Second-order adjoint state methods for Full Waveform Inversion

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

1 ISTerre - Institut des Sciences de la Terre
2 GEOAZUR 6526 - Géoazur

Full Waveform Inversion (FWI) is becoming an efficient tool to derive high resolution quantitative models of the subsurface parameters. The method relies on the minimization, through an iterative procedure, of the residual between recorded data and synthetic data computed by solving the two-way wave equation in a subsurface model. The growth of available computational resources and recent developments of the method makes now possible applications to 2D and 3D data in the acoustic approximation (see for example Prieux et al., 2011; Plessix et al., 2010) and even in the elastic approximation (Brossier et al 2009). Most of the FWI applications rely on fast optimization schemes as preconditioned steepest descent or preconditioned conjugate-gradient methods (PCG). Second-order information provided by the Hessian is often neglected in FWI, due to the high computational cost to build this matrix and solve the normal equation system. However, a significant improvement of the results can be obtained using this information: Pratt et al. (1998) have shown the improved resolution of Gauss-Newton method compared to the steepest descent one in a canonical application. Hu et al. (2011) have shown results improvement provided by a non-diagonal truncated Hessian in PCG. Brossier et al. (2009) have shown the estimated Hessian's impact of a quasi-Newton l-BFGS (Nocedal, 1980), on image resolution and convergence speed compared to PCG. Epanomeritakis et al. (2008); Fichtner and Trampert (2011) have also discussed the interest of Hessian for inversion and uncertainty estimation, and also the prohibitive cost of Hessian computation and storage. In this study, we develop the mathematical framework to propose an efficient matrix-free Hessian-vector product algorithm for FWI, and give an illustration of the interest of accounting for the exact Hessian in the inversion process. The final aim is to tackle Gauss-Newton and Full-Newton method for large scale applications. Our development relies on a general second-order adjoint-state formula, valid either in the time or in the frequency domain.

Mots clés: nonlinear optimization; inverse problems; seismic imaging; Full Waveform Inversion

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

Ludovic Métivier, Romain Brossier, Stéphane Operto, Jean Virieux. Second-order adjoint state methods for Full Waveform Inversion. EAGE 2012 - 74th European Association of Geoscientists and Engineers Conference and Exhibition, Jun 2012, Copenhagen, Denmark. ⟨hal-00826614⟩