A massively parallel frequency‐domain full‐waveform inversion algorithm for imaging acoustic media: Application to a dense OBS data set

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.

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Source‐independent full‐waveform inversion of seismic data

Geophysics ◽

10.1190/1.1635054 ◽

2003 ◽

Vol 68 (6) ◽

pp. 2010-2015 ◽

Cited By ~ 63

Author(s):

Ki Ha Lee ◽

Hee Joon Kim

Keyword(s):

Frequency Domain ◽

Seismic Data ◽

Waveform Inversion ◽

Source Spectrum ◽

Full Waveform Inversion ◽

Source Inversion ◽

Inversion Algorithm ◽

Source Information ◽

Full Waveform ◽

Precise Knowledge

A rigorous full‐waveform inversion of seismic data has been a challenging subject, partly because of the lack of precise knowledge of the source. Since currently available approaches involve some form of approximations to the source, inversion results are subject to the quality and choice of the source information used. We propose a new full‐waveform inversion methodology that does not involve source spectrum information. Thus, potential inversion errors from source estimation can be eliminated. A gather of seismic traces is first Fourier transformed into the frequency domain, and a normalized wavefield is obtained for each trace in the frequency domain. Normalization is done with respect to the frequency response of a reference trace selected from the gather, so the complex‐valued normalized wavefield is dimensionless. The source spectrum is eliminated during the normalization procedure. With its source spectrum eliminated, the normalized wavefield lets us construct an inversion algorithm without the source information. The inversion algorithm minimizes misfits between a measured normalized wavefield and a numerically computed normalized wavefield. The proposed approach has been demonstrated successfully using a simple 2D scalar problem.

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Three-dimensional frequency-domain full-waveform inversion with an iterative solver

Geophysics ◽

10.1190/1.3211198 ◽

2009 ◽

Vol 74 (6) ◽

pp. WCC149-WCC157 ◽

Cited By ~ 122

Author(s):

René-Édouard Plessix

Keyword(s):

Frequency Domain ◽

Waveform Inversion ◽

Three Dimensional ◽

Iterative Solvers ◽

Full Waveform Inversion ◽

Ocean Bottom ◽

Ocean Bottom Seismometer ◽

Iterative Solver ◽

Data Set ◽

Full Waveform

With the acquisition of wide-aperture seismic data sets, full-waveform inversion is an attractive method for deriving velocity models. Three-dimensional implementations require an efficient solver for the wave equation. Computing 3D time-harmonic responses with a frequency-domain solver is complicated because a large linear system with negative and positive eigenvalues must be solved. Time-domain schemes are an alternative. Nevertheless, existing frequency-domain iterative solvers with an efficient preconditioner are a viable option when full-waveform inversion is formulated in the frequency domain. An iterative solver with a multigrid preconditioner is competitive because of a high-order spatial discretization. Numerical examples illustrated the efficiency of the iterative solvers. Three dimensional full-waveform inversion was then studied in the context of deep-water ocean-bottom seismometer acquisition. Three dimensional synthetic data inversion results showed the behavior of full-waveform inversion with respect to the initial model and the minimum frequency available in the data set. Results on a 3D real ocean-bottom seismometer data set demonstrated the relevance of full-waveform inversion, especially to image the shallow part of the model.

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3D frequency domain Full Waveform Inversion via a massively parallel structured multifrontal solver

10.1190/segam2012-0212.1 ◽

2012 ◽

Author(s):

Shen Wang ◽

Maarten V. de Hoop ◽

Jianlin Xia

Keyword(s):

Frequency Domain ◽

Waveform Inversion ◽

Massively Parallel ◽

Full Waveform Inversion ◽

Full Waveform

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Performances of 3D Frequency-Domain Full-Waveform Inversion Based on Frequency-Domain Direct-Solver and Time-Domain Modeling: Application to 3D OBC Data from the Valhall Field

10.2523/16881-ms ◽

2013 ◽

Cited By ~ 1

Author(s):

Romain Brossier ◽

Vincent Etienne ◽

Guanghui Hu ◽

Stephane Operto ◽

Jean Virieux

Keyword(s):

