The imaging condition usually adopted for reverse time migration gives good results when applied to acoustic data. However, when dealing with multi-component data, it is important to take into account the vectorial nature of the wave fields recorded. We show how the imaging condition can be formulated to include these vector wave fields. We also apply this formulation to the 2D Marmousi 2 synthetic model and obtain multi-parameter images that can be applied for structural interpretation or as a part of a multi-parameter inversion scheme.
Presentation Date: Monday, October 17, 2016
Start Time: 3:45:00 PM
Presentation Type: ORAL
We implement multiparameter full-waveform inversion (FWI) in the isotropic acoustic media with the nonlinear conjugate gradient (CG) method. The performance of the FWI is evaluated using di erent combinations of acoustic parameters, including velocity, density and acoustic impedance. Simultaneous inversion of velocity and density leads to smoother results than simultaneous inversion of velocity and acoustic impedance. We apply FWI to a time-lapse (4D) seismic inverse problem, and show gradient based methods cannot e ciently resolve velocity and density change simultaneously because of the crosstalk between parameters. We show a second order method is promising in time-lapse FWI by applying the approximated inverse of the Hessian to the gradient.
Presentation Date: Monday, October 17, 2016
Start Time: 4:35:00 PM
Location: Lobby D/C
Presentation Type: POSTER
Interpretation of sharp salt boundaries can be achieved by using level sets to define the boundary as an isocontour of a higher dimensional implicit surface. Using shape optimization, we can evolve this surface and the boundary it represents. We derive an update for the implicit surface that uses second-order information in the Hessian of the FWI objective function, taking into account the effects of the acquisition, as well as scattering and transmission energy. This approach helps us avoid local minima and more effectively converges on the true model, both in terms of the data and model residual norms. We demonstrate this idea using a Gauss-Newton approximation of the Hessian on synthetic examples.
Presentation Date: Tuesday, October 18, 2016
Start Time: 9:15:00 AM
Location: Lobby D/C
Presentation Type: POSTER
Level set methods can provide a sharp interpretation of the salt body by defining the boundary as an isocontour of a higher dimensional implicit surface. We can use shape optimization to derive a gradient update that evolves the implicit surface to minimize the Full-Waveform Inversion (FWI) objective function. We can decompose the update gradient into separate partitions with individual scaling parameters to better avoid local minima, and more effectively converge on the true model. Using our approach on synthetic examples, we can achieve reasonable convergence of the residual L2 norm, as well as the evolution of the velocity toward the true model, demonstrating the feasibility of this approach. Ultimately, this method could be integrated into processing work-flows to improve the building and refining of the velocity models used for imaging.
Some previous approaches to performing salt body segmentation use a shape optimization approach for identifying salt body boundaries (Guo and de Hoop (2013); Lewis et al. (2012)), by applying a global step parameter to the update gradient. However, the back-propagation of the residuals can create boundary updates that lead to a local minima when applied this way. We show how decomposing the update gradient can help avoid this problem. I will discuss the general derivation, the fundamental problem that we address, the algorithm we apply, and the results we obtain.
The boundaries of a salt body can be represented as the zero isocontour of a higher dimensional surface ø (for example, a 2D boundary as a contour of a 3D surface). A gradient can be derived to evolve the surface ø according to the FWI objective function:
Unlike the smooth boundaries produced by tomographic approaches, the isocontour resulting from the shape optimization provides a sharp boundary, which is a more appropriate way to classify most salt-sediment interfaces.
Derivation of the evolution equation
While it may seem counter-intuitive to add an extra dimension to our problem, by doing so, we gain the advantage of easily merging/separating bodies as the evolution proceeds, as well as the ability to handle sharp corners and cusps in the lowerdimensional (2D) plane on which the boundary exists.
We present a field data application of the technique proposed by Maharramov and Biondi (2015) for reconstructing production-induced subsurface model changes from timelapse seismic data using full-waveform inversion (FWI). The technique simultaneously inverts multiple survey vintages with total-variation (TV) regularization of the model differences. After describing the method, we discuss its application to the Gulf of Mexico, Genesis Field data. We resolve negative velocity changes associated with overburden dilation and demonstrate that the results are stable with respect to the amount of regularization and consistent with earlier estimates of time strain in the overburden.
