On the relation between the propagator matrix and the Marchenko focusing function

The propagator matrix “propagates” a full wave field from one depth level to another, accounting for all propagation angles and evanescent waves. The Marchenko focusing function forms the nucleus of data-driven Marchenko redatuming and imaging schemes, accounting for internal multiples. These seemingly different concepts appear to be closely related to each other. With this insight, the strong aspects of the propagator matrix (such as the handling of evanescent waves) can be transferred to the focusing function. Vice-versa, the propagator matrix inherits from the focusing function that it can be retrieved from the reflection response, which reduces its sensitivity to the subsurface model.

Impacts of model resolution on multiple prediction

Despite theoretical advancements in multiple identification and elimination, the application and success of these advancements is questionable in some cases and is limited to marine environments, especially deep water. In land seismic, however, a clear understanding of the internal multiple generators is not readily available and thus efforts to attenuate them are often quite ineffective. In this paper, we analyze, in the case of many thin layers, how the primaries and multiples are affected by fine-scale variations in the velocity model. Cross-coherence is used to measure the similarity of the original primaries/multiples and the ones generated from upscaled velocity models. The combined use of kurtosis and the cross-coherence method enables us to precisely quantify the impact of fine layering on multiples. Test results demonstrate that both surface-related multiples and internal multiples are much more sensitive than the primaries to thickness variations of the velocity model. As the thickness of each upscaled layer varies from 1m to 21m, multiples change rapidly, while primaries are almost the same. The high sensitivity of internal multiples on fine layering suggests that the detailed model information should be considered in model parameterization in the internal multiple removal, especially for model-driven methods.

Time-lapse difference inversion based on the modified reflectivity method with differentiable Hyper-Laplacian blocky constraint

Time-lapse (TL) seismic has great potential in monitoring and interpreting time-varying variations in reservoir fluid properties during hydrocarbon exploitation. Obtaining the disparities of reservoir elastic parameters by inversion is essential for TL reservoir monitoring. Conventional TL inversion is carried out by stages without coupling processing and leads to inaccuracy of the results. We directly use the differences in seismic data responses from different vintages, namely difference inversion, to improve the results credibility. It may reduce the deviations of the subtraction of base and monitor inversions in traditional methods. Moreover, most existing studies involving pre-stack inversion methods use the Zoeppritz equation or its approximants, which failed to consider the wave propagation effects. Here, we propose a new TL difference inversion based on the modified reflectivity method (MRM), the internal multiples and transmission losses are taken into consideration to fine-tune the characterization of the seismic wave propagating underground. The new method is modified on the basis of reflectivity method (RM) making it feasible in TL difference inversion, and derived from the Bayesian theorem. For further delineating the boundaries between layers, the differentiable Hyper-Laplacian blocky constraint (DHLBC) is introduced into the prior information of Bayesian framework, which heightens the sparseness in the vertical gradients of inversion results and leads to sharp interlayer boundaries of difference parameters. The synthetic and field data examples demonstrate that the proposed TL difference inversion method has clear advantages in accuracy and resolution compared to Zoeppritz method and MRM without DHLBC.

3D adaptive internal multiples modeling based on globally optimised Fourier finite-difference method

Numerical methods have been widely applied to simulate seismic wave propagation. However, few studies have focused on internal multiples modeling. The formation mechanism and response of internal multiples are still unclear. Therefore, we develop a weighted-optimised-based internal multiples simulation method under 3D conditions. Using a one-way wave equation and full-wavefield method, the different-order internal multiples are computed numerically in a recursive manner. The traditional Fourier finite-difference (FFD) method has low numerical accuracy in a horizontal direction. A globally optimised FFD (OFFD) method is used to improve the lateral propagation accuracy of the seismic waves. Meanwhile, we adopt an adaptive variable-step technique to improve computational efficiency. The 3D internal multiples modeling technique is capable of calculating the different-order multiple reflections in complex structures. We use the present method to simulate internal multiples in several models. Theoretical analyses are consistent with the numerical results. Numerical examples demonstrate that the 3D internal multiples modeling technique has superior performance when adapting to lateral velocity changes and steep dip. This also implies that our method is fit for the simulation of internal multiples propagation in a 3D complex medium and can assist in identifying the internal multiples from full-wavefield data.

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.

Full Wavefield Least-Squares Reverse Time Migration

Waveform inversion based on Least-Squares Reverse Time Migration (LSRTM) usually involves Born modelling, which models the primary-only data. As a result the inversion process handles only primaries and corresponding multiple elimination pre-processing of the input data is required prior to imaging and inversion. Otherwise, multiples left in the input data are mapped as false reflectors, also known as crosstalk, in the final image. At the same time the developed Full Wavefield Migration (FWM) methodology can handle internal multiples in an inversion-based imaging process. However, because it is based on the framework of the one-way wave equation, it cannot image dips close to and beyond 90 degrees. Therefore, we aim at upgrading LSRTM framework by bringing functionality of FWM to handle internal multiples. We have discovered that the secondary source term, used in the original formulation of FWM to define a wavefield relationship that allows to model multiple scattering via reflectivity, can be injected into a pressure component when simulating the two-way wave equation using finite-difference modelling. We use this modified forward model for estimating the reflectivity model with automatic crosstalk supression and validate the method on both synthetic and field data containing visible internal multiples.

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.

Sub-basalt Marchenko imaging with offshore Brazil field data

Sub-basalt 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 geological 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 present a successful application of direct Marchenko imaging for sub-basalt de-multiple and imaging with an offshore Brazil field dataset. The internal multiples in this example are generated from the seabed and basalt layers, causing severe artifacts in conventional seismic images. We demonstrate that these artifacts are largely suppressed with Marchenko imaging and propose a general work flow for data pre-processing and regularization of marine streamer datasets. We show that horizontally propagating waves can also be reconstructed by the Marchenko method at far offsets.