In this paper, we investigate the elastic wave
full-waveform inversion (FWI) based on the trust region method. The FWI is an
optimization problem of minimizing the misfit between the observed data and
simulated data. Usually, the line
search method is used to update the model parameters iteratively. The line
search method generates a search direction first and then finds a suitable step
length along the direction. In the trust region method, it defines a trial step
length within a certain neighborhood of the current iterate point and then
solves a trust region subproblem. The theoretical methods for the trust region
FWI with the Newton type method are described. The algorithms for the truncated
Newton method with the line search strategy and for the Gauss-Newton method
with the trust region strategy are presented. Numerical computations of FWI for
the Marmousi model by the L-BFGS method, the Gauss-Newton method and the
truncated Newton method are completed. The comparisons between the line search
strategy and the trust region strategy are given and show that the trust region
method is more efficient than the line search method and both the Gauss-Newton
and truncated Newton methods are more accurate than the L-BFGS method.
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