One of the limitations in seismic waveform inversion is that inversion results are very sensitive to initial guesses, which may be because the gradients computed at each frequency are not properly weighted depending on given models. Analyzing the conventional waveform inversion algorithms using the pseudo-Hessian matrix as a pre-conditioner shows that the gradients do not properly describe the feature of given models or high- and low-end frequencies do not contribute the model parameter updates due to banded spectra of source wavelet. For a better waveform inversion algorithm, we propose applying weighting factors to gradients computed at each frequency. The weighting factors are designed using the source-deconvolved back-propagated wavefields. Numerical results for the SEG/EAGE salt model show that the weighting method improves gradient images and its inversion results are compatible with true velocities even with poorly estimated initial guesses.


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