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Velocity estimation

Resolving the effects of production-induced overburden dilation using simultaneous TV-regularized time-lapse FWI [SRC]
Musa Maharramov, Biondo Biondi and Mark Meadows
We present a field data application of the technique proposed by Maharramov and Biondi (2015) for reconstructing production-induced subsurface model changes from time-lapse seismic data using full-waveform inversion (FWI). The technique simultaneously inverts multiple survey vintages with total-variation (TV) regularization of the model differences. We apply it to the Gulf of Mexico, Genesis Field data, and successfully 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.
Residual-moveout-based wave-equation migration velocity analysis --- field data example [SRC]
Yang Zhang and Biondo Biondi
We apply our residual-moveout-based (RMO-based) wave-equation migration velocity analysis (WEMVA) method to an industry scale 3-D marine streamers wide-azimuth data set --- E-Octopus III in the Gulf of Mexico. This 3-D field data set poses many challenges for our implementation, including irregular geometry, abnormal traces, complex 3-D salt geometry, and more importantly, huge data volume and large domain dimensions. To overcome these hurdles, we apply careful data regularization and preprocessing, and employ a target-oriented inversion scheme that focuses on the update of sediment velocities in specific regions of interest. Such target-oriented scheme significantly reduces the computational cost, allowing us to make our WEMVA method affordable on our academic cluster. Our experiment result on a subsalt sediments target region shows that the angles of illumination on the subsalt sediments are very limited (less than 25 degrees) because of the complex salt overburden and the depth of the target. Although the lack of angular illumination in this region severely reduces the capability of any reflection tomography method that tries to resolve a better velocity model, our RMO-based WEMVA method is still able to detect the curvatures of the angle gathers and produce good velocity model updates that further flatten the angle gathers and improve the quality of the structural image in the target region.
Amplitude normalization in TFWI [SRC]
Ali Almomin
Tomographic Full Waveform Inversion (TFWI) provides a robust and accurate method to invert the seismic data by simultaneously inverting all scales of the model. However, maintaining simultaneous inversion of scales is hindered when the modeling operator cannot accurately match the amplitudes of the data. In this paper, I modify TFWI to increase robustness against amplitude inaccuracies in the modeling operator by normalizing the objective function using a running-window filter. Finally, I test the proposed algorithm on the Marmousi. The results of the modified TFWI show a major improvement in the accuracy and convergence rate of the inversion.
Domain decomposition in shape optimization for segmenting salt bodies [SRC]
Taylor Dahlke, Biondo Biondi and Robert Clapp
Level set methods can provide a sharp interpretation of the salt body by defining the boundary as an isocontour of a higher dimensional implicit representation, and then evolving that surface to minimize the Full Waveform Inversion objective function. I propose to take advantage of the benefits that the shape optimization approach has to offer. First, because the implicit surface update gradient is based on the tomographic update gradient, there is potential to utilize it to update the background velocity concurrently with the salt boundary. Second, we can decompose the update gradient into separate partitions with individual scaling parameters in order to better avoid local minima in our search and more effectively converge on the true model. Using a shape optimization approach on synthetic examples, we can achieve reasonable convergence both in terms of the residual L2 norm, as well as the evolution of the salt boundary and background velocity towards the true model, demonstrating the feasibility of this approach. Ultimately, this method can be integrated into the processing work flow as a tool that provides improved building and refining of the velocity models used for imaging.
Addressing the effects of inaccurate top-salt delineation on subsalt seismic imaging [SRC]
Guillaume Barnier and Biondo Biondi
Imaging in the presence of salt bodies is important for the oil and gas industry but, it is also very difficult. Current seismic imaging techniques may still fail to capture the fine-scale details of a rugose boundary between the top of a salt body and its overlying sediments. This lack of accuracy can have a destructive effect on images of potentially hydrocarbon-bearing layers located underneath the salt. In this paper, we give an overview of the main challenges encountered by the oil and gas industry in terms of subsalt imaging, and we explain the importance of addressing the problem of top-salt boundary delineation. We conduct synthetic tests, and show that a slight misinterpretation of a top-salt boundary significantly damages the image quality of underlying layers. Image gathers may become incoherent and uninterpretable, which prevents us from using standard migration velocity analysis techniques to improve imaging. There is a need to develop a technique that enables us to refocus the subsalt images. We propose an approach for future research.

