A seismic processing workflow based on iterative migration/inversion and target-oriented postprocessing of the migrated image is developed for fine-scale quantitative characterization of reflectors. The first step of the workflow involves linear iterations of the migration/inversion. The output of the first step is a true-amplitude migrated image parameterized by velocity perturbations. In a second step, postprocessing of the migrated image is performed through a random search with a very-fast simulated annealing (VFSA) algorithm. The forward problem of the global optimization is a simple convolutional model that linearly relates a vertical profile of the band-limited migrated image after depth-to-time conversion to a 1D velocity model composed of a stack of homogeneous layers of arbitrary velocity and thickness. The aim of the postprocessing is to eliminate the limited bandwidth effects of the source from the migrated image for resolution improvement and enhanced geological interpretation of selected targets. The global optimization approach allows for uncertainty analysis required by the intrinsic nonuniqueness of the velocity model output by the postprocessing. The relevance of the convolutional model when applied to the output of the migrated inversion is first illustrated with a one-layer model. The accuracy and the robustness of the workflow to image geologically complicated models are then illustrated with an application to the synthetic Marmousi model. Some practical issues (e.g., the source wavelet estimate and the scaling of the migrated image required by the VFSA optimization) are discussed with an application to a 2D real seismic multichannel reflection data set collected in the Gulf of Guayaquil (Ecuador). The postprocessing is applied to derive the fine-scale velocity structure of a décollement zone on top of the subduction channel. The postprocessing allows for mapping structural variations along different segments of the décollement, which can be associated with changes in fluid content and porosity.