Electromagnetic Marchenko scheme based internal multiple elimination for lossless media

Due to shale-carbonate alternating successions with a gentle structure, primary reflections are severely interfered by various orders of strong and complex internal multiples from the overburden to reservoir levels in carbonate fields in the Middle East. These factors make the existing techniques ineffective, and still pose various geophysical challenges. This study aims to demonstrate an innovative scheme to eliminate internal multiples based on the Marchenko equation, originated from a basis of the inverse scattering theory. The extension of the Marchenko equation to surface seismic data enables a retrieval of upgoing and downgoing Green’s functions between a virtual source in a given subsurface location and receivers at the surface. Such a key feature in the Marchenko method is capable of identifying and/or eliminating internal multiples in a data-driven fashion, without the need for explicit subsurface models or numerical modelling. The technique estimates all the downgoing reflections from the overburden level, interfering primaries in the target level as internal multiples, which are subsequently subtracted from the input data to derive internal-multiple free data. To thoroughly assess the value of the Marchenko method, a numerical study was conducted. The realistic earth model that incorporates subsurface contexts in a carbonate field in the Middle East was derived to generate synthetic data through finite-difference modelling. The Marchenko-based internal multiple elimination was applied to synthesized data followed by reverse time migration. As true subsurface responses are known here, this trial properly revealed the effectiveness of the algorithm. For a comparison purpose, we also performed another processing flow using conventional internal multiple elimination that makes use of periodicity and velocity discrimination. The Marchenko scheme successfully estimates various types of internal multiples, such as over- and under-corrected multiples and even flat internal multiples, regardless of their periodicities, at once. Despite its ability to effectively suppress internal multiples, the final imaging results indicate that underlaying primary events are still preserved. The technique also leads to notable improvements in the imaging quality as compared to conventional processing flow. In addition to the effectiveness of the Marchenko method, we also describe a dedicated workflow adapted in this study to deal with strong and complex internal multiples. The unique advantage of the Marchenko scheme over existing approaches is its ability to predict internal multiples in a data-driven manner without precisely specifying multiple generators, assuming behaviors of internal multiples, or requiring prior knowledge of subsurface context. The Marchenko method can be also implemented for various ways such as redatuming, target oriented imaging and velocity estimation, source inversion problem, passive seismic, and electromagnetic, which will certainly provide several aspects of additional value.

Summary Multiples are real reflections from the underground interface, and if internal multiples can be effectively used, it can assist in illuminating shadowed areas that cannot be reached by primary., which is of great research value for the exploration and development of complex structural reservoirs. The single internal multiples imaging method is difficult to extract remove the illusion. Therefore, it is of great significance to study the joint imaging method of primary and internal multiples. In this paper, the feasibility of the joint imaging of primary and internal multiples is firstly verified. Then, the problem of opposite polarity between primary and internal multiples imaging is studied, and the problem of inconsistent polarity is well solved, so that the energy at the imaging interface is effectively compensated.

Recent work on retrieving the Green’s function with the Marchenko equation shows how these functions for a virtual source in the subsurface can be obtained from reflection data. The response to the virtual source is the Green’s function from the location of the virtual source to the surface. The Green’s function is retrieved using only the reflection response of the medium and an estimate of the first arrival at the surface from the virtual source. Current techniques, however, only include primaries and internal multiples. Therefore, all surface-related multiples must be removed from the reflection response prior to Green’s function retrieval. We have extended the Marchenko equation to retrieve the Green’s function that includes primaries, internal multiples, and free-surface multiples. In other words, we have retrieved the Green’s function in the presence of a free surface. The information needed for the retrieval is the same as the current techniques, with the only difference being that the reflection response now also includes free-surface multiples. The inclusion of these multiples makes it possible to include them in the imaging operator, and it obviates the need for surface-related multiple elimination. This type of imaging with Green’s functions is called Marchenko imaging.

