Common‐angle migration: A strategy for imaging complex media

Abstract

International audienceComplex velocity models characterized by strong lateral variations are certainly a great motivation, but also a great challenge, for depth imaging. In this context, some unexpected results can occur when using depth imaging algorithms. In general, after a common shot or common offset migration, the resulting depth images are sorted into common‐image gathers (CIG), for further processing such as migration‐based velocity analysis or amplitude‐variation‐with‐offset analysis. In this paper, we show that CIGs calculated by common‐shot or common‐offset migration can be strongly affected by artifacts, even when a correct velocity model is used for the migration. The CIGs are simply not flat, due to unexpected curved events (kinematic artifacts) and strong lateral variations of the amplitude (dynamic artifacts). Kinematic artifacts do not depend on the migration algorithm provided it can take into account lateral variations of the velocity model. This can be observed when migrating the 2‐D Marmousi dataset either with a wave‐equation migration or with a multivalued Kirchhoff migration/inversion. On the contrary, dynamic artifacts are specific to multi‐arrival ray‐based migration/inversion. This approach, which should provide a quantitative estimation of the reflectivity of the model, provides in this context dramatic results. In this paper, we propose an analysis of these artifacts through the study of the ray‐based migration/inversion operator. The artifacts appear when migrating a single‐fold subdata set with multivalued ray fields. They are due to the ambiguous focusing of individual reflected events at different locations in the image. No information is a priori available in the single‐fold data set for selecting the focusing position, while migration of multifold data would provide this information and remove the artifacts by the stack of the CIGs. Analysis of the migration/inversion operator provides a physical condition, the imaging condition, for insuring artifact free CIGs. The specific cases of common‐shot and common‐offset single‐fold gathers are studied. It appears clearly that the imaging condition generally breaks down in complex velocity models for both these configurations. For artifact free CIGs, we propose a novel strategy: compute CIGs versus the diffracting/reflecting angle. Working in the angle domain seems the natural way for unfolding multivalued ray fields, and it can be demonstrated theoretically and practically that common‐angle imaging satisfies the imaging condition in the great majority of cases. Practically, the sorting into angle gathers can not be done a priori over the data set, but is done in the inner depth migration loop. Depth‐migrated images are obtained for each angle range. A canonical example is used for illustrating the theoretical derivations. Finally, an application to the Marmousi model is presented, demonstrating the relevance of the approach

Kinematics of prestack shot‐geophone migration

“…In particular, depth extrapolation per se is not the source of the good kinematic properties of shot-geophone migration. Note also that angle imaging via shot-geophone migration, is not equivalent, even kinematically, to the surface-oriented common angle imaging described by Xu et al (2001);BrandsbergDahl et al (2003) -indeed, the latter typically generates kinematic artifacts when multiple ray paths carry important energy.…”

“…for which each data bin creates an independent image. This category includes many variants of common shot, common offset and common scattering angle migration -see Symes (1996, 1997); Xu et al (2001); Brandsberg-Dahl et al (2003); Stolk and Symes (2004).…”

High Resolution/High Fidelity Seismic Imaging and Parameter Estimation for Geological Structure and Material Characterization

“…Therefore the imaging and image amplitude correction have to be done in the angle-domain, which makes ray-based methods more convenient than wave-equation based methods since the angle information is inherently embedded in ray-based methods. The theory and method of true-reflection imaging has been developed based on high-frequency asymptotic theory (ray theory) and is traditionally carried out through Kirchhoff prestack depth migration (e.g., Bleistein et al, 1987;Hubral et al, 1991;Hanitzsch, 1995;Xu et al, 2001;Audebert et al, 2002;Brandsberg-Dahl et al, 2003). However, the results may contain large errors in complex areas due to the high-frequency approximation and singularity problems therein.…”

An amplitude-preserved adaptive focused beam seismic migration method

“…Ray-based Kirchhoff migration has been developed from 2D to 3D (Hubral et al 1996;Epili and McMechan 1996;Sun et al 2000), from single-arrival migration (including first arrival, most energy arrival etc.) to multi-arrival migration (Brandsberg-Dahl et al 2001;Xu et al 2001) and from kinematic migration to true-amplitude migration (Schleicher et al 1993;Albertin et al 1999;Xu and Lambaré 2006). Due to its high efficiency and flexibility, Kirchhoff migration is still the workhorse in practical applications, especially for land seismic data.…”