Fast Gauss-Newton full-wavefield migration

Since the appearance of wave-equation migration, many have tried to push this technology to the limits of its capacity. Least-squares wave-equation migration is one of those attempts that tries to fill the gap between the migration assumptions and reality in an iterative manner. However, these iterations do not come cheap. A proven solution to limit the number of iterations is to correct the update direction in every iteration via a proper but cheap preconditioner that approximates the second-order partial derivatives, known as Hessian, of the data-error functional employed in the least-squares formulation. In this study, we will address this issue, namely the cheap computation of the Hessian inverse in the context of our one-way wave-equation-based migration method, cited as full wavefield migration. To do so, we will build and apply the Hessian inverse matrix depth by depth, reducing the Hessian matrix size considerably each time it is calculated. We prove the validity of our proposed method by two numerical examples.