Horizontal contraction in image domain for velocity inversion

A kinematically correct choice of velocity focuses subsurface offset image gathers at a zero offset. Infinitesimal warping from the current image toward its focus can be approximated by a horizontal contraction. The image residual can then be 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. We evaluated a warping scheme based on the radial image derivative in the subsurface offset. We found that the corresponding gradient was free of the diffraction edge effect. We further enhanced the efficiency of the velocity update procedure via the use of a diagonal Hessian approximation. We developed a sequence of synthetic examples leading to a salt body inversion. The limitation of the method was argued and analyzed in the presence of refracting structures.