Prevalent practice of time-lapse seismic processing relies on picking time displacements and changes in reflectivity amplitudes between migrated baseline and monitor images, and converting them into impedance changes and subsurface deformation (Johnston, 2013). This approach requires a significant amount of manual interpretation and quality control. An alternative approach is based on using the high-resolution power of full-waveform inversion (Sirgue et al., 2010a) to reconstruct production-induced changes from wide-offset seismic acquisitions (Routh et al., 2012; Zheng et al., 2011; Asnaashari et al., 2012; Raknes et al., 2013; Maharramov and Biondi, 2014a; Yang et al., 2014). However, while potentially reducing the amount of manual interpretation, time-lapse FWI is sensitive to repeatability issues (Asnaashari et al., 2012), with both coherent and incoherent noise potentially masking important production- induced changes. The joint time-lapse FWI proposed by Maharramov and Biondi (2013, 2014a) addressed repeatability issues by joint inversion of multiple vintages with modeldifference regularization based on the 𝑳 2-norm and produced improved results when compared to the conventional time-lapse FWI techniques. Maharramov and Biondi (2015) extended this joint inversion approach to include edge-preserving totalvariation (TV) model-difference regularization. The new method was shown to achieve a dramatic improvement over alternative techniques by significantly reducing oscillatory artifacts in the recovered model difference for synthetic data with repeatability issues. In this work, we apply this TV-regularized simultaneous inversion technique to the Gulf of Mexico, Genesis Field data and demonstrate a stable recovery of productioninduced model changes.
Passive seismic arrays on land provide the opportunity to push the use of ambient noise cross-correlation techniques to frequencies well beyond the microseism band. Using data recorded by a dense array in Long Beach, California, we demonstrate that high-frequency (> 3 Hz) fundamental- and first-order-mode Rayleigh waves generated by traffic noise can be extracted from the ambient noise field and used for tomographic studies. Here, we show group velocity maps derived from travel times of the fundamental-mode Rayleigh waves at 3.00 Hz and 3.50 Hz. The velocity trends in our results correlate well with lithologies outlined in a geologic map of the survey region. As expected, less-consolidated materials display relatively low velocities, while more-consolidated materials display relatively high velocities.
The extraction of surface waves from the ambient noise field for use in tomographic studies is well-established at the regional and continental scales (eg. Shapiro et al., 2005; Yang et al., 2008; Bensen et al., 2008). The success of these studies has encouraged investigation of this technique at the exploration scale. In ocean-bottom environments, de Ridder et al. (2014) and Mordret et al. (2014) obtained reliable time-lapse group and phase velocity maps, respectively, of the Valhall overburden, while de Ridder et al. (2015) recovered phase velocity and anisotropy maps representative of subsidence patterns at Ekofisk. In these cases, the examined frequencies were less than 2 Hz. In land environments, passive seismic arrays of sufficient density, size, and duration for these sorts of studies are rare.
One array that does meet these requirements is located in Long Beach, California (map in Figure 1). Deployed in January 2012 by NodalSeismic, the array spans an 8.5 ⨯ 4 km2 region and consists of approximately 2400 vertical-component geophones. With an average geophone spacing of 100 m and a continuous 3-month recording period, the array is well-suited for exploration-scale tomography using ambient noise. Dahlke et al. (2014) were able to create phase velocity maps at lowfrequencies (approximately 1 Hz) that resolved the location of the Newport-Inglewood fault. At the neighboring array, Lin et al. (2013) were able to create similar Rayleigh-wave phase velocity maps for frequencies up to 2 Hz that successfully imaged the same fault.
Tomographic Full Waveform Inversion (TFWI) provides a robust but expensive method to invert the seismic data. Scale separation of the model greatly reduces the cost but adds complexity to theory and the implementation of the inversion. In addition, maintaining simultaneous inversion of scales is hindered when the modeling operator cannot accurately match the amplitudes of the data. In this paper, I provide two improvements that reduce the complexity of TFWI and increase robustness against amplitude inaccuracies in the modeling operator. First, I rederive TFWI with one model in an abstract formulation that is applicable to any form of the wave-equation. Then, I modify the objective function using a running-window normalization. Finally, we test the proposed algorithm on the SEG 2014 blind test data. The results of the modified TFWI show a major improvement in the accuracy and convergence rate of the inversion.
Previously, we reduced the cost of TFWI by separating the extended model into two components: a non-extended smooth background and an extended rough perturbation (Almomin and Biondi, 2013; Biondi and Almomin, 2013). This might have caused some confusion on the resulting relationship and balance between these two parameters and their relationship to the original model. Furthermore, the interpretation of these two parameters limited the way we could separate them and increased the difficulty of moving to different wave-equations, such as the elastic.
Another limitation to TFWI is when the amplitude of the data cannot be accurately matched by the modeling operator. TFWI, similar to other data-space inversion method, produces highly accurate results due to matching both the phase and amplitude of the data. One solution is to only match the phase using a single frequency per iteration (Pratt, 1999; Shin and Ha, 2008). Using phase only will prevent simultaneous inversion of scales. Another approach is to normalize each trace by its norm, as presented in Shen (2014). The issue with trace normalization is that it does not take into account the large difference in amplitude behavior between the transmission and reflection data, which makes it only usable when inverting a few events to match.
To overcome these limitations, I first derive the “original” TFWI using the two-parameter approach. Next, I rederive TFWI while keeping one abstract model that makes it applicable to different forms of the wave-equation. Then, I generalize the amplitude normalization inversion to use any nonlinear weighting function that is based on the data. Finally, I propose using a running window normalization that uses a Gaussian function to extract the local amplitude of the data.
