Migration velocity analysis (MVA) using diffracted events is not a new concept. Harlan (1986) addresses this problem and proposes methods to isolate diffraction events around faults, quantifies focusing using statistical tools, and introduces MVA techniques applicable to simple geology, e.g. constant velocity or v(z). Similarly, de Vries and Berkhout (1984) use the concept of minimum entropy to evaluate diffraction focusing and apply this methodology to MVA, again for the case of simple geology. Soellner and Yang (2002) estimate interval velocities from focusing of diffractions simulated using data-darived parameters.
Sava and Biondi (2004a,b) introduce a method of migration velocity analysis using wave-equation techniques (WEMVA), which aims to improve the quality of migrated images, mainly by correcting moveout inaccuracies of specular energy. WEMVA finds a slowness perturbation which corresponds to an image perturbation. Thus, it is similar to ray-based migration tomography Al-Yahya (1989); Etgen (1993); Stork (1992), where the slowness perturbation is derived from depth errors, and to wave-equation tomography Dahlen et al. (2000); Pratt (1999); Tarantola (1986); Woodward (1992) where the slowness perturbation is derived from measured wavefield perturbations.
The moveout information given by the specular energy is not the only information contained by an image migrated with the incorrect slowness. Non-specular diffracted energy is present in the image and clearly indicates slowness inaccuracies. Traveltime-based MVA methods cannot easily deal with the diffraction energy, and are mostly concerned with moveout analysis. In contrast, a difference between an inaccurate image and a perfectly focused target image contains both specular and non-specular energy; therefore WEMVA is naturally able to derive velocity updates based on both these types of information. Our proposed method can benefit, and thus be used in conjunction with, methods to isolate diffracted energy from the seismic data, such as the one proposed by Khaidukov et al. (2004).
In this paper, we use WEMVA to estimate slowness updates based on focusing of diffracted energy using residual migration. One possible application of this technique in seismic imaging concerns areas with abundant, clearly identifiable diffractions. Examples include highly fractured reservoirs, carbonate reservoirs, rough salt bodies and reservoirs with complicated stratigraphic features. Another application is related to imaging of zero-offset Ground-Penetrating Radar (GPR) data, where moveout analysis is simply not an option.
Of particular interest is the case of salt bodies. Diffractions can help estimate more accurate velocities at the top of the salt, particularly in the cases of rough salt bodies. Moreover, diffraction energy may be the most sensitive velocity information we have from under the salt, since most of the reflected energy we record at the surface has only a narrow range of angles of incidence at the reflector, rendering the analysis of moveout ambiguous.
We begin with a summary of the wave-equation MVA methodology, specialized to diffraction focusing, followed by synthetic and real-data examples from seismic and GPR applications.