scholarly journals Hybrid frequency-domain full-waveform inversion using ray+Born sensitivity kernels

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. R339-R347
Author(s):  
Ramzi Djebbi ◽  
Tariq Alkhalifah
Keyword(s):  
Frequency Domain ◽  
Ray Tracing ◽  
Waveform Inversion ◽  
Hybrid Approach ◽  
Computational Cost ◽  
Equation Modeling ◽  
Inversion Method ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Full Waveform

Full-waveform inversion (FWI) using the scattering integral (SI) approach is an explicit formulation of the inversion optimization problem. The inversion procedure is straightforward, and the dependence of the data residuals on the model parameters is clear. However, the biggest limitation associated with this approach is the huge computational cost in conventional exploration seismology applications. Modeling from each of the source and receiver locations is required to compute the update at every iteration, and that is prohibitively expensive, especially for 3D problems. To deal with this issue, we have developed a hybrid implementation of frequency-domain FWI, in which forward modeling is combined with ray tracing to compute the update. We use the sensitivity kernels computed from dynamic ray tracing to build the gradient. The data residual is still computed using finite-difference wavefield modeling. With ray theory, the Green’s function can be approximated using a coarser grid compared to wave-equation modeling. Therefore, the memory requirements, as well as the computational cost, are reduced significantly. Considering that in transmission FWI long-to-intermediate wavelengths are updated during the early iterations, we obtain accurate inverted models. The inversion scheme captured the anomaly embedded in the homogeneous background medium. For more complex models, the hybrid inversion method helps in improving the initial model with little cost compared with conventional SI inversion approaches. The accuracy of the inversion results shows the effectiveness of the hybrid approach for 3D realistic problems.

Extending the useful angle range for elastic inversion through the amplitude-versus-angle full-waveform inversion method

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. R213-R226 ◽  
Author(s):  
Sérgio A. M. Oliveira ◽  
Igor L. S. Braga ◽  
Murillo B. Lacerda ◽  
Geovane F. Ouverney ◽  
Anderson W. P. de Franco
Keyword(s):  
Incidence Angle ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Reliable Estimate ◽  
Inversion Method ◽  
Full Waveform Inversion ◽  
Angle Of Incidence ◽  
Data Set ◽  
Full Waveform ◽  
Amplitude Versus

We have developed the amplitude versus angle full-waveform inversion (AVA-FWI) method. This method considers the complete seismic response of the layered medium, and so it is capable of correctly handling seismic amplitudes from prestack data with a wide angle range. This capability is very important because a reliable estimate of the elastic parameters and the density requires an incidence angle that goes beyond 30°. Our method inputs seismic traces from prestack time-migrated gathers ordered by angle of incidence and works under the local 1D assumption. AVA-FWI is a nonlinear inversion based on forward modeling by the reflectivity method, which substantially increases its computational cost with respect to conventional AVA inversion. To address this problem, we developed an efficient routine for angle gather modeling and a new method for differential seismogram generation that greatly reduces the amount of computation involved in this task. The AVA-FWI method was applied to synthetic data and to a geophysical reservoir characterization case study using the North Viking Graben open data set.

scholarly journals Frequency Domain Full Waveform Inversion Method of Acquiring Rock Wave Velocity in Front of Tunnels

2021 ◽  
Vol 11 (14) ◽  
pp. 6330
Author(s):  
Kai Wang ◽  
Meiyan Guo ◽  
Qingxia Xiao ◽  
Chuanyi Ma ◽  
Lingli Zhang ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Wave Velocity ◽  
Waveform Inversion ◽  
Inversion Method ◽  
Full Waveform Inversion ◽  
Tunnel Face ◽  
Detection Range ◽  
Seismic Prospecting ◽  
Full Waveform ◽  
Geological Conditions

Ahead geological prospecting, which can estimate adverse geology ahead of the tunnel face, is necessary in the process of tunnel construction. Due to its long detection range and good recognition effect on the interface, the seismic method is widely used in tunnel ahead prospecting. However, the observation space in tunnels is quite narrow compared to ground seismic prospecting, which leads to some problems in the acquisition of wave velocity, including: the velocity of the direct wave is used to replace the wave velocity of the forward rock approximately; the arrival time information of seismic waves is the main factor in time-travel inversion or the tomography method, which is sufficient to provide a simple model rather than deal with complex geological conditions. In view of the above problems, the frequency domain full waveform inversion method in ground prospecting is introduced to tunnel seismic prospecting. In addition, the optimized difference format is given according to the particularity of the tunnel environment. In this method, the kinematics and dynamics of the seismic wavefield are fully used to obtain more accurate wave velocity results. Simultaneously, forward modeling and inversion simulations on tunnel samples with typical adverse geological bodies are given here, which verified the validity and reliability of the proposed method.

