Sequential inversion methods are performed by velocity estimation for a low-wavenumber model followed by imaging for a high-wavenumber model. Given a known background velocity, the computation of synthetic seismograms from different impedance models is a quasi-linear problem if we neglect multiple reflection and guided energy. This suggests a simplification of the original nonlinear inverse problem into a nonlinear formulation for the background velocity and, given this background, a linearized formulation for the impedance contrasts.
Many techniques for obtaining the background velocity have been proposed. A standard robust technique, normal moveout (NMO) stacking velocity analysis Taner and Koehler (1969), can be insufficient in complex media because of its simplified layered velocity model. Since background velocity information is contained in traveltimes, many algorithms are based on traveltime tomography, which matchs the fit between observed and calculated traveltimes. Each algorithm in tomographic velocity analysis can be characterized according to the domain it uses for traveltime picking. Conventional tomography Bishop et al. (1985); Stork (1988) picks the traveltime in the prestack data. In order to reduce the number, errors, and bias of picking, the semblance velocity stack panel or time-migrated section can be used for information about traveltime errors Fowler (1988); Toldi (1985). The result of those two types of the time domain picking can be achieved similarly in the image domain after prestack migration by picking events for every offset van Trier (1990) or by picking the best residual moveout (RMO) velocity along the events in the stack images Al-Yahya (1987); Etgen (1990).
After obtaining the low-wavenumber component of the velocity model by using the tomographic techniques explained above, we obtain the high-wavenumber component of the velocity model by migration which locates reflector position correctly. Conventional migration uses a simplified imaging condition that results in a zero-offset reflectivity. In order to extract more information from the seismic data, one needs to retrieve the angle-dependent reflectivity. To achieve this goal, de Bruin et al. 1990 propose an imaging condition in the wavenumber domain after shot-profile migration using depth extrapolation Claerbout (1985) and Cunha Filho 1992 proposes plane-wave-response imaging after reverse time migration using time extrapolation.