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Alkhalifah, Tariq Ali (12)

Sava, Paul C. (2)Stovas, A. (2)Choi, Yun Seok (1)Fomel, Sergey (1)View MoreDepartmentEarth Science and Engineering Program (12)Environmental Science and Engineering Program (12)Physical Sciences and Engineering (PSE) Division (12)Journal
Geophysical Prospecting (12)

PublisherWiley (12)SubjectAnisotropy (3)Angle gathers (2)Migration (2)Anelliptical (1)Anisotropic (1)View MoreTypeArticle (12)Year (Issue Date)2014 (4)2013 (3)2012 (4)2010 (1)Item AvailabilityMetadata Only (12)

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Anisotropy signature in reverse-time migration extended images

Sava, Paul C.; Alkhalifah, Tariq Ali (Geophysical Prospecting, Wiley, 2014-11-04) [Article]

Reverse-time migration can accurately image complex geologic structures in anisotropic media. Extended images at selected locations in the Earth, i.e., at common-image-point gathers, carry rich information to characterize the angle-dependent illumination and to provide measurements for migration velocity analysis. However, characterizing the anisotropy influence on such extended images is a challenge. Extended common-image-point gathers are cheap to evaluate since they sample the image at sparse locations indicated by the presence of strong reflectors. Such gathers are also sensitive to velocity error that manifests itself through moveout as a function of space and time lags. Furthermore, inaccurate anisotropy leaves a distinctive signature in common-image-point gathers, which can be used to evaluate anisotropy through techniques similar to the ones used in conventional wavefield tomography. It specifically admits a V-shaped residual moveout with the slope of the "V" flanks depending on the anisotropic parameter η regardless of the complexity of the velocity model. It reflects the fourth-order nature of the anisotropy influence on moveout as it manifests itself in this distinct signature in extended images after handling the velocity properly in the imaging process. Synthetic and real data observations support this assertion.

Prestack exploding reflector modelling and migration for anisotropic media

Alkhalifah, Tariq Ali (Geophysical Prospecting, Wiley, 2014-10-09) [Article]

The double-square-root equation is commonly used to image data by downward continuation using one-way depth extrapolation methods. A two-way time extrapolation of the double-square-root-derived phase operator allows for up and downgoing wavefields but suffers from an essential singularity for horizontally travelling waves. This singularity is also associated with an anisotropic version of the double-square-root extrapolator. Perturbation theory allows us to separate the isotropic contribution, as well as the singularity, from the anisotropic contribution to the operator. As a result, the anisotropic residual operator is free from such singularities and can be applied as a stand alone operator to correct for anisotropy. We can apply the residual anisotropy operator even if the original prestack wavefield was obtained using, for example, reverse-time migration. The residual correction is also useful for anisotropic parameter estimation. Applications to synthetic data demonstrate the accuracy of the new prestack modelling and migration approach. It also proves useful in approximately imaging the Vertical Transverse Isotropic Marmousi model.

Source-receiver two-way wave extrapolation for prestack exploding-reflector modelling and migration

Alkhalifah, Tariq Ali; Fomel, Sergey; Wu, Zedong (Geophysical Prospecting, Wiley, 2014-10-08) [Article]

Most modern seismic imaging methods separate input data into parts (shot gathers). We develop a formulation that is able to incorporate all available data at once while numerically propagating the recorded multidimensional wavefield forward or backward in time. This approach has the potential for generating accurate images free of artiefacts associated with conventional approaches. We derive novel high-order partial differential equations in the source-receiver time domain. The fourth-order nature of the extrapolation in time leads to four solutions, two of which correspond to the incoming and outgoing P-waves and reduce to the zero-offset exploding-reflector solutions when the source coincides with the receiver. A challenge for implementing two-way time extrapolation is an essential singularity for horizontally travelling waves. This singularity can be avoided by limiting the range of wavenumbers treated in a spectral-based extrapolation. Using spectral methods based on the low-rank approximation of the propagation symbol, we extrapolate only the desired solutions in an accurate and efficient manner with reduced dispersion artiefacts. Applications to synthetic data demonstrate the accuracy of the new prestack modelling and migration approach.

