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AuthorAlkhalifah, Tariq Ali (4)Schuster, Gerard T. (3)Li, Jing (2)Liu, Zhaolun (2)chen, fuqiang (1)View MoreDepartmentEarth Science and Engineering Program (9)Physical Sciences and Engineering (PSE) Division (9)Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (1)Extreme Computing Research Center (1)JournalSEG Technical Program Expanded Abstracts 2018 (8)GEOPHYSICS (1)PublisherSociety of Exploration Geophysicists (9)Subject

inversion (9)

full-waveform inversion (4)dispersion (3)near surface (2)surface wave (2)View MoreTypeConference Paper (8)Article (1)Year (Issue Date)
2018 (9)

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Open Access (9)

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A misfit function based on entropy regularized optimal transport for full-waveform inversion

chen, fuqiang; Peter, Daniel (SEG Technical Program Expanded Abstracts 2018, Society of Exploration Geophysicists, 2018-08-27) [Conference Paper]

Given two probability distributions, the classical theorem of optimal transport aims to determine a transport plan which can map one distribution to the other such that the transport cost is minimized. The general functions such as seismic traces do not satisfy all properties of probability distribution. Therefore, we normalize the seismic traces by an exponential function prior to applying the optimal transport to define the distance between seismic traces. In this abstract, we report some results of full waveform inversion from an alternative misfit function based on entropy regularized optimal transport. The regularization gives a smooth approximation to the original optimal transport and the regularized optimum can be found efficiently though. Numerical examples demonstrate the proposed misfit function can invert the data with super lower frequency unavailable from a rough initial model.

Image-guided wavefield tomography for VTI media

Li, Vladimir; Guitton, Antoine; Tsvankin, Ilya; Alkhalifah, Tariq Ali (SEG Technical Program Expanded Abstracts 2018, Society of Exploration Geophysicists, 2018-08-27) [Conference Paper]

Transversely isotropic (TI) models have become essential in generating accurate depth images from seismic data. Here, we develop image-domain tomography (IDT) for building acoustic VTI (TI with a vertical symmetry axis) models from P-wave reflection data. Based on a separable dispersion relation, the modeling operator extrapolates only P-wavefields without the shear-wave artifacts. The inversion algorithm includes least-squares reverse-time migration (LSRTM), which improves the quality of the extended images and accuracy of parameter estimation. Whereas the zero-dip NMO velocity (V) and anellipticity parameter η are updated by focusing energy in space-lag LSRTM gathers, the Thomsen parameter δ is constrained by image-guided interpolation between two or more boreholes. We also apply image-guided smoothing to the IDT gradients of V and η to steer the inversion towards geologically plausible models. To mitigate the trade-off between V and η, we adopt a multistage approach that gradually relaxes the constraints on the spatial η-variation. The robustness of the algorithm is demonstrated on the elastic VTI Marmousi-II model. We also present preliminary inversion results for a line from a 3D data set acquired in the Gulf of Mexico.

Multiscale and layer-stripping wave-equation dispersion inversion of Rayleigh waves

Liu, Zhaolun; Huang, Lianjie (SEG Technical Program Expanded Abstracts 2018, Society of Exploration Geophysicists, 2018-08-27) [Conference Paper]

Rayleigh-wave inversion could converge to a local minimum of its objective function for a complex subsurface model. We develop a multiscale strategy and a layer-stripping method to alleviate the local minimum problem of wave-equation dispersion inversion of Rayleigh waves, and improve the inversion robustness. We first invert the high-frequency and near-offset data for the shallow S-velocity model, and gradually incorporate the lower-frequency components of data with longer offsets to reconstruct the deeper regions of the model. We demonstrate the efficacy of this multiscale and layer-stripping method using synthetic and field Rayleigh-wave data.

Dispersion inversion of guided P-waves in a waveguide of arbitrary geometry

Li, Jing; Hanafy, Sherif; Schuster, Gerard T. (SEG Technical Program Expanded Abstracts 2018, Society of Exploration Geophysicists, 2018-08-27) [Conference Paper]

We present the theory for wave equation inversion of dispersion curves obtained from traces containing guided P waves. The misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves, and the inverted result is a high-resolution estimate of the near-surface P-velocity model. This procedure, denoted as the wave equation dispersion inversion of guided P waves (WDG), is valid for near-surface waveguides with irregular layers. It is less prone to the cycle skipping problems of full waveform inversion (FWI) and can sometimes provide velocity models with higher resolution than wave-equation traveltime tomography (WT). The synthetic and field data examples demonstrate that WDG for guided P waves can accurately reconstruct the P-wave velocity distribution in laterally heterogeneous media.

3D wave-equation dispersion inversion of surface waves

Liu, Zhaolun; Li, Jing; Hanafy, Sherif M.; Schuster, Gerard T. (SEG Technical Program Expanded Abstracts 2018, Society of Exploration Geophysicists, 2018-08-27) [Conference Paper]

The 2D wave-equation dispersion inversion (WD) methodology is extended to the inversion of three-dimensional data for a 3D shear-wave velocity model. The objective function of 3D WD is the sum of the squared wavenumber differences along each azimuth angle between the predicted and observed 3D dispersion curves. The 3D dispersion curves are obtained by wavenumber-frequency analysis of the fundamental Rayleigh waves in each 3D shot gather. The S-wave velocity update is computed by a weighted zero-lag crosscorrelation between the source wavefield and the back-projected receiver-side wavefield for each azimuth angle. The synthetic and field data examples demonstrate that the 3D WD method can accurately estimate the 3D S-wave velocity model in laterally heterogeneous media.

