Selecting an optimal aperture in Kirchhoff migration using dip-angle images

Introduction

Kirchhoff migration remains a popular tool for seismic imaging (Leveille et al., 2011). It handles every input trace separately, enabling the user to work with data sets of any configuration (including irregular geometry) and to apply target-oriented analysis. One of the features of Kirchhoff migration is its global aperture. The migration operator distributes energy throughout a wide area described by an impulse-response surface. However, a seismic image is constructed only by a local part of the surface that touches a reflector. The remainder does not make a constructive contribution and, even worse, may generate image artifacts (Hertweck et al., 2003; Sun, 1998).

The artifact problem can be solved by limiting migration aperture. Schleicher et al. (1997) analyzed influence of aperture parameters on imaging results and proposed a technique based on projected Fresnel zones for shortening the migration curve. After preliminary picking of target reflections and computing diffraction curves, they estimated the migration-aperture size by analytical equations. Sun (1998) analyzed the structure of a seismic image and proposed rules for its optimal construction. Two main principles were identified: (1) the tangent point between a diffraction curve and a reflector must be located in the central part of the aperture and (2) the aperture must be at least as large as the first Fresnel zone. Several methods were proposed to achieve these two objectives. Tillmanns and Gebrande (1999) detected instantaneous slowness in the data domain. Sun and Schuster (2001) described wave-path migration smearing energy within a small zone centered on the specular reflection point and defined under a stationary-phase approximation. Lüth et al. (2005) smeared migrated multicomponent data only inside a Fresnel volume built around rays computed using polarization of the wavefield. Buske et al. (2009) constructed a Fresnel volume for single-component seismic data, determining the emergent angle by local slowness analysis. Tabti et al. (2004) worked with diffraction-operator panels and picked Fresnel apertures after preliminary low-pass filtering. Kabbej et al. (2007) introduced an attribute that characterizes the distance between a common-midpoint position and a currently imaged depth point then migrated the attribute and used it for weighting-function construction. Spinner and Mann (2007) used the common-reflection-surface operator to determine parameters for the optimal migration aperture. Alerini and Ursin (2009) estimated horizon slopes in the image domain.

The migrated dip-angle domain has properties that are favorable for taking both issues -- the aperture position and its width -- into consideration. In this domain, a reflection event has a concave shape with an apex whose position corresponds to the reflector dip (Landa et al., 2008; Audebert et al., 2002; Klokov and Fomel, 2012). The event summation in the dip-angle direction produces an image in accordance with the stationary-point principle (Bleistein et al., 2001). To limit aperture in the dip-angle domain and to restrict summation to stationary points, Bienati et al. (2009) applied an automatic slope estimation followed by muting. Aperture size was defined on the basis of wavelet bandwidth. Dafni and Reshef (2012) proposed analyzing migrated gathers simultaneously in dip-angle and scattering-angle directions.

A seismic wavefield may contain reflections and diffractions. There are a number of important differences between these two components (Klem-Musatov, 1994). One of the differences is that reflections require a narrow migration aperture, whereas diffractions require an aperture as wide as possible (while allowing matching of a diffraction curve). Therefore, all methods that imply migration-aperture limiting are oriented toward optimal imaging of reflection boundaries and not diffraction objects. Diffractions characterize small but important geological objects and play a significant role in imaging of rough reflection boundaries (Khaidukov et al., 2004). Their attenuation may cause a significant loss of resolution (Neidell, 1997). For image resolution to be preserved, a migration-optimization method should aim to protect the diffraction component. In this paper, we demonstrate an approach that allows us to achieve an optimal aperture size for reflection boundaries while also protecting the diffraction component. The main idea is analyzing slope information in constant-dip partial images.

Selecting an optimal aperture in Kirchhoff migration using dip-angle images