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Wave-equation Migration Velocity Analysis

Subsalt velocity analysis by target-oriented wavefield tomography: A 3-D field-data example[paper][source]
Yaxun Tang and Biondo Biondi
We apply target-oriented wavefield tomography to a 3-D field data set acquired from the Gulf of Mexico. Instead of using the original surface-recorded data set, we use a new data set synthesized specifically for velocity analysis to update subsalt velocities. The new data set is generated based on an initial unfocused target image and by a novel application of 3-D generalized Born wavefield modeling, which correctly preserves velocity kinematics by modeling non-zero subsurface-offset-domain images. We show that the target-oriented inversion strategy drastically reduces the data size and the computation domain for 3-D wavefield tomography, greatly improving its efficiency and flexibility. We apply differential semblance optimization (DSO) using the synthesized new data set to optimize subsalt velocities. The updated velocity model significantly improves the continuity of subsalt reflectors and yields flattened angle-domain common-image gathers.
Migration velocity analysis for anisotropic models[paper][source]
Yunyue (Elita) Li and Biondo Biondi
Anisotropic models are recognized as more realistic representations of the subsurface in complex geological environments. These models are widely needed by many kinds of migration and interpretation schemes. However, anisotropic model building is still a challenging problem in the industry. In this paper, we propose an approach to building anisotropic models from surface seismic data based on the theory of Wave-Equation Migration Velocity Analysis (WEMVA). Because of the ambiguity between depth and Thomsen parameter δ, we parametrize our model space using only NMO velocity (Vnmo) and the anellipticity parameter η. We tested the anisotropic WEMVA on a shallow part of the Hess synthetic VTI model. The results show that anisotropic WEMVA is effective in resolving some of the anisotropic perturbation. However, a unique solution to the inversion requires additional constraining information.
Correlation-based wave-equation migration velocity analysis[paper][source]
Ali Almomin
Wave-equation migration velocity analysis (WEMVA) is a family of techniques that aim to improve the subsurface velocity model by minimizing the residual in the image space. Since the true image is unknown, measuring the residual in the image space is a challenge for WEMVA techniques. In this paper, I present a new method of measuring the image perturbation that is based on the cross-correlation of the observed image with a reference image in reflection angle gathers. I derive the gradient of this technique and show some synthetic examples that compare it to the optimum WEMVA gradient. I then modify the gradient in order to handle multiple events and show that it becomes immune to the problem of cycle skipping. I finally show a synthetic example of the modified gradient and compare it to the optimum gradient.
Moveout-based wave-equation migration velocity analysis[paper][source]
Yang Zhang and Biondo Biondi
We propose a new method to perform wave-equation migration velocity analysis using angle-domain common image gathers. Instead of maximizing the image-stack-power objective function directly with respect to the slowness, we link the objective function to the slowness indirectly through an intermediate moveout parameter. Since this approach is robust against the cycle-skipping problem, it produces more reasonable gradients. Also the proposed method does not require explicit picking of the moveout parameters. Our data examples shows the great potential of this method.
Migration velocity analysis by one-parameter residual moveout fitting in presence of strong lateral velocity anomalies[paper][source]
Biondo Biondi
The analysis of a simple synthetic data set recorded above a strong velocity anomaly and a flat reflector illustrates the challenges that can be encountered when performing residual-moveout analysis using a family of curves described by a single parameter. Overcoming these challenges is important if we want to use automatic velocity analysis methods that rely on the derivative of the stack power with respect to the residual-moveout parameter to compute velocity gradients. My analysis shows how, at some reflector locations, the stack-power may have a poorly defined peak because the residual moveout is more complex than the one-parameter model assumes. At other reflector locations, the peak of the stack-power is sharp but it is too far from the value of the parameter corresponding to no residual moveout. Consequently, the derivatives are unreliable, and possibly have even the wrong sign. More robust information could be provided by migrating data with lower frequencies, when available. A more general solution is smoothing the stack power along the residual-moveout parameter before evaluating its derivatives.