Multiscale full-waveform inversion using flux-corrected transport

Kalita, Mahesh; Alkhalifah, Tariq Ali (SEG Technical Program Expanded Abstracts 2018, Society of Exploration Geophysicists, 2018-08-27) [Conference Paper]

Full-waveform inversion (FWI) iteratively recovers the unknown model parameters from seismic data. In practice, a successful FWI implementation often follows a multistage recovery approach: starting from the retrieval of the lower model wavenumbers (tomography) followed by the higher resolution ones (imaging). On that account, we propose a new method based on the flux-corrected transport (FCT) technique, used often in computational fluid dynamics owing to the removal of instabilities in a shock profile. FCT involves three finite-difference steps: a transport, a diffusion, and followed by an anti-diffusion. The third step, however, involves nonlinear operators such as maximum and minimum, which are non-differentiable in a classic sense. However, since the seismic source wavelet and the corresponding wavefield are relatively smooth and continuous in nature, and does not yield any strong ripples like shock waves, we unsubscribe to the non-linear step from FCT, which allows us to evaluate the FWI gradient. As a result, it accentuates no trouble in achieving a converging FWI model by gradually reducing the diffusive flux-correction amount. Those features are demonstrated on a dataset from the Marmousi II model with no frequency content less that 5 Hz. We initiate the inversion process for the remaining full-bandwidth of the dataset with a linear v(z) model. In addition, we show the versatility of the FCT based FWI on a marine field dataset from offshore Australia.

Image-domain Q inversion

Chen, Yuqing; Dutta, Gaurav; Schuster, Gerard T. (SEG Technical Program Expanded Abstracts 2018, Society of Exploration Geophysicists, 2018-08-27) [Conference Paper]

Seismic waves traveling in the earth experience amplitude loss and velocity dispersion associated with strong subsurface attenuation. To compensate for these effects, the Q model should be first estimated and the data can be corrected. However, Q estimation from the data can be challenging if the data have a poor signal-to-noise ratio. To mitigate this problem, we develop a wave-equation Q inversion method in the image domain. This method seeks a Q model which minimizes the local wavenumber differences between a reference image without Q effects, and a Q migration image computed with the current Q model. Numerical tests on synthetic data demonstrate that the Q model inverted by this image-domain Q inversion method can lead to a noticeable improvement in the migration image quality.

The application of an optimal transport to a preconditioned data matching function for robust waveform inversion

Sun, Bingbing; Alkhalifah, Tariq Ali (SEG Technical Program Expanded Abstracts 2018, Society of Exploration Geophysicists, 2018-08-27) [Conference Paper]

Full Waveform Inversion updates the subsurface model iteratively by minimizing a misfit function, which measures the difference between observed and predicted data. The conventional l norm misfit function is widely used as it provides a simple, sample by sample, high resolution misfit function. However it is susceptible to local minima if the low wavenum-ber components of the initial model are not accurate. A deconvolution of the predicted and observed data offers an extend space comparison, which is more global. The matching filter calculated from the deconvolution has energy focussed at zero lag, like a Dirac Delta function, when the predicted data matches the observed ones. We use the Wasserstein distance to measure the difference between the matching filter and a Dirac Delta function. Unlike data, the matching filter can be easily transformed to a distribution satisfying the requirement of optimal transport theory. Compared with the conventional normalized penalty applied to non-zero lag energy in the matching filter, the new misfit function is a metric and has solid mathematical foundation based on optimal transport theory. Both synthetic and real data examples verified the effectiveness of the proposed misfit function.

Selective data extension for full-waveform inversion: An efficient solution for cycle skipping

Wu, Zedong; Alkhalifah, Tariq Ali (GEOPHYSICS, Society of Exploration Geophysicists, 2018-02-23) [Article]

Standard full-waveform inversion (FWI) attempts to minimize the difference between observed and modeled data. However, this difference is obviously sensitive to the amplitude of observed data, which leads to difficulties because we often do not process data in absolute units and because we usually do not consider density variations, elastic effects, or more complicated physical phenomena. Global correlation methods can remove the amplitude influence for each trace and thus can mitigate such difficulties in some sense. However, this approach still suffers from the well-known cycle-skipping problem, leading to a flat objective function when observed and modeled data are not correlated well enough. We optimize based on maximizing not only the zero-lag global correlation but also time or space lags of the modeled data to circumvent the half-cycle limit. We use a weighting function that is maximum value at zero lag and decays away from zero lag to balance the role of the lags. The resulting objective function is less sensitive to the choice of the maximum lag allowed and has a wider region of convergence compared with standard FWI. Furthermore, we develop a selective function, which passes to the gradient calculation only positive correlations, to mitigate cycle skipping. Finally, the resulting algorithm has better convergence behavior than conventional methods. Application to the Marmousi model indicates that this method converges starting with a linearly increasing velocity model, even with data free of frequencies less than 3.5 Hz. Application to the SEG2014 data set demonstrates the potential of our method.

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