Geophysics and Geophysical Exploration (지구물리와물리탐사)

Korean Society of Earth and Exploration Geophysicists (한국지구물리·물리탐사학회)
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Review on the Three-Dimensional Inversion of Magnetotelluric Date

MT 자료의 3차원 역산 개관

  • Kim Hee Joon (Department of Environmental Exploration Engineering, Pukyong National University) ;
  • Nam Myung Jin (School of Civil, Urban & Geosystem Engineering Seoul National University) ;
  • Han Nuree (School of Civil, Urban & Geosystem Engineering Seoul National University) ;
  • Choi Jihyang (School of Civil, Urban & Geosystem Engineering Seoul National University) ;
  • Lee Tae Jong (Korea Institute of Geoscience and Mineral Resources) ;
  • Song Yoonho (Korea Institute of Geoscience and Mineral Resources) ;
  • Suh Jung Hee (School of Civil, Urban & Geosystem Engineering Seoul National University)
  • 김희준 (부경대학교 환경탐사공학과) ;
  • 남명진 (서울대학교 지구환경시스템공학부) ;
  • 한우리 (서울대학교 지구환경시스템공학부) ;
  • 최지향 (서울대학교 지구환경시스템공학부) ;
  • 이태종 (한국지질자원연구원) ;
  • 송윤호 (한국지질자원연구원) ;
  • 서정희 (서울대학교 지구환경시스템공학부)
  • Published : 2004.08.01
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Abstract

This article reviews recent developments in three-dimensional (3-D) magntotelluric (MT) imaging. The inversion of MT data is fundamentally ill-posed, and therefore the resultant solution is non-unique. A regularizing scheme must be involved to reduce the non-uniqueness while retaining certain a priori information in the solution. The standard approach to nonlinear inversion in geophysis has been the Gauss-Newton method, which solves a sequence of linearized inverse problems. When running to convergence, the algorithm minimizes an objective function over the space of models and in the sense produces an optimal solution of the inverse problem. The general usefulness of iterative, linearized inversion algorithms, however is greatly limited in 3-D MT applications by the requirement of computing the Jacobian(partial derivative, sensitivity) matrix of the forward problem. The difficulty may be relaxed using conjugate gradients(CG) methods. A linear CG technique is used to solve each step of Gauss-Newton iterations incompletely, while the method of nonlinear CG is applied directly to the minimization of the objective function. These CG techniques replace computation of jacobian matrix and solution of a large linear system with computations equivalent to only three forward problems per inversion iteration. Consequently, the algorithms are efficient in computational speed and memory requirement, making 3-D inversion feasible.

자기지전류(MT) 자료의 3차원 역산에 대해 소개한다. MT 자료의 역산 문제는 기본적으로 악조건이므로 유일한 해가 존재하지 않는다. 이러한 비유일성을 줄이고 정확한 역산해를 구하기 위해서는 역산 시 사전정보를 추가하는 제약조건을 가해야 한다. 물리탐사 분야에서 비선형 역산에 사용되는 가장 일반적인 방법은 일련의 선형화된 역산문제를 푸는 Gauss-Newton법이다. 이 알고리듬은 수렴 시, 모델 공간에서 역산문제에 대한 목적함수를 최소화하는 최적해를 준다. 그러나 이러한 반복적 선형화기법은 3차원 MT 역산의 경우 Jacobian 행렬을 구하기 힘들기 때문에 그 유용성에 한계가 있다. 이러한 어려움은 CG법에 의해 완화할 수 있다. 선형 CG법은 Gauss-Newton 반복의 각 단계를 근사적으로 풀기 위해서 사용된다. 한편 비선형 CG법은 목적함수의 최소화에 직접적으로 적용된다. 이들 CG법은 Jacobian 행렬의 계산 및 대형 선형방정식의 해를 반복 당 세 번의 모델링으로 대치할 수 있어서 3차원 역산에 적합하다.