Frequency Domain ◽

Time Domain ◽

Waveform Inversion ◽

Full Waveform Inversion ◽

Domain Modeling ◽

Direct Solver ◽

Full Waveform ◽

Time Domain Modeling

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Application of an Improved Ultrasound Full-Waveform Inversion in Bone Quantitative Measurement

Symmetry ◽

10.3390/sym13020260 ◽

2021 ◽

Vol 13 (2) ◽

pp. 260

Author(s):

Meng Suo ◽

Dong Zhang ◽

Yan Yang

Keyword(s):

Nonlinear Equations ◽

Waveform Inversion ◽

Optimal Solution ◽

Inversion Method ◽

Full Waveform Inversion ◽

Inversion Algorithm ◽

Elastic Wave Equation ◽

Full Waveform ◽

Ultrasonic Propagation ◽

Joint Velocity

Inspired by the large number of applications for symmetric nonlinear equations, an improved full waveform inversion algorithm is proposed in this paper in order to quantitatively measure the bone density and realize the early diagnosis of osteoporosis. The isotropic elastic wave equation is used to simulate ultrasonic propagation between bone and soft tissue, and the Gauss–Newton algorithm based on symmetric nonlinear equations is applied to solve the optimal solution in the inversion. In addition, the authors use several strategies including the frequency-grid multiscale method, the envelope inversion and the new joint velocity–density inversion to improve the result of conventional full-waveform inversion method. The effects of various inversion settings are also tested to find a balanced way of keeping good accuracy and high computational efficiency. Numerical inversion experiments showed that the improved full waveform inversion (FWI) method proposed in this paper shows superior inversion results as it can detect small velocity–density changes in bones, and the relative error of the numerical model is within 10%. This method can also avoid interference from small amounts of noise and satisfy the high precision requirements for quantitative ultrasound measurements of bone.

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

Journal of Geophysics and Engineering ◽

10.1093/jge/gxz062 ◽

2019 ◽

Vol 16 (6) ◽

pp. 1017-1031 ◽

Cited By ~ 5

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.

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A new parameter set for anisotropic multiparameter full-waveform inversion and application to a North Sea data set

Geophysics ◽

10.1190/geo2015-0349.1 ◽

2016 ◽

Vol 81 (4) ◽

pp. U25-U38 ◽

Cited By ~ 32

Author(s):

Nuno V. da Silva ◽

Andrew Ratcliffe ◽

Vetle Vinje ◽

Graham Conroy

Keyword(s):

North Sea ◽

Waveform Inversion ◽

Real Data ◽

Model Parameters ◽

Full Waveform Inversion ◽

Radiation Patterns ◽

Data Set ◽

Full Waveform ◽

Seismic Image ◽

Central North Sea

Parameterization lies at the center of anisotropic full-waveform inversion (FWI) with multiparameter updates. This is because FWI aims to update the long and short wavelengths of the perturbations. Thus, it is important that the parameterization accommodates this. Recently, there has been an intensive effort to determine the optimal parameterization, centering the fundamental discussion mainly on the analysis of radiation patterns for each one of these parameterizations, and aiming to determine which is best suited for multiparameter inversion. We have developed a new parameterization in the scope of FWI, based on the concept of kinematically equivalent media, as originally proposed in other areas of seismic data analysis. Our analysis is also based on radiation patterns, as well as the relation between the perturbation of this set of parameters and perturbation in traveltime. The radiation pattern reveals that this parameterization combines some of the characteristics of parameterizations with one velocity and two Thomsen’s parameters and parameterizations using two velocities and one Thomsen’s parameter. The study of perturbation of traveltime with perturbation of model parameters shows that the new parameterization is less ambiguous when relating these quantities in comparison with other more commonly used parameterizations. We have concluded that our new parameterization is well-suited for inverting diving waves, which are of paramount importance to carry out practical FWI successfully. We have demonstrated that the new parameterization produces good inversion results with synthetic and real data examples. In the latter case of the real data example from the Central North Sea, the inverted models show good agreement with the geologic structures, leading to an improvement of the seismic image and flatness of the common image gathers.

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