# A Preconditioned truncated Newton method for Full Waveform Inversion

#### Séminaire Modèles et Algorithmes Déterministes: EDP-MOISE

8/03/2012 - 11:00
Mr Ludovic Metivier *(ISTerre, Université Joseph Fourier)*
Salle 1 - Tour IRMA

Full Waveform Inversion (FWI) is a promising tool for seismic imaging. This method aims at estimating subsurface parameters such as the pressure wave velocity, the shear wave velocity, or the density, from local measurements of the wavefield. Based on a wave propagation model, the FWI method consists in minimizing the distance between this measurements and the predicted data given by the wave propagation model. Classical procedures such as the preconditioned steepest descent, or more recently the quasi-Newton l-BFGS method are used to perform this minimization. We are interested in the design of a method that accounts more accurately for the influence of the second order derivatives. The Hessian operator has a strong impact on the quality of the reconstructed parameters, in terms of amplitude estimation and image resolution. We thus investigate the possibility of using a truncated Newton method. In this framework, the Newton descent direction is computed at each iteration by solving a linear system using a matrix-free Conjugate Gradient (CG) algorithm. The algorithm results in two interlocked loops : at each outer nonlinear Newton iteration, a linear system is solved using the CG algorithm. This approach requires however - the capability of computing efficiently Hessian-vector products, - a well-suited stopping criterion for the CG inner iterations - a preconditioner for the CG inner iterations In this study, we present these three key ingredients. Numerical results on a 2D benchmark model demonstrate that an interesting speed-up in convergence can be obtained, compared to the l-BFGS algorithm.