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AuthorAlkhalifah, Tariq Ali (11)Schuster, Gerard T. (5)Guo, Bowen (3)Wu, Zedong (3)Zhang, Zhendong (3)View MoreDepartmentEarth Science and Engineering Program (18)Physical Sciences and Engineering (PSE) Division (18)Extreme Computing Research Center (2)Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (1)King Abdullah University of Science and Technology (KAUST).. (1)Journal

GEOPHYSICS (18)

KAUST Grant NumberUAPN#2605-CRG4 (1)PublisherSociety of Exploration Geophysicists (18)SubjectFull-waveform inversion (5)full-waveform inversion (4)crosscorrelation (2)Inversion (2)Least-squares migration (2)View MoreType
Article (18)

Year (Issue Date)
2018 (18)

Item AvailabilityOpen Access (18)

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Full-intensity waveform inversion

Liu, Yike; He, Bin; Lu, Huiyi; Zhang, Zhendong; Xie, Xiao-Bi; Zheng, Yingcai (GEOPHYSICS, Society of Exploration Geophysicists, 2018-10-23) [Article]

Many full-waveform inversion schemes are based on the iterative perturbation theory to fit the observed waveforms. When the observed waveforms lack low frequencies, those schemes may encounter convergence problems due to cycle skipping when the initial velocity model is far from the true model. To mitigate this difficulty, we have developed a new objective function that fits the seismic-waveform intensity, so the dependence of the starting model can be reduced. The waveform intensity is proportional to the square of its amplitude. Forming the intensity using the waveform is a nonlinear operation, which separates the original waveform spectrum into an ultra-low-frequency part and a higher frequency part, even for data that originally do not have low-frequency contents. Therefore, conducting multiscale inversions starting from ultra-low-frequency intensity data can largely avoid the cycle-skipping problem. We formulate the intensity objective function, the minimization process, and the gradient. Using numerical examples, we determine that the proposed method was very promising and could invert for the model using data lacking low-frequency information.

Normalized nonzero-lag crosscorrelation elastic full-waveform inversion

Zhang, Zhendong; Alkhalifah, Tariq Ali; Wu, Zedong; Liu, Yike; He, Bin; Oh, Juwon (GEOPHYSICS, Society of Exploration Geophysicists, 2018-11-23) [Article]

Full-waveform inversion (FWI) is an attractive technique due to its ability to build high-resolution velocity models. Conventional amplitude-matching FWI approaches remain challenging because the simplified computational physics used does not fully represent all wave phenomena in the earth. Because the earth is attenuating, a sample-by-sample fitting of the amplitude may not be feasible in practice. We have developed a normalized nonzero-lag crosscorrelataion-based elastic FWI algorithm to maximize the similarity of the calculated and observed data. We use the first-order elastic-wave equation to simulate the propagation of seismic waves in the earth. Our proposed objective function emphasizes the matching of the phases of the events in the calculated and observed data, and thus, it is more immune to inaccuracies in the initial model and the difference between the true and modeled physics. The normalization term can compensate the energy loss in the far offsets because of geometric spreading and avoid a bias in estimation toward extreme values in the observed data. We develop a polynomial-type weighting function and evaluate an approach to determine the optimal time lag. We use a synthetic elastic Marmousi model and the BigSky field data set to verify the effectiveness of the proposed method. To suppress the short-wavelength artifacts in the estimated S-wave velocity and noise in the field data, we apply a Laplacian regularization and a total variation constraint on the synthetic and field data examples, respectively.

Interferometric full-waveform inversion

Sinha, Mrinal; Schuster, Gerard T. (GEOPHYSICS, Society of Exploration Geophysicists, 2018-12-04) [Article]

Velocity errors in the shallow part of the velocity model can lead to erroneous estimates of the full-waveform inversion (FWI) tomogram. If the location and topography of a reflector are known, then such a reflector can be used as a reference reflector to update the underlying velocity model. Reflections corresponding to this reference reflector are windowed in the data space. Windowed reference reflections are then crosscorrelated with reflections from deeper interfaces, which leads to partial cancellation of static errors caused by the overburden above the reference interface. Interferometric FWI (IFWI) is then used to invert the tomogram in the target region, by minimizing the normalized waveform misfit between the observed and predicted crosscorrelograms. Results with synthetic and field data with static errors above the reference interface indicate that an accurate tomogram can be inverted in areas lying within several wavelengths of the reference interface. IFWI can also be applied to synthetic time-lapse data to mitigate the nonrepeatability errors caused by time-varying overburden variations. The synthetic- and field-data examples demonstrate that IFWI can provide accurate tomograms when the near surface is ridden with velocity errors.

