SS: The Future of Seismic Imaging; Reverse Time Migration an Full Wavefield Inversion - Wave equation based model building and imaging in complex settings
Authors: ten Kroode Fons , Plessix René-Edouard , Perkins Colin , Clippard Jim 
Published: July 2009

Abstract
In complex geological environments encountered in today's exploration practice there is a need for model building and imaging schemes based on an as accurate a description as possible of wave propagation in the earth. In this paper we discuss the most advanced members of a family of wave equation based imaging and model building schemes, namely Reverse Time Migration and Full Waveform Inversion. We illustrate the potential of these schemes by results obtained on an OBS survey in the Gulf of Mexico.

Introduction
Seismic imaging consists of two steps. One starts by building a subsurface velocity model and follows this by creating the actual reflection image by a depth migration in this velocity model.
Of these two steps depth migration is well understood. It is based on a single scattering description of wave propagation in the earth. This description provides a linear relationship between the reflectivity in the subsurface and the reflection data measured at the surface of the earth. Depth migration boils down to constructing the inverse of this relationship on the reflection data and thus constructs an image of the reflectivity in the subsurface. Obviously, because of the single scattering assumption, this does not deal with multiple reflections, which therefore have to be attenuated before migration. The most advanced depth migration algorithm in use today is Reverse Time Migration.
The velocity model building problem is much harder, as it is inherently a non-linear problem. The standard approach is to exploit the redundancy in the seismic data, for example the offset between source and receiver. One migrates subsets of the data with fixed values of the redundant coordinates (" minimal datasets??) and requires that at each horizontal location (x,y) the depth of an imaged reflector does not vary with the redundant coordinate. If it does, the variations are used to update the velocity model iteratively. This leads to a family of well known reflection tomography schemes, which go under the name of migration velocity analysis. Although most of them are based on some form of raytracing, these methods do have a natural generalization towards the wave equation domain, see e.g. Symes 2008. It is important to stress that they are based on primary reflections only. These methods therefore all rely on effective multiple attenuation and/or interpreter based identification of the primaries. The latter is still one of the most important bottlenecks of migration velocity analysis, especially in poor signal to noise situations, such as subsalt.
Full Waveform Inversion is another, completely different method for estimating the velocity model. In this approach one tries to find the model by requiring that the data calculated by solving the wave equation in this model optimally resemble the measured data in a seismic survey. The great advantage of this formulation is that it should work for all wave types, not only for primary reflections.
In this paper we will take a closer look at Reverse Time Migration and Full Waveform Inversion.