Robust time-domain full waveform inversion with normalized zero-lag cross-correlation objective function
File(s)
Published version
Author(s)
Type
Journal Article
Abstract
In full waveform inversion (FWI) with the least-squares (L2) norm, the direct amplitude matching is never perfect and the accurate estimation of the seismic source strength is not always available. In contrast, the normalized zero-lag cross-correlation objective function relaxes on the amplitude constraints and emphasizes the phase information when measuring the closeness between the simulated and observed data. This FWI method becomes insensitive to differences in amplitude. Based on this property, we investigate the effectiveness and robustness of FWI with the normalized zero-lag cross-correlation function (CFWI) against the noise and unpredictable amplitude of the data that cannot be modeled by the wavefield extrapolation operator. The effectiveness is firstly tested by noise-free data and data contaminated by Gaussian white noise. In addition, CFWI can invert the data set with incorrect source strength when compared with the L2 norm. Moreover, the data set with incorrect source signature illustrates that CFWI is slightly more insensitive to the error in source signature than the L2 norm. However, a source inversion is still needed when the source signature is severely erroneous. With non-Gaussian noise data, such as contaminated by strong ground motion noise and even by spike-type noise, CFWI provides a comparable result with that of the robust Huber norm. Numerical experiments with non-Gaussian noise also indicate that CFWI can suppress noise in data to produce clearer images when compared with the Huber norm. Besides, CFWI is free of the threshold criterion that controls the transition between the L2 and L1 norms used with the Huber and Hybrid norms and therefore free from tedious trial-and-error tests. Several numerical examples support that CFWI is an alternative and reliable inversion method. However, a numerical test with a one-dimensional initial model confirms that CFWI is more sensitive to the cycle-skipping problem caused by less-accurate initial velocity model than the L2 norm, which is due to the wrong matched events contributing to spurious local minima of the objective function of CFWI, but to an increase in the objective function used with the L2 nrom.
Date Issued
2017-04-01
Date Acceptance
2016-12-22
Citation
GEOPHYSICAL JOURNAL INTERNATIONAL, 2017, 209 (1), pp.106-122
ISSN
0956-540X
Publisher
OXFORD UNIV PRESS
Start Page
106
End Page
122
Journal / Book Title
GEOPHYSICAL JOURNAL INTERNATIONAL
Volume
209
Issue
1
Copyright Statement
© The Authors 2016. Published by Oxford University Press on behalf of The Royal Astronomical Society.
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000396820600007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Geochemistry & Geophysics
Inverse theory
Waveform inversion
Seismology
ADJOINT-STATE METHOD
SEISMIC DATA
FREQUENCY-DOMAIN
SENSITIVITY KERNELS
FIELD INVERSION
REAL DATA
TOMOGRAPHY
NORM
TRANSMISSION
STRATEGY
Publication Status
Published