In Kirchhoff-type migration, two dynamic ray-tracing computations are usually needed for computing the complex weighting (Green's) functions necessary for recovering the source pulse with true amplitude. One computation is from the source point to the image point, the other is from the receiver point to the image point. Since it is a time-consuming procedure, dynamic ray tracing is a main factor slowing down the performance speed of weighted diffraction stack migration. Here, the known weighting function for a common-shot configuration is revisited and a new, alternative formula is developed. Because only the takeoff angles of rays are involved in this alternative formula, the module of the