Effective 2D Full Waveform Inversion for 3D Seismic Data using Plane-Wave Transformation

doi:10.12972/ksmer.2016.53.2.164

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2016 Vol.53, Issue 2 Preview Page Next Page

Research Paper

Effective 2D Full Waveform Inversion for 3D Seismic Data using Plane-Wave Transformation 평면파 변환을 이용한 3차원 탄성파자료의 효과적인 2차원 완전파형역산: 권택현·설순지·변중무
Taekhyun Kwon, Soon Jee Seol, Joongmoo Byun

30 April 2016. pp. 164-174

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Abstract

Full waveform inversion (FWI) provides accurate velocity information of subsurface media. FWI can update velocity as reducing the residual between the observed and estimated data which can be obtained by solving wave equation. Therefore, when we carry out 2D FWI with 3D data acquired in a field, critical problems happen in FWI, because 2D and 3D wave equations have different green functions. To overcome the problem we suggest 2D plane-wave FWI method using plane-wave gathers, which are transformed from 3D data, as observed data. Since plane-wave data follow 1D green function, the differences of amplitude and phase do not occur, it means that we can implement FWI by using different dimension data. In addition, this method has advantage that computational cost is considerably reduced. To verifythe validity of this method, we applied it to 3 layer model and 3D SEG/EAGE overthrust model and obtained reasonable inversion results.

Keywords

Plane-wave

Full waveform inversion

Green function

완전파형역산은 정확한 파동방정식의 해에 의해 얻어진 예측자료와 관측자료와의 잔차를 줄여가며 속도모델을 업데이트 시키는 자료처리 방법이다. 그러나 실제 현장자료는 3차원적 송신원에 의해 얻어지게 되어 2차원 파동방정식을 이용한 2차원 역산을 수행하면 서로 다른 그린함수로 인해 역산 수행에 근본적인 문제가 발생한다. 이 연구에서는 이러한 문제를 해결하기 위해 3차원 자료를 평면파자료로 변환하여 2차원 평면파 완전파형역산을 수행하는 방법을 제안하였다. 평면파자료는 1차원 그린함수를 따르는 해가 되므로 그린함수의 차이에 의한 문제가 발생되지 않고 이 방법을 적용 시 계산비용이 줄어드는 장점도 갖게 된다. 제안한 방법의 효용성을 확인하기 위해 3층 층서모델 및 3차원 SEG/EAGE 충상단층(overthrust) 모델에 적용하였고 수치 실험 결과 평면파 완전파형역산이 성공적으로 수행됨을 확인하였다.

