FWI: The role of the imaging frequencies and the number of iterations in the reduction of the sensibility to noise

The full waveform inversion is a nonlinear inverse problem in which the values of physical properties recovered from seismic data are sensitive with respect to noise in data. The problem becomes more critical when the number of parameters increases or different kind of physical parameters are searched. The multi-scale approach is one of the most used strategies to make the solution process more stable. Tikhonov and other kinds of regularization are also used. However, these strategies have some drawbacks. The regularization operators and parameters influence the solution and the optimal ones are expensive to estimate. The multi-scale approach demands the choice of imaging frequencies and number of iterations for each frequency or other stop criteria. The knowledge of the misfit level to stop minimizing is a good stop criterion to avoid fit noise in data. The main objective of this work is to present some numerical experiments of acoustic inversion in the context of multi-scale approach considering the same total number of iterations but with a different number of imaging frequencies for the same bandwidth. The experiments show that the results can be less sensitive to noise in data if the number of iterations for each frequency is reduced and the number of frequencies is increased. The results are compared with images recovered from noise free data in order to show the effect of different settings.