Wave-equation migration velocity analysis (WEMVA) is a velocity estimation technique designed to invert for velocity information using migrated images. Its capacity for handling multi-pathing makes it appropriate in complex subsurface regions characterized by strong velocity variation. WEMVA operates by establishing a linear relation between a velocity model perturbation and a corresponding migrated image perturbation. The linear relationship is derived from conventional extrapolation operators and it inherits the main properties of frequency-domain wavefield extrapolation. A key step in implementing WEMVA is to design an appropriate procedure for constructing image perturbations. Using time-lag extended images, one can characterize the error in migrated images by defining the focusing error as the shift of the focused reflection along the time-lag axis. Under the linear approximation, the focusing error can be transformed into an image perturbation by multiplying it with an image derivative taken relative to the time-lag parameter. The resulting image perturbation is thus a mapping of the velocity error in image space. This approach is computationally efficient and simple to implement, and no further assumptions about smoothness and homogeneity of the velocity model and reflector geometry are needed. Synthetic examples demonstrate the successful application of our method to a complex velocity model.


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