Current state-of-the-art subsurface imaging techniques have based upon two-way wave propagation solutions. At the beginning of the 2000s, reverse-time migration constituted the ``main character" of the imaging toolbox: the ultimate solution for geologically complex areas. Nowadays it represents the main ``engine" working under the hood of the most acclaimed and researched imaging techniques, such as linearized waveform inversion (a.k.a. least-squares migration) for the estimation of the subsurface reflectivity, migration velocity analysis for the estimation of the subsurface background component, and full-waveform inversion for the estimation of both components as a single model parameter set. The latter is arguably the most ambitious attempt to obtain a complete and accurate picture of the subsurface. Unfortunately, it is vulnerable to cycle-skipping, which drives the optimization process to convergence into local minima. Strategies to attack this problem include better acquisition, data processing, and different implementations of the full-waveform inversion algorithm. In this thesis, I explore a different and certainly less ambitious approach, which consists of the joint inversion of the subsurface reflectivity and the subsurface background component as different parameter sets. During the early stages of my research, I posed the problem as a linear optimization problem. However, this approach does not have the expected properties. Maintaining the migration image nonlinear with respect to the background model corrected the problem. I test this new optimization problem scheme in synthetic 2D data and a 3D ocean-bottom node dataset from the Gulf of Mexico.

%One philosophy behind this approach is reusing some components of the operator, such as the Gauss-Newton Hessian of full-waveform inversion by selective linearizations. Other components, such as wave-equation migration velocity analysis, are actively recalculated. This concept is tested in both 2D synthetic data and in an 3D ocean-bottom node dataset from the Gulf of Mexico.