In this abstract, we present some initial results on a specific nonlinear pseudoacoustic wave equation in anisotropic media, including forward modeling, linearization, and the adjoint method. Our objective is to find a robust and efficient method for anisotropic full-waveform inversion (FWI). The forward modeling equation is solved discretely by the rotated staggered finite difference scheme. The first-order Born modeling operator is obtained by linearizing the forward equation. Following adjoint methods, we derived the adjoint equation and tested it on simple models. Our results demonstrate a possibility for waveform inversion in anisotropic media.
Though anisotropy has been recognized to play an important role in seismic imaging and the industry has routinely incorporated transverse isotropy in seismic processing, building anisotropic models remains a great challenge because of its multiparameter nature. With elastic inversion under development, the acoustic approximation is still in use (Alkhalifah, 1998). This approximation results in a linear pseudodifferential equation for P-wave in vertical transverse isotropy (VTI) written in frequency-wavenumber domain as follows:
where u is the pressure wavefield, ω is the angular frequency, k is the wave vector, and vpz is the vertical P-wave velocity. S is a pseudodifferential operator, whose expression is:
where n is the unit wave vector and n2/a =(1+2ε)n2/x+n2/z, with ε and δ being the familiar Thomsen parameters (Thomsen, 1986). Physically, S controls the degree of anisotropy along different propagation directions. For isotropic media, S = 1.
Equation 1 can be computationally expensive to solve (Song and Alkhalifah, 2013; Le and Levin, 2014) because S incorporates all the anisotropic parameters. To overcome the computational intensity of solving Equation 1, Xu and Zhou (2014) introduced an approximation:
(3) By regarding the wavefront normal, n, as the direction of greatest change in the pressure wavefield, ⊽u, this approximation ignores any amplitude variation with angle, but is exactly correct for plane waves. For this reason, the approximation 3 might be called plane-wave approximation. Assuming local homogeneity, the linear pseudodifferential Erefeq:dispersion now becomes a nonlinear differential equation:
To produce a reliable Q model, we present a new method for wave-equation migration Q analysis in angle-domain common image gathers. We develop two ways of choosing the reference images for the objective function: one using the near angles of each angle gather and one using the near angles of the reference angle gather. We apply our methods to two 2D synthetic tests. The results show that the inverted Q anomalies are well retrieved. Compared with Q analysis from the stacked image, Q estimation using pre-stack gathers can obtain a higher resolution result. In addition, Q estimation from pre-stack gathers mitigates the side lobe problems that arise in the stacked gather.
Shen et al. (2013) and Shen et al. (2014) presented a new method, wave-equation migration Q analysis (WEMQA), to produce a reliable Q model. This method analyzes attenuation effects from the image space, which uses wavefield-continuation imaging with Q to stack out noise, focus and simplify events, and provide a direct link between the model perturbation and the image perturbation. In addition, this method uses waveequation Q tomography to handle complex wave propagation.
However, our previous method is performed on the stacked image, which presents limitations. First, to remove the influence of the reflectivities on the spectra, large windows are used for the image-space spectral analysis. The use of large windows makes the spectra of the windowed reflectivities statistically identical. This generates low resolution through model building and fails when the events in the stacked image have strong horizontal variation. Second, the spectra of the image are stretched differently at different velocities, which requires spectral unstretching before spectral analysis. Third, this method stacks the pre-stack image over the offset/angle, which causes problems for the model updating. For example, the updates shown in Figure 1(a) cannot restore the shape of the true Q model in Figure 2, even when a true image perturbation is applied. The strong side lobes are the result of information loss after stacking.
In this paper we present WEMQA on the pre-stack image, with angle-domain common image gather (ADCIG), to mitigate the problem that the stacked image presents. First, if a correct velocity model is used for migration, the events in the angle gathers are flat. Therefore, this method can obtain a high resolution result without requiring large windows for the spectral analysis, and avoid the spectral differences caused by the strongly horizontal varied events. Second, no spectral correction based on the velocity is required because each depth corresponds to one velocity in the angle gathers. Third, unlike stacked images, ADCIGs preserve all the data information, which makes it possible to update the model more correctly. Figure 1(b) shows that the Q updates retrieve the shape of the true Q model in Figure 2 using a true image perturbation.
We show that ambient seismic noise can be used to detect long-term velocity changes in Scholte-wave velocities at microseism frequencies. Two approaches to detect a time-lapse change in Scholte-wave velocities are tested: a data-domain and an image-domain approach. We rely on straight-ray tomography of perturbed traveltimes for imaging. The first approach is based on differentiating phase traveltime changes in the data domain. The second approach is based on differentiating group velocities in the image domain. Both methods work very well and compare well to a time-lapse image computed from controlled-source data. The time-lapse response is dominated by near-surface geomechanical effects of production-induced reservoir compaction.