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Direct and indirect inversions

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Abstract

A bridge is highlighted between the direct inversion and the indirect inversion. They 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. However, it is possible to obtain similar structures for model perturbation, and we shall focus on P-wave velocity reconstruction. This bridge is built up through the Born approximation linearizing the forward problem with respect to model perturbation and through asymptotic approximations of the Green functions of the wave propagation equation. We first describe the direct inversion and its ingredients and then we focus on a specific misfit function design leading to a indirect inversion. Finally, 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. This bridge has been proposed by the group led by Raul Madariaga in the early nineties, emphasizing his leading role in efficient imaging workflows for seismic velocity reconstruction, a drastic requirement at that time.

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Acknowledgments

This study was granted access to the HPC resources of the Froggy platform of the CIMENT infrastructure (https://ciment.ujf-grenoble.fr), which is supported by the Rhône-Alpes region (GRANT CPER07_13 CIRA), the OSUG@2020 labex (reference ANR10 LABX56), and the Equip@Meso project (reference ANR-10-EQPX-29-01) of the programme Investissements d’Avenir supervised by the Agence Nationale pour la Recherche, and the HPC resources of CINES/IDRIS under the allocation 046091 made by GENCI. This study was partially funded by the SEISCOPE consortium, sponsored by BP, CGG, CHEVRON, EXXON-MOBIL, JGI, PETROBRAS, SAUDI ARAMCO, SCHLUMBERGER, SHELL, SINOPEC, STATOIL, TOTAL, and WOODSIDE (http://seiscope2.osug.fr).

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Authors and Affiliations

  1. ISTerre, Université Grenoble Alpes, BP 53, 38041, Grenoble, CEDEX 09, France

    Jean Virieux & Romain Brossier

  2. LJK, Université Grenoble Alpes, BP 53, 38041, Grenoble, CEDEX 09, France

    Ludovic Métivier

  3. GeoAzur, CNRS, IRD UNS, 250 Rue Albert Einstein, 06560, Valbonne, France

    Stéphane Operto & Alessandra Ribodetti

Authors
  1. Jean Virieux
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  2. Romain Brossier
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  3. Ludovic Métivier
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  4. Stéphane Operto
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  5. Alessandra Ribodetti
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Correspondence to Jean Virieux.

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Virieux, J., Brossier, R., Métivier, L. et al. Direct and indirect inversions. J Seismol 20, 1107–1121 (2016). https://doi.org/10.1007/s10950-016-9587-3

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  • DOI: https://doi.org/10.1007/s10950-016-9587-3

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