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Alkhalifah, Tariq Ali (14)

Zhang, Zhendong (5)Wu, Zedong (3)Guo, Qiang (2)Kalita, Mahesh (2)View MoreDepartmentEarth Science and Engineering Program (14)Physical Sciences and Engineering (PSE) Division (14)JournalSEG Technical Program Expanded Abstracts 2018 (14)PublisherSociety of Exploration Geophysicists (14)Subjectfull-waveform inversion (8)acoustic (3)elastic (3)inversion (3)velocity analysis (3)View MoreType
Conference Paper (14)

Year (Issue Date)
2018 (14)

Item AvailabilityOpen Access (14)

Now showing items 1-10 of 14

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Subspace methods for time-lapse elastic full-waveform inversion

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

The application of elastic full waveform inversion on time-lapse seismic data is arising from the boom in conventional full waveform inversion. In the past few years, many different inversion strategies are introduced for the time-lapse case, taking advantage of the power of FWI in capturing small changes. However, all methods tend to suffer from the imperfect repeatability of the data acquisition and the weakness in FWI in focussing on the affected areas (i.e. the reservoir). Thus, we modify the subspace method and apply it to time-lapse elastic full waveform inversion. A soft mask calculated using the gradients of the baseline and monitoring data, which acts as a pre-conditioner, is introduced to localize the update area to the affected regions. Specifically, we suppress the similarities of the two gradients and at the same time highlight their differences when calculating the soft mask. The calculated soft mask can reduce the dimensionality of the inverse problem with a delicately selected threshold, which provides a feasible way to calculate the reduced Hessian matrix. Besides, it is a data-driven approach free of human intervention or apriori knowledge. For comparison, we also use a hard mask surrounding the injection area. The numerical example shows that the proposed soft mask performs better than the hard mask.

Adaptive data-selection elastic full-waveform inversion

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

The multiscale inversion strategy is widely used to mitigate the cycle-skipping problem in full waveform inversion. There are many different approaches to implement the multiscale inversion and the widely used low-to-high frequency continuation is not applicable when the observed data lack low frequencies. As an alternative to multiple frequencies, offsets continuation is also able to suppress the cycle-skipping problem when the initial model is not perfect. We improve the multiscale strategy of offset-selection by introducing a local similarity criterion. Thus, we formulate an adaptive data-driven selection process that is better than conventional offset continuation approaches. The global-crosscorrelation objective function used here aims to maximize the similarity of two data sets instead of subtracting one from another and it is more consistent with the selection strategy. Besides, the crosscorrelation-based objective function is more sensitive to the phase information of the data and thus is more applicable to field data. We use a modified elastic Marmousi example to verify the effectiveness of the proposed method.

A robust full-waveform inversion based on a shifted correlation of the envelope of wavefields

Wu, Zedong; Alonaizi, Faisal; Alkhalifah, Tariq Ali; Zhang, Zhendong; Almalki, Majed (SEG Technical Program Expanded Abstracts 2018, Society of Exploration Geophysicists, 2018-08-27) [Conference Paper]

The standard full waveform inversion (FWI) attempts to minimize the difference between the observed and modeled data. When the initial velocity is kinematically accurate, FWI often converges to to the best velocity model, usually of a high-resolution nature. However, when the modeled data using an initial velocity is far from the observed data, conventional local gradient based methods converge to a solution near the initial velocity instead of the global minimum. This is also known as the cycle skipping problem, which results in a zero correlation when observed and modeled data are not correlated. To reduce the cycle-skipping problem, we can compare the envelope of the modeled and observed data instead of the original data. However, when the initial velocity is not good enough, the correlation of the envelope of the modeled and observed data do not contribute accurately to the gradient. To mitigate this issue, we suggest to maximize not only the zero-lag correlation of the envelope but also the non-zero-lag correlation of the envelope. A weighting function, which has its maximum value at zero lag and decays away from zero lag, is proposed 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 radius of convergence compared to standard FWI and envelope inversions. The implementation has the same computational complexity as conventional FWI as the only difference in the calculation is related to the modified adjoint source. We implement this algorithm on the AMD GPU based on OPENCL and obtained about a 14 fold speed up compared to a CPU implementation based on OPENMP. At last, several numerical examples are shown to demonstrate the proper convergence of the proposed method. Application to the Marmousi model shows that this method converges starting with a linearly increasing velocity model, even with data free of frequencies below 3 Hz.

A partial-low-rank method for solving acoustic wave equation

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

Numerical solutions of the acoustic wave equation, especially in anisotropic media, is crucial to seismic modeling, imaging and inversion as it provides efficient, practical, and stable approximate representation of the medium. However, a clean implementation (free of shear wave artifacts and dispersion) of wave propagation, especially in anisotropic media, requires an integral operator, the direct evaluation of which is extremely expensive. Recently, the low-rank method was proposed to provide a good approximation to the integral operator utilizing Fourier transforms. Thus, we propose to split the integral operator into two terms. The first term provides a differential operator that approximates that can be approximated with a standard finite-difference method. We, then, apply the lowrank approximation on the residual term of the finite-difference operator. We implement the two terms in two complementing steps, in which the spectral step corrects for any errors admitted by the finite difference step. Even though we utilize finite-difference approximations, the resulting algorithm admits spectral accuracy. Also, through the finite difference step, the method can deal approximately with the free surface and absorbing boundary conditions in a straight forward manner. Numerical examples show that the method is of high accuracy and efficiency.