Frequency domain multi-parameter acoustic inversion for transversely isotropic media with a vertical axis of symmetry

Djebbi, Ramzi; Alkhalifah, Tariq Ali (GEOPHYSICS, Society of Exploration Geophysicists, 2018-12-04) [Article]

Multi-parameter full waveform inversion (FWI) for transversely isotropic (TI) media with a vertical axis of symmetry (VTI) suffers from the trade-off between the parameters. The trade-off results in the leakage of one parameter’s update into the other. It affects the accuracy and convergence of the inversion. The sensitivity analyses suggested a parameterization using the horizontal velocity vh, Thomsen’s parameter ϵ and the an-elliptic parameter η to reduce the trade-off for surface recorded seismic data. We aim to invert for this parameterization using the scattering integral (SI) method. The available Born sensitivity kernels, within this approach, can be used to calculate additional inversion information. We mainly compute the diagonal of the approximate Hessian, used as a conjugate-gradient preconditioner, and the gradients step lengths. We consider modeling in the frequency domain. The large computational cost of the scattering integral method can be avoided with direct Helmholtz equation solvers.We apply the proposed method to the VTI Marmousi II model for various inversion strategies. We show that we can invert the vh accurately. For the ϵ parameter, only the short wavelengths are well recovered. On the other hand, the η parameter impact is weak on the inversion results and can be fixed. However, a good background η, with accurate long wavelengths, is needed to correctly invert for vh.Furthermore, we invert a real data set acquired by CGG from offshore Australia. We invert simultaneously all three parameters using the proposed inversion approach. The velocity model is improved and additional layers are recovered. We confirm the accuracy of the results by comparing them with well-log information, as well as, looking at the data and angle gathers.

Wave-equation Traveltime Inversion with Multi-Frequency Bands: Synthetic and Land Data Examples

Yu, Han; Hanafy, Sherif M.; Schuster, Gerard T. (GEOPHYSICS, Society of Exploration Geophysicists, 2018-10-11) [Article]

A wave-equation traveltime inversion method with multifrequency bands is proposed to invert for the shallow or intermediate subsurface velocity distribution. Similar to the classical wave equation traveltime inversion, this method searches for the velocity model that minimizes the squared sum of the traveltime residuals using source wavelets with progressively higher peak frequencies. Wave-equation traveltime inversion can partially avoid the cycle skipping problem by recovering the low-wavenumber parts of the velocitymodel. However, we also utilize the frequency information hidden in the traveltimes for obtaining a more highly resolved tomogram. Therefore, we employ different frequency bands when calculating the Fréchet derivatives so that tomograms with better resolution can be reconstructed. Results are validated by the zero offset gathers from the raw data associated with moderate geometrical irregularities. The improved wave-equation traveltime method is robust and merely needs a rough estimate of the startingmodel. Numerical tests on both the synthetic and field data sets validate the above claims.

One-step data-domain least-squares reverse time migration

Liu, Qiancheng; Peter, Daniel (GEOPHYSICS, Society of Exploration Geophysicists, 2018-07-02) [Article]

Least-squares reverse time migration (LSRTM) is an iterative inversion algorithm for estimating the broadband-wavenumber reflectivity model. Although it produces superior results compared with conventional reverse time migration (RTM), LSRTM is computationally expensive. We have developed a one-step LSRTM method by considering the demigrated and observed data to design a deblurring preconditioner in the data domain using the Wiener filter. For the Wiener filtering, we further use a stabilized division algorithm via the Taylor expansion. The preconditioned observed data are then remigrated to obtain a deblurred image. The total cost of this method is about two RTMs. Through synthetic and real data experiments, we see that one-step LSRTM is able to enhance image resolution and balance source illumination at low computational costs.

