Migration can be formulated as optimization problem involving forward and adjoint simulations, much like inversion. While inversions usually require many model update iterations, conventional migration involve only a single iteration.
Given a velocity model as input, the forward simulation returns synthetic traces as output, just as in an inversion.
In our terminology, pre-processing includes all operations performed on seismic traces prior to the adjoint simulation. Signal processing operations, comparison of obervations and synthetics, and creation of adjoint traces fall into this category.
Given adjoint traces as input, the adjoint simulations returns sensitivity kernels as output.
In our terminology post-processing includes all operations performed on sensitivity kernels following the adjoint simulation. Summation, projection, regularization, and preconditioning fall into this category.
In conventional migration, only a single iteration is carried out. Optionally, additional iterations can be performed using the same type of optimization procedure as in seismic waveform inversion.