An efficient frequency-domain full waveform inversion method using simultaneous encoded sources

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. R109-R124 ◽  
Author(s):  
Hafedh Ben-Hadj-Ali ◽  
Stéphane Operto ◽  
Jean Virieux
Keyword(s):  
Frequency Domain ◽  
Case Studies ◽  
Waveform Inversion ◽  
Random Phase ◽  
Inversion Method ◽  
Multiscale Approach ◽  
Full Waveform Inversion ◽  
Computational Domain ◽  
Multiple Sources ◽  
Full Waveform

Three-dimensional full waveform inversion (FWI) still suffers from prohibitively high computational costs that arise because of the seismic modeling for multiple sources that is performed at each nonlinear iteration of FWI. Building supershots by assembling several sources allows mitigation of the number of simulations per FWI iteration, although it adds crosstalk artifacts because of interference between the individual sources of the supershots. These artifacts themselves can be reduced by encoding each individual source with a random phase shift during assembling of the sources. The source encoding method is applied to an efficient frequency-domain FWI, in which a limited number of discrete frequencies or coarsely sampled frequency groups are inverted successively following a multiscale approach. Random codes can be regenerated at each FWI iteration or for each frequency of a group during each FWI iteration, to favor the destructive summation of crosstalk artifacts over FWI iterations. Either a limited number of sources (partial assembling) or the total number of sources (full assembling) can be combined into supershots. Wide-aperture acquisition geometries such as land or marine node acquisitions are considered, to allow one to stack a large number of shots in the full computational domain and to test different partial assembling strategies involving sources that are close to or distant from each other. Two-dimensional case studies show that partial-source assembling of distant shots has a limited sensitivity to noise, for a computational saving that is roughly proportional to the number of shots assembled into the supershots. On the other hand, full assembling is more sensitive to noise, and it requires successive inversions of finely sampled frequency groups with a large number of FWI iterations. In contrast, refining the shot interval to improve the fold degrades the models when full assembling is applied to noisy data. Preliminary 3D application of the method leads to the same conclusions that 2D case studies do, with regard to the footprint of crosstalk noise in the imaging.

Full-waveform inversion for signal enhancement of weak amplitude phases using beamforming and adjoint methods

2020 ◽  
Author(s):  
Maria Koroni ◽  
Andreas Fichtner
Keyword(s):  
Epicentral Distance ◽  
Average Distance ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Signal Enhancement ◽  
Time Shift ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Phase Alignment

<p>In this study, we develop a new adjoint- and full-waveform inversion approach for low-amplitude seismic phases that are typically below noise in individual recordings. The methodology aims at enhancing weak signals from body wave phases, which can be used in full-waveform inversion for inferring structural and boundary parameters in the earth. The new approach is based on the formulation of misfit functionals and corresponding adjoint sources for stacks of suitably time-shifted recordings. </p><p>To tackle this problem, we compute synthetic waveforms using spectral-elements for models with and without topographic variations along mantle discontinuities. We focus on global underside reflections which are reportedly almost always undetectable in real seismograms due to their low amplitudes and are considerably affected by topography. We enforce phase alignment on a chosen reference seismogram recorded at an average distance among the selected stations. A time shift towards the reference is applied to all seismograms according to their epicentral distance calculated by 1-D ray tracing. A set of time shifts is calculated by cross-correlation in time windows around predicted traveltimes of the desired phase. Using this set of time shifts, we sum the waveforms creating the main stack for each model.</p><p>We use the two linear stacks as <em>observed</em> and <em>synthetic</em> (with and without topography, respectively) and develop a least-squares misfit measurement which gives rise to an adjoint source determined by the time shift between stacks. The expectation is that computing the traveltime Fréchet kernel with respect to volumetric and boundary model parameters will show the exact sensitivity of the enhanced signal and save time from computing each station kernel separately. Upon achieving signal enhancement of the desired phases, we can ensure that these can be used for better informing updates of the initial model given the higher quality measurement of the observable.</p><p>This method once fully developed will allow us to leverage information of many recordings by reducing incoherent signal and enhancing weak seismic phases. The computation of sensitivity kernels in our study has a twofold importance. Firstly, it helps us realise whether the stacking technique indeed enhances the desired signal and whether it is ideal for precursor waves. Secondly, the exact sensitivity kernels show us the way of incorporating finite-frequency effects of weak but informative phases and introducing non-linear inversion for improving imaging while reducing some computational cost. </p><p> </p>

A Bayesian approach to estimate uncertainty for full-waveform inversion using a priori information from depth migration

