Comment on: “Application of the variable projection scheme for frequency-domain full-waveform inversion” (M. Li, J. Rickett, and A. Abubakar, Geophysics, 78, no. 6, R249–R257)

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. X11-X15 ◽  
Author(s):  
Tristan van Leeuwen ◽  
Aleksandr Y. Aravkin ◽  
Felix J. Herrmann
Keyword(s):  
Frequency Domain ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Variable Projection ◽  
Projection Scheme ◽  
Full Waveform

Application of the variable projection scheme for frequency-domain full-waveform inversion

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. R249-R257 ◽  
Author(s):  
Maokun Li ◽  
James Rickett ◽  
Aria Abubakar
Keyword(s):  
Frequency Domain ◽  
Waveform Inversion ◽  
Simulated Data ◽  
Calibration Procedure ◽  
Full Waveform Inversion ◽  
Inversion Algorithm ◽  
Unknown Parameters ◽  
Variable Projection ◽  
Full Waveform ◽  
Data Calibration

We found a data calibration scheme for frequency-domain full-waveform inversion (FWI). The scheme is based on the variable projection technique. With this scheme, the FWI algorithm can incorporate the data calibration procedure into the inversion process without introducing additional unknown parameters. The calibration variable for each frequency is computed using a minimum norm solution between the measured and simulated data. This process is directly included in the data misfit cost function. Therefore, the inversion algorithm becomes source independent. Moreover, because all the data points are considered in the calibration process, this scheme increases the robustness of the algorithm. Numerical tests determined that the FWI algorithm can reconstruct velocity distributions accurately without the source waveform information.

scholarly journals Multi-scale time-frequency domain full waveform inversion with a weighted local correlation-phase misfit function

2019 ◽  
Vol 16 (6) ◽  
pp. 1017-1031 ◽  
Author(s):  
Yong Hu ◽  
Liguo Han ◽  
Rushan Wu ◽  
Yongzhong Xu
Keyword(s):  
Frequency Domain ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Full Waveform Inversion ◽  
Local Correlation ◽  
Time Frequency ◽  
Model Dependence ◽  
Full Waveform ◽  
Frequency Components

Abstract Full Waveform Inversion (FWI) is based on the least squares algorithm to minimize the difference between the synthetic and observed data, which is a promising technique for high-resolution velocity inversion. However, the FWI method is characterized by strong model dependence, because the ultra-low-frequency components in the field seismic data are usually not available. In this work, to reduce the model dependence of the FWI method, we introduce a Weighted Local Correlation-phase based FWI method (WLCFWI), which emphasizes the correlation phase between the synthetic and observed data in the time-frequency domain. The local correlation-phase misfit function combines the advantages of phase and normalized correlation function, and has an enormous potential for reducing the model dependence and improving FWI results. Besides, in the correlation-phase misfit function, the amplitude information is treated as a weighting factor, which emphasizes the phase similarity between synthetic and observed data. Numerical examples and the analysis of the misfit function show that the WLCFWI method has a strong ability to reduce model dependence, even if the seismic data are devoid of low-frequency components and contain strong Gaussian noise.

Acoustic multiscale full waveform inversion of frequency domain based on FCG

2015 ◽  
Author(s):  
Changlu Sun* ◽  
Guangzhi Zhang ◽  
Xinpeng Pan ◽  
Xingyao Yin
Keyword(s):  
Frequency Domain ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform

scholarly journals Velocity model building by 3D frequency-domain, full-waveform inversion of wide-aperture seismic data

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE101-VE117 ◽  
Author(s):  
Hafedh Ben-Hadj-Ali ◽  
Stéphane Operto ◽  
Jean Virieux
Keyword(s):  
High Resolution ◽  
Frequency Domain ◽  
Distributed Memory ◽  
Waveform Inversion ◽  
Steepest Descent Method ◽  
Frequency Domain Method ◽  
Full Waveform Inversion ◽  
Direct Solver ◽  
Velocity Models ◽  
Full Waveform

We assessed 3D frequency-domain (FD) acoustic full-waveform inversion (FWI) data as a tool to develop high-resolution velocity models from low-frequency global-offset data. The inverse problem was posed as a classic least-squares optimization problem solved with a steepest-descent method. Inversion was applied to a few discrete frequencies, allowing management of a limited subset of the 3D data volume. The forward problem was solved with a finite-difference frequency-domain method based on a massively parallel direct solver, allowing efficient multiple-shot simulations. The inversion code was fully parallelized for distributed-memory platforms, taking advantage of a domain decomposition of the modeled wavefields performed by the direct solver. After validation on simple synthetic tests, FWI was applied to two targets (channel and thrust system) of the 3D SEG/EAGE overthrust model, corresponding to 3D domains of [Formula: see text] and [Formula: see text], respectively. The maximum inverted frequencies are 15 and [Formula: see text] for the two applications. A maximum of 30 dual-core biprocessor nodes with [Formula: see text] of shared memory per node were used for the second target. The main structures were imaged successfully at a resolution scale consistent with the inverted frequencies. Our study confirms the feasibility of 3D frequency-domain FWI of global-offset data on large distributed-memory platforms to develop high-resolution velocity models. These high-velocity models may provide accurate macromodels for wave-equation prestack depth migration.

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