Summary Recent work on autofocusing with the Marchenko equation has shown how the Green's function for a virtual source in the subsurface can be obtained from reflection data. The response to the virtual source is the Green's function from the location of the virtual source to the surface. The Green's function is retrieved using only the reflection response of the medium and an estimate of the first arrival at the surface from the virtual source. Current techniques, however, only include primaries and internal multiples. Therefore, all surface-related multiples must be removed from the reflection response prior to Green's function retrieval. Here, we extend the Marchenko equation to retrieve the Green's function that includes primaries, internal multiples, and free-surface multiples. In other words, we retrieve the Green's function in the presence of a free surface. We use the associated Green's function for imaging the subsurface. The information needed for the retrieval are the reflection response at the surface and an estimate of the first arrival at the surface from the virtual source. The reflection response, in this case, includes the free-surface multiples; this makes it possible to include these multiples in the imaging operator and it obviates the need for surface-related multiple elimination.

Recent work on autofocusing with the Marchenko equation has shown how the Green's function for a virtual source in the subsurface can be obtained from reflection data. The response to the virtual source is the Green's function from the location of the virtual source to the surface. The Green's function is retrieved using only the reflection response of the medium and an estimate of the first arrival at the surface from the virtual source. Current techniques, however, only include primaries and internal multiples. Therefore, all surface-related multiples must be removed from the reflection response prior to the Green's function retrieval. Here, we present a new scheme that includes primaries, internal multiples, and free-surface multiples. In other words, we retrieve the Green's function in the presence of the free surface. The information needed for the retrieval are the reflection response at the acquisition surface and an estimate of the first arrival at the surface from the virtual source. The reflection response, in this case, includes the free-surface multiples; this makes it possible to include these multiples in the imaging operator and it obviates the need for surface-related multiple elimination.

Internal multiples severely reduce seismic imaging quality and interpretation accuracy. With the continuous advancement of seismic imaging toward higher resolution, the accurate suppression of internal multiples has become increasingly critical. The concept of virtual events provides a fully data-driven approach for suppressing internal multiples. However, when energy interference occurs between internal multiples and primaries, the process of adaptive subtraction using matching filters may lead to damage to primaries. Building on the conventional virtual-events theory, an adaptive iterative method for the internal multiple suppression had been developed that reduces the dependency on the matching algorithm to some extent. Nonetheless, it remains unable to fundamentally prevent the loss of primary energy. To address this issue, we propose a waveform inversion-based internal multiple suppression method by constructing virtual events. Based on the theoretical foundation of the traditional virtual-events theory, we formulate an inversion objective function to estimate internal multiples via waveform inversion, thereby avoiding the requirement for the adaptive subtraction process. This approach achieves effective suppression of internal multiples while better preserving the primary energy. Comparing results with traditional methods, we demonstrate that the proposed method exhibits superior performance in both accuracy of multiple suppression and preservation of primary amplitude, providing a more reliable data foundation for subsequent seismic processing and geological interpretation.

Internal multiples deteriorate the image when the imaging procedure assumes only single scattering, especially if the velocity model does not reproduce such scattering in the Green’s function. If properly imaged, internal multiples (and internally-scattered energy) can enhance the seismic image and illuminate areas otherwise neglected or poorly imaged by conventional single-scattering approaches. Conventionally, in order to image internal multiples, accurate, sharp contrasts in the velocity model are required to construct a Green’s function with all the scattered energy. As an alternative, we develop a three-step procedure, which images the first-order internal scattering using the background Green’s function (from the surface to each image point), constructed from a smooth velocity model: We first back-propagate the recorded surface data using the background Green’s function, then cross-correlate the back-propagated data with the recorded data and finally cross-correlate the result with the original background Green’s function. This procedure images the contribution of the recorded first-order internal multiples and is almost free of the single-scattering recorded energy. This image can be added to the conventional single-scattering image, obtained e.g. from Kirchhoff migration, to enhance the image. Application to synthetic data with reflectors illuminated by multiple scattering only demonstrates the effectiveness of the approach.