Modeling and imaging

Inverse demigration for simultaneous source separation [SRC]
Chris Leader and Biondo Biondi
Separating simultaneously acquired seismic data is the link between more efficient acquisition and conventional imaging techniques. Existing methods for separation rely on coherency measurements and work only for randomly delayed sources. By using the extended image space, data blended with a variety of time delay sequences can be well separated. Demigration will then output the separated, conventionally equivalent, dataset. A single pass of demigration can adequately recreate kinematic information. For amplitude balancing, however, an inverse process is required. By introducing a blending operator into a linearised inverse system posed in the extended image space, accurate data separation is observed for a variety of blending schemes, without the need for an accurate velocity model. Furthermore, such a system can be easily adapted to include velocity model updates, since extended imaging has already been applied.
Inadequacy of inverse theory for images [SRC]
Jon Claerbout and Antoine Guitton
Prior information generally enters inverse theory as regularization. In large scale problems such as image estimation where iteration does not continue to completion, an additional way to introduce a prior model is as the starting model. This lesson, hard won at Galilee, is widely applicable.
Adjoint formulation for the elastic wave equation [SRC]
Gustavo Alves
I present the formulation for the forward non-linear elastic wave equation and the linearized Born modeling approximation. The methodolgy used is similar to the adjoint formulation presented for the acoustic case by Almomin (2013). I also demonstrate how a perfectly matched absorbing layer (PML) can be applied to the formulation and derive the necessary adjoints for implementing inversion methods. Finally, I show results for a synthetic model using the linear approximation and compare it to the non-linear solution for a small localized perturbation. The linear solution converges to the non-linear one when the perturbation is small in relation to the background model.
Reverse-time migration using the rapid expansion method (REM) [SRC]
Alejandro Cabrales-Vargas
Reverse-time migration using the rapid expansion method allows the use of coarse time steps, and can be used as an alternative to high-order finite difference schemes. Its implementation using the pseudospectral method avoids the occurrence of frequency dispersion artifacts, and can be easily adapted to handling anisotropy. I use random boundary conditions to reduce memory usage. Tests in two-dimensional synthetic models show the ability of this method to handle strong velocity and anisotropy contrasts in the presence of complex geology, regardless of the time resolution of the data.