키워드

평면파

완전파형역산

그린함수

3차원

References

Aminzadeh, F., Brac, J. and Kunz, T., 1997, 3-D Salt and Overthrust Models, SEG/EAGE 3-D Modeling Series No.1., SEG.
Ben-Hadj-Ali, H., Operto, S. and Virieux, J., 2008, “Velocity model building by 3D frequency-domain, full-waveform inversion of wide-aperture seismic data,” Geophysics, Vol. 73, No. 5, pp. 101-117.
Ben-Hadj-Ali, H., Operto, S. and Virieux, J., 2011, “An efficient frequency-domain full waveform inversion method using simultaneous encoded sources,” Geophysics, Vol. 76, No. 4, pp. R109-R124.
Brossier, R, Operto, S. and Virieux, J., 2009, “Seismic imaging of complex onshore structures by 2D elastic frequency- domain full-waveform inversion,” Geophysics, Vol. 74, No. 6, pp. WCC105-WCC118.
Choi, J., Byun, J., Seol, S.J. and Kim, Y., 2014, “Wavelet based interpolation by matching pursuit and multicomponent streamer data,” 84th SEG, Expanded Abstracts, pp. 1-5.
Crase, E., Pica, A., Noble, M., McDonald, J. and Tarantola, A., 1990, “Robust elastic nonlinear waveform inversion: Application to real data,” Geophysics, Vol. 55, No. 5, pp. 527-538.
Joo, Y., Seol, S.J. and Byun, J., 2009, “Full waveform inversion of surface seismic data using damped least-squares method,” J. of Mineral and Energy Resources, Vol. 46, No. 3, pp. 322-331.
Krebs, J.R., Anderson, J.E., Hinkley, D., Neelamani, R., Lee, S., Baumstein, A. and Lacasse, M.D., 2009, “Fast full- wavefield seismic inversion using encoded sources,” Geophysics, Vol. 74, No. 6, pp. WCC177-WCC188.
Kwon, T., Seol, S.J. and Byun, J, 2015, “Efficient full waveform inversion with normalized plane-wave data,” Geophys. J. Int., Vol. 201, No. 1, pp. 53-60.
Marfurt, K.J., 1984, “Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations,” Geophysics, Vol. 49, No. 5, pp. 533-549.
Pica, A., Diet, J.P. and Tarantola A., 1990, “Nonlinear inversion of seismic reflection data in a laterally invariant medium,” Geophysics, Vol. 55, No. 3, pp. 284-292.
Plessix, R., 2009, “Three-dimensional frequency-domain full-waveform inversion with an iterative solver,” Geophysics, Vol. 74, No. 6, pp. WCC149-WCC157.
Pratt, R.G., 1999, “Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model,” Geophysics, Vol. 64, No. 3, pp. 888-901.
Pratt, R.G., Shin, C. and Hicks, G.J., 1998, “Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion,” Geophys. J. Int., Vol. 133, No. 2, pp. 341-362.
Pyun, S., Son, W. and Shin, C., 2011, “3D acoustic waveform inversion in the Laplace domain using an iterative solver,” Geophysical Prospecting, Vol. 59, No. 3, pp. 386-399.
Sears, T.J., Barton, P.J. and Singh, S.C., 2010, “Elastic full waveform inversion of multicomponent ocean-bottom cable seismic data: Application to Alba Field, U. K. North Sea,” Geophysics, Vol. 75, No. 6, pp. R109-R119.
Shin, C., Yoon, K., Marfurt, K.J., Park, K., Yang, D., Lim, H.Y., Chung, S. and Shin, S., 2001, “Efficient calculation of a partial-derivative wavefield using reciprocity for seismic imaging and inversion,” Geophysics, Vol. 66, No 6, pp. 1856-1863.
Shipp, R. and Singh, S., 2002, “Two-dimensional full wavefield inversion of wide-aperture marine seismic streamer data,” Geophys. J. Int., Vol. 151, No. 2, pp. 325-344.
Sirgue, L. and Pratt, R.G., 2004, “Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies,” Geophysics, Vol. 69, No. 1, pp. 231-248.
Song, Z., Williamson, P.R. and Pratt, R., 1995, “Frequency- domain acoustic‐wave modeling and inversion of crosshole data: Part II-Inversion method, synthetic experiments and real-data results,” Geophysics, Vol. 60, No. 3, pp. 796-809.
Tao, Y. and Sen, M., 2013, “Frequency-domain full waveform inversion with plane-wave data,” Geophysics, Vol. 78, No. 1, pp. R13-R23.
Vigh, D. and Starr, E.W., 2008, “3D prestack plane-wave, full-waveform inversion,” Geophysics, Vol. 73, No. 5, pp. VE135-VE144.
Vigh, D., Jiao, K., Watts, D. and Sun, D., 2014, “Elastic full-waveform inversion application using multicomponent measurements of seismic data collection,” Geophysics, Vol. 79, No. 2, pp. R63-R77.
Wang, H., Singh, S. and Calandra, H., 2014, “Integrated inversion using combined wave-equation tomography and full waveform inversion,” Geophys. J. Int, Vol. 198, No. 1, pp. 430-446.
Warner, M., Ratcliffe, A., Nangoo, T., Morgan, J., Umpleby, A., Shah, N., Vinje, V., Stekl, I., Guasch, L., Win, C., Conroy, G. and Bertrand, 2013, “Anisotropic 3D full-waveform inversion,” Geophysics, Vol. 78, No. 2, pp. R59-R80.
Watanabe, K., 2014, Lecture Notes in Applied and Computational Mechanics-Integral Transform Techniques for Green’s Function, 2^nd edition, Vol. 71, Springer, Switzerland, pp. 11-42.
Xiong, J.L., Lin, Y., Abubakar, A. and Habashy, T.M., 2013, “2.5-D forward and inverse modelling of full-waveform elastic seismic survey,” Geophys. J. Int., Vol. 193, No. 2, pp. 938-948.

Information

Publisher :The Korean Society of Mineral and Energy Resources Engineers
Publisher(Ko) :한국자원공학회
Journal Title :Journal of the Korean Society of Mineral and Energy Resources Engineers
Journal Title(Ko) :한국자원공학회지
Volume : 53
No :2
Pages :164-174
DOI :https://doi.org/10.12972/ksmer.2016.53.2.164

[1] Aminzadeh, F., Brac, J. and Kunz, T., 1997, 3-D Salt and Overthrust Models, SEG/EAGE 3-D Modeling Series No.1., SEG.

[2] Ben-Hadj-Ali, H., Operto, S. and Virieux, J., 2008, “Velocity model building by 3D frequency-domain, full-waveform inversion of wide-aperture seismic data,” Geophysics, Vol. 73, No. 5, pp. 101-117.

[3] Ben-Hadj-Ali, H., Operto, S. and Virieux, J., 2011, “An efficient frequency-domain full waveform inversion method using simultaneous encoded sources,” Geophysics, Vol. 76, No. 4, pp. R109-R124.

[4] Brossier, R, Operto, S. and Virieux, J., 2009, “Seismic imaging of complex onshore structures by 2D elastic frequency- domain full-waveform inversion,” Geophysics, Vol. 74, No. 6, pp. WCC105-WCC118.

[5] Choi, J., Byun, J., Seol, S.J. and Kim, Y., 2014, “Wavelet based interpolation by matching pursuit and multicomponent streamer data,” 84th SEG, Expanded Abstracts, pp. 1-5.