Full Waveform Inversion & velocity

A new waveform inversion workflow: Application to near-surface velocity estimation in Saudi Arabia [paper][source]
Xukai Shen, Thierry Tonellot, Yi Luo, Tim Keho, and Robert Ley
Waveform inversion is a more accurate near-surface velocity estimation tool than ray-based methods. It is able to solve complex near-surface velocity structure where conventional ray-based methods fail. If errors in the initial model are too large, waveform inversion will fail to converge to the correct model. This convergence problem is particularly obvious for large near-surface velocity contrasts and velocity inversions. We propose to address this issue with a new inversion workflow that adds a wave-equation traveltime inversion step prior to waveform inversion. The performance of our approach is evaluated on both synthetic and field data.
Combining forward-scattered and back-scattered wavefields in velocity analysis[paper][source]
Ali Almomin, Biondo Biondi, and Robert Clapp
Wave-Equation Migration Velocity Analysis (WEMVA) is a family of techniques that aims to improve the subsurface velocity model by minimizing the residual in the image space. This process is performed iteratively by linearizing the imaging operator in order to relate image perturbations to model updates. However, WEMVA techniques only utilize the kinematics in the forward-scattered wavefield. Ignoring the back-scattered wavefield results in model updates that have low vertical resolution. I present a method that combines the forward-scattered wavefield information from WEMVA with the back-scattered wavefield information from full-waveform inversion (FWI). This can be done by first decomposing the FWI gradient into forward- and back-scattered gradients, and then applying the proper weights to combine the back-scattered FWI gradient with the WEMVA gradient. These weights aim to enhance the components of the FWI gradients that overlap with the WEMVA gradient. Preliminary results show that the combined gradient converges faster and to a better solution.
Random boundary condition for low-frequency wave propagation[paper][source]
Xukai Shen and Robert G. Clapp
In this paper we present a random boundary that is effective at both high-frequencies (Reverse Time Migration) and low-frequencies (waveform inversion). This boundary condition uses larger, irregularly-shaped randomized velocity grains that are effective in introducing incoherency in wavefronts at a large range of wavelengths. We use source functions with a range of peak frequencies to compare this boundary condition to alternative implementations.

Linearized wave-equation inversion

Subsalt imaging by target-oriented wavefield least-squares migration: A 3-D field-data example [paper][source]
Yaxun Tang and Biondo Biondi
We pose the reflectivity-imaging problem as a linear inversion problem and solve it in the image domain in a target-oriented fashion. The most computationally intensive part of the image-domain inversion is the explicit computation of the Hessian matrix. We show how we can overcome the cost issue by using the phase-encoding technique in the 3-D conical-wave domain. We apply the inversion-based imaging methodology to a 3-D field data set acquired from the Gulf of Mexico (GOM), and we precondition the inversion with non-stationary dip filters, which naturally incorporate interpreted geological information. Numerical examples demonstrate that imaging by regularized inversion successfully recovers the reflectivities from the effects of uneven illumination, yielding images with more balanced amplitudes and higher spatial resolution.
Wave-equation inversion of time-lapse seismic data sets[paper][source]
Gboyega Ayeni
We propose a linearized wave-equation inversion formulation for time-lapse seismic data sets. Our method poses time-lapse imaging as a joint least-squares problem that utilizes target-oriented approximations to the Hessian of the objective function. Because our method accounts for illumination mismatches -caused by differences in acquisition geometries- and for band-limited wave-propagation effects, it provides better estimates of production-related changes in reservoir acoustic properties than conventional time-lapse processing methods. Using data sets from a North Sea field, we demonstrate how our method can be used to image differences between time-lapse data sets. Furthermore, we show that obstruction artifacts may be attenuated by wave-equation inversion.
Least-squares reverse time migration for the Cascadia ocean-bottom dataset[paper][source]
Mandy Wong, Shuki Ronen, and Biondo Biondi
We present a method based on least-squares reverse time migration (LSRTM) for imaging ocean-bottom data. We show that by using LSRTM, we not only enhance the resolution of the image but also suppress the migration artifacts. Furthermore, LSRTM also raise the relative amplitude of true reflectors in the subsurface. This method can also be extended to imaging with higher-order multiples. In certain geometries, LSRTM with multiples can further improve the image with a larger aperture. We demonstrate the concept and methodology in 2D and apply our proposed scheme to an ocean-bottom field survey located in the northern Cascadia continental margin.