Anisotropy and attenuation

Image-based Q tomography using reverse time Q migration [SRC]
Yi Shen and Tieyuan Zhu
We have developed a technique to tomographically estimate a Q model from migrated images using two-way wavefield continuation. When compared with our previously proposed technique that uses a one-way downward-continuation method, this technique better handles steep structures, e.g. salt flanks. Numerical results on a complex model with a salt body demonstrate the effectiveness of our two-way method for resolving attenuation in the presence of steep and overturned structures.
Approximating Q propagation to speed up finite differences [SRC]
Robert G. Clapp
Propagating wave-fields using explicit finite difference is the kernel for Reverse Time Migration (RTM) and high end velocity analysis algorithms. To avoid grid dispersion artifacts, the cost of propagation is proportional to the frequency of the energy being propagated raised to the fourth power. Attenuation in the earth tends to decrease usable frequencies as a function of time. By using an approximation to the wave equation for attenuated media, to save computation, we can approximate the earth's behavior. As a result we can use coarser sampling at large time. Combined with limiting grid propagation to around the source at early times we can achieve large speedups in modeling, migration, and potentially velocity analysis.
Using a nonlinear wave equation for anisotropic inversion [SRC]
Huy Le, Biondo Biondi, Robert G. Clapp and Stewart A. Levin
We present some preliminary results on a specific nonlinear pseudo-acoustic wave equation in anisotropic media, including forward modeling, linearization, and adjoint method. Our objective is to find a robust and efficient method for anisotropic full-waveform inversion (FWI). The wave equation is solved discretely by the rotated staggered finite-difference scheme (RSFD) in time and space domains. The solution is more accurate than the one obtained using the centered finite-difference (CFD) scheme. The linearized equation is derived by taking only the first-order dependence of the wavefield with respect to medium parameters. The nonlinearity of the pseudo-acoustic wave equation introduces an additional term in the linearized equation. The adjoint method provides a mean to compute the gradients of the least-squares misfit objective function with respect to medium parameters through the adjoint wavefield. As a result of solving the forward equation by RSFD, the medium parameters are located on two different grids. We show that the gradients computed by the derived adjoint equation are in fact collocated consistently with the medium parameters. Applications on simple models, in both vertically transverse isotropic (VTI) and orthorhombic media, show that they also lead to the correct update directions. These results show the potential of our method for anisotropic parameter estimation.
Pseudo-acoustic modeling for tilted anisotropy with pseudo-source injection [SRC]
Musa Maharramov and Stewart A. Levin
We provide a general framework for deriving fast finite-difference algorithms for the numerical modeling of acoustic wave propagation in anisotropic media. We specialize this framework to the case of tilted transversely isotropic media to implement a kinematically accurate fast finite-difference modeling method. This results in a significant reduction of the shear artifacts compared to similar kinematically accurate finite-difference methods.
Using rock physics to improve Qp quantification in seismic data [SRC]
Yi Shen and Jack Dvorkin
We derived an approximate closed-form solution relating Vp to Qp using rock physics modeling. This solution is validated using well data in which the elastic properties were measured and Q was derived numerically using rock physics. We applied our new Qp-Vp equation to synthetic seismic data, which produced an improved Q model.

Passive seismic

Rayleigh-wave group velocity tomography using traffic noise at Long Beach, CA [SRC]
Jason P. Chang and Biondo Biondi
Anthropogenic sources recorded by passive seismic arrays provide the opportunity for ambient noise cross-correlation techniques to effectively use 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 use travel times of the fundamental-mode Rayleigh waves in a straight-ray tomography procedure to derive group velocity maps at 3.00 Hz and 3.50 Hz. The velocity trends in our results correspond to shallow depths and 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. Our results suggest important implications for research investigations concerned with the near-surface.
Applying interferometry to ambient seismic noise recorded by a trenched distributed acoustic sensing array [SRC]
Eileen Martin, Jonathan Ajo-Franklin, Nate Lindsey, Tom Daley, Barry Freifeld, Michelle Robertson, Craig Ulrich, Shan Dou and Anna Wagner
We deployed a shallow trenched distributed acoustic sensing (DAS) array consisting of multiple fiber optic cables and casings to assess the suitability of DAS to recording ambient noise for near-surface characterization. We briefly describe the acquisition of an ambient noise dataset, our processing workflow, and preliminary results of interferometry on a small data subset. The approximate virtual source responses show reasonable Rayleigh wave velocity estimates compared to geophones. The results of several types of cable casings are comparable, which is encouraging for surveys deployed in conditions requiring durable materials. We show coherent virtual source responses at a relatively high frequency range and short recording period relative to most passive seismic surveys.
Fast dispersion curves from ambient noise [SRC]
Eileen Martin
To calculate dispersion curves, phase velocity vs. frequency, from ambient seismic noise, many researchers calculate virtual source responses in the time domain, then stack. This algorithm scales as O(n2), where n is the number of sensors. If the data are regularly sampled in space and time, an existing O(nlogn) algorithm involves an F-K transform of the data cube followed by a transform into velocity vs frequency. I propose a new O(n) algorithm which only takes the Fourier transform of the data in time. The new algorithm is conceptually simple, parallelizes easily, and does not require regular spacing between sensors. I show similar results for dispersion curves resulting from both the O(n) algorithm and the O(n2) algorithm applied to data collected in a field trial of a trenched distributed acoustic sensing array at the Richmond Field Station. There are fewer opportunities for accumulating numerical error in the new O(n) algorithm, so it yields a sharper image than the O(n2) algorithm.

