Wave-Equation Migration Velocity Analysis with Dip Contraction in the Subsurface Offset Common Image Gather

Abstract

Wave-equation migration velocity analysis extracts unfocused or unflattened information from the common image gather and projects the information into velocity space to get the update direction. It's often formulated as a non-linear inverse problem. The progress to solve this inverse problem can be taken as velocity updates along with image focusing or flattening flow. The key point of this progress is to compute the image residual, which should be the difference between the reference image and the current image. Previous methods, like classic differential semblance optimization or differential residual migration method, suffer from gradient artifacts or non-trivial manual picking. To provide an artifact-free gradient automatically, we compute the image residual using image warping operators, namely dip contraction in the common image gather, to approximate the reference image. Least-squares fitting of the effect of a velocity perturbation to this image warping perturbation produces a tomographic velocity update, which can be explained as one step of Gauss-Newton method to solve the original non-linear inverse problem. We further enhance the efficiency of the velocity update procedure via use of a diagonal Hessian approximation. Numerical tests demonstrate that our proposed method is free of gradient artifacts and should be convergent to optimal solution efficiently.