Keywords

References

  1. 송윤호, 이태종, 이성곤, Uchida , T., Mitsuhata, Y, and Graham, G. B., 2004, 포항지역 지열개발을 위한 3차원 MT탐사, 대한지구물리학회.한국물리탐사학회 공동 학술발표회
  2. Constable, S. C., Parker, R L., and Constable, C. G., 1987, Occam's inversion: A practical algorithm for generating smooth models from electromagnetic sounding data, Geophysics, 52, 289-300
  3. deGroot-Hedlin, C, 1991, Removal of static shift in two dimensions by regularized inversion, Geophysics, 56, 21022106
  4. Farquharson, C. G., Oldenburg, D. W, and Haber, E., 2002, An algorithm for the three-dimensional inversion of magnetotelluric data, Expanded Abstract, 72nd Ann. Internat. Mtg., Soc. Expl. Geophys.,649-652
  5. Golubev, N., Zhdanov, M. S., and Chernobay, B., 2002, Threedimensionalinversion of array magnetotelluric data based on quasi-analytical approximation, Expanded Abstract, 72nd Ann. Internat. Mtg., Soc. Expl. Geophys., 637-640
  6. Habashy, T. M., Groom, R. W, and Spies, B., 1993, Beyond the Born and Rytov approximation: A nonlinear approach to electromagnetic scattering, J. Geophys. Res., 98, 1759-1775
  7. Hursan, G., and Zhdanov, M. S., 2001, Rapid 3-D magnetotelluric and CSAMT inversion, Expanded Abstract, 7I st Ann. Internat. Mtg., Soc. Expl. Geophys., 1493-1496
  8. Lee, T. J., Uchida, T., Sasaki, Y, and Song, Y, 2003, Characteristics of static shift in 3-D MT inversion, MulliTamsa, 6, 199-206
  9. Mackie, R L., Rodi, W, and Watts, M. D., 2001, 3-D magnetotelluric inversion for resource exploration, Expanded Abstract, 7Ist Ann. Internat. Mtg., Soc. Expl. Geophys., 1501-1504
  10. Mackie, R L., and Madden, T. R, 1993, Three-dimensional magnetotelluric inversion using conjugate gradients, Geophys. J. Int., 115, 215-229
  11. McGillivary, P. R, Oldenburg, D. W, Ellis, R G., and Habashy, T M., 1994, Calculation of sensitivities for the frequency domain electromagnetic problem, Geophys. J. Int., 116, 1-4
  12. Newman, G. A, and Alumbaugh, D. L., 2000, Three-dimensional magnetotelluric inversion using non-linear conjugate gradients, Geophys. J. Int., 140,410-424
  13. Ogawa, Y, and Uchida, T, 1996, A two-dimensional magnetotelluric inversion assuming Gaussian static shift, Geophys. J. Int., 126, 69-76
  14. Press, W H., Teukolsky, S. A, Vetterling, W T, and Flannery, B. P., 1992, Numerical Recipes in Fortran: The Art of Scientific Computing, Cambridge Univ. Press
  15. Sasaki, Y, 2001, Three-dimensional inversion of static-shifted magnetotelluric data, Proc. 5th SEGJ Int. Symp., 185-190
  16. Scales, J. A, Gersztenkorn, A, and Treitel, S., 1988, Fast lp solution of large, sparse, linear systems: application to seismic travel time tomography, J. Comput. Phys., 75, 314333
  17. Uchida, T, 1993, Smooth 2-D inversion for magnetotelluric data based on statistical criterion ABIC, J. Geomag. Geoelect., 45, 841-858
  18. Uchida, T, Lee, T J., Sasaki, Y, Honda, M., Andan, A, and Andan, A, 2001, Three-dimensional inversion of magnetotelluric data at the Bajawa geothermal field, eastern Indonesia, Expanded Abstract, 7Ist Ann. Internat. Mtg., Soc. Expl. Geophys., 1497-1500
  19. Uchida, T, and Sasaki, Y, 2003, Stable 3-D inversion of MT data and its application to geothermal exploration: in Macnae, J. and Liu, G., eds., 'Three-Dimensional Electromagnetics III', ASEG, Paper 12,1-10
  20. Weidelt, P, 1975, Inversion of two-dimensional conductivity structures, Phys. Earth Planet Inten, 10, 282-291
  21. Yamane, K., Kim, H. J., and Ashida, Y, 2000, Three-dimensional magnetotelluric inversion using a generalized RRI method and its application, Butsuri-Tansa, 53, 234-244
  22. Zhdanov, M. S., and Fang, S., 1996, Quasi-linear approximation in 3-D electromagnetic modeling, Geophysics, 61, 646-665
  23. Zhdanov, M. S., Fang, S., and Hursan, G., 2000a, Electromagnetic inversion using quasi-linear approximation, Geophysics, 65, 1501-1513
  24. Zhdanov, M. S., Dmitriev, V. I., Fang, S., and Hursan, G., 2000b, Quasi-analytic approximations and series in electromagnetic modeling, Geophysics, 65, 1746-1757