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Alkhalifah, Tariq Ali (12)

Wu, Zedong (12)

Cheng, Jiubing (1)Fomel, Sergey (1)Guo, Qiang (1)DepartmentEarth Science and Engineering Program (12)Physical Sciences and Engineering (PSE) Division (12)Environmental Science and Engineering Program (5)JournalProceedings 76th EAGE Conference and Exhibition 2014 (3)79th EAGE Conference and Exhibition 2017 (2)SEG Technical Program Expanded Abstracts 2013 (2)SEG Technical Program Expanded Abstracts 2016 (2)EAGE Workshop on High Performance Computing for Upstream (1)View MorePublisherEAGE Publications (7)Society of Exploration Geophysicists (5)Subjectdepth migration (2)prestack (2)anisotropy (1)common midpoint (1)decomposition (1)View MoreType
Conference Paper (12)

Year (Issue Date)2017 (2)2016 (2)2014 (5)2013 (3)Item AvailabilityOpen Access (7)Metadata Only (5)

Now showing items 1-10 of 12

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Full waveform inversion based on the optimized gradient and its spectral implementation

Wu, Zedong; Alkhalifah, Tariq Ali (Proceedings 76th EAGE Conference and Exhibition 2014, EAGE Publications, 2014) [Conference Paper]

Full waveform inversion (FWI) despite it's potential suffers from the ability to converge to the desired solution due to the high nonlinearity of the objective function at conventional seismic frequencies. Even if frequencies necessary for the convergence are available, the high number of iterations required to approach a solution renders FWI as very expensive (especially in 3D). A spectral implementation in which the wavefields are extrapolated and gradients are calculated in the wavenumber domain allows for a cleaner more efficient implementation (no finite difference dispersion errors). In addition, we use not only an up and down going wavefield decomposition of the gradient to access the smooth background update, but also a right and left propagation decomposition to allow us to do that for large dips. To insure that the extracted smooth component of the gradient has the right decent direction, we solve an optimization problem to search for the smoothest component that provides a negative (decent) gradient. Application to the Marmousi model shows that this approach works well with linear increasing initial velocity model and data with frequencies above 2Hz.

Waveform inversion for acoustic VTI media in frequency domain

Wu, Zedong; Alkhalifah, Tariq Ali (SEG Technical Program Expanded Abstracts 2016, Society of Exploration Geophysicists, 2016-09-06) [Conference Paper]

Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the background model using a single scattered wavefield from an inverted perturbation. However, current RWI methods are mostly based on isotropic media assumption. We extend the idea of the combining inversion for the background model and perturbations to address transversely isotropic with a vertical axis of symmetry (VTI) media taking into consideration of the optimal parameter sensitivity information. As a result, we apply Born modeling corresponding to perturbations in only for the variable e to derive the relative reflected waveform inversion formulation. To reduce the number of parameters, we assume the background part of η = ε and work with a single variable to describe the anisotropic part of the wave propagation. Thus, the optimization variables are the horizontal velocity v, η = ε and the e perturbation. Application to the anisotropic version of Marmousi model with a single frequency of 2.5 Hz shows that this method can converge to the accurate result starting from a linearly increasing isotropic initial velocity. Application to a real dataset demonstrates the versatility of the approach.

Practical waveform inversion in anisotropic media: The natural combination of the data and image objectives

Alkhalifah, Tariq Ali; Wu, Zedong (SEG Technical Program Expanded Abstracts 2016, Society of Exploration Geophysicists, 2016-09-06) [Conference Paper]

Addressing anisotropy in full wavenumber inversion (FWI) is crucial to obtaining credible models, and it is extremely challenging considering the multi parameter nature of the inversion. A successful FWI in anisotropic media takes into account the sensitivity of the data (or the wave) to the long and short wavelength components of the anisotropic parameters. Considering the low sensitivity of FWI to the anellipticity parameter ? when parametrizing the acoustic transversely isotropic model with the horizontal velocity, η and ε, we develop a combined FWI and reflection waveform inversion (RWI) to invert for the anisotropic parameters that influence surface seismic data. This practical waveform inversion (PWI) separates the parameters to their resolvable scales, with information accessed from the data fitting (FWI) and the image focusing (RWI) objectives. With this parametrization, the RWI role is to obtain a smooth ηmodel, as well as velocity, while FWI focusses on the scattering potential of the horizontal velocity. The parameter η is used to produce the Born scattered wavefield for the RWI part and eventually fit the amplitude for the imperfect physics in the FWI part.

Spectral implementation of full waveform inversion based on reflections

Wu, Zedong; Alkhalifah, Tariq Ali (Proceedings 76th EAGE Conference and Exhibition 2014, EAGE Publications, 2014) [Conference Paper]

Using the reflection imaging process as a source to model reflections for full waveform inversion (FWI), referred to as reflection FWI (RFWI), allows us to update the background component of the model, and avoid using the relatively costly migration velocity analysis (MVA), which usually relies on extended images. However, RFWI requires a good image to represent the current reflectivity, as well as, some effort to obtain good smooth gradients. We develop a spectral implementation of RFWI where the wavefield extrapolations and gradient evaluation are performed in the wavenumber domain, obtaining clean dispersion free and fast extrapolations. The gradient, in this case, yields three terms, two of which provide us with each side of the rabbit ear kernel, and the third, often ignored, provides a normalization of the reflectivity within the kernel, which can be used to obtain a reflectivity free background update. Since the image is imperfect (it is an adjoint, not an inverse), an optimization process for the third term scaling is implemented to achieve the smoothest gradient update. A rare application of RFWI on the reflectivity infested Marmousi model shows some of the potential 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.

