@conference {min2012EAGEefwi,
	title = {Frequency-domain elastic waveform inversion using weighting factors related to source-deconvolved residuals},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2012},
	month = {06},
	abstract = {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.Analyzingthe conventional waveform inversion algorithms using the pseudo-Hessian matrix as a pre-conditioner shows that the gradientsdo 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.},
	keywords = {EAGE, elastic, frequency-domain, waveform inversion, weighting factors},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2012/min2012EAGEefwi/min2012EAGEefwi.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=59623},
	author = {Ju-Won Oh and Dong-Joo Min and Felix J. Herrmann}
}
@conference {min2012CSEGrgfe,
	title = {Re-establishment of gradient in frequency-domain elastic waveform inversion},
	booktitle = {CSEG Annual Conference Proceedings},
	year = {2012},
	month = {02},
	abstract = {To obtain solutions close to global minimum in waveform inversion, the gradients computed at each frequency need to be weighted to appropriately describe the residuals between modeled and field data. While the low-frequency components of the gradients should be weighted to recover the long-wavelength structures, the high-frequency components of the gradients need to be weighted when the short-wavelength structures are restored. However, the conventional elastic waveform inversion algorithms cannot properly weight the gradients computed at each frequency. When gradients are scaled using the pseudo-Hessian matrix inside the frequency loop, gradients obtained at high frequencies are over-emphasized. When the gradients are scaled outside the frequency loop, gradients are weighted by the source spectra. In this study, we propose applying weighting factors to the gradients obtained at each frequency so that gradients can properly reflect the differences between the true and assumed models satisfying the general inverse theory. The weighting factors are composed by the backpropagated residuals. Numerical examples for the simple rectangular-shaped model and the modified version of the Marmousi-2 model show that the weighting method enhances gradient images and inversion results compared to the conventional inversion algorithms.},
	keywords = {elastic, frequency-domain, waveform inversion, weighting factors},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/CSEG/2012/min2012CSEGrgfe/min2012CSEGrgfe.pdf},
	author = {Ju-Won Oh and Dong-Joo Min and Felix J. Herrmann}
}
