In the past decade, the kinematic or ray-geometric principles underlying the DMO process have been well established. It is only recently, however, that the associated amplitude aspects have received attention. The aim of this paper is to extend the Kirchhoff-style TZO and DMO processes to elastic media, and to develop dynamically correct transformations of wavefield data. We accomplish this goal with the aid of the generalized Radon transform (GRT). We consider general, anisotropic media, and provide closed-form expressions for the constant-background-medium case.