The internal multiples, which are generated with strong reflection interfaces, have bothered the oil and gas exploration for a long time because of their complicated propagation paths and high costs in suppression. Considering that internal multiples are also real reflections from the underground interfaces, and reverse time migration can realize the correct imaging of multiples, a joint imaging method of primary and internal multiples is studied in order to reduce the calculation cost of multiple suppression and improve imaging accuracy. Firstly, the imaging condition for the data containing both primaries and internal multiples is analyzed and modified. Then, the corresponding solutions to the image artifacts introduced in the process of imaging are proposed, and the high-precision imaging for the seismic data containing both primaries and internal multiples is realized. Finally, the feasibility and effectiveness of the research method are verified by numerical tests.

Incorrect imaging of internal multiples can lead to substantial imaging artifacts. It is estimated that most seismic images available to exploration and production companies have had no direct attempt at internal multiple removal. Previously, we have considered the role of sparsity promoting transforms for improving practical prediction quality for algorithms derived from the inverse scattering series (ISS). Furthermore, we have developed a demigration-migration approach to perform multidimensional internal multiple prediction with migrated data and provided a synthetic proof of concept. Now, we consider application of the demigration-migration approach to field data from the Norwegian Sea and compare it to a poststack method (from a previous related work). Beyond application to a wider range of data with our approach, we consider algorithmic and implementational optimizations of the ISS prediction algorithms to further improve the applicability of the multidimensional formulations.

Subbasalt imaging for hydrocarbon exploration faces challenges with the presence of multiple scattering, attenuation, and mode conversion as seismic waves encounter highly heterogeneous and rugose basalt layers. A combination of modern seismic acquisition that can record densely sampled data and advanced imaging techniques make imaging through basalt feasible. Yet, the internal multiples, if not properly handled during seismic processing, can be mapped to reservoir layers by conventional imaging methods, misguiding geologic interpretation. Traditional internal multiple elimination methods suffer from the requirement of picking horizons of multiple generators and/or a top-down adaptive subtraction process. Marchenko imaging provides an alternative solution to directly remove the artifacts due to internal multiples, without the need of horizon picking or subtraction. In this paper, we evaluate a successful application of direct Marchenko imaging for subbasalt demultiple and imaging with an offshore Brazil field data set. The internal multiples in this example are generated from the seabed and basalt layers, causing severe artifacts in conventional seismic images. We have determined that these artifacts are largely suppressed with Marchenko imaging, and we have developed a general workflow for data preprocessing and regularization of marine streamer data sets. We find that horizontally propagating waves also can be reconstructed by the Marchenko method at far offsets.

SUMMARY Short-period internal multiples, resulting from closely spaced interfaces, may interfere with their generating (bandlimited) primaries, and hence they pose a long-standing challenge in their prediction and removal. A recently proposed method based on the Marchenko equation enables removal of the entire overburden-related scattering by means of calculating an inverse transmission response. However, the method relies on time windowing and can thus be inexact in the presence of short-period internal scattering. In this work, we present a detailed analysis of the impact of band-limitation on the Marchenko method. We show the influence of an incorrect first guess, and that adding multidimensional energy conservation and a minimum phase principle may be used to correctly account for both long- and short-period internal multiple scattering. The proposed method can currently only be solved for media with a laterally invariant overburden, since a multidimensional minimum phase condition is not well understood for truly 2-D and 3-D media. We demonstrate the virtue of the proposed scheme with a complex acoustic numerical model that is based on sonic log measurements in the Middle East. The results suggest not only that the conventional scheme can be robust in this setting, but that the ‘augmented’ Marchenko method is superior, as the latter produces a structural image identical to one where the finely layered overburden is missing. This is the first demonstration of a data-driven method to account for short-period internal multiples beyond 1-D.

