The fundamental definition of A from equation equ6 allows analytic computations of its inner product elements. The challenge is then to solve for the inverse of A. First, we write the solution for from equation equ3 in terms of A as
where is the filtered input given by the substitution:
Solving for , we then need to compute the inverse of . This is essentially the first step of the solution, i.e., the data-equalization step. After filtering, we merely need to apply the imaging operator to the equalized data to obtain the final image. At this stage, any true-amplitude imaging process could be applied, e.g., prestack Kirchhoff migration.