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.

Time-lapse waveform inversion regularized by spectral constraints and Sobolev space norm

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

Imperfect illumination from surface seismic data due to lack of aperture and frequency content leads to ambiguity and resolution loss in seismic images and in full-waveform inversion (FWI) results. The resolution of time-lapse velocity updates can, however, be improved enforcing the sparsity of the parameter changes. Edge-preserving regularizations and constraints are typically used to promote sparsity. However, different choice of regularization parameters leads to different inversion results and optimal parameters are hard to identify, especially for real data. In particular it is not straightforward to balance the inversion between sparsity constraint and data fit. Fortunately, it is possible to estimate local spatial wavenumbers in a velocity model that are best illuminated by the data. We propose to constrain part of the model difference spectrum that is well illuminated by the data and optimize the rest of the spectrum to enhance sparsity. We approximate correctly retrieved model wavenumbers by simply picking large enough values in the inverted spectrum and constrain that part of model spectrum. Then we adjust the rest of the wavenumbers to reduce the value of a Sobolev space norm (SSN). SSN reduction promotes sparsity of time-lapse updates, while spectral constraints ensure that the part of the modeled spectrum retrieved from the data is completely retained. Application to synthetic noisy data for a perturbation of the Marmousi II model shows that the model resolution can be improved by using our method to extrapolate the model spectrum.

Subsurface wavefields based on the generalized internal multiple imaging

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

Accessing full Green's functions between image points and the location of our recording surface is crucial to obtaining accurate subsurface wavefields and accurate images beyond the single scattering assumption. A direct approach to do so is oered by utilizing the recorded data combined with a background model. The process includes extrapolating the recorded data back in time followed by a simple interferometric crosscorrelation of the back propagated wavefield with the recorded data. This interferometric step oers the opportunity to extract subsurface Green's functions with the first order scattering forming the transmission component, and the second-order scattering becomes the leading scattering term. A crosscorrelation of the resulting, assumed upgoing, wavefield with a forward modeled down going wavefield highlights the double scattered reflectivity in a process referred to as the generalized internal multiple imaging (GIMI). The resulting image is vulnerable to crosstalk between dierent order multiples interacting with each other. Thus, we develop the adjoint GIMI that takes us from image to data, and use it to formulate a least square optimization problem to fit the image to the data. The result is reduced crosstalk and cleaner higher resolution multiple scattering images. We also extract space extensions of the image, which oers the opportunity to evaluate the focussing capability of the velocity model, and formulate updates for that model based on double scattering.

Waveform inversion based target-oriented redatuming

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

Finding a velocity model that produces simulated data that fits the observed one is the main objective of full waveform inversion (FWI). To meet such an objective we often need to solve for a high-resolution delineation of the subsurface medium. The current algorithms are usually implemented over the entire model space with a consistent discretization and physical assumptions, which can be both complex and costly in practice. Alternatively, we develop an FWI framework that utilizes a split model to an overburden, like the medium above a reservoir, and the underlying represented by data at a datum at the bottom of the overburden. We simultaneously invert for the velocity model above the datum level, which effects the redatuming process but often owns to more simple physics, and the corresponding data at that datum, which may represent a complex reservoir region. We formulate the redatuming operator using a modified expression of the extended Born representation, which is a multi-dimensional crosscorrelation. The resulting modeling needed in such an inversion includes wavefields from a source and those ignited at the datum level. We estimate the overburden velocity using low-wavenumber updates along the modeled reflection wavepaths. The dimensionality of the model extension and the retrieved data helps us match data on the surface, which results in a robust implementation. Tests on a simple model and the Marmousi show that our method can build a good velocity model and also obtain redatumed data with reasonable amplitude accuracy.

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.

An approximate method for the acoustic attenuating orthorhombic eikonal equation

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

Solving the eikonal equation is used widely in traveltime calculation, tomography, Kirchhoff migration etc. The complex eikonal equation governs the traveltimes in an attenuating medium, where the real and imaginary parts of the traveltimes are associated with the phase and energy-absorption, respectively. Attenuating orthorhombic anisotropy can be used to explain the azimuthal variation of velocity- and attenuation-anisotropy measured from surface seismic data. We present an approximate method to solve the acoustic eikonal equation for an attenuating orthorhombic medium. We combine perturbation theory and Shanks transform in different ways to derive the analytic solutions in the case of homogeneous media. We design a fast marching scheme to solve the acoustic eikonal equation numerically. We share some numerical examples to demonstrate the effectiveness of the complex eikonal equation in predicting attenuation.

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