Sparse and L1 optimization

Double-difference time-lapse FWI with a total-variation regularization [SRC]
Musa Maharramov, Yinbin Ma and Biondo Biondi
In this paper we study double-difference FWI with a total-variation (TV) model-difference regularization (Maharramov and Biondi, 2014c). This data-space technique reduces the sensitivity of time-lapse FWI to inaccurate velocity model reconstruction. We describe a computational framework for conducting a TV-regularized double-difference FWI both as a simultaneous inversion and as an extension of single-model inversion. The method is demonstrated on linearized time-lapse waveform inversion of production effects for a synthetic example of compacting sub-salt reservoirs. We demonstrate the resolution of production effects and discuss stability of the results with respect to inaccuracies in the background velocity model.
Total-variation minimization with bound constraints [SRC]
Musa Maharramov and Stewart A. Levin
We present a powerful and easy-to-implement algorithm for solving constrained optimization problems that involve L1/total-variation regularization terms, and both equality and inequality constraints. We discuss the relationship of our method to earlier works of Goldstein and Osher (2009) and Chartrand and Wohlberg (2010), and demonstrate that our approach is a combination of the augmented Lagrangian method with splitting and model projection. We test the method on a geomechanical problem and invert highly compartmentalized pressure change from noisy surface uplift observations. We conclude the paper with a discussion of possible extension to a wide class of regularized optimization problems with bound and equality constraints.
Illumination compensation by L1 regularization and steering filters [SRC]
Yinbin Ma, Musa Maharramov, Robert Clapp and Biondo Biondi
L1/L2-regularization techniques often generate better results than the conventional least-squares solutions for inverse problem in geophysics. We implement a method to combine L1 regularization with steering filters. We obtain steering filters iteratively from input data without using any prior information. The numerical examples show significant improvement in comparison with the standard least squares. We demonstrate our method is robust with respect to inaccurate steering filters.
Time Lapse seismic imaging with L1 regularization and steering filters [SRC]
Yinbin Ma, Musa Maharramov, Robert Clapp and Biondo Biondi
We propose a new L1-regularized simultaneous time-lapse linearized waveform inversion method. We test the proposed method on models exhibiting production induced reservoir compaction and overburden dialation. We demonstrate that L1 regularization and steering filters significantly improve image quality in the presence of acquisition nonrepeatability issues, such as those caused by different acquisition parameters.

Acquisition processing and integration

Acquiring rotation data on the ocean bottom without rotation sensors [SRC]
Ohad Barak, Kerry Key, Steven Constable, Paul Milligan and Shuki Ronen
There are currently no widely available rotation sensors that can operate on the ocean-bottom. We derive rotation data on the ocean bottom from two surveys that were not originally designed to record them: 1) from geophone recordings in the Moere Vest ocean-bottom survey by differencing adjacent geophones; and 2) from magnetometer recordings in the SERPENT CSEM ocean-bottom survey by extrapolating from the deviations in magnetic field projections on the magnetometer components.
Toward PZ summation without Z [SRC]
Ettore Biondi and Stewart A. Levin
We examine the possibility of separating up-going and down-going wavefields of ocean-bottom data using only one component. This possibility relies on differential static shifts of the up-going events caused by near sea-bottom inhomogeneities. We downward continue a survey to the sea bottom to recover these shifts while leaving nonprimary arrivals smoothly curved. We then explore whether or not these static shifts are detectable in the curvelet domain. In addition, we show how suppressing fine-scale curvelet coefficients affects an event distributed along a disrupted hyperbolic curve. From our synthetic examples, we demonstrate that the curvelet domain has the potential to separate up-going from down-going events.

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