@article{fdi:010068345,
  title = {{D}irect and indirect inversions},
  author = {{V}irieux, {J}. and {B}rossier, {R}. and {M}etivier, {L}. and {O}perto, {S}. and {R}ibodetti, {A}lessandra},
  editor = {},
  language = {{ENG}},
  abstract = {{A} bridge is highlighted between the direct inversion and the indirect inversion. {T}hey are based on fundamental different approaches: one is looking after a projection from the data space to the model space while the other one is reducing a misfit between observed data and synthetic data obtained from a given model. {H}owever, it is possible to obtain similar structures for model perturbation, and we shall focus on {P}-wave velocity reconstruction. {T}his bridge is built up through the {B}orn approximation linearizing the forward problem with respect to model perturbation and through asymptotic approximations of the {G}reen functions of the wave propagation equation. {W}e first describe the direct inversion and its ingredients and then we focus on a specific misfit function design leading to a indirect inversion. {F}inally, we shall compare this indirect inversion with more standard least-squares inversion as the {FWI}, enabling the focus on small weak velocity perturbations on one side and the speed-up of the velocity perturbation reconstruction on the other side. {T}his bridge has been proposed by the group led by {R}aul {M}adariaga in the early nineties, emphasizing his leading role in efficient imaging workflows for seismic velocity reconstruction, a drastic requirement at that time.},
  keywords = {{S}eismology ; {S}eismics ; {S}eismic inversion ; {S}eismic migration},
  booktitle = {},
  journal = {{J}ournal of {S}eismology},
  volume = {20},
  numero = {4},
  pages = {1107--1121},
  ISSN = {1383-4649},
  year = {2016},
  DOI = {10.1007/s10950-016-9587-3},
  URL = {https://www.documentation.ird.fr/hor/fdi:010068345},
}