[6] Crase, E., Pica, A., Noble, M., McDonald, J. and Tarantola, A., 1990, “Robust elastic nonlinear waveform inversion: Application to real data,” Geophysics, Vol. 55, No. 5, pp. 527-538.

[7] Joo, Y., Seol, S.J. and Byun, J., 2009, “Full waveform inversion of surface seismic data using damped least-squares method,” J. of Mineral and Energy Resources, Vol. 46, No. 3, pp. 322-331.

[8] Krebs, J.R., Anderson, J.E., Hinkley, D., Neelamani, R., Lee, S., Baumstein, A. and Lacasse, M.D., 2009, “Fast full- wavefield seismic inversion using encoded sources,” Geophysics, Vol. 74, No. 6, pp. WCC177-WCC188.

[9] Kwon, T., Seol, S.J. and Byun, J, 2015, “Efficient full waveform inversion with normalized plane-wave data,” Geophys. J. Int., Vol. 201, No. 1, pp. 53-60.

[10] Marfurt, K.J., 1984, “Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations,” Geophysics, Vol. 49, No. 5, pp. 533-549.

[11] Pica, A., Diet, J.P. and Tarantola A., 1990, “Nonlinear inversion of seismic reflection data in a laterally invariant medium,” Geophysics, Vol. 55, No. 3, pp. 284-292.

[12] Plessix, R., 2009, “Three-dimensional frequency-domain full-waveform inversion with an iterative solver,” Geophysics, Vol. 74, No. 6, pp. WCC149-WCC157.

[13] Pratt, R.G., 1999, “Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model,” Geophysics, Vol. 64, No. 3, pp. 888-901.

[14] Pratt, R.G., Shin, C. and Hicks, G.J., 1998, “Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion,” Geophys. J. Int., Vol. 133, No. 2, pp. 341-362.

[15] Pyun, S., Son, W. and Shin, C., 2011, “3D acoustic waveform inversion in the Laplace domain using an iterative solver,” Geophysical Prospecting, Vol. 59, No. 3, pp. 386-399.

[16] Sears, T.J., Barton, P.J. and Singh, S.C., 2010, “Elastic full waveform inversion of multicomponent ocean-bottom cable seismic data: Application to Alba Field, U. K. North Sea,” Geophysics, Vol. 75, No. 6, pp. R109-R119.

[17] Shin, C., Yoon, K., Marfurt, K.J., Park, K., Yang, D., Lim, H.Y., Chung, S. and Shin, S., 2001, “Efficient calculation of a partial-derivative wavefield using reciprocity for seismic imaging and inversion,” Geophysics, Vol. 66, No 6, pp. 1856-1863.

[18] Shipp, R. and Singh, S., 2002, “Two-dimensional full wavefield inversion of wide-aperture marine seismic streamer data,” Geophys. J. Int., Vol. 151, No. 2, pp. 325-344.

[19] Sirgue, L. and Pratt, R.G., 2004, “Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies,” Geophysics, Vol. 69, No. 1, pp. 231-248.

[20] Song, Z., Williamson, P.R. and Pratt, R., 1995, “Frequency- domain acoustic‐wave modeling and inversion of crosshole data: Part II-Inversion method, synthetic experiments and real-data results,” Geophysics, Vol. 60, No. 3, pp. 796-809.

[21] Tao, Y. and Sen, M., 2013, “Frequency-domain full waveform inversion with plane-wave data,” Geophysics, Vol. 78, No. 1, pp. R13-R23.

[22] Vigh, D. and Starr, E.W., 2008, “3D prestack plane-wave, full-waveform inversion,” Geophysics, Vol. 73, No. 5, pp. VE135-VE144.

[23] Vigh, D., Jiao, K., Watts, D. and Sun, D., 2014, “Elastic full-waveform inversion application using multicomponent measurements of seismic data collection,” Geophysics, Vol. 79, No. 2, pp. R63-R77.

[24] Wang, H., Singh, S. and Calandra, H., 2014, “Integrated inversion using combined wave-equation tomography and full waveform inversion,” Geophys. J. Int, Vol. 198, No. 1, pp. 430-446.

[25] Warner, M., Ratcliffe, A., Nangoo, T., Morgan, J., Umpleby, A., Shah, N., Vinje, V., Stekl, I., Guasch, L., Win, C., Conroy, G. and Bertrand, 2013, “Anisotropic 3D full-waveform inversion,” Geophysics, Vol. 78, No. 2, pp. R59-R80.

[26] Watanabe, K., 2014, Lecture Notes in Applied and Computational Mechanics-Integral Transform Techniques for Green’s Function, 2^nd edition, Vol. 71, Springer, Switzerland, pp. 11-42.

[27] Xiong, J.L., Lin, Y., Abubakar, A. and Habashy, T.M., 2013, “2.5-D forward and inverse modelling of full-waveform elastic seismic survey,” Geophys. J. Int., Vol. 193, No. 2, pp. 938-948.

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