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Original Articles

A wavelet multiscale method for the inverse problems of a two-dimensional wave equation

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Pages 643-656 | Received 02 Sep 2003, Accepted 02 Mar 2004, Published online: 16 Aug 2006

  • Ameur, HB, and Kaltenbacher, B, 2003. Regularization of parameter estimation by adaptive discretization using refinement and coarsening indicators, J. Inv. Ill-posed Problems 10 (2003), pp. 561–584.
  • Ascher, UM, and Haber, E, 2003. A mutigrid method for distributed parameter estimation problem, Electronic Transactions on Numerical Analysis 15 (2003), pp. 1–17.
  • Bunks, C, Saleck, FM, Zaleski, S, and Chavent, G, 1995. Multiscale seismic waveform inversion, Geophysics 60 (1995), pp. 1457–1473.
  • Daubechies, I, 1992. Ten Lectures on Wavelets, SIAM. Philadelphia. 1992.
  • Dicken, V, and Romeo, F, 1996. A wavelet-Galerkin methods for ill-posed problems, J. Inv. Ill-posed Problems 4 (1996), pp. 203–222.
  • Ghanem, R, and Romeo, F, 2001. A wavelet-based approach for model and parameter identification of non-linear systems, International J. Non-linear Mech. 36 (2001), pp. 835–859.
  • Hackbusch, W, 1985. Multi-Grid Methods and Applications, Spinger-Verlag. Berlin. 1985.
  • Kold, P, Collino, F, and Lailly, P, 1984. Pre-stack inversion of a 1-D medium, Proc. IEEE 74 (1984), pp. 498–508.
  • Lindgren, J, 1992. "Waveform inversion of seismic reflection data through local optimization methods: PhD thesis". In: Institute Physique du Globe. Paris, France. 1992, The Geophysical Tomography Group, Periodical Rep., no. 21.
  • Lindgren, J, Mora, P, and Tarantola, A, 1989. "Nonlinear wave form inversion of seismic data: retrieving both long and short wavelength velocity information: The Geophysical Tomography Group Periodical Rep". In: Institute be physique du Globe. Vol. 7. Paris, France. 1989. p. pp. 2.1–2.23.
  • Liu, J, 1993. A multiresolution method for distributed parameter estimation, SIAM J. Sci. Comput 14 (1993), pp. 389–405.
  • Reginka, T, and Elden, L, 2000. Stability and convergence of the wavelet-Galerkin method for the sideways heat equation, J. Inv. Ill-Posed Problems 8 (2000), pp. 31–49.
  • Rieder, A, 1997. A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization, Numer. Math. 75 (1997), pp. 501–522.
  • Saleck, FM, Bunks, C, Zaleski, C, and Chavent, G, 1993. "Combining the multigrid and gradient methods to solve the seismic inversion problem: 63rd Ann. Intern. Mty, Soc. Expl. Gephoys". In: Abstracts. 1993. pp. 688–691.
  • Tikhonov, AN, and Aresenin, VY, 1977. Solution of Ill-posed Problems, John Wiley and Sons, Inc. 1977.
  • Wang, SD, Liu, JQ, and Xie, G, 1996. 2-D acoustic wave equation inversion combining plane-wave seismograms with well logs, Geophysics 61 (1996), pp. 735–741.

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