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Alkhalifah, Tariq Ali (11)

Choi, Yun Seok (3)Waheed, Umair bin (3)Aldawood, Ali (1)Djebbi, Ramzi (1)View MoreDepartmentEarth Science and Engineering Program (11)Physical Sciences and Engineering (PSE) Division (11)Environmental Science and Engineering Program (9)KAUST Solar Center (KSC) (3)Earth Fluid Modeling and Prediction Group (1)Journal
London 2013, 75th eage conference en exhibition incorporating SPE Europec (11)

PublisherEAGE Publications (11)Subjectanisotropic eikonal equation (1)anisotropy (1)parameter estimations (1)traveltimes (1)View MoreType
Conference Paper (11)

Year (Issue Date)2013 (11)Item AvailabilityMetadata Only (9)Open Access (2)

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Wave equation tomography using the unwrapped phase - Analysis of the traveltime sensitivity kernels

Djebbi, Ramzi; Alkhalifah, Tariq Ali (London 2013, 75th eage conference en exhibition incorporating SPE Europec, EAGE Publications, 2013) [Conference Paper]

Full waveform inversion suffers from the high non-linearity in the misfit function, which causes the convergence to a local minimum. In the other hand, traveltime tomography has a quasi-linear misfit function but yields low- resolution models. Wave equation tomography (WET) tries to improve on traveltime tomography, by better adhering to the requirements of our finite-frequency data. However, conventional (WET), based on the crosscorelaion lag, yields the popular hallow banana sensitivity kernel indicating that the measured wavefield at a point is insensitive to perturbations along the ray theoretical path at certain finite frequencies. Using the instantaneous traveltime, the sensitivity kernel reflects more the model-data dependency we grown accustom to in seismic inversion (even phase inversion). Demonstrations on synthetic and the Mamousi model support such assertions.

Refraction traveltime tomography with irregular topography using the unwrapped phase inversion

Choi, Yun Seok; Alkhalifah, Tariq Ali (London 2013, 75th eage conference en exhibition incorporating SPE Europec, EAGE Publications, 2013) [Conference Paper]

Traveltime tomography has long served as a stable and efficient tool for velocity estimation, especially for the near surface. It, however, suffers from some of limitations associated with ray tracing and high-frequency traveltime in velocity inversion zones and ray shadow regions. We develop a tomographic approach based on traveltime solutions obtained by tracking the phase (instantaneous traveltime) of the wavefield solution of the Helmholtz wave equation. Since the instantaneous-traveltime does not suffer from phase wrapping, the inversion algorithm using the instantaneous-traveltime has the potential to generate robust inversion results. With a high damping factor, the instantaneous-traveltime inversion provides refraction tomography similar results, but from a single frequency. Despite the Helmholtz-based solver implementation, the tomographic inversion handles irrgular topography. The numerical examples show that our inversion algorithm generates a convergent smooth velocity model, which looks very much like a tomographic result. Next, we plan to apply the instantaneous-traveltime inversion algorithm to real seismic data acquired from the near surface with irregular topography.

Near-surface traveltime tomographic inversion using multiple first break picks

Saragiotis, Christos; Choi, Yun Seok; Keho, T.; Alkhalifah, Tariq Ali (London 2013, 75th eage conference en exhibition incorporating SPE Europec, EAGE Publications, 2013) [Conference Paper]

The input data for refraction traveltime tomography are the traveltimes of the first breaks, which are picked using automatic pickers. Although automatic pickers perform satisfactorily overall, no one automatic picker can be characterized as the best one; one picker might fail for traces for which other pickers are accurate and vice versa for other traces. We introduce an iterative method for traveltime tomography, which takes as input traveltimes from a number of pickers. During the inversion scheme inconsistent traveltimes are replaced with more meaningful ones to obtain a smooth near-surface velocity model. The scheme is easily parallelizable and a byproduct of the inversion scheme is a set of consistent traveltimes which is close to the actual traveltimes of the first breaks.

Selective interferometric imaging of internal multiples

Zuberi, M. A H; Alkhalifah, Tariq Ali (London 2013, 75th eage conference en exhibition incorporating SPE Europec, EAGE Publications, 2013) [Conference Paper]

Internal multiples deteriorate the image when the imaging procedure assumes only single scattering, especially if the velocity model does not reproduce such scattering in the Green’s function. If properly imaged, internal multiples (and internally-scattered energy) can enhance the seismic image and illuminate areas otherwise neglected or poorly imaged by conventional single-scattering approaches. Conventionally, in order to image internal multiples, accurate, sharp contrasts in the velocity model are required to construct a Green’s function with all the scattered energy. As an alternative, we develop a three-step procedure, which images the first-order internal scattering using the background Green’s function (from the surface to each image point), constructed from a smooth velocity model: We first back-propagate the recorded surface data using the background Green’s function, then cross-correlate the back-propagated data with the recorded data and finally cross-correlate the result with the original background Green’s function. This procedure images the contribution of the recorded first-order internal multiples and is almost free of the single-scattering recorded energy. This image can be added to the conventional single-scattering image, obtained e.g. from Kirchhoff migration, to enhance the image. Application to synthetic data with reflectors illuminated by multiple scattering only demonstrates the effectiveness of the approach.

