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

Ludovic Métivier (1, 2) , Romain Brossier (2) , Quentin Mérigot (3) , Edouard Oudet (4) , Jean Virieux (2)

1 EDP - Equations aux Dérivées Partielles
2 ISTerre - Institut des Sciences de la Terre
3 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
4 CVGI - Calcul des Variations, Géométrie, Image

Full waveform inversion using the conventional $L^2$ 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 $L^2$ 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.

Mots clés: Inverse theory; Wave propagation; Computational seismology; Controlled source seismology; Numerical approximation and analysis

Domaines: Géométrie algorithmique [cs.CG]; Modélisation et simulation; Géophysique [physics.geo-ph]

Ludovic Métivier, Romain Brossier, Quentin Mérigot, Edouard Oudet, Jean Virieux. Measuring the misfit between seismograms using an optimal transport distance: application to full waveform inversion. Geophysical Journal International, 2016, 205 (1), pp.345 - 377. ⟨10.1093/gji/ggw014⟩. ⟨hal-01499531⟩