LJKDeterministic Models and Algorithms: EDPMOISE Seminar

On Thursday March 8 2012 at 11h00 in Salle 1  Tour IRMA

Seminary of Mr Ludovic METIVIER (ISTerre, Université Joseph Fourier)

A Preconditioned truncated Newton method for Full Waveform Inversion

Summary

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 quasiNewton lBFGS 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 matrixfree 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 Hessianvector products,
 a wellsuited 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 speedup in convergence can be obtained, compared to the lBFGS algorithm.
