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Diffraction-focusing WEMVA example

Migration velocity analysis (MVA) using diffracted events is not a new concept. (43) 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, (112) use the concept of minimum entropy to evaluate diffraction focusing and apply this methodology to MVA, again for the case of simple geology. (99) use focusing of diffractions simulated using data-derived parameters to estimate interval velocities.

In wemva, I 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, that is similar to ray-based migration tomography (104; 3; 33), where the slowness perturbation is derived from depth errors, and to wave-equation inversion (108) or tomography (114; 28; 72) 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.

In this section, I 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. The first example concerns a synthetic dataset obtained by acoustic finite-difference modeling over a salt body. Although in this example I use the WEMVA technique to constrain the top of the salt, I emphasize that we can use the same technique in any situation where diffractions are available. For example, in sub-salt regions where angular coverage is small, uncollapsed diffractions carry substantial information which is disregarded in typical MVA methodologies.

The second example is a real dataset of single-channel, Ground-Penetrating Radar (GPR) data. Many GPR datasets are single-channel and no method has thus far been developed to estimate a reasonable interval velocity models in the presence of lateral velocity variations. Typically, the velocity estimated by Dix inversion at sparse locations along the survey line is smoothly extrapolated, although this is not optimal from an imaging point of view.