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First EAGE/SBGf Workshop on Least-Squares Migration
- Conference date: November 27-28, 2018
- Location: Rio de Janeiro, Brazil
- Published: 27 November 2018
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North Sea Examples of Kirchhoff Least-squares Migration for Quantitative Interpretation
Authors C. Leone, M. Shadrina, K. Ramani, M. Cavalca and R. FletcherSummary3D borehole-related seismic data has superior quality and higher-frequency content compared to surface seismic data. These unique properties make it possible to produce high-resolution images and accurate velocity models especially around the borehole. However, using conventional imaging algorithms, that assume primary reflection energy, will retrieve only a limited area around the borehole. This problem can be overcome by including surface-related and internal multiples in the imaging algorithm to enhance the illumination of the. In addition, on-the-fly the velocity model can be updated using the so-called Joint Migration Inversion (JMI) process, which explains the full wavefield seismic data in terms of reflectivity and a propagation velocity model. To augment the results, datasets from different wells in the area can reinforce each other by simultaneous inversion to assure the consistency and improve the quality of the results. To steer and constrain the velocity estimation, the estimated reflectivity in the JMI process can be used as additional constraint for the velocity updating process.
In this paper we have deployed the full wavefield of the 3D borehole data, from two different wells, containing all orders scattering, both up- and down-going wavefields, in one integrated inversion-imaging process as proposed by the JMI methodology. The final result is a smooth accurate background velocity model along with a true amplitude reflectivity image with high resolution and maximum lateral extent.
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Pre-stack Least-Squares Reverse Time Migration in Presence of Strong Velocity Contrasts
More LessSummaryLeast-Squares Migrations have been well studied for the last few decades and are essentially known for their good properties in improving the signal-to-noise ratio, increasing the resolution and giving more accurate and better-balanced amplitudes. We focus on Least-Square Reverse Time Migration for its ability to handle complex velocity fields with sharp velocity contrasts. In this paper we present a short list of issues faced on real data cases. We propose solutions to overcome them but mainly detail the problems coming from the limitations of Born modelling in such cases. We describe an innovative solution based on the use of an adaptive subtraction algorithm to deal with strong velocity contrasts in the background model. The efficiency of this method is proven on a simple synthetic example. Subsequent application on a real field will exhibit the potential of our approach for producing images with fewer artefacts and better reflectivity updates.
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Image-domain Least-Squares Migration in Rapidly-Varying Media: Practical Considerations
Authors M. Cavalca, R.P Fletcher and D NicholsSummaryLeast-squares migration implemented in the image domain by approximating the blurring operator through a set of point spread functions has proven to be a viable method to mitigate the blurring effects present in depth migrated data. Yet, rapidly-changing media can challenge the accuracy/cost trade-off required for practical application of the approach, especially if the lithology justifies the inclusion of high contrasts in the velocity model (e.g. at salt boundaries). In this paper we discuss several methods to mitigate inaccuracies arising from such media, whilst keeping the cost affordable. We propose to work with irregularly-sampled PSFs and to rely on a masked linear interpolation that prevents interpolating PSFs across high velocity contrasts. Furthermore, when two-way wavefield propagators are employed, we propose two complementary approaches to mitigate high-order scattering artefacts arising at high velocity contrasts and distorting point spread functions close to these contrasts. We show that the combination of these approaches can help approximate the blurring operator more reliably, leading to improved inversion results.
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Least-Squares Migration Beyond Primaries
Authors N. Chemingui, F Liu and S LuSummaryWe present a least-squares inversion solution for Full Wavefield Migration (FWM). The algorithm is capable of imaging all reflection modes in the data consisting of primaries and multiples. The inversion approach is key to improving the resolution of seismic images and compensating for the illumination variations due to incomplete acquisitions. The least-squares method also attenuates the artifacts caused by the crosstalk between different orders of reflections. At its core, the inversion uses a Born modelling kernel capable of propagating the full reflection wavefield from seismic records. The algorithm solves for the earth reflectivity by means of data residual reduction in an iterative fashion. Successful applications to field data from different geological settings demonstrate the effectiveness of the solution in imaging the full seismic wavefield beyond primaries.
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Iterative Least-Squares Migration in Practice, Application to a Narrow Azimuth North Sea Dataset
Authors Ø Korsmo and A.A ValencianoSummaryA case study was carried out over the Viking Graben in the North Sea, were Least-Squares Wave-Equation Migration was used to obtain an optimal global image as well as revealing complex and subtle sand systems better than conventional migration. We address two main practical issues with the technology: errors in the background velocity model and cost. Accounting for un-resolved velocity effects in the data and evaluating different reflectivity models as input to the inversion.