Reverse time migration & Angle gathers

Imaging using compressive sensing[paper][source]
Robert G. Clapp
Constructing 3-D angle gathers is quickly becoming the computational bottleneck in Reverse Time Migration (RTM). Both the expansion in volume size (120-900x) and the cost of cross-correlating wavefields greatly increase the cost of RTM. Both the storage and computational cost can be greatly reduced by reformulating the imaging process as a compressive sensing problem. Preliminary results show that this approach holds promise but finding an acceptable L-1 inversion approach is still problematic.
Memory efficient 3D reverse time migration[paper][source]
Chris Leader and Robert Clapp
Reverse time migration in three dimensions has two key bottlenecks - wavefield computation and IO limitations due to mass data transfer. Wave propagation and correlation in three dimensions imposes large computational constraints, both in terms of the number of floating point operations and the size of objects that need to be allocated. Furthermore, wavefields must be constantly written and read from disk since memory cannot possibly hold them all, this causes conventional RTM to become IO bound quickly. To address the computation requirements GPU propagation kernels are used to greatly reduce the computation time for source side modeling, achieving speeds in excess of 2.5 gigapoints calculated per second. Additionally, data handling requirements are vastly reduced by imposing pseudo-random boundaries on the velocity field, allowing time reversable source propagation. Achieving time reversable source propagation alleviates the requirement of checkpointing or boundary reinjection; this minimal data transfer results in GPU on-device operations becoming further accelerated.
Reverse-time migration using wavefield decomposition[paper][source]
Kittinat Taweesintananon
Reverse-time migration (RTM) is capable of imaging very steeply dipping reflectors and overhangs. However, it usually produces strong artifacts that contaminate the shallow parts of the migrated images. These artifacts can be suppressed using an imaging condition with appropriate decomposed source and receiver wavefields. In this paper, such a technique is applied and examined. This imaging condition keeps only energy at the points where strong backscattering originates. The results show that RTM using wavefield decomposition is a promising remedy for attenuating artifacts compared to the implementation of a low-cut filter. However, some artifacts still remain in the decomposed RTM image. These residual artifacts are caused by the cross-correlation between the upgoing component of the direct source wavefield and the backscattered component of the receiver wavefield.
Elastic wavefield directionality vectors[paper][source]
Ohad Barak
The direction of energy propagation at every point in a wavefield propagated using an elastic finite-difference method can be deduced from the displacement vectors. The pressure-wave amplitude and displacements can be separated from the shear-wave amplitude and displacements using a separation operator. Amplitude separation can be used to create a more informative image by correctly imaging converted waves. Displacement separation enables calculation of the propagation direction, which can be used to create angle gathers without utilizing extended imaging conditions.

