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Measuring the misfit between seismograms using an optimal transport distance: application to full waveform inversion

Métivier, Ludovic; Brossier, Romain; Mérigot, Quentin; Oudet, Edouard; Virieux, Jean (2016), Measuring the misfit between seismograms using an optimal transport distance: application to full waveform inversion, Geophysical Journal International, 205, 1, p. 345 - 377. 10.1093/gji/ggw014

Type
Article accepté pour publication ou publié
Date
2016
Journal name
Geophysical Journal International
Volume
205
Number
1
Pages
345 - 377
Publication identifier
10.1093/gji/ggw014
Metadata
Show full item record
Author(s)
Métivier, Ludovic
Laboratoire Jean Kuntzmann [LJK]
Institut des Sciences de la Terre [ISTerre]
Brossier, Romain cc
Institut des Sciences de la Terre [ISTerre]
Mérigot, Quentin
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Oudet, Edouard
Laboratoire Jean Kuntzmann [LJK]
Virieux, Jean
Institut des Sciences de la Terre [ISTerre]
Abstract (EN)
Full waveform inversion using the conventional L2 distance to measure the misfit between seismograms is known to suffer from cycle skipping. An alternative strategy is proposed in this study, based on a measure of the misfit computed with an optimal transport distance. This measure allows to account for the lateral coherency of events within the seismograms, instead of considering each seismic trace independently, as is done generally in full waveform inversion. The computation of this optimal transport distance relies on a particular mathematical formulation allowing for the non-conservation of the total energy between seismograms. The numerical solution of the optimal transport problem is performed using proximal splitting techniques. Three synthetic case studies are investigated using this strategy: the Marmousi 2 model, the BP 2004 salt model, and the Chevron 2014 benchmark data. The results emphasize interesting properties of the optimal transport distance. The associated misfit function is less prone to cycle skipping. A workflow is designed to reconstruct accurately the salt structures in the BP 2004 model, starting from an initial model containing no information about these structures. A high-resolution P-wave velocity estimation is built from the Chevron 2014 benchmark data, following a frequency continuation strategy. This estimation explains accurately the data. Using the same workflow, full waveform inversion based on the L2 distance converges towards a local minimum. These results yield encouraging perspectives regarding the use of the optimal transport distance for full waveform inversion: the sensitivity to the accuracy of the initial model is reduced, the reconstruction of complex salt structure is made possible, the method is robust to noise, and the interpretation of seismic data dominated by reflections is enhanced.
Subjects / Keywords
Inverse theory; Numerical approximation and analysis; Controlled source seismology; Computational seismology; Wave propagation

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