f Extension of reflectivity to smooth media

Propagation of elastic waves in 1D layered media can be modeled exactly with the well known reflectivity technique (Kennet, 1983). It consists in the computerion of the response of the layers to plane waves of different temporal frequency and ray parameter (reflectivity function) and the summation of these responses through the Sommerfeld integral. Computation time is proportional to the number of layers. Modeling of continuous variations in depth is accomplished by discretization in a set of uniform layers. The thickness must be smaller than the predominant wavelength to ensure accuracy The number of layers can become quite large and the computation cumbersome.