Reflection wave equation for seismic reflection wave and its application for migration

Summary Wave equation is the basis of seismic wave modeling, inversion and migration imaging. In this study, we present a set of reflection wave equations with source term of product of reflectivity and the first order time derivative of incident wavefield for the scalar-, acoustic- and elastic primary seismic reflection wave, based on the scattering theory, the high frequency approximation of wave phenomena and its generalization to the medium parameter. By viewing the variations of medium parameter as a constant under the high frequency approximation, the incident wave directional derivative can be expressed in term of local wavenumber of incident wave direction. Defining the reflectivity as the incident wave directional derivative of medium parameter perturbation. We show the application of scalar reflection wave equation for migration.