The future in seismic exploration and seismic monitoring is the inclusion of all orders of scattering in the imaging and inversion algorithms. Using the full wavefield in an inversion process allows us to surpass imprints provided by incomplete acquisition and provide more accurate information on the subsurface, as noise becomes signal. We describe an inversion process that does not use the standard parameters from finite-difference-type modeling (being local velocity and density) but that describes the seismic data in terms of elastic reflectivity operators and propagation operators. With these operators, our full-wavefield modeling process builds the complete two-way seismic response. A major advantage of our alternative to the traditional full-waveform inversion methodology is that reflectivity operators are traveltime-free and propagation operators are scattering-free, making the inversion problem significantly more linear. A major advantage of our algorithm is (1) that multiples are utilized to improve both image and velocity accuracy, and (2) that both image and velocities are utilized to make a contribution in the nonlinear migration process. Hence, in joint migration inversion, multiples have a twofold active role.