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Exploring Inversion Strategies in Image Domain Least Squares Migration
Authors B Pereira-Dias, C Guerra, A Bulcão and R. de M DiasSummaryThis work explores different approaches for the image domain least-squares migration with Point Spread Functions (PSFs) computed in pre-stack and post-stack domain, using both Reverse Time Migration (RTM) and Kirchhoff migration engines. We also present two applications in 3D datasets of deepwater offshore of Brazil. Both strategies showed that least-squares migration provide an uplift in the migration amplitudes and resolution even on geologically complex models.
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Neural Network Least Squares Migration
Authors Zhaolun Liu and Gerard SchusterSummarySparse least squares migration (SLSM) estimates the reflectivity distribution that honors a sparsity condition. This problem can be reformulated by finding both the sparse coefficients and basics functions from the data to predict the migration image. This is designated as neural network least squares migration (NLSM), which is a more general formulation of SLSM. This reformulation opens up new thinking for improving SLSM by adapting ideas from the machine learning community.
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Applying Least-Squares Migration Methods in Time Imaging: Marine and Land Data Example
Authors S Dell, M Gloeckner, C Vanelle and D GajewskiSummaryTime migration is an attractive tool to produce subsurface images because it is very fast, less sensitive to the model errors than depth migration and, usually, massively parallelized technique. However, the time-migration operator is derived by considering many assumptions, among others a straight ray propagation, regularly sampled seismic data and infinite migration aperture which frequently results in deteriorated images. Least-squares techniques can also be applied within the time-migration framework to tackle the imaging problems. As migration/demigration strongly depends on the velocity model, we first apply an iterative time-migration model building based on kinematic wavefield attributes and a thresholding approach followed by interpolation and smoothing. In this paper, we investigate three least-squares time-migration methods: the conventional approach using conjugate gradient (L-BFGS) optimization, a single-iteration approach using Hessian filter and CRS data conditioning, an iterative approach using preconditioning by diffraction correlation matrix. All least-squares methods lead to an enhancement of the image resolution and mitigating migration artifacts.
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Application of Single-Iteration Least-Squares Migration to the Brazilian Pre-Salt
More LessSummaryReverse-time migration (RTM) is the state-of-the-art imaging technology for complex structures. The most important plays nowadays in Brazil are in the pre-salt region. The complex overburden above them, with salt bodies, volcanics and/or shallow carbonates, produces illumination variations thus generating amplitude distortions in the migrated image. Least-squares RTM aims at approximating the inverse of the forward modeling operator, and as such it promises to reduce migration artifacts and compensate for illumination variations due to both acquisition geometry and complex overburden. We apply CHF-based LS-RTM to two field datasets in the Santos basin, acquired using narrow-azimuth streamer geometry.
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Iterative Least-Squares Migration without Cycle Skipping
More LessSummaryLeast-squares reverse-time migration (LSRTM) has been shown to improve image quality over conventional RTM by enhancing the resolution, balancing illumination, and suppressing migration artefacts. However, it is also known to be sensitive to velocity errors. In the presence of velocity errors, predicted data show different moveouts from the observed data, which will hinge LSRTM convergence and yield sub-optimal results. To mitigate velocity errors, we propose to apply dynamic time warping (DTW) to the observed data and shift them towards the predicted data to improve data matching and subsequently images. In this paper, we show 2 synthetic examples and 1 real data example to demonstrate the advantages of dynamic time warping. Our observations show that dynamic time warping helps with event focusing, corrects phase distortion, improves event amplitudes, and thus improves event continuity.
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Zero-Offset Sections with a Deblurring Filter in the Time Domain
Authors Shihang Feng, Oz Yilmaz, Yuqing Chen and Gerard SchusterSummaryWe present a velocity independent workflow for constructing a zero-offset reflection section that preserves most of the reflections and diffractions. This workflow constructs a migration image volume by prestack time migration (PSTM) using a series of constant-velocity models. A deblurring filter for each constant-velocity model is applied to each time migration image to get a deblurred image volume. In order to preserve all events in the image volume, each deblurred image panel is demigrated and then summed over the velocity axis. The resulting demigration section is equivalent to a zero-offset reflection section. Compared with the workflow without deblurring filter, the composite zero-offset reflection section has higher resolution. A more accurate estimate of the velocity distribution can be obtained from this workflow using time-migration velocity analysis, which can then used as the velocity model to migrate the zero-offset section. Numerical tests are used to validate the effectiveness of this method with 3D synthetic data.