A New Wave Equation Based Source Location Method with Full-waveform Inversion

Wu, Zedong; Alkhalifah, Tariq Ali (79th EAGE Conference and Exhibition 2017, EAGE Publications, 2017-05-26) [Conference Paper]

Locating the source of a passively recorded seismic event is still a challenging problem, especially when the velocity is unknown. Many imaging approaches to focus the image do not address the velocity issue and result in images plagued with illumination artifacts. We develop a waveform inversion approach with an additional penalty term in the objective function to reward the focusing of the source image. This penalty term is relaxed early to allow for data fitting, and avoid cycle skipping, using an extended source. At the later stages the focusing of the image dominates the inversion allowing for high resolution source and velocity inversion. We also compute the source location explicitly and numerical tests show that we obtain good estimates of the source locations with this approach.

Simulating propagation of decomposed elastic waves using low-rank approximate mixed-domain integral operators for heterogeneous transversely isotropic media

Cheng, Jiubing; Wu, Zedong; Alkhalifah, Tariq Ali (SEG Technical Program Expanded Abstracts 2014, Society of Exploration Geophysicists, 2014-08-05) [Conference Paper]

In elastic imaging, the extrapolated vector fields are decomposed into pure wave modes, such that the imaging condition produces interpretable images, which characterize reflectivity of different reflection types. Conventionally, wavefield decomposition in anisotropic media is costly as the operators involved is dependent on the velocity, and thus not stationary. In this abstract, we propose an efficient approach to directly extrapolate the decomposed elastic waves using lowrank approximate mixed space/wavenumber domain integral operators for heterogeneous transverse isotropic (TI) media. The low-rank approximation is, thus, applied to the pseudospectral extrapolation and decomposition at the same time. The pseudo-spectral implementation also allows for relatively large time steps in which the low-rank approximation is applied. Synthetic examples show that it can yield dispersionfree extrapolation of the decomposed quasi-P (qP) and quasi- SV (qSV) modes, which can be used for imaging, as well as the total elastic wavefields.

FWI and MVA the natural way

Alkhalifah, Tariq Ali; Wu, Zedong (Proceedings 76th EAGE Conference and Exhibition 2014, EAGE Publications, 2014) [Conference Paper]

Integrating migration velocity analysis (MVA) and full waveform inversion (FWI) can help reduce the high nonlinearity of the classic FWI objective function. The combination of inverting for the long and short wavelength components of the velocity model using a dual objective function that is sensitive to both components is still very expensive and have produced mixed results. We develop an approach that includes both components integrated to complement each other. We specifically utilize the image to generate reflections in our synthetic data only when the velocity model is not capable of producing such reflections. As a result, we get the MVA working when we need it, and mitigate it's influence when the velocity model produces accurate reflections (possible first for the low frequencies). Applications to a layered model, as well as, the Marmousi model demonstrate some of the approach features.

Velocity Building by Reflection Waveform Inversion without Cycle-skipping

Guo, Qiang; Alkhalifah, Tariq Ali; Wu, Zedong (79th EAGE Conference and Exhibition 2017, EAGE Publications, 2017-05-26) [Conference Paper]

Reflection waveform inversion (RWI) provides estimation of low wavenumber model components using reflections generated from a migration/demigration process. The resulting model tends to be a good initial model for FWI. In fact, the optimization images to combine the migration velocity analysis (MVA) objectives (given here by RWI) and the FWI ones. However, RWI may still encounter cycle-skipping at far offsets if the velocity model is highly inaccurate. Similar to MVA, RWI is devoted to focusing reflection data to its true image positions, yet because of the cycle skipping potential we tend to initially use only near offsets. To make the inversion procedure more robust, we introduce the extended image into our RWI. Extending the model perturbations (or image) allows us to better fit the data at larger offsets even with an inaccurate velocity. Thus, we implement a nested approach to optimize the velocity and extended image simultaneously using the objective function of RWI. We slowly reduce the extension, as the image becomes focused, to allow wavepath updates from far offsets to near as a natural progression from long wavelength updates to shorter ones. Applications on synthetic data demonstrate the effectiveness of our method without much additional cost to RWI.

Exploring imaging capabilities of the extended prestack wavefield

Alkhalifah, Tariq Ali; Wu, Zedong; Fomel, Sergey (SEG Technical Program Expanded Abstracts 2013, Society of Exploration Geophysicists, 2013-08-19) [Conference Paper]

The dynamic form of the double square-root (DSR) equation provides a mechanism to extrapolate prestack wavefields by moving the sources and receivers in space with respect to a potential image (scatterer) point. Its classical implementation for imaging often assumes sources and receivers are at the same horizontal surface. Reverse time migration (RTM), as well as common shot migrations in general, through its separate treatment of the sources and receivers, allows for more exibility in source and receiver configurations. A simple modication to the classical DSR equation provides such exibility. Specically, we define a 7-dimensional prestack wavefield for 3-D media that includes the vertical source and receiver offset. The corresponding dispersion relation can be used to extrapolate such wavefields. However, the cost for such a definition and extrapolation can be prohibitive, considering the high dimensionality of the problem. We reduce the dimensionality by recognizing that the sources and receivers often share the same horizontal plane, and thus, obtain the conventional DSR formulation. An efficient implementation of DSR in time yields extrapolation speeds that nominally exceed those obtained from reverse time migration. We can also reduce the dimensionality by setting the horizontal offset between the source and receiver at the image point to zero, or using a DSR-like formulation to correct for source-receiver vertical offset or topography.

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