A focusing function is a specially constructed field that will come into focus at a specified subsurface position upon back propagation (injection) into the medium. The concept of focusing functions is a key ingredient in the Marchenko method and its applications such as retrieving Green’s function, redatuming, imaging with multiples, and creating virtual sources/receivers. In this study, we show how the focusing function and its corresponding focused response at a specified subsurface position are heavily influenced by the data aperture at the surface. Such effects can be explained by considering focusing function in the context of time-domain imaging and its usual assumptions. In particular, we show that the focused response in the time-imaging domain radiates in the direction perpendicular to the line drawn from the center of the surface data aperture to the focused position. The corresponding direction in the Cartesian domain is simply then a combination of the time-domain direction and the directional change due to time-to-depth conversion. Therefore, the result from this study provides insights towards a better understanding of focusing function and may have meaningful implications in applications such as the construction of virtual subsurface source, where the directionality of the focused response is important.
Presentation Date: Tuesday, October 16, 2018
Start Time: 1:50:00 PM
Location: Poster Station 12
Presentation Type: Poster
The Marchenko method represents a constructive technique toobtain Green�s functions between the acquisition surface andany arbitrary point in the medium. The process generally involvessolving an inversion starting with a direct-wave Green's function from the desired subsurface position, which is typicallyobtained using an approximate velocity model. In thisstudy, we first propose to formulate the Marchenko method inthe time-imaging domain. We recognize that the traveltimeof the direct-wave Green�s function is related to the Cheop�straveltime pyramid commonly used in time-domain processingand can be readily obtained from the local slopes of thecommon-midpoint (CMP) gathers. This observation allowsus to substitute the need for a prior velocity model with thedata-driven slope estimation process. Moreover, we show thatworking in the time-imaging domain allows for the specificationof the desired subsurface position in terms of vertical time,which is connected to the Cartesian depth position via the timeto-depth conversion. Our results suggest that the prior velocitymodel is only required when specifying the position in depthbut this requirement can be circumvented by making use of thetime-imaging domain and its usual assumptions. Provided thatthose assumptions are satisfied, the estimated Green�s functionsfrom the proposed method have comparable quality tothose obtained with the knowledge of a prior velocity model.
Presentation Date: Wednesday, October 17, 2018
Start Time: 1:50:00 PM
Location: 211A (Anaheim Convention Center)
Presentation Type: Oral
The Biot theory provides a general framework for describing the seismic response of porous media. Proper boundary conditions must be specified for the following three cases: the elastic-poroelastic interface, the acoustic-poroelastic interface and the poroelastic-poroelastic interface for accurate modeling and inversion of seismic data. In this study, we first review the expressions for reflection coefficients for all three cases from plane-wave analysis. We subsequently benchmark the first two cases against spectral element method (SEM) forward modeling to verify and ensure consistency between finite-frequency wavelets. We show with numerical examples, that both methods lead to comparable results within frequency range between 5Hz and 80Hz, which is of relevance to exploration seismology.
Presentation Date: Monday, October 15, 2018
Start Time: 1:50:00 PM
Location: Poster Station 15
Presentation Type: Poster
The Marchenko redatuming approach reconstructs wavefields at depth that contain not only primary reflections, but also multiply-scattered waves. While such fields in principle contain additional subsurface information, conventional imaging approaches cannot tap into the information encoded in internal multiples in a trivial manner. We discuss a new approach that uses the full information contained in Marchenko-redatumed fields, whose output are local reflection and transmission responses that fully enclose a target volume at depth, without contributions from over- or under-burden structures. To obtain the Target-Enclosing Extended Images (TEEIs) we solve a multi-dimensional deconvolution (MDD) problem that can be severely ill-posed, so we offer stable estimates to the MDD problem that rely on the physics of the Marchenko scheme. We validate our method on ocean-bottom field data from the North Sea. In our field data example, we show that the TEEIs can be used for reservoir-targeted imaging using reflection and, for the first time, local transmission responses, shown to be the direct by-product of using internal multiples in the redatuming scheme. Finally, we present local, TEEI-derived reflection and transmission images of the target volume at depth that are structurally consistent with a benchmark image from conventional migration of surface data.
Presentation Date: Monday, September 25, 2017
Start Time: 2:40 PM
Presentation Type: ORAL
The goal of Marchenko redatuming is to reconstruct, from single-sided reflection data, wavefields at virtual subsurface locations containing transmitted and reflected primaries and internal multiples, while relying on limited or no knowledge of discontinuties in subsurface properties. Here, we address the limitations of the current Marchenko scheme in retrieving waves in highly heterogeneous media, such as subsalt or subbasalt. We focus on the initial focusing function that plays a key role in the iterative scheme, and propose an alternative focusing function that uses an estimate of the inverse transmission operator from a reference model that contains sharp contrasts (e.g., salt boundaries). Using a physics-driven estimate of the inverse transmission operator, we demonstrate that the new approach retrieves improved subsurface wavefields, including enhanced amplitudes and internal multiples, in a subsalt environment.
