Weighted pseudo-Hessian matrix for frequency-domain elastic full waveform inversion

2014 ◽  
Author(s):  
Hyunggu Jun* ◽  
Jangwoo Kim ◽  
Changsoo Shin
Keyword(s):  
Frequency Domain ◽  
Hessian Matrix ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform

Frequency-domain full waveform inversion with plane-wave data

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. R13-R23 ◽  
Author(s):  
Yi Tao ◽  
Mrinal K. Sen
Keyword(s):  
Plane Wave ◽  
Frequency Domain ◽  
Model Updating ◽  
Linear Time ◽  
Hessian Matrix ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Adjoint State ◽  
The Cost

We derived an efficient frequency-domain full waveform inversion (FWI) method using plane-wave encoded shot records. The forward modeling involved application of position dependent linear time shifts at all source locations. This was followed by propagation of wavefields into the medium from all shotpoints simultaneously. The gradient of the cost function needed in the FWI was calculated first by transforming the densely sampled seismic data into the frequency-ray parameter domain and then backpropagating the residual wavefield using an adjoint-state approach. We used a Gauss-Newton framework for model updating. The approximate Hessian matrix was formed with a plane-wave encoding strategy, which required a summation over source and receiver ray parameters of the Green’s functions. Plane-wave encoding considerably reduces the computational burden and crosstalk artifacts are effectively suppressed by stacking over different ray parameters. It also has the advantage of directional illumination of the selected targets. Numerical examples show the accuracy and efficiency of our method.

2D frequency-domain elastic full-waveform inversion using the block-diagonal pseudo-Hessian approximation

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. R247-R259 ◽  
Author(s):  
Yuwei Wang ◽  
Liangguo Dong ◽  
Yuzhu Liu ◽  
Jizhong Yang
Keyword(s):  
Frequency Domain ◽  
Wave Velocity ◽  
Hessian Matrix ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Trade Off ◽  
Full Waveform ◽  
Trade Offs ◽  
Block Diagonal

Elastic full-waveform inversion (EFWI) of multicomponent seismic data is a powerful tool for estimating the subsurface elastic parameters with high accuracy. However, the trade-offs between multiple parameters increase the nonlinearity of EFWI. Although the conventional diagonal-approximate Hessian matrix describes the illumination and limited bandwidth effects, it ignores the trade-off effects and decreases the convergence rate of EFWI. We have developed a block-diagonal pseudo-Hessian operator for 2D frequency-domain EFWI to take into account the approximate trade-offs among the P-wave (compressional-wave) velocity, S-wave (shear-wave) velocity, and density without extra computational costs on forward simulations. The Hessian matrix tends toward a block-diagonal matrix as the frequency grows to infinity; thus, the proposed block-diagonal pseudo-Hessian matrix is more accurate at higher frequencies. The inverse of the block-diagonal pseudo-Hessian matrix is used as a preconditioner for the nonlinear conjugate-gradient method to simultaneously reconstruct P- and S-wave velocities and density. This approach effectively mitigates the crosstalk artifacts by correcting the gradients from the trade-off effects and produces more rapid inversion convergence, which becomes more significant at higher frequencies. Synthetic experiments on an inclusion model and the elastic Marmousi2 model demonstrate its feasibility and validity in EFWI.

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.

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.

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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