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Fast line-search for full waveform inversion in the Huber norm

XIAONA MA
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Institute of Geophysics, China Earthquake Administration, Beijing 100081, P.R. China.,
JSE 2021, 30(4), 347–364;
Submitted: 8 July 2019 | Accepted: 10 February 2021 | Published: 1 August 2021
© 2021 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

Ma, X., 2021. Fast line-search for full waveform inversion in the Huber norm. Journal of Seismic Exploration, 30: 347-364. The misfit functions decide the robust performance of full-waveform inversion (FWD) when the data is contaminated by noise. Huber norm combines the L2 norm when residuals are small and L1 norm when residuals are large, which compromise the merits of them. It not only improves the anti-noise ability with the L1 norm, but also keeps smoothness for small residuals with the L2 norm. Line searches are always important for FWI process. Step-length can typically be calculated using an inexact or exact line-search method. Optimal step-length can prevent the over- or under-estimations, and make FWI to reach a global minimum along searching direction with fast convergence rate. Exact line searches for local optimization methods can be performed very efficiently for computing solutions in robust norms, thereby promoting convergence rate of FWI. Therefore, we derive an exact line search method, i.e., the analytical step-length method (ASLM), for the Huber norm. Through numerical tests on noise-free and noisy data of Overthrust model, we demonstrate the efficiency of ASLM for Huber norm. In addition, we also compare Huber with L2 norm on the data contaminated by non-Gaussian noise, such as ground-motion noise. We think that ASLM is an efficient optimal step-length estimation method for the Huber norm in FWI. Meanwhile, the Huber norm makes the FWI more robust than the L2 norm alone.

Keywords
time-domain full waveform inversion
Huber norm
exact line-search method
analytical step-length method
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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