Geodesic
Hierarchical approach to seismic full waveform inversion
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 2, pp. 119-130 
A. Asnaashari; R. Brossier; С. Castellanos; B. Dupuy; V. Etienne; Y. Gholami; G. Hu; L. Métivier; S. Operto; D. Pageot; V. Prieux; A. Ribodetti; A. Roques; J. Virieux. Hierarchical approach to seismic full waveform inversion. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 2, pp. 119-130. http://geodesic.mathdoc.fr/item/SJVM_2012_15_2_a0/
@article{SJVM_2012_15_2_a0,
     author = {A. Asnaashari and R. Brossier and {\CYRS}. Castellanos and B. Dupuy and V. Etienne and Y. Gholami and G. Hu and L. M\'etivier and S. Operto and D. Pageot and V. Prieux and A. Ribodetti and A. Roques and J. Virieux},
     title = {Hierarchical approach to seismic full waveform inversion},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {119--130},
     year = {2012},
     volume = {15},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2012_15_2_a0/}
}
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%A J. Virieux
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Voir la notice de l'article provenant de la source Math-Net.Ru

Full waveform inversion (FWI) of seismic traces recorded at the free surface allows the reconstruction of the physical parameters structure on the underlying medium. For such reconstruction, an optimization problem is defined where synthetic traces, obtained through numerical techniques as finite-difference or finite-element methods in a given model of the subsurface, should match the observed traces. The number of data samples is routinely around 1 billion for 2D problems and 1 trillion for 3D problems, while the number of parameters ranges from 1 million to 10 million degrees of freedom. Moreover, if one defines the mismatch as the standard least-squares norm between values sampled in time/frequency and space, the misfit function has a significant number of secondary minima related to the ill-posedness and non-linearity of the inversion problem linked to the so-called cycle skipping. Taking into account the size of the problem, we consider a local linearized method where the gradient is computed using the adjoint formulation of the seismic wave propagation problem. Starting for an initial model, we consider a quasi-Newton method which allows us to formulate the reconstruction of various parameters, such as P and S wave velocities, density, or attenuation factors. A hierarchical strategy is based on an incremental increase in the data complexity starting from low-frequency content to high-frequency content, from initial wavelets to later phases in the data space, from narrow azimuths to wide azimuths, and from simple observables to more complex ones. Different synthetic examples of realistic structures illustrate the efficiency of this strategy based on data manipulation. This strategy is related to the data space, and has to be inserted into a more global framework, where we could improve significantly the probability of convergence to the global minimum. When considering the model space, we may rely on the construction of the initial model or add constraints, such as smoothness of the searched model and/or prior information collected by other means. An alternative strategy concerns building the objective function, and various possibilities must be considered which may increase the linearity of the inversion procedure.

[1] Asnaashari A., Brossier R., Garambois S., Audebert F., Thore P., Virieux J., “Sensitivity analysis of time-lapse images obtained by differential waveform inversion with respect to reference model”, Expanded Abstracts, Soc. Expl. Geophys., 2011, 2482–2486 | DOI

[2] Beydoun W. B., Tarantola A., “First Born and Rytov approximation: Modeling and inversion conditions in a canonical example”, J. of the Acoustical Society of America, 83 (1988), 1045–1055 | DOI | MR

[3] Billette F., Lambaré G., “Velocity macro-model estimation from seismic reection data by stereotomography”, Geophysical J. International, 135:2 (1998), 671–680 | DOI

[4] Brenders A. J., Pratt R. G., “Efficient waveform tomography for lithospheric imaging: implications for realistic 2D acquisition geometries and low frequency data”, Geophysical J. International, 168:1 (2007), 152–170 | DOI

[5] Brossier R., Operto S., Virieux J., “Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion”, Geophysics, 74:6 (2009), WCC63–WCC76 | DOI

[6] Brossier R., Operto S., Virieux J., “Two-dimensional seismic imaging of the Valhall model from synthetic OBC data by frequency-domain elastic full-waveform inversion”, SEG Technical Program Expanded Abstracts (Houston), 28:1 (2009), 2293–2297 | DOI

[7] Brossier R., Roux P., “Seismic imaging by frequency-domain double-beamforming full-waveform inversion”, 73th Annual EAGE Conference Exhibition, Expanded Abstracts, Vienna, 2011

[8] Bunks C., Salek F. M., Zaleski S., Chavent G., “Multiscale seismic waveform inversion”, Geophysics, 60:5 (1995), 1457–1473 | DOI

[9] Crase E., Pica A., Noble M., McDonald J., Tarantola A., “Robust elastic non-linear waveform inversion: application to real data”, Geophysics, 55 (1990), 527–538 | DOI

[10] Djikpéssé H. A., Tarantola A., “Multiparameter $l_1$ norm waveform fitting: Interpretation of gulf of mexico reflection seismograms”, Geophysics, 64:4 (1999), 1023–1035 | DOI

[11] Gelis C., Virieux J., Grandjean G., “2D elastic waveform inversion using Born and Rytov approximations in the frequency domain”, Geophysical J. International, 168 (2007), 605–633 | DOI

[12] Improta L., Zollo A., Herrero A., Frattini R., Virieux J., DellÁversana P., “Seismic imaging of complex structures by non-linear traveltimes inversion of dense wide-angle data: application to a thrust belt”, Geophysical J. International, 151 (2002), 264–278 | DOI

[13] Kolb P., Collino F., Lailly P., “Prestack inversion of 1-D medium”, Proceedings of IEEE, 74, 1986, 498–508 | DOI

[14] Kommedal J. H., Barkved O. I., Howe D. J., “Initial experience operating a permanent 4C seabed array for reservoir monitoring at Valhall”, SEG Technical Program Expanded Abstracts, 23:1 (2004), 2239–2242 | DOI

[15] Munns J. W., “The Valhall field: a geological overview”, Marine and Petroleum Geology, 2 (1985), 23–43 | DOI

[16] Nocedal J., “Updating Quasi-Newton matrices with limited storage”, Mathematics of Computation, 35:151 (1980), 773–782 | DOI | MR | Zbl

[17] Plessix R.-E., “A review of the adjoint-state method for computing the gradient of a functional with geophysical applications”, Geophysical J. International, 167:2 (2006), 495–503 | DOI

[18] Pratt R. G., “Seismic waveform inversion in the frequency domain, part I: theory and verification in a physic scale model”, Geophysics, 64 (1999), 888–901 | DOI

[19] Pratt R. G., Shin C., Hicks G. J., “Gauss–Newton and full Newton methods in frequency-space seismic waveform inversion”, Geophysical J. International, 133 (1998), 341–362 | DOI

[20] Prieux V., Operto S., Lambaré G., Virieux J., “Building starting model for full waveform inversion from wide-aperture data by stereotomography”, SEG Technical Program Expanded Abstracts, 29:1 (2010), 988–992 | DOI

[21] Rost S., Thomas C., “Array seismology: methods and applications”, Reviews of Geophysics, 40:3 (2002), 1008 | DOI

[22] Sears T., Singh S., Barton P., “Elastic full waveform inversion of multi-component OBC seismic data”, Geophysical Prospecting, 56:6 (2008), 843–862 | DOI

[23] Shin C., Min D.-J., “Waveform inversion using a logarithmic wavefield”, Geophysics, 71:3 (2006), R31–R42 | DOI

[24] Sirgue L., Pratt R. G., “Efficient waveform inversion and imaging: a strategy for selecting temporal frequencies”, Geophysics, 69:1 (2004), 231–248 | DOI

[25] Tarantola A., “Inversion of seismic reflection data in the acoustic approximation”, Geophysics, 49:8 (1984), 1259–1266 | DOI

[26] Tarantola A., Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation, Elsevier, New York, 1987 | MR | Zbl

[27] Tarantola A., Inverse Problem Theory and Methods for Model Parameter Estimation, Society for Industrial and Applied Mathematics, Philadelphia, 2005 | MR

[28] Thurber C., Ritsema J., Inverse Methods and Seismic Tomography, Elsevier, 2007

[29] 1976 | MR | Zbl

[30] Vigh D., Starr E. W., “3D prestack plane-wave, full-waveform inversion”, Geophysics, 73:5 (2008), VE135–VE144 | DOI