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. R307-R323 ◽  
Author(s):  
Hejun Zhu ◽  
Siwei Li ◽  
Sergey Fomel ◽  
Georg Stadler ◽  
Omar Ghattas
Keyword(s):  
Waveform Inversion ◽  
Computational Cost ◽  
Covariance Operator ◽  
Maximum A Posteriori ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Posterior Distributions ◽  
A Posteriori ◽  
Model Uncertainties ◽  
Full Waveform

Full-waveform inversion (FWI) enables us to obtain high-resolution subsurface images; however, estimating model uncertainties associated with this technique is still a challenging problem. We have used a Bayesian inference framework to estimate model uncertainties associated with FWI. The uncertainties were assessed based on an a posteriori covariance operator, evaluated at the maximum a posteriori model. For the prior distribution, we have used a spatially nonstationary covariance operator based on a plane-wave construction with local dips measured from migrated images. Preconditioned frequency-domain FWI was used to estimate the maximum a posteriori model. Efficient manipulation of the posterior covariance was based on a low-rank approximation of the data misfit Hessian preconditioned by the prior covariance operator. The strong decay of the singular values indicated that data were mostly informative about a low-dimensional subspace of model parameters. To reduce computational cost of the randomized singular value decomposition, we have used a Hessian approximation based on point-spread functions. The 2D numerical examples with synthetic data confirmed that the method can effectively estimate uncertainties for FWI. Visual comparisons of random samples drawn from the prior and posterior distributions have allowed us to evaluate model uncertainties. Furthermore, we found out how statistical quantities, such as means and pointwise standard deviation fields, can be efficiently extracted from the prior and posterior distributions. These fields helped us to objectively assess subsurface images provided by FWI.

A numerical study of 3D frequency-domain elastic full-waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. R99-R108 ◽  
Author(s):  
Guangdong Pan ◽  
Lin Liang ◽  
Tarek M. Habashy
Keyword(s):  
Frequency Domain ◽  
Message Passing ◽  
Message Passing Interface ◽  
Numerical Study ◽  
Waveform Inversion ◽  
Seismic Profile ◽  
Total Variation Regularization ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Full Waveform

We have developed a 3D elastic full-waveform inversion (FWI) algorithm with forward modeling and inversion performed in the frequency domain. The Helmholtz equation is solved with a second-order finite-difference method using an iterative solver equipped with an efficient complex-shifted incomplete LU-based preconditioner. The inversion is based on the minimization of the data misfit functional and a total variation regularization for the unknown model parameters. We implement the Gauss-Newton method as the optimization engine for the inversions. The codes are parallelized with a message passing interface based on the number of shots and receivers. We examine the performance of this elastic FWI algorithm and workflow on synthetic examples including surface seismic and vertical seismic profile configurations. With various initial models, we manage to obtain high-quality velocity images for 3D earth models.

scholarly journals Full-waveform inversion in acoustic orthorhombic media and application to a North Sea data set

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. C179-C193 ◽  
Author(s):  
Nabil Masmoudi ◽  
Tariq Alkhalifah
Keyword(s):  
North Sea ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Model Inversion ◽  
Multistage Model ◽  
Full Waveform ◽  
Trade Offs

Full-waveform inversion (FWI) in anisotropic media is challenging, mainly because of the large computational cost, especially in 3D, and the potential trade-offs between the model parameters needed to describe such media. By analyzing the trade-offs and understanding the resolution limits of the inversion, we can constrain FWI to focus on the main parameters the data are sensitive to and push the inversion toward more reliable models of the subsurface. Orthorhombic anisotropy is one of the most practical approximations of the earth subsurface that takes into account the natural horizontal layering and the vertical fracture network. We investigate the feasibility of a multiparameter FWI for an acoustic orthorhombic model described by six parameters. We rely on a suitable parameterization based on the horizontal velocity and five dimensionless anisotropy parameters. This particular parameterization allows a multistage model inversion strategy in which the isotropic, then, the vertical transverse isotropic, and finally the orthorhombic model can be successively updated. We applied our acoustic orthorhombic inversion on the SEG-EAGE overthrust synthetic model. The observed data used in the inversion are obtained from an elastic variable density version of the model. The quality of the inverted model suggests that we may recover only four parameters, with different resolution scales depending on the scattering potential of these parameters. Therefore, these results give useful insights on the expected resolution of the inverted parameters and the potential constraints that could be applied to an orthorhombic model inversion. We determine the efficiency of the inversion approach on real data from the North Sea. The inverted model is in agreement with the geologic structures and well-log information.

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

Symmetry ◽  
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.

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.

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