Applying Gauss-Newton and Exact Newton method to Full Waveform Inversion

Ludovic Métivier (1, 2) , Romain Brossier (2) , Stéphane Operto (3) , Jean Virieux (2)

1 EDP - Equations aux Dérivées Partielles
2 Ondes et Structures
3 GEOAZUR 6526 - Géoazur

Full Waveform Inversion (FWI) applications classically rely on efficient first-order optimization schemes, as the steepest descent or the nonlinear conjugate gradient optimization. However, second-order information provided by the Hessian matrix is proven to give a useful help in the scaling of the FWI problem and in the speed-up of the optimization. In this study, we propose an efficient matrix-free Hessian-vector formalism, that should allow to tackle Gauss-Newton (GN) and Exact-Newton (EN) optimization for large and realistic FWI targets. Our method relies on general second order adjoint formulas, based on a Lagrangian formalism. These formulas yield the possibility of computing Hessian-vector products at the cost of 2 forward simulations per shot. In this context, the computational cost (per shot) of one GN or one EN nonlinear iteration amounts to the resolution of 2 forward simulations for the computation of the gradient plus 2 forward simulations per inner linear conjugate gradient iteration. A numerical test is provided, emphasizing the possible improvement of the resolution when accounting for the exact Hessian in the inversion algorithm.

Domaines: Géophysique [physics.geo-ph]; Géophysique [physics.geo-ph]; Milieux et Changements globaux; Optimisation et contrôle [math.OC]

Ludovic Métivier, Romain Brossier, Stéphane Operto, Jean Virieux. Applying Gauss-Newton and Exact Newton method to Full Waveform Inversion. EAGE 2012 - European Association of Geoscientists and Engineers, Jun 2012, Copenhaguen, Denmark. pp.1-5. ⟨hal-00944435⟩