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Tomographic Full Waveform Inversion via Iterative Least-Squares Migration by Variable Projection Method
Authors G. B. Barnier, E. B. Biondi and B. B. BiondiSummaryWe present a velocity independent workflow for constructing a zero-offset reflection section that preserves most We tackle the well-known global convergence issue associated to any full waveform inversion (FWI) approach by solving an extended-image space least-squares migration problem to remove any local minima present in the FWI objective function. We discuss the connection between the reflectivity and migration velocity inversion and show the importance of combing the two problems using one objective function. Moreover, we show the full separability of the two inverse problems by using the variable projection method.
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Least-Squares Migration Using Surface-Related Multiples on Data with Large Acquisition Gaps
Authors A. Nath and D.J. VerschuurSummarySeismic acquisition in an area can often get hindered by reasons such as complex topography, infrastructure (e.g. platforms) or lack of access due to legal and environmental reasons. Such areas with possibilities of large data gaps may deter exploration or monitoring, as the conventional imaging strategies would either provide bad seismic images or turn out to be very expensive. Surface-related multiples travel different paths compared to primaries, illuminating a wider subsurface area. This property makes the surface-related multiples particularly important in case of data with large gaps. In this paper we show different strategies of using surface-related multiples to get around the problem of imaging with a large data gap. Conventional least-squares imaging methods that incorporate surface-related multiples do so by re-injecting the measured wavefield, which makes it sensitive to missing data. Therefore, we present a ‘non-linear’ imaging method that models all the surface-related multiples in the unacquired section from the original source field. Eventually we also demonstrate a ‘hybrid’ method that combines the ‘non-linear’ imaging method with the conventional ‘linear’ multiple imaging method, which further improves our imaging result. We test the methods on synthetic as well as field data. Despite large acquisition gaps, our method gives promising results.
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Multiparameter Deblurring Filter and its Application to Elastic Migration and Inversion
Authors Z.F. Feng and G.S. SchusterSummaryWe present a multiparameter deblurring filter that approximates the Hessian inverse. This filter considers the coupling between different parameters by using stationary local filters to approximate the submatrices of the Hessian inverse for the same and different types of parameters. Numerical tests with elastic migration and inversion show that the multiparameter deblurring filter not only reduces the footprint noise, balances the amplitude and increases the resolution of the elastic migration images, but also mitigates the crosstalk artifacts. When used as a preconditioner, it also accelerates the convergence rate for elastic inversion.
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Onshore Mexico Example of Least-Squares Migration for Improved Imaging and Inversion
SummaryIn oil exploration today, many easy targets are exhausted and seismic imaging is often relied on in areas that suffer from variable illumination due to complex overburden heterogeneity. At the same time, seismic data are increasingly expected to reveal subsurface rock properties and fluid information. To achieve this, rock physics analysis and property estimation using seismic inversion are essential, but these methods assume that changes in seismic amplitudes reflect changes in lithology, which may not be the case for an onshore seismic dataset formed from a merge of different acquisitions and affected by complex overthrust with large velocity contrasts. In this case study we demonstrate how least-squares migration in the image domain was successful in improving seismic images and inversion results for an onshore Mexico project.
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Onshore Mexico Example of Least-Squares Migration for Improved Imaging and Inversion
Authors Y. Chen and G. SchusterSummaryViscoacoustic migration can significantly compensate for the amplitude loss and phase distortion in migration images computed from highly attenuated data. However, solving the viscoacoustic wave equation requires a significant amount of storage space and computation time, especially for least-squares migration methods. To mitigate this problem, we use acoustic reverse time migration (RTM) instead of viscoacoustic migration to migrate the viscoacoustic data, and then correct the amplitude and phase distortion by hybrid deblurring filters in the image domain. Numerical tests on synthetic and field data demonstrate that acoustic RTM combined with hybrid deblurring filters can compensate for the attenuation effects and produce images with high resolution and balanced amplitudes. This procedure requires less than 1/3 of the storage space and N/2 of the computation time compared to the viscoacoustic migration. Here the N indicates the iteration number of the least-square migration method. This procedure can be extended to 3D migration at even a greater cost saving.
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