In the inversion of focusing operators an attempt is made to combine both stabilizing methods; the adjustment of parameterization is based on the covariance after optimization; the a posteriori covariance. Model parameters that have a high variance are removed, and in regions containing low variance parameters, extra parameters can be added. In this way, the inversion problem is well determined and over-parameterization is avoided. Moreover, all the available information within the data will be translated to the model, as the parameterization adapts to the data.
If the data is used to determine the parameterization, as a consequence the obtained parameterization tells something about the data. A coarse parameterization exposes for example that more focus points should positioned in that region (of course this is only possible if data related to the focus point is available). On the other hand, when updated focus points are positioned very close to each other, it might be wise to remove/shift them, as they will only duplicate information.
Figure 5 Strategy flowchart for inversion if focusing operators with data dependent parameterization. The extra steps w.r.t. Figure 3 are underlined.