Marchenko methods use seismic data acquired at or near the surface of the earth to estimate seismic signals as if the receiver (now a virtual receiver) was at an arbitrary point inside the subsurface of the earth. This process is called redatuming, and it is central to subsurface imaging. Marchenko methods estimate the multiply scattered components of these redatumed signals, which is not the case for most other redatuming techniques that are based on single-scattering assumptions. As a result, images created using Marchenko redatumed signals contain a reduction in the artifacts that usually contaminate migrated seismic images due to improper handling of internal multiples. We exploit recent theoretical advances that enable virtual sources and virtual receivers to be placed at arbitrary points inside the subsurface as a means to incorporate vertical seismic profile (VSP) data into Marchenko methods. The advantage of including this type of data is that the additional acquisition boundary increases subsurface illumination, which in turn enables vertical interfaces and steeply dipping structures to be imaged. We develop this methodology using two synthetic data sets. The first is created using a simple variable density but constant velocity subsurface model. In this example, we find that our newly devised VSP Marchenko imaging methodology enables imaging of horizontal and vertical structures and that optimal results are achieved by combining these images with those created using standard Marchenko imaging. A second example demonstrates that the method can be applied to more realistic subsurface structures, in this case a modified version of the Marmousi 2 model. We determine the applicability of the methods to image fault structures with the final imaging result containing reduced contamination due to internal multiples and an improvement in the imaging of fault structures when compared to other standard imaging methods alone.

The growth of seismic surveys using small airgun sources and short streamers has significantly reduced the costs and environmental impacts, but may limit the quality of reflection images. Using a 2D deep marine reflection survey in the South Atlantic with two small airguns and a 600-m-long streamer, we examine the challenges and solutions to imaging deep seafloor structures. The two main challenges are low signal-to-noise ratio and poor seismic illumination. In response, we performed noise attenuation methods such as de-swell and de-bubble to suppress noise through different processing steps. We also evaluate the impact of illumination on reverse-time migration and finite-difference migration methods. Furthermore, more challenges arise in association with limited source energy, short streamers, bio-interruptions, and 2D rather than 3D acquisition geometry. The data collected from such low-energy and short-streamer surveys require dedicated efforts to preserve seismic image fidelity against artifacts and position error. For imaging deep ocean sediments, our onboard monitoring based on brute stacks allowed timely identification of imaging issues, while post-survey processing focused on suppressing image artifacts due to airgun bubble reverberation, internal multiples, and sideswipe.

Some of the important petroleum reservoirs accumulate beneath the seas and oceans. Marine seismic reflection method is the most efficient method and is widely used in the petroleum industry to map and interpret the potential of petroleum reservoirs. Multiple reflections are a particular problem in marine seismic reflection investigation, as they often obscure the target reflectors in seismic profiles. Multiple reflections can be categorized by considering the shallowest interface on which the bounces take place into two types: internal multiples and surface-related multiples. Besides, the multiples can be categorized on the interfaces where the bounces take place, a difference between long-period and short-period multiples can be considered. The long-period surface-related multiples on 2D marine seismic data of the East Coast of the United States-Southern Atlantic Margin were focused on this research. The seismic profile demonstrates the effectiveness of the results from predictive deconvolution and the combination of surface-related multiple eliminations (SRME) and parabolic Radon filtering. First, predictive deconvolution applied on conventional processing is the method of multiple suppression. The other, SRME is a model-based and data-driven surface-related multiple elimination method which does not need any assumptions. And the last, parabolic Radon filtering is a moveout-based method for residual multiple reflections based on velocity discrimination between primary and multiple reflections, thus velocity model and normal-moveout correction are required for this method. The predictive deconvolution is ineffective for long-period surface-related multiple removals. However, the combination of SRME and parabolic Radon filtering can attenuate almost long-period surface-related multiple reflections and provide a high-quality seismic images of marine seismic data.

In this paper, we propose a fully automatic and efficient algorithm for realistic 3D face reconstruction by fusing multiple 2D face images. Firstly, an efficient multi-view 2D face alignment algorithm is utilized to localize the facial points of the face images; and then the intrinsic shape and texture models are inferred by the proposed Syncretized Shape Model (SSM) and Syncretized Texture Model (STM), respectively. Compared with other related works, our proposed algorithm has the following characteristics: 1) the inferred shape and texture are more realistic owing to the constraints and co-enhancement among the multiple images; 2) it is fully automatic, without any user interaction; and 3) the shape and pose parameter estimation is efficient via EM approach and unit quaternion based pose representation, and is also robust as a result of the dynamic correspondence approach. The experimental results show the effectiveness of our proposed algorithm for 3D face reconstruction.