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

(1) |

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:

(2) |

where () is the shot (receiver) coordinate, and is
the total traveltime from source to reflection point to receiver.
*A*_{s} (*A*_{r})
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.

Figure 1

11/17/1997