Geophysics and Geophysical Exploration (지구물리와물리탐사)

Korean Society of Earth and Exploration Geophysicists (한국지구물리·물리탐사학회)
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Improved full-waveform inversion of normalised seismic wavefield data

정규화된 탄성파 파동장 자료의 향상된 전파형 역산

  • Kim, Hee-Joon (Department of Environmental Exploration Engineering, Pukyong National University) ;
  • Matsuoka, Toshifumi (Department of Civil and Earth Resource Engineering, Kyoto University)
  • 김희준 (부경대학교, 환경탐사공학과) ;
  • Published : 2006.02.28
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Abstract

The full-waveform inversion algorithm using normalised seismic wavefields can avoid potential inversion errors due to source estimation required in conventional full-waveform inversion methods. In this paper, we have modified the inversion scheme to install a weighted smoothness constraint for better resolution, and to implement a staged approach using normalised wavefields in order of increasing frequency instead of inverting all frequency components simultaneously. The newly developed scheme is verified by using a simple two-dimensional fault model. One of the most significant improvements is based on introducing weights in model parameters, which can be derived from integrated sensitivities. The model-parameter weighting matrix is effective in selectively relaxing the smoothness constraint and in reducing artefacts in the reconstructed image. Simultaneous multiple-frequency inversion can almost be replicated by multiple single-frequency inversions. In particular, consecutively ordered single-frequency inversion, in which lower frequencies are used first, is useful for computation efficiency.

정규화된 파동장을 이용하는 탄성파 전파형 역산법은 기존의 전파형 역산법에서 필요로 하는 탄성파원 예측으로 인해 야기되는 잠재적인 역산오차를 피할 수 있다. 본 논문에서는 이러한 전파형 역산법에 가중 평활화제약을 추가하여 분해능을 높였으며, 모든 주파수성분을 동시에 역산하지 않고 주파수 별로 순차적으로 역산하도록 수정하였다. 새로운 방법은 간단한 2 차원 단층모델에 적용하여 검증하였다. 가장 큰 개선점은 적분감도에 기초하여 결정한 가중계수를 모델변수에 도입한 점이다. 모델변수에 가중계수를 적용하면 평활화제약을 선택적으로 완화할 수 있기 때문에 영상화 재구성 시 잘못된 영상을 줄이는데 효과적이다. 다중 단일주파수 역산은 다중주파수 동시역산을 대치할 수 있으며, 특히 작은 주파수부터 먼저 사용하는 순차적인 단일주파수 역산은 계산효율면에서 유용하다.