Effective wavefield extrapolation in anisotropic media: Accounting for resolvable anisotropy

Alkhalifah, Tariq Ali (Geophysical Prospecting, Wiley, 2014-04-30) [Article]

Spectral methods provide artefact-free and generally dispersion-free wavefield extrapolation in anisotropic media. Their apparent weakness is in accessing the medium-inhomogeneity information in an efficient manner. This is usually handled through a velocity-weighted summation (interpolation) of representative constant-velocity extrapolated wavefields, with the number of these extrapolations controlled by the effective rank of the original mixed-domain operator or, more specifically, by the complexity of the velocity model. Conversely, with pseudo-spectral methods, because only the space derivatives are handled in the wavenumber domain, we obtain relatively efficient access to the inhomogeneity in isotropic media, but we often resort to weak approximations to handle the anisotropy efficiently. Utilizing perturbation theory, I isolate the contribution of anisotropy to the wavefield extrapolation process. This allows us to factorize as much of the inhomogeneity in the anisotropic parameters as possible out of the spectral implementation, yielding effectively a pseudo-spectral formulation. This is particularly true if the inhomogeneity of the dimensionless anisotropic parameters are mild compared with the velocity (i.e., factorized anisotropic media). I improve on the accuracy by using the Shanks transformation to incorporate a denominator in the expansion that predicts the higher-order omitted terms; thus, we deal with fewer terms for a high level of accuracy. In fact, when we use this new separation-based implementation, the anisotropy correction to the extrapolation can be applied separately as a residual operation, which provides a tool for anisotropic parameter sensitivity analysis. The accuracy of the approximation is high, as demonstrated in a complex tilted transversely isotropic model. © 2014 European Association of Geoscientists & Engineers.

Research Note: Full-waveform inversion of the unwrapped phase of a model

Alkhalifah, Tariq Ali (Geophysical Prospecting, Wiley, 2013-12-06) [Article]

Reflections in seismic data induce serious non-linearity in the objective function of full- waveform inversion. Thus, without a good initial velocity model that can produce reflections within a half cycle of the frequency used in the inversion, convergence to a solution becomes difficult. As a result, we tend to invert for refracted events and damp reflections in data. Reflection induced non-linearity stems from cycle skipping between the imprint of the true model in observed data and the predicted model in synthesized data. Inverting for the phase of the model allows us to address this problem by avoiding the source of non-linearity, the phase wrapping phenomena. Most of the information related to the location (or depths) of interfaces is embedded in the phase component of a model, mainly influenced by the background model, while the velocity-contrast information (responsible for the reflection energy) is mainly embedded in the amplitude component. In combination with unwrapping the phase of data, which mitigates the non-linearity introduced by the source function, I develop a framework to invert for the unwrapped phase of a model, represented by the instantaneous depth, using the unwrapped phase of the data. The resulting gradient function provides a mechanism to non-linearly update the velocity model by applying mainly phase shifts to the model. In using the instantaneous depth as a model parameter, we keep track of the model properties unfazed by the wrapping phenomena. © 2013 European Association of Geoscientists & Engineers.

Mapping of moveout in tilted transversely isotropic media

Stovas, A.; Alkhalifah, Tariq Ali (Geophysical Prospecting, Wiley, 2013-09-09) [Article]

The computation of traveltimes in a transverse isotropic medium with a tilted symmetry axis tilted transversely isotropic is very important both for modelling and inversion. We develop a simple analytical procedure to map the traveltime function from a transverse isotropic medium with a vertical symmetry axis (vertical transversely isotropic) to a tilted transversely isotropic medium by applying point-by-point mapping of the traveltime function. This approach can be used for kinematic modelling and inversion in layered tilted transversely isotropic media. © 2013 European Association of Geoscientists & Engineers.

