The theory underlying this study is more fully discussed in Lumley and Beydoun (1991) and Lumley (1993). I assume a forward model for a ``generalized'' PP reflectivity, , which combines elements of plane wave reflection and Rayleigh-Sommerfeld diffraction theory. I define a differential volume element of as
for , and zero otherwise. Here, w is angular frequency, is compressional velocity, is the Zoeppritz PP plane wave reflection coefficient and () is the angle between the incident source (receiver) ray and the specular ray in Figure . is the specular angle of reflection. Equation (1) can be integrated over the subsurface volume to model the reflected scalar wavefield:
where () is the shot (receiver) coordinate, and is the total traveltime from source to reflection point to receiver. As (Ar) is the WKBJ amplitude factor along the source (receiver) leg of the raypath to the subsurface reflection point , and incorporates the amplitude effects of source (receiver) directivity, geometric spreading, transmission loss, and intrinsic high-frequency Q attenuation. All of these quantities are obtained by raytracing through the background migration velocity model.