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Pseudo-Hessian matrix for the logarithmic objective function in full waveform inversion

WANSOO HA1 ,  WOOKEEN CHUNG2 ,  CHANGSOO SHIN1
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1 Department of Energy Systems Engineering, Seoul National University, Seoul 151-742, South Korea.,
2 Department of Energy and Resources Engineering, Korea Maritime University, Busan 606-791, South Korea. wkchung@hhu.ac.kr,
JSE 2012, 21(3), 201–214;
Submitted: 27 December 2011 | Accepted: 29 March 2012 | Published: 1 August 2012
© 2012 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

Ha, W.S., Chung, W.K. and Shin, C.S., 2012. Pseudo-Hessian matrix for the logarithmic objective function in full waveform inversion. Journal of Seismic Exploration, 21: 201-214. The pseudo-Hessian matrix of the J, objective function has been used in previous inversion studies because it was observed to yield satisfactory results in both the frequency and Laplace domains. However, there are fundamental differences between the pseudo-Hessian of the logarithmic objective function and that of the J, objective function. In this study, we first derive the pseudo-Hessian matrix for full waveform inversion using the logarithmic objective function. We then compare the two pseudo-Hessian matrices in both Laplace-and frequency-domain waveform inversions using the logarithmic objective function. A Laplace-domain inversion using the pseudo-Hessian of the logarithmic objective function yields a better result than that obtained using the pseudo-Hessian of the /, objective function. On the other hand, frequency domain inversion results using the two pseudo-Hessians yield similar results. The differences originate from the different behaviour of wavefields in the Laplace and frequency domains.

Keywords
pseudo-Hessian matrix
logarithmic objective function
frequency domain
waveform inversion
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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