Time-shift imaging condition in seismic migration |

Migration velocity analysis after migration by wavefield extrapolation requires image decomposition in scattering angles relative to reflector normals. Several methods have been proposed for such decompositions (Soubaras, 2003; Rickett and Sava, 2002; Xie and Wu, 2002; Biondi and Symes, 2004; Fomel, 2004; Prucha et al., 1999; Mosher and Foster, 2000; de Bruin et al., 1990; Sava and Fomel, 2003). These procedures require decomposition of extrapolated wavefields in variables that are related to the reflection angle.

A key component of such image decompositions is the imaging condition. A careful implementation of the imaging condition preserves all information necessary to decompose images in their angle-dependent components. The challenge is efficient and reliable construction of these angle-dependent images for velocity or amplitude analysis.

In migration with wavefield extrapolation, a prestack imaging condition based on spatial shifts of the source and receiver wavefields allows for angle-decomposition (Rickett and Sava, 2002; Sava and Fomel, 2005). Such formed angle-gathers describe reflectivity as a function of reflection angles and are powerful tools for migration velocity analysis (MVA) or amplitude versus angle analysis (AVA). However, due to the large expense of space-time cross-correlations, especially in three dimensions, this imaging methodology is not used routinely in data processing.

This paper presents a different form of imaging condition. The key idea of this new method is to use time-shifts instead of space-shifts between wavefields computed from sources and receivers. Similarly to the space-shift imaging condition, an image is built by space-time cross-correlations of subsurface wavefields, and multiple lags of the time cross-correlation are preserved in the image. Time-shifts have physical meaning that can be related directly to reflection geometry, similarly to the procedure used for space-shifts. Furthermore, time-shift imaging is cheaper to apply than space-shift imaging, and thus it might alleviate some of the difficulties posed by costly cross-correlations in 3D space-shift imaging condition.

The idea of a time-shift imaging condition is related to the idea of depth focusing analysis (MacKay and Abma, 1993; Faye and Jeannot, 1986; Nemeth, 1995,1996; MacKay and Abma, 1992). The main novelty of our approach is that we employ time-shifting to construct angle-domain gathers for prestack depth imaging.

The time-shift imaging concept is applicable to Kirchhoff migration, migration by wavefield extrapolation, or reverse-time migration. We present a theoretical analysis of this new imaging condition, followed by a physical interpretation leading to angle-decomposition. Finally, we illustrate the method with images of the complex Sigsbee 2A dataset (Paffenholz et al., 2002).

Time-shift imaging condition in seismic migration |

2007-04-08