Multidimensional linearized inversion and seismic migration

This paper discusses the close relationship between seismic migration and multidimensional inversion according to the linearized inverse scattering theory. The linearized inverse scattering approach represents a mixed modeling-inversion procedure. Unlike seismic migration, the actual inversion process is carried out on the difference between a modeled reference response and the actually measured data. The output is generally presented in terms of the elastic parameters of the medium. Siesmic migration represents a direct inversion method: the downward extrapolation process is carried out directly on the measured data. Output is presented in terms of reflectivity. If the reference medium has been chosen in such a way that (1) the total wave field in the reference medium can be split into a downward traveling source wave field and an upward traveling response (the propagation of both wave fields being defined by the one-way wave equation) and that, (2) the upward traveling response in the reference medium can be neglected with respect to the upward traveling response in the actual medium, then seismic migration and linearized inversion define identical inversion processes. Typically, the above conditions are fulfilled in a homogeneous reference medium. In iterative multidimensional inversion, the full inverse scattering problem is approached by a number of linearized inversion steps. I show that each linear step consists of a prestack migration process and a prestack modeling process, the modeling output being used to remove the contribution of multiple scattering. Finally, I argue that for a proper inversion process, information on the elastic parameters outside the seismic frequency bandwidth (temporarily and spatially) should be accounted for in the reference medium.