Keywords

References

  1. Cerveny, v., and Soares, J.E.P., 1992, Fresnel volume ray tracing: Geophysics, 57, 902-915 https://doi.org/10.1190/1.1443303
  2. Constable, S.e., Parker, R.L., and Constable, e.G., 1987, A practical algorithm for generating smooth models from electromagnetic sounding data: Geophysics, 52, 289-300 https://doi.org/10.1190/1.1442303
  3. deGroot-Hedlin, C., and Constable, S., 1990, Occam's inversion to generate smooth, two-dimensional models from magnetotelluric data: Geophysics, 55, 1613-1624 https://doi.org/10.1190/1.1442813
  4. de Lugao, P., Portniaguaine, 0., and Zhdanov, M.S., 1997, Fast and stable twodimensional inversion of magnetotelluric data: Journal of Geomagnetism and Geoelectricity,49, 1437-1454
  5. Frazer, L.N., Sun, X., and Wilkens, R.H., 1997, Inversion of sonic waveforms with unknown source and receiver functions: Geophysical Journal International, 129, 579-586 https://doi.org/10.1111/j.1365-246X.1997.tb04494.x
  6. Frazer, L.N., and Sun, X., 1998, New objective functions for waveform inversion: Geophysics, 63, 213-222 https://doi.org/10.1190/1.1444315
  7. Humphreys, E., and Clayton, RW., 1988, Application of back-projection tomography to seismic traveltime problems: Journal of Geophysical Research, 93, 1073-1085 https://doi.org/10.1029/JB093iB02p01073
  8. Huber, PJ., 1964, Robust estimation of a location parameter: Annals of Mathematical Statistics, 35, 73-101 https://doi.org/10.1214/aoms/1177703732
  9. Kim, H.J., Fujisaki, 0., and Takeuchi, M., 1996, Two-dimensional resistivity inversion with robust estimation: Butsuri-Tansa, 49, 110-116
  10. Kormendi, F., and Dietrich, M., 1991, Nonlinear waveform inversion of plane-wave seismograms in stratified elastic media: Geophysics, 56, 664-674 https://doi.org/10.1190/1.1443083
  11. Lee, K.H., and Kim, H.J., 2003, Source-independent full-waveform inversion of seismic data: Geophysics, 68, 2010-2015 https://doi.org/10.1190/1.1635054
  12. Lines, L.R, and Treitel, S., 1984, Tutorial: A review of least-squares inversion and its application to geophysical problems: Geophysical Prospecting, 32, 159-186 https://doi.org/10.1111/j.1365-2478.1984.tb00726.x
  13. inkoff, S.E., and Symes, W.W., 1997, Full waveform inversion of marine reflection data in the plane-wave domain: Geophysics, 62, 540-553 https://doi.org/10.1190/1.1444164
  14. Nolet, G., 1985, Solving or resolving inadequate and noisy tomographic systems: Journal of Computational Physics, 61, 463-482 https://doi.org/10.1016/0021-9991(85)90075-0
  15. Parker, RL., 1980, The inverse problem of electromagnetic induction: existence and construction of solutions based upon incomplete data: Journal of Geophysical Research, 85, 4421--4425 https://doi.org/10.1029/JB085iB08p04421
  16. Parker, R.L., 1994, Geophysical Inverse Theory, Princeton University Press. Peterson, J.E., Paulson, B.N.P., and McEvilly, T.V, 1985, Applications of algebraic reconstruction techniques to crosshole seismic data: Geophysics, 50, 1566-1580 https://doi.org/10.1190/1.1441847
  17. Plessix, R.-E., and Bork, 1., 1998, A full waveform inversion example in VTI media: 68th Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts, 1562-1565
  18. Pratt, R.G., 1999, Seismic waveform inversion in frequency domain, Part 1: Theory and verification in physical scale model: Geophysics, 64, 888-901 https://doi.org/10.1190/1.1444597
  19. Pratt, R.G., and Shipp, R.M., 1999, Seismic waveform inversion in frequency domain, Part 2: Fault delineation in sediments using crosshole data: Geophysics, 64, 902-914 https://doi.org/10.1190/1.1444598
  20. Sasaki, Y, 1989, Two-dimensional joint inversion of magnetotelluric and dipoledipole resistivity data: Geophysics, 54, 254-262 https://doi.org/10.1190/1.1442649
  21. Scales, J.A., Gersztenkom, A., and Treitel, S., 1988, Fast solution of large sparse, linear systems: Application to seismic traveltime tomography: Journal of Computational Physics, 75, 314-333 https://doi.org/10.1016/0021-9991(88)90115-5
  22. Sen, M.K., and Stoffa, P.L., 1991, Nonlinear one-dimensional seismic waveform inversion using simulated annealing: Geophysics, 56,1624-1638 https://doi.org/10.1190/1.1442973
  23. Sheng, J., and Schuster, G.T., 2000, Finite-frequency resolution limits of traveltime tomography for smoothly varying velocity models: 70th Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts" 21342137
  24. Song, Z.-M., Williamson, P.R., and Pratt, R.G., 1995, Frequency-domain acoustic wave modeling and inversion of crosshoJe data: Part II-inversion method, synthetic experiments and real-data results: Geophysics, 60, 796-809 https://doi.org/10.1190/1.1443818
  25. Tikhonov, A.N., and Arsenin, VY, 1977, Solutions to Ill-Posed Problems, John Wiley and Sons, Inc
  26. Torres-Verdin, c., Druskin, VD., Fang, S., Knizhnerman, L.A., and Malinverno, A., 2000, A dual-grid nonlinear inversion technique with applications to the interpretation of de resistivity data: Geophysics, 65, 1733-1745 https://doi.org/10.1190/1.1444858
  27. Vasco, D.W., 1991, Bounding seismic velocities using a tomographic method: Geophysics, 56, 472--482 https://doi.org/10.1190/1.1443064
  28. Vasco, D.W., Peterson, Jr., J.E., and Majer, E.L., 1995, Beyond ray tomography: wavepatns and Fresnel volumes: Geophysics, 60,1790-1804 https://doi.org/10.1190/1.1443912
  29. Williamson, P.R., 1991, A guide to the limits of resolution imposed by scattering in ray tomography: Geophysics, 56, 202-207 https://doi.org/10.1190/1.1443032
  30. Yi, M.-J., Kim, J.-H., Song, Y, Cho, S.-J., Chung, S.-H., and Suh, J.-H., 2001, Threedimensional imaging of subsurface structures using resistivity data: Geophysical Prospecting, 49, 483--497 https://doi.org/10.1046/j.1365-2478.2001.00269.x
  31. Yokota, T., and Matsushima, J., 2004, Seismic waveform tomography in the frequency-space domain: selection of the optimal temporal frequency for inversion: Exploration Geophysics, 35, 19-24 https://doi.org/10.1071/EG04019
  32. Zhou, B., and Greenhalgh, S.A., 2003, Crosshole seismic inversion with normalized full-waveform amplitude data: Geophysics, 68, 1320-1330 https://doi.org/10.1190/1.1598125
  33. Zhou, c., Schuster, G.T., Hassanzadeh, S., and Harris, J.M, 1997, Elastic wave equation traveltime and wavefield inversion of crosswell data: Geophysics, 62, 853-868 https://doi.org/10.1190/1.1444194