Since accurate imaging of reflections is more important in the neighborhood of the reservoir, a target-oriented strategy can be applied to estimate the wave-equation least-squares inverse image by explicitly computing the Hessian. The main contributions of the Hessian occurs around the diagonal, that is why additional computational savings can be obtain by limiting the its computation to only few elements around it. The least-squares inverse image is then computed as the solution, using a conjugate gradient algorithm, of a non-stationary least-squares filtering problem. This approach allows to perform the number of iterations necessary to achieve the convergence.
Results on the constant velocity model show that the inversion recovers the correct image amplitudes. In this case a filter size of is enough to obtain a good result. However, something different happens in the Gaussian anomaly velocity model case, where the inversion gives noisy results if a filter size of is used. After adding more coefficients to the filter (filter size of ) a more stable result was obtained.