    Article  Google Scholar 

  • Loke, M. H. and R. D. Barker, Practical techniques for 3D resistivity surveys and data inversion, Geophys. Prosp., 44, 499–523, 1996.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Mackie, R. L., T. R. Madden, and P. E. Wannamaker, Three-dimensional magnetotelluric modelling using difference equations: Theory and comparisons to integral equation solutions, Geophysics, 58, 215–226, 1993.

    Article  Google Scholar 

  • Mackie, R. L., J. T. Smith, and T. R. Madden, Three-dimensional electromagnetic modeling using finite difference equations: The magnetotelluric example, Radio Sci., 29, 923–935, 1994.

    Article  Google Scholar 

  • Marquardt, D. W., An algorithm for least-squares estimation of nonlinear parameters, J. Soc. Indust. Appl. Math., 2, 431–441, 1963.

    Article  Google Scholar 

  • McGillivray, P. R., D. W. Oldenburg, R. G. Ellis, and T. M. Habashy, Calculation of sensitivities for the frequency-domain electromagnetic problem, Geophys. J. Int., 116, 1–4, 1994.

    Article  Google Scholar 

  • Newman, G. A. and D. L. Alumbaugh, Frequency-domain modelling of airborne electromagnetic responses using staggered finite differences, Geophys. Prospec., 43, 1021–1042, 1995.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ogawa, Y. and T. Uchida, A two-dimensional magnetotelluric inversion assuming Gaussian static shift, Geophys. J. Int., 126, 69–76, 1996.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Sasaki, Y., 3-D resistivity inversion using the finite-element method, Geophysics, 59, 1839–1848, 1994.

    Article  Google Scholar 

  • Siripunvaraporn, W. and G. Egbert, An efficient data-subspace inversion method for 2-D magnetotelluric data, Geophysics, 65, 791–803, 2000.

    Article  Google Scholar 

  • Smith, J. T., Conservative modeling of 3-D electromagnetic fields, Part I: properties and error analysis, Geophysics, 61, 1308–1318, 1996a.

    Article  Google Scholar 

  • Smith, J. T., Conservative modeling of 3-D electromagnetic fields, Part II: Biconjugate gradient solution and an accelerator, Geophysics, 61, 1319–1324, 1996b.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Tarantola, A., Inverse Problem Theory: Method for Data Fitting and Model Parameter Estimation, Elsevier, New York, 1987.

    Google Scholar 

  • Torres-Verdin, C., V. L. Druskin, S. Fang, L. A. Knizhnerman, and A. Malinverno, A dual-grid nonlinear inversion technique with applications to the interpretation of dc resistivity data, Geophysics, 65, 1733–1745, 2000.

    Article  Google Scholar 

  • Uchida, T. and Y. Sasaki, Stable 3-D inversion of MT data and its application for geothermal exploration, in Three-Dimensional Electromagnetics III, edited by J. Macnae and G. Liu, ASEG, 12, 1–10, 2003.

    Google Scholar 

  • Uchida, T., Y. Ogawa, S. Takakura, and Y. Mitsuhata, Three-dimensionality of magnetotelluric data in the Kakkonda geothermal field, northern Japan, edited by P. E. Wannamaker and M. S. Zhdanov, Proc. Second Internat. Symposium on Three-dimensional Electromagnetics (3DEM-2), Salt Lake City, 285–288, 1999.

    Google Scholar 

  • Uchida, T., T. J. Lee, Y. Sasaki, M. Honda, Ashari, and A. Andan, 3-D interpretation of magnetotelluric data at the Bajawa geothermal field, Indonesia, Geothermal Resources Council Transaction, 25, 433–438, 2001.

    Google Scholar 

  • Wannamaker, P. E., G. W. Hohmann, and S. H. Ward, Magnetotelluric responses of three-dimensional bodies in layered earths, Geophysics, 49, 1517–1533, 1984.

    Article  Google Scholar 

  • Weidelt, P., Inversion of two-dimensional conductivity structure, Phys. Earth Planet Inter., 10, 282–291, 1975.

    Article  Google Scholar 

  • Yamane, K., H. J. Kim, and Y. Ashida, Three-dimensional magnetotelluric inversion using a generalized RRI method and its applications, Butsuri-Tansa (Geophysical Exploration), 53, 234–244, 2000.

    Google Scholar 

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

    Article  Google Scholar 

Download references

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Affiliations

  1. Department of Earth Resources Engineering, Kyushu University, Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan

    Yutaka Sasaki

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  1. Yutaka Sasaki
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Correspondence to Yutaka Sasaki.

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Sasaki, Y. Three-dimensional inversion of static-shifted magnetotelluric data. Earth Planet Sp 56, 239–248 (2004). https://doi.org/10.1186/BF03353406

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  • DOI: https://doi.org/10.1186/BF03353406

Key words

  • Magnetotellurics
  • 3-D inversion
  • static shift
  • Gauss-Newton method