The next generation of seismic imaging algorithms will use full wavefield migration, which regards multiple scattering as indispensable information. These algorithms will also include autonomous velocity-updating in the migration process, called joint migration inversion. Full wavefield migration and joint migration inversion address industrial requirements to improve the images of highly complex reservoirs as well as the industrial ambition to produce these images more automatically (automation in seismic processing). In these vision papers on seismic imaging, full wavefield migration and joint migration inversion are formulated in terms of a closed-loop, estimation algorithm that can be physically explained by an iterative double-focusing process (full wavefield Common Focus Point technology). A critical module in this formulation is forward modelling, allowing feedback from the migrated output to the unmigrated input ('closing the loop'). For this purpose, a full wavefield modelling module has been developed, which uses an operator description of complex geology. Full wavefield modelling is pre-eminently suited to function in the feedback path of a closed-loop migration algorithm. 'The Future of Seismic Imaging' is presented as a coherent trilogy of papers that propose the migration framework of the future. In Part I, the theory of full wavefield modelling is explained, showing the fundamental distinction with the finite-difference approach. Full wavefield modelling allows the computation of complex shot records without the specification of velocity and density models. Instead, an operator description of the subsurface is used. The capability of full wavefield modelling is illustrated with examples. Finally, the theory of full wavefield modelling is extended to full wavefield reverse modelling (FWMod(-1)), which allows accurate estimation of (blended) source properties from (blended) shot records.
