Wavefield extrapolation methods are powerful for handling strong lateral velocity variations. However, they require an accurate velocity model to produce good images. There are many different migration velocity methods; but most of them make some simplifying assumptions about the subsurface, which reduces their ability to exploit the power of wavefield extrapolation methods.
In this report, we reformulate some well-known migration velocity methods, like residual curvature analysis (RCA), depth focusing analysis (DFA), and common focus point (CFP) analysis into mathematical hypotheses. This reformulation puts them in the same context, so they are easier to understand and compare. Further, by restating the methods as mathematical hypotheses, they are easier to relate to other disciplines such as mathematics and physics.
We also combine different aspects of the RCA, DFA, and CFP methods into a new migration velocity analysis approach called the common image cube analysis (CICA). Instead of simply taking the zero-lag crosscorrelation at each depth level, we store all the crosscorrelation lags. The result is a cube that contains more prestack information than the other methods. Slicing this cube at different lags forms a series of common image gathers (CIGs), where the conventional CIG can be obtained by slicing the cube at the zero lag.
When the background velocity model used for migration is different from the true velocity model, the best-focused CIG is not at zero lag. Searching the cube at other lags for the most focused CIG gives the traveltime shift that is needed to approximately equalize the traveltimes of the upgoing and downgoing wavefields. From the updated traveltimes, the true velocity can be estimated. This approach is tested on models with constant velocity as well as velocity varying with depth, and the results show that it can be used to yield an accurate estimate of the true velocity when the wrong velocity model is used for migration.
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