Conventional AVO analysis extracts the intercept and slope from NMO-corrected CMP gathers. Since no imaging capability is incorporated, diffraction energy is not properly analyzed. Diffraction-corrupted intercept and slope sections may lead to false hydrocarbon indications.
The influence of migration/inversion on AVO analysis has been addressed by several authors Dong and Keys (1997); Lumley et al. (1995); Mosher et al. (1996). Lumley et al. (1995) use the conventional common-offset prestack time migration to collapse the diffraction energy. Mosher et al. (1996) also use the prestack time migration technique. In order to improve the lateral resolution and spatial positioning of AVO anomalies, they choose common-angle sections instead of common-offset sections. The most important problem with the time migration schemes is that they cannot handle large lateral velocity and structure variations easily. The time imaging error will consequently produce mispositioning of AVO anomalies in the spatial domain. Dong and Keys (1997) propose a prestack depth inversion scheme. They assume that the earth satisfies a locally 1-D layered velocity model to make the algorithm efficient. The inversion is of Kirchhoff-typed and implemented in the common-midpoint gather. This locally 1-D assumption restricts their schemes to handle only moderate lateral velocity and structure variations.
In this paper, we propose an AVO inversion scheme for 2-D media. The WKBJ Green's function is calculated by a finite-difference algorithm. A 2.5-D Kirchhoff integral is used in the inversion. Common-image gathers (CIG) are produced as a by-product, that can be used to quality-control the accuracy of velocity model. We first derive a new form of the 2.5-D Kirchhoff integral formula in V(x,z) media and relate it to the WKBJ Green's function. Then we discuss the characteristics of the weighting function in the Kirchhoff integral. We show the effect of the integral aperture on the estimated amplitude of the reflection coefficient. Finally, we discuss the results of applying the new algorithm to synthetic and field data.