Full model wavenumber inversion: Identifying sources of information for the elusive middle model wavenumbers

Alkhalifah, Tariq Ali; Sun, Bing Bing; Wu, Zedong (GEOPHYSICS, Society of Exploration Geophysicists, 2018-10) [Article]

We recognized over the years that our conventional surface seismic recording can effectively identify two main features of the earth: its seismic propagation attributes and those attributes resulting in echoes or reflections. Thus, the resulting expression of the earth is dominated by the generally smooth (long-wavelength) features that control wave propagation, which we use to invert for the short-wavelength features causing reflections in a process we refer to as migration velocity analysis and imaging, respectively. The features of the earth that fall in between these two model scales - the middle wavenumbers - have been elusive, which is a dilemma for full-waveform inversion because we need to build the full velocity model (a broad band of model wavenumbers). We analyze the middle model wavenumber gap, but we focus more here on potential sources of information for such middle model wavenumbers. Such sources include regularization, objective function enhancements, and multiscattered energy. Regularization, provided by a total variation (TV) constraint admits middle and high model wavenumber components into the model to enforce the model's compliance with such a constraint. As opposed to minimizing the TV, such a constraint merely reduces the model space, and thus, these injected middle model wavenumbers are as good as the projected data information to the reduced model space. Such data information includes large offsets, but also multiscattered energy, in which the energy through wavepath and scattering updates can admit more of the elusive middle-wavenumber information that comes from the data. The combination of the right level of allowable model variations with the added data information from large offsets and multiscattering can help in filling the elusive middle model wavenumber gap and admit plausible models.

A hybrid finite-difference/lowrank solution to anisotropy acoustic wave equations

Zhang, Zhendong; Alkhalifah, Tariq Ali; Wu, Zedong (GEOPHYSICS, Society of Exploration Geophysicists, 2018-12-05) [Article]

P-wave extrapolation in anisotropic media suffers from SVwave artifacts and computational dependency on the complexity of anisotropy. The anisotropic pseudodifferential wave equation cannot be solved using an efficient time-domain finite-difference (FD) scheme directly. The wavenumber domain allows us to handle pseudodifferential operators accurately; however, it requires either smoothly varying media or more computational resources. In the limit of elliptical anisotropy, the pseudodifferential operator reduces to a conventional operator. Therefore, we have developed a hybrid-domain solution that includes a spacedomain FD solver for the elliptical anisotropic part of the anisotropic operator and a wavenumber-domain low-rank scheme to solve the pseudodifferential part. Thus, we split the original pseudodifferential operator into a second-order differentiable background and a pseudodifferential correction term. The background equation is solved using the efficient FD scheme, and the correction term is approximated by the low-rank approximation. As a result, the correction wavefield is independent of the velocity model, and, thus, it has a reduced rank compared with the full operator. The total computation cost of our method includes the cost of solving a spatial FD time-step update plus several fast Fourier transforms related to the rank. The accuracy of our method is of the order of the FD scheme. Applications to a simple homogeneous tilted transverse isotropic (TTI) medium and modified BP TTI models demonstrate the effectiveness of the approach.

Optimal full-waveform inversion strategy for marine data in azimuthally rotated elastic orthorhombic media

Oh, Juwon; Alkhalifah, Tariq Ali (GEOPHYSICS, Society of Exploration Geophysicists, 2018-06-08) [Article]

The orthorhombic (ORT) anisotropic description of earth layers can allow the capture of much of the earth's anisotropic complexity. The inversion for high-resolution azimuthal variation of anisotropy is important for reservoir characterization, among other applications. A high-resolution description of the azimuth of fractures can help us to predict flow preferences. To verify the feasibility of multiparameter full-waveform inversion (FWI) for marine data assuming azimuthally rotated elastic ORT media, we have analyzed the radiation patterns and gradient directions of ORT parameters to the reflection data. First, we express the gradient direction of the ORT parameters considering the azimuthal rotation of the symmetric planes. Then, to support our observations in the gradient direction, the radiation patterns of the partial derivative wavefields from each parameter perturbation are also derived under the rotated elastic ORT assumption. To find an optimal parameterization, we compare three different parameterizations: monoclinic, velocity-based, and hierarchical parameterizations. Then, we suggest an optimal multistage update strategy by analyzing the behavior of the rotation angle as a FWI target. To analyze the trade-off among parameters in different parameterizations, we calculate the gradient direction from a hockey-puck model, in which each parameter is perturbed at the different location on a horizontal layer. The trade-off analysis supports that the hierarchical parameterization provides us with more opportunities to build up subsurface models with less trade-off between parameters and less influence of the azimuthal rotation of ORT anisotropy. The feasibility of the proposed FWI strategy is examined using synthetic marine streamer data from a simple 3D reservoir model with a fractured layer.

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

Masmoudi, Nabil; Alkhalifah, Tariq Ali (GEOPHYSICS, Society of Exploration Geophysicists, 2018-07-18) [Article]

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.

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