Migration Velocity Analysis techniques suffer from the presence of artefacts in reflectivity models obtained by standard migration. To overcome this difficulty, recent studies suggest determining the reflectivity by inversion instead of migration, either through pseudo-inverse formulas or by iterative minimisation of a least-squares data misfit. The advantage of the iterative approach is the possible introduction of multiple reflections in MVA techniques, usually restricted to primary reflection data. In this nested optimisation process, we pay attention at the computation of the gradient with respect to the background velocity model. From a numerical point of view, we show that this gradient appears to be unstable: in particular, gradients computed with very close reflectivity models may exhibit significant differences. To obtain a more stable procedure, we introduce a slight modification in the MVA objective function. The robustness of the approach is illustrated on simple 2D models, first in the case of primaries only, then with primaries and first-order surface-related multiples.


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  1. Chauris, H. and Cocher, E.
    [2017] From Migration to Inversion Velocity Analysis. Accepted for publication in Geophysics.
    [Google Scholar]
  2. Hou, J. and Symes, W.W.
    [2015] An Approximate Inverse to the Extended Born Modeling Operator. Geophysics, 80(6), R331–R349.
    [Google Scholar]
  3. Huang, Y.
    [2016] Born Waveform Inversion in Shot Coordinate Domain. Ph.D. thesis, Rice University.
    [Google Scholar]
  4. Métivier, L., Brossier, R., Virieux, J. and Operto, S.
    [2013] Full Waveform Inversion and the Truncated Newton Method. SIAM Journal on Scientific Computing, 35(2), B401–B437.
    [Google Scholar]
  5. Mulder, W.A. and ten Kroode, F.
    [2002] Automatic Velocity Analysis by Differential Semblance Optimization. Geophysics, 67(4), 1184–1191.
    [Google Scholar]
  6. Plessix, R.E.
    [2006] A Review of the Adjoint-State Method for Computing the Gradient of a Functional with Geophysical Applications. Geophysical Journal International, 167(2), 495–503.
    [Google Scholar]
  7. Shen, P. and Symes, W.W.
    [2008] Automatic Velocity Analysis via Shot Profile Migration. Geophysics, 73(5), VE49–VE59.
    [Google Scholar]
  8. Symes, W.W.
    [2008] Migration Velocity Analysis and Waveform Inversion. Geophysical Prospecting, 56(6), 765–790.
    [Google Scholar]
  9. ten Kroode, F.
    [2012] A Wave-Equation-Based Kirchhoff Operator. Inverse Problems, 28(11), 115013.
    [Google Scholar]

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