The most common migration velocity analysis algorithms, iterative profile migration, focusing analysis, and stack power analysis are based on restrictive subsurface assumptions that may cause the methods to break down in the presence of lateral velocity variations. Typically, the subsurface is assumed to have either a constant velocity, or at most, a depth variable velocity. Recent innovations include the use of traveltime inversion philosophy to invert migration measurements of the curvature as a function of offset exhibited by an event following migration. Traveltime inversion makes few assumptions regarding the subsurface, but is a rather unstable process. Thus, an important question is, 'Under what conditions do the traditional methods break down and make the use of traveltime inversion methods mandatory?'Marrying the common migration analysis with tomography results in a set of equations that, while useful for generating updates from migration measurements, are too complex for answering the above question. However, by restricting the subsurface to low relief structures and assuming small angle wave propagation, these updating equations can be approximated by forms that are identical to the traditional updating equations, except for a factor that is dependent upon the magnitude, position, and spatial wavelength of potential lateral velocity variations. These simpler equations indicate that even relatively long wavelength anomalies can cause updates to point in the wrong direction and iterative procedures to diverge, and under certain conditions, cause the accuracy of these updates to decrease dramatically.

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