The retrieval of wavefields within the earth’s subsurface where no receivers or sources are available is a key component of wave-equation imaging and inversion; however, retrieving fullwave responses containing internal multiples with improved amplitudes has long presented a challenge to imaging practice. The method of Marchenko redatuming or autofocusing (Broggini et al., 2011; Wapenaar et al., 2013) proposes to retrieve such wave responses inside the subsurface, while using relatively little information about the earth’s properties. The fields retrieved by Marchenko redatuming can, in principle, be used to improve imaging beyond current capabilities, as discussed by Behura et al. (2012), van der Neut et al. (2013), Broggini et al. (2014), Slob et al. (2014),Wapenaar et al. (2014a) and Vasconcelos et al. (2014). Recently, Ravasi et al. (2015) validated the imaging capabilities of the method on oceanbottom field data. While indeed capable of retrieving internal multiples and correcting amplitudes, recent studies in the presence of highly complex media brought forth some limitations of the current Marchenko scheme (van der Neut et al., 2014a; Wapenaar et al., 2014b). With the aim of applying Marchenko redatuming in geologically complex media such as subsalt, we review the limitations of the existing approach and propose an alternative scheme capable of accounting for higher medium complexity.
We describe a method for source deghosting after imaging. The method consists of a multi-dimensional deterministic deconvolution of a standard migrated image using non-Hessian form operators. The operators, created by modelling with ghost effects followed by standard migration, compensate for both dip dependent illumination and ghost effects, and provide an estimation of the reflectivity. Applying a standard modelling then migration operator to the estimated reflectivity yields the 3D deghosted image.
We illustrate the post-imaging deghosting approach on 2D and 3D synthetic data modelled over complex salt structures. In both examples the image of the no-ghost data compares well with the deghosted image. The sensitivity of the post-imaging deghosting approach to the migration velocity model is also briefly discussed. We see a potential application of this method for source side deghosting.
Wapenaar, Kees (Delft University of Technology) | Thorbecke, Jan (Delft University of Technology) | van der Neut, Joost (Delft University of Technology) | Vasconcelos, Ivan (Schlumberger Gould Research) | van Manen, Dirk-Jan (ETH Zürich) | Ravasi, Matteo (University of Edinburgh)
Despite the close links between the fields of time-reversed acoustics, seismic interferometry and Marchenko imaging, a number of subtle differences exist. This paper reviews the various focusing conditions of these methods, the causality/acausality aspects of the corresponding focusing wavefields, and the requirements with respect to omnidirectional/single- sided acquisition.
It has been noted by various authors that there exists a close link between time-reversed acoustics and seismic interferometry (Derode et al., 2003; Wapenaar et al., 2005; van Manen et al., 2005; Bakulin and Calvert, 2006). More recently, similar links have been discovered between seismic interferometry and autofocusing, also known as Marchenko imaging (Broggini and Snieder, 2012; Wapenaar et al., 2012). All these methods have in common that recorded wavefields are focused onto a point inside the medium, either by actually emitting these fields into the real medium or by processing them in the computer. The aim of this paper is to discuss a number of subtle differences between the focusing conditions in the various methods and to point out the causality/acausality aspects of the corresponding focusing wavefields.
Recently, a novel iterative scheme was proposed to retrieve Green’s functions in an unknown medium from its single-sided reflection response and an estimate of the propagation velocity. In Marchenko imaging, these Green’s functions are used for seismic imaging with complete wavefields, including internal multiple reflections. In this way, common artifacts from these internal reflections are avoided and illumination of the subsurface can potentially be improved. However, Marchenko imaging requires accurate input data, with correct amplitudes, a deconvolved source signature, without free-surface multiples and source / receiver ghosts. Hence, a significant amount of preprocessing is required, which should be done accurately. To relax these requirements, we propose a scheme to remove artifacts due to internal multiples from inverse-extrapolated wavefields, by adaptively subtracting an estimate of these artifacts that is constructed with the Marchenko equation.
Time-lapse seismic surveys have become a powerful reservoir monitoring tool. The basic approach in time-lapse surveys is to image the changes in the reservoir by subtracting separated-in-time seismic images of the reservoir. Recently FWI has been used as an alternative time-lapse monitoring tool. However, in practice nonlinear gradient-based FWI is limited due to its notorious sensitivity to the choice of the starting model. Kernel decomposition based on scattering theory allows to break the acoustic-wavefield sensitivity kernels with respect to model parameters into background and singular parts, which should help to address model-convergence issues in FWI. In this work we apply scattering theory to the time-lapse problem, considering the time-lapse change as a perturbation of the singular part of the model. In the framework of time-lapse differential-waveform inversion, and under application of scattering-based decomposition of the sensitivity kernel, we take advantage of the additional illumination of the time-lapse change provided by multiple-scattering phenomena to improve the perturbation estimates from FWI.
Halliday, David (Schlumberger Cambridge Research) | Vasconcelos, Ivan (Schlumberger Cambridge Research) | Laws, Robert (Schlumberger Cambridge Research) | Robertsson, Johan O.A. (ETH Zürich) | van Manen, Dirk-Jan (WesternGeco) | Özdemir, Kemal (WesternGeco) | Grønaas, Halvor (WesternGeco)
In this paper, we introduce multicomponent marine seismic sources generating monopole and dipole responses in the water. We describe a few different alternatives for generating such a source using existing technology. Three different application areas are described in some detail: source-side deghosting, source-side wavefield reconstruction and, finally, a vector-acoustic reverse-time imaging approach that requires monopole and dipole data on both the source and receiver side of the acquisition. Introduction Robertsson et al. (2008a) introduced the concept of a fourcomponent (4C) streamer. Such a streamer includes recording elements of monopole character (the hydrophones) as well as elements of dipole character (3C particle velocity/acceleration sensors).