Since the wavefield is differently affected by the low- and high-frequency components of the model, we would expect that the estimation of one can be made independent of the other. In fact, some standard techniques employed to estimate the average properties (solve the kinematics) are based on the assumption of a dynamically passive system. For instance, conventional methods, for estimating the optimum NMO velocity field assume that the reflectivity should ideally be a constant function of the offset instead of satisfying an specific angle dependence. These methods have proved to be completely adequate to almost all practical applications.

On the other hand, most methods for acoustic and elastic inversion (solve the dynamics) try to solve both problems at the same time (Hindlet and Kolb, 1988; Mora, 1987; Snieder et al., 1988). The coupling between the kinematically and dynamically related parts of the system is responsible for both an unnecessary increase in the time needed for the inversion and an increase in the instability of the problem (Demirbag and Coruh, 1989). To separate the two problems, we must look at the crucial point, that is, the characterization of the model.

The usual way is to model the earth as a stack of layers with fixed elastic properties. As a result of this structure, a change in the model affects not only amplitudes, but also traveltimes. Therefore, both average and local properties of the subsurface medium (and consequently, kinematics and dynamics) will be coupled from the beginning--in the model itself.

In an attempt to separate the two problems, de Haas and Berkhout (1988), propose the introduction of a macro model (responsible for the kinematics) and a target zone, composed of a stack of layers (responsible for dynamics). This characterization of the model space results in a reduction of the cost and an increase in the stability of the inversion. The target zone, however, remains characterized by the same stack-of-layers scheme.

A more consistent method for solving the dynamics problem should be able to completely separate the local from the average properties of the subsurface media. One way of doing that is to impose constraints on the possible changes of the model, so that the kinematics remains unaffected. I propose a method in which the uncoupling is performed in the model itself. One part of the model (which I will refer as background) is an apriori estimation of the smoothly varying elastic properties of the subsurface. Of course, a pure kinematic method should be used to construct this part of the model, which remains unchanged during the inversion process. The other part consists of sparse perturbation layers, which affect only the dynamically-related features of the wavefield.

1/13/1998