Wave-equation migration velocity analysis
Wave-equation migration velocity analysis is a technique for estimating the perturbations of the velocity model by observing perturbations of the migrated images. It employs wavefield extrapolation and thus it is a close companion of migration by wavefield extrapolation. For a correctly migrated image, all events are focused, both spatially and function of the offset at depth. For angle-domain common image gathers, correctly migrated events are flat. For an incorrectly migrated image, the events are not focused (non flat). By estimating the direction in which we need to change an image to increase its focusing, we can estimate an image perturbation. One possibility is to run residual migration and scan a range of possible velocities. The image perturbations can be transformed to velocity perturbations by a linear wave-equation MVA operator.
Wave-equation MVA operates in the image space and thus it is different from wave-equation tomography which is formulated in the data space. The objective function increases focusing of the image, thus it is guaranteed to converge, unless assumptions related to the Born approximation are violated.
Monochromatic WEMVA example:
Wideband WEMVA example:
ReferencesSava, P.C., Biondi, B., 2004, Wave-equation migration velocity analysis - I: Theory, Geophysical Prospecting, v. 52, pp. 593-606. (PDF)
Sava, P.C., Biondi, B., 2004, Wave-equation migration velocity analysis - II: Subsalt imaging example, Geophysical Prospecting, v. 52, pp. 607-623. (PDF)
Sava, P.C., Biondi, B., Etgen, J., 2005, Wave-equation migration velocity analysis by focusing of diffractions and reflections, Geophysics, v. 70, no. 3, U19-U27. (PDF)
Sava, P.C., Vlad, I., 2008, Numeric implementation of wave-equation migration velocity analysis operators, Geophysics, v. 73, pp. VE145-VE159. (PDF)