Velocity estimation and model building

Ambient seismic noise eikonal tomography for near-surface imaging at Valhall[paper][source]
Sjoerd de Ridder and Joe Dellinger
We demonstrate that in three passive seismic datasets recorded by an ocean-bottom-cable array at the Valhall field in the Norwegian North Sea, virtual-source interferometry over the frequency range 0.35-1.75 Hz produces strong omnidirectional Scholte-wave sources. We then use these virtual-sources gathers to image the shallow structure in high resolution using eikonal traveltime tomography. Unlike conventional tomography, which determines velocities between source and receiver using an inversion scheme, eikonal tomography computes the local traveltime gradient at each receiver, and thus directly estimates the local velocity in the neighborhood of each receiver. The Scholte-wave images produced from imaging the passive noise reveal many of the same features visible in the active P-wave data. These results suggest that a permanent recording system using passive seismic noise might be useful for real-time surveillance of shallow shear-wave velocity anomalies.
Interpreter input for seismic image segmentation[paper][source]
Adam Halpert
While automatic segmentation of seismic images can dramatically speed up interpretation of salt bodies and alleviate a major model-building bottleneck, human expertise at this task is valuable and should be included. Here, I demonstrate a strategy to incorporate such expertise into the highly-efficient Pairwise Region Comparison (PRC) segmentation algorithm. By supplying a limited manual interpretation of the salt boundary, interpreters can correct local inaccuracies and guide the automatic result in both two and three dimensions. In the 3D case, accuracy of the segmentation improves even in areas far from the manual picks. Examples from a wide-azimuth Gulf of Mexico survey demonstrate the effectiveness of this procedure.
Anisotropic tomography with rock physics constraints[paper][source]
Yunyue Li, Dave Nichols, Konstantin Osypov, and Ran Bachrach
Anisotropic model building is a challenging problem, well-known for its non-linear and underdetermined nature. To reduce the null-space and stabilize the inversion, we propose a new preconditioning scheme in linearized tomography to include rock physics prior information. We introduce the rock physics information in the form of covariance among P-wave vertical velocity (v0), ε and δ, and is generated by stochastic realizations of a compacting shale model. We design a VSP synthetic survey with the common industry geometry on two different examples, of which one fulfills the assumption of our rock physics model and the other does not. The results show that by utilizing the proper rock physics prior information, tomography can better resolve the anisotropy parameters, especially in the area where inversion is poorly constrained by the data. However, precautions should be taken when the lithology of the subsurface is largely unknown. Finally, we perform a posterior uncertainty analysis to evaluate the contribution of the rock physics prior information. The results show that the null-space is greatly reduced by introducing the prior information.
Model-building with image segmentation and fast image updates[paper][source]
Adam Halpert and Gboyega Ayeni
An accurate salt interpretation is an essential component of velocity model-building in areas dominated by complicated salt geology. The Pairwise Region Comparison (PRC) image segmentation algorithm can automatically pick salt bodies on seismic images, and be used as part of an iterative sediment-flood and salt-flood model-building workflow. In areas where the salt interpretation is highly uncertain, however, human expertise is needed to judge the relative accuracy of two or more possible models. We demonstrate a fast image updating scheme based on shot-profile migration that can be used to investigate how different salt interpretations provided by the PRC algorithm affect the final image. With further efficiency improvements, this process could allow for an interactive interpretation, model-building, and imaging workflow that substantially reduces cycle time for large-scale iterative imaging projects.

Bidirectional deconvolution

A new algorithm for bidirectional deconvolution[paper][source]
Yi Shen, Qiang Fu, and Jon Claerbout
We introduce a new algorithm for bidirectional deconvolution. In our method, we estimate the causal filters and anti-causal filters simultaneously instead of alternately. We test three data examples (1D synthetic, 2D synthetic and 2D field data). The results show that the wavelet can be compressed almost into a spike using our method. The two filters can be estimated equally when we are dealing with a zero-phase wavelet. In addition, our method has a lower computational cost and faster convergence rate than the method discussed by Zhang and Claerbout (2010).
An approximation of the inverse Ricker wavelet as an initial guess for bidirectional deconvolution [paper][source]
Qiang Fu, Yi Shen, and Jon Claerbout
Bidirectional deconvolution is a powerful tool for performing blind deconvolution on a signal that contains a mixed-phase wavelet, such as seismic data. Previously, we used a prediction error filter (PEF) as the minimum-phase filter and an impulse function as the maximum-phase filter as initial guesses. This surprised us by apparent instability as the solution would jump from spiking the first pulse of a Ricker wavelet to get larger middle pulse. In this paper, we propose new initial guesses for the causal and anti-causal deconvolution filters that are more effective on data with a Ricker-like wavelet. We test these on both synthetic data and field data. The results demonstrate that the new starting filters do a better job than the previous initial guesses.
A log spectral approach to bidirectional deconvolution [paper][source]
Jon Claerbout, Qiang Fu, and Yi Shen
The blind-deconvolution problem for non-minimum-phase-source was established in the time domain. This is a Fourier domain formulation. Changing variables from A(Z)B(1/Z) to U(Z)=ln(A(Z)B(1/Z)) leads to a different kind of whiteness - the output being orthogonal to its shifted soft clip.

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