The numerical implementation of the inversion is carried out in the Fourier domain. After log stretch and Fourier transform, we solve the linear system of equations equ1 for each frequency slice. The unknown is a common-offset section regularly sampled at the nominal CMP spacing. We use an iterative solution to estimate the inverse of A. This solves a set of simultaneous equations without the need for writing down the matrix of coefficients. The iterative technique is based on the conjugate gradient method, which produces a good result at a reasonable cost.
For estimating the model-space inverse we need to invert for an AMO matrix, A, whose size is the square of the model-space. Whereas computing the data-space inverse requires the inversion of a matrix that is the size of the data space squared. Since there are more traces in the unstacked volume than the stacked model, estimating the data space inverse is generally, computationally more expensive than for the model-space inverse.