To enable the analysis of the Residual Moveout (RMO) in Angle-Domain Common Image Gathers (ADCIGs) after anisotropic wavefield-continuation migration, I develop the fundamental concepts for quantitatively relating perturbations in anisotropic parameters to the corresponding reflector movements in ADCIGs. I then apply the general methodology to the particular case of RMO analysis of reflections from flat reflectors in a Vertical Transverse Isotropic (VTI) medium. This analysis shows that the RMO in migrated ADCIGs is a function of both the phase aperture angle and the group aperture angle.
Several numerical examples demonstrate the accuracy of the RMO curves predicted by my kinematic analysis. The synthetic examples also show that the approximation of the group angles by the phase angles may lead to substantial errors for events reflected at wide aperture angles.
The results obtained by migrating a 2-D line extracted from a Gulf of Mexico 3-D data set confirm the accuracy of the proposed method. The RMO curves predicted by the theory exactly match the RMO function observed in the ADCIGs computed from the real data.
The analysis of Residual Moveout (RMO) in Common Image Gathers (CIGs) after prestack migration is an essential step for updating migration velocity. When the migration velocity is inaccurate, the inconsistency of the migrated events along either the offset axis or the aperture-angle axis is proportional to the migration velocity errors. Measuring the RMO in ADCIGs provides the quantitative information necessary to update the velocity function in a Migration Velocity Analysis (MVA) procedure.
Today, MVA is the procedure most commonly employed to estimate isotropic migration velocity in complex media. The technology for anisotropic MVA is much less mature than for isotropic MVA. Recently, important progress has been made toward the development of anisotropic MVA in conjunction with Kirchhoff migration. Sarkar and Tsvankin (2003, 2004b) analyze the effect of velocity errors on offset-domain CIGs produced by Kirchhoff migration. They demonstrate the effectiveness of their method by successfully applying it to a West Africa data set Sarkar and Tsvankin (2004a). Krebs et al. (2003) and Bear et al. (2003) integrate borehole-seismic data and nonseismic information in an MVA process based on Kirchhoff migration.
Wavefield-continuation is capable of producing better images than Kirchhoff migration does in the presence of complex overburden that causes multipathing of the propagating wavefield, as often it occurs when imaging below or in proximity of salt bodies. To perform MVA after wavefield-continuation the RMO function is measured from Angle Domain Common Image Gathers (ADCIGs) Biondi and Sava (1999); Clapp and Biondi (2000). Since all the present methods for computing ADCIGs in conjunction with wavefield migration are limited to isotropic migration, the quantitative analysis of RMO in ADCIGs is also limited to the isotropic case Biondi and Symes (2003); Biondi and Tisserant (2004). In this paper, I provide the basic analytical tools necessary to perform anisotropic migration velocity analysis by analyzing the RMO function in ADCIGs. This paper builds on the results presented in a companion paper Biondi (2005) that develops a method for computing ADCIGs after anisotropic migration and lays the foundations for the kinematic analysis of anisotropic ADCIGs. I apply the general theory to the specific case of defining the RMO function measured from flat reflectors in VTI media, because in this case the methodology is simple both to derive and to apply. However, the same concepts could be applied to more general situations, though at the expense of additional complexities that could obfuscate the fundamental concepts.
In Biondi (2005) I show that in anisotropic media the ADCIGs are approximately functions of the phase aperture angle, and exactly so for flat reflectors in VTI media. In this paper I demonstrate that the RMO function depends on both the phase and the group aperture angles. This dependency of the RMO function on the group angles adds some complexity to the RMO analysis because the computation of group angles from phase angles, which are measured from the ADCIGs, depends on the background anisotropic velocity evaluated at the reflector point. The synthetic-data examples show that neglecting the dependency on the group angles, and assuming that group angles are equal to phase angles, leads to substantial inaccuracy in the predicted RMO function. Fortunately, the additional computational cost of computing group angles is negligible, and thus it should not be an obstacle to the application of the proposed methodology.