The optimizied expansion method for wavefield extrapolation

Wu, Zedong; Alkhalifah, Tariq Ali (London 2013, 75th eage conference en exhibition incorporating SPE Europec, EAGE Publications, 2013) [Conference Paper]

Spectral methods are fast becoming an indispensable tool for wave-field extrapolation, especially in anisotropic media, because of its dispersion and artifact free, as well as highly accurate, solutions of the wave equation. However, for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain operator.In this abstract, we propose an optimized expansion method that can approximate this operator with its low rank representation. The rank defines the number of inverse FFT required per time extrapolation step, and thus, a lower rank admits faster extrapolations. The method uses optimization instead of matrix decomposition to find the optimal wavenumbers and velocities needed to approximate the full operator with its low rank representation.Thus,we obtain more accurate wave-fields using lower rank representation, and thus cheaper extrapolations. The optimization operation to define the low rank representation depends only on the velocity model, and this is done only once, and valid for a full reverse time migration (many shots) or one iteration of full waveform inversion. Applications on the BP model yielded superior results than those obtained using the decomposition approach. For transversely isotopic media, the solutions were free of the shear wave artifacts, and does not require that eta>0.

Compressed-sensing application - Pre-stack kirchhoff migration

Aldawood, Ali; Hoteit, Ibrahim; Alkhalifah, Tariq Ali (London 2013, 75th eage conference en exhibition incorporating SPE Europec, EAGE Publications, 2013) [Conference Paper]

Least-squares migration is a linearized form of waveform inversion that aims to enhance the spatial resolution of the subsurface reflectivity distribution and reduce the migration artifacts due to limited recording aperture, coarse sampling of sources and receivers, and low subsurface illumination. Least-squares migration, however, due to the nature of its minimization process, tends to produce smoothed and dispersed versions of the reflectivity of the subsurface. Assuming that the subsurface reflectivity distribution is sparse, we propose the addition of a non-quadratic L1-norm penalty term on the model space in the objective function. This aims to preserve the sparse nature of the subsurface reflectivity series and enhance resolution. We further use a compressed-sensing algorithm to solve the linear system, which utilizes the sparsity assumption to produce highly resolved migrated images. Thus, the Kirchhoff migration implementation is formulated as a Basis Pursuit denoise (BPDN) problem to obtain the sparse reflectivity model. Applications on synthetic data show that reflectivity models obtained using this compressed-sensing algorithm are highly accurate with optimal resolution.

Q-P Wave traveltime computation by an iterative approach

Ma, Xuxin; Alkhalifah, Tariq Ali (London 2013, 75th eage conference en exhibition incorporating SPE Europec, EAGE Publications, 2013) [Conference Paper]

In this work, we present a new approach to compute anisotropic traveltime based on solving successively elliptical isotropic traveltimes. The method shows good accuracy and is very simple to implement.

Efficient Traveltime Solutions of the TI Acoustic Eikonal Equation

Waheed, Umair bin; Alkhalifah, Tariq Ali (London 2013, 75th eage conference en exhibition incorporating SPE Europec, EAGE Publications, 2013-05-31) [Conference Paper]

Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for integral imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order nonlinearity of the TI eikonal equation, which requires solving a quartic polynomial at each computational step. Using perturbation theory, we approximate the first-order discretized form of the TI eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution in terms of the anellipticity anisotropy parameter. Such perturbation, applied to the discretized form of the eikonal equation, does not impose any restrictions on the complexity of the perturbed parameter field. Therefore, it provides accurate traveltime solutions even for the anisotropic Marmousi model, with complex distribution of velocity and anellipticity anisotropy parameter. The formulation allows tremendous cost reduction compared to using the exact TI eikonal solver. Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy of the proposed approximation, without any addition to the computational cost.

Diffraction Traveltime Approximation to Estimate Anisotropy Parameters in Complex TI Media

Waheed, Umair bin; Alkhalifah, Tariq Ali (London 2013, 75th eage conference en exhibition incorporating SPE Europec, EAGE Publications, 2013-05-31) [Conference Paper]

Diffracted waves carry valuable information that can help improve our velocity modeling capability for better imaging of the subsurface. They are especially useful for anisotropic media as they inherently possess a wide range of dips necessary to resolve the angular dependence of velocity. We develop a scheme for diffraction traveltime computations based on perturbation theory for transverse isotropic media with tilted axis of symmetry (TTI). The formulation has advantages on two fronts: firstly it alleviates the computational complexity associated with solving the TTI eikonal equation and secondly it provides a mechanism to scan for the best fit anellipticity parameter without the need for repetitive modeling of traveltimes. The accuracy of such an expansion is further enhanced by the use of Shanks transform. We establish the effectiveness of the proposed formulation with tests on a homogeneous TTI model and the BP TTI model.

Efficient anisotropic wavefield extrapolation using effective isotropic models

Alkhalifah, Tariq Ali; Ma, X.; Waheed, Umair bin; Zuberi, Mohammad (London 2013, 75th eage conference en exhibition incorporating SPE Europec, EAGE Publications, 2013-05-31) [Conference Paper]

Isotropic wavefield extrapolation is more efficient than anisotropic extrapolation, and this is especially true when the anisotropy of the medium is tilted (from the vertical). We use the kinematics of the wavefield, appropriately represented in the high-frequency asymptotic approximation by the eikonal equation, to develop effective isotropic models, which are used to efficiently and approximately extrapolate anisotropic wavefields using the isotropic, relatively cheaper, operators. These effective velocity models are source dependent and tend to embed the anisotropy in the inhomogeneity. Though this isotropically generated wavefield theoretically shares the same kinematic behavior as that of the first arrival anisotropic wavefield, it also has the ability to include all the arrivals resulting from a complex wavefield propagation. In fact, the effective models reduce to the original isotropic model in the limit of isotropy, and thus, the difference between the effective model and, for example, the vertical velocity depends on the strength of anisotropy. For reverse time migration (RTM), effective models are developed for the source and receiver fields by computing the traveltime for a plane wave source stretching along our source and receiver lines in a delayed shot migration implementation. Applications to the BP TTI model demonstrates the effectiveness of the approach.

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