Internal multiple prediction using inverse-scattering series with sparsity promotion — Part 1: Background, analysis, and synthetic modeling

The presence of internal multiples in seismic data can lead to artefacts in subsurface images ob-tained by conventional migration algorithms. This problem can be ameliorated by removing themultiples prior to migration, if they can be reliably estimated. Recent developments have renewedinterest in the plane wave domain formulations of the inverse scattering series (ISS) internal multipleprediction algorithms. We build on this by considering sparsity promoting plane wave transformsto minimize artefacts and in general improve the prediction output. Furthermore, we argue forthe usage of demigration procedures to enable multidimensional internal multiple prediction withmigrated images, which also facilitate compliance with the strict data completeness requirementsof the ISS algorithm. We believe that a combination of these two techniques, sparsity promotingtransforms and demigration, pave the way for a wider application to new and legacy datasets.

Internal multiple prediction using inverse scattering series withsparsity promotionPart II: Application strategy and field data examples

Incorrect imaging of internal multiples can lead to substantial imaging artefacts. It is estimatedthat the majority of seismic images available to exploration and production companies have had nodirect attempt at internal multiple removal. In Part I of this article we considered the role of spar-sity promoting transforms for improving practical prediction quality for algorithms derived fromthe inverse scattering series (ISS). Furthermore, we proposed a demigration-migration approach toperform multidimensional internal multiple prediction with migrated data and provided a syntheticproof of concept. In this paper (Part II) we consider application of the demigration-migration approach to field data from the Norwegian Sea, and provide a comparison to a post-stack method (froma previous related work). Beyond application to a wider range of data with the proposed approach,we consider algorithmic and implementational optimizations of the ISS prediction algorithms tofurther improve the applicability of the multidimensional formulations.

Enhancing internal multiple prediction by using the inverse scattering series: methodology and field application

We introduce four approaches that dramatically enhance the application of the inverse scattering series method for field data internal multiple prediction. The first approach aims to tackle challenges related to input data conditioning and interpolation. We addressed this through an efficient and fit-for-purpose data regularization strategy, which in this work was a nearest-neighbor search followed by differential moveout to accommodate various acquisition configurations. The second approach addresses cost challenges through applying angle constraints over both the dip angle and opening angle, reducing computational cost without compromising the model’s quality. We also propose an automatic solution for parameterization. The third approach segments the prediction by limiting the range of the multiple’s generator, which can benefit the subsequent adaptive subtraction. The fourth approach works on improving predicted model quality. The strategy includes correctly incorporating the 3D source effect and obliquity factor to enhance the amplitude fidelity of the predicted multiples in terms of frequency spectrum and angle information. We illustrate challenges and report on the improvements in cost, quality or both from the new innovative approaches, using examples from synthetic data and from three field data 2D lines representative of shallow and of deep water environments.

Comparison of monotonicity challenges encountered by the inverse scattering series and the Marchenko demultiple method for elastic waves

The reflection response of strongly scattering media often contains complicated interferences between primaries and (internal) multiples, which can lead to imaging artifacts unless handled correctly. Internal multiples can be kinematically predicted, for example by the Jakubowicz method or by the inverse scattering series (ISS), as long as monotonicity, that is, “correct” temporal event ordering, is obeyed. Alternatively, the (conventional) Marchenko method removes all overburden-related wavefield interactions by formulating an inverse problem that can be solved if the Green’s and the so-called focusing functions are separable in the time domain, except for an overlap that must be predicted. For acoustic waves, the assumptions of the aforementioned methods are often satisfied within the recording regimes used for seismic imaging. However, elastic media support wave propagation via coupled modes that travel with distinct velocities. Compared to the acoustic case, not only does the multiple issue become significantly more severe, but also violation of monotonicity becomes much more likely. By quantifying the assumptions of the conventional Marchenko method and the ISS, unexpected similarities as well as differences between the requirements of the two methods come to light. Our analysis demonstrates that the conventional Marchenko method relies on a weaker form of monotonicity. However, this advantage must be compensated by providing more prior information, which in the elastic case is an outstanding challenge. Rewriting, or remixing, the conventional Marchenko scheme removes the need for prior information but leads to a stricter monotonicity condition, which is now almost as strict as for the ISS. Finally, we introduce two strategies on how the remixed Marchenko solutions can be used for imperfect, but achievable, demultiple purposes.