ARTICLE

Frequency-domain reverse time migration using the L1-norm

JEEEUN LEE1 YOUNGSEO KIM2 CHANGSOO SHIN1
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1 Seoul National University, Department of Energy Resources Engineering, 151-744/ 36-2061, College of Engineering, Seoul National Univ., Daehak-dong Gwanak-gu, Seoul, South Korea.,
2 Seoul National University, Research Institute of Energy and Resources 151-744/ Building 135, College of Engineering, Seoul National Univ., Daehak-dong Gwanak-gu, Seoul, South Korea. kysgood@snuaekr,
JSE 2012, 21(3), 281–300;
Submitted: 5 February 2012 | Accepted: 1 June 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/ )
Abstract

Lee, J., Kim, Y. and Shin, C., 2012. Frequency-domain reverse time migration using the L,-norm. Journal of Seismic Exploration, 21: 281-300. Waveform inversion algorithms generally use the L,-norm. However, previous work indicates that the L,-norm objective function can produce better results than the L,-norm objective function because the Li-norm is more robust against outliers. Moreover, because field data always contain some outliers, adopting the L,-norm objective function for waveform inversion would therefore be beneficial. Thus, we consider adopting the L,-norm for reverse time migration, since the algorithm structure of reverse time migration is identical to that of waveform inversion. Thus, we propose introducing the L,-norm into frequency domain reverse time migration for 2D acoustic media. To verify the effectiveness of our algorithm, we compare the results with those from the conventional algorithm. First, we apply both algorithms to synthetic data drawn from the Marmousi model. We also apply both algorithms to synthetic data on which we add artificial random outliers. Considering the data without outliers, both algorithms yield similar results regardless of the norm used. However, when we consider the data containing outliers, our algorithm using the L,-norm yields better results. We then apply the same algorithm to field data obtained from an area in the Gulf of Mexico. As expected from the synthetic test, our algorithm yields superior results. Through these experiments, we conclude that the newly proposed algorithm would be useful for performing reverse time migration on data containing considerable outliers, thus eliminating some preprocessing steps through the use of the L,-norm.

Keywords
reverse time migration
frequency domain
2D
L
-norm
outlier
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing