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Subsurface Domain Image Warping by Horizontal Contraction and its Application to Wave-Equation Migration Velocity Analysis

A kinematically correct choice of velocity focuses subsurface offset image gathers at zero offset. Infinitesimal warping from the current image towards its focus can be approximated by a horizontal contraction. The image residual can be then taken as the difference between the warped and the original image to account for the velocity error. Least squares fitting of the effect of a velocity perturbation to this image warping perturbation produces a tomographic velocity update. This paper describes the warping scheme based on the radial image derivative in subsurface offset. We show the corresponding gradient is free of the diffraction edge effect. We further enhance the efficiency of the velocity update procedure via use of a diagonal Hessian approximation.