Imaging by forward propagating the data: Theory and application

Zuberi, Akbar; Alkhalifah, Tariq Ali (Geophysical Prospecting, Wiley, 2013-02-27) [Article]

The forward (modelled) wavefield for conventional reverse time migration (RTM) is computed by extrapolating the wavefield from an estimated source wavelet. In the typical case of a smooth subsurface velocity, this wavefield lacks the components, including surface reflections, necessary to image multiples in the observed data. We, instead, introduce the concept of forward propagating the recorded data, including direct arrivals, as part of RTM. We analyse the influence of the main components of the data on the imaging process, which include direct arrivals, primaries and surface-related multiples. In our RTM methodology, this implies correlating the forward extrapolated recorded data wavefield with its reversely extrapolated version prior to applying the zero-lag cross-correlation imaging condition. The interaction of the data components with each other in the cross-correlation process will image primaries and multiples, as well as introduce cross-talk artefact terms. However, some of these artefacts are present in conventional RTM implementation and they tend to be relatively weak. In fact, for the surface seismic experiment, forward propagating the direct arrivals is almost equivalent to forward propagating a source and it tends to contribute the majority of the data imaging energy. In addition, primaries and multiples recorded in the data become multiples of one higher order. Forward propagating the recorded data to recreate the source will relieve us from the requirement of estimating the source function. It will also include near-surface information necessary to improve the image in areas with near-surface complexity. Data from a simple synthetic layered model, as well as the Marmousi model, are used to demonstrate some of these features. © 2013 European Association of Geoscientists & Engineers.

Wide-azimuth angle gathers for anisotropic wave-equation migration

Sava, Paul C.; Alkhalifah, Tariq Ali (Geophysical Prospecting, Wiley, 2012-10-15) [Article]

Extended common-image-point gathers (CIP) constructed by wide-azimuth TI wave-equation migration contain all the necessary information for angle decomposition as a function of the reflection and azimuth angles at selected locations in the subsurface. The aperture and azimuth angles are derived from the extended images using analytic relations between the space- and time-lag extensions using information which is already available at the time of migration, i.e. the anisotropic model parameters. CIPs are cheap to compute because they can be distributed in the image at the most relevant positions, as indicated by the geologic structure. If the reflector dip is known at the CIP locations, then the computational cost can be reduced by evaluating only two components of the space-lag vector. The transformation from extended images to angle gathers is a planar Radon transform which depends on the local medium parameters. This transformation allows us to separate all illumination directions for a given experiment, or between different experiments. We do not need to decompose the reconstructed wavefields or to choose the most energetic directions for decomposition. Applications of the method include illumination studies in complex areas where ray-based methods fail, and assuming that the subsurface illumination is sufficiently dense, the study of amplitude variation with aperture and azimuth angles. © 2012 European Association of Geoscientists & Engineers.

A tilted transversely isotropic slowness surface approximation

Stovas, A.; Alkhalifah, Tariq Ali (Geophysical Prospecting, Wiley, 2012-05-09) [Article]

The relation between vertical and horizontal slownesses, better known as the dispersion relation, for transversely isotropic media with a tilted symmetry axis (TTI) requires solving a quartic polynomial equation, which does not admit a practical explicit solution to be used, for example, in downward continuation. Using a combination of the perturbation theory with respect to the anelliptic parameter and Shanks transform to improve the accuracy of the expansion, we develop an explicit formula for the vertical slowness that is highly accurate for all practical purposes. It also reveals some insights into the anisotropy parameter dependency of the dispersion relation including the low impact that the anelliptic parameter has on the vertical placement of reflectors for a small tilt in the symmetry angle. © 2012 European Association of Geoscientists & Engineers.

Application of multi-source waveform inversion to marine streamer data using the global correlation norm

Choi, Yun Seok; Alkhalifah, Tariq Ali (Geophysical Prospecting, Wiley, 2012-05-02) [Article]

Conventional multi-source waveform inversion using an objective function based on the least-square misfit cannot be applied to marine streamer acquisition data because of inconsistent acquisition geometries between observed and modelled data. To apply the multi-source waveform inversion to marine streamer data, we use the global correlation between observed and modelled data as an alternative objective function. The new residual seismogram derived from the global correlation norm attenuates modelled data not supported by the configuration of observed data and thus, can be applied to multi-source waveform inversion of marine streamer data. We also show that the global correlation norm is theoretically the same as the least-square norm of the normalized wavefield. To efficiently calculate the gradient, our method employs a back-propagation algorithm similar to reverse-time migration based on the adjoint-state of the wave equation. In numerical examples, the multi-source waveform inversion using the global correlation norm results in better inversion results for marine streamer acquisition data than the conventional approach. © 2012 European Association of Geoscientists & Engineers.

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