Construction the pseudo-Hessian matrix in Gauss-Newton Method and Seismic Waveform Inversion

Gauss-Newton 방법에서의 유사 Hessian 행렬의 구축과 이를 이용한 파형역산

  • 하태영 (서울대학교 수리과학부)
  • Published : 2004.08.01

Abstract

Seismic waveform inversion can be solved by using the classical Gauss-Newton method, which needs to construct the huge Hessian by the directly computed Jacobian. The property of Hessian mainly depends upon a source and receiver aperture, a velocity model, an illumination Bone and a frequency content of source wavelet. In this paper, we try to invert the Marmousi seismic data by controlling the huge Hessian appearing in the Gauss-Newton method. Wemake the two kinds of he approximate Hessian. One is the banded Hessian and the other is the approximate Hessian with automatic gain function. One is that the 1st updated velocity model from the banded Hessian is nearly the same of the result from the full approximate Hessian. The other is that the stability using the automatic gain function is more improved than that without automatic gain control.

References

  1. Gauthier, O., Virieux, J., and Tarantola, A., 1986, Twodimensional non-linear inversion of seismic waveforms, Numerical results, Geophysics, 51, 1387-1403
  2. Geller, R. J., and Hara, T., 1993, Two efficient algorithms for iterative linearized inversion of seismic waveform data, Geophys. J Int., 115, 699-710
  3. Kolb, P, 1983, Pre-stack inversion of a I-D medium, Proc. IEEE, 74,498-508
  4. Lailly, P, 1986, The seismic inverse problem as a sequence of before stack migration, in Bednar, J. B., Redner, R., Robinson, E., and Weglein, A., Eds., Conference on Inverse Scattering, Theory and Application, Soc. Industr. Appl. Math
  5. Pratt, R. G., 1999, Seismic waveform inversion in the frequency domain I-Theory and verification in a physical scale model, Geophysics, 64, 888-901
  6. Pratt, R. G., Shin, C. S., and Hicks, G. J., 1998, Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion, Geophys. J. lnt., 133, 341-362
  7. Shin, C., Jang, S. and Min, D. J., 2001a, Improved amplitude preservation for pres tack depth migration by inverse scattering theory, Geophys. Prosp., 49, 592-606
  8. Shin, C. Yoon, K., Markurt, K. J. Park, Young, D. Lim, H. Chung, S., and Shin, S., 2001b, Efficient calculation of a partial-derivative wavefield using reciprocity for seismic imaging and inversion, Geophysics, 66, 1-8
  9. Tarantola, A., 1984, Inversion of seismic reflection data in the acoustic approximation, Geophysics, 49, 1259-1266
  10. Tarantola, A., 1987, Inverse Problem Theory: Methods for data fitting and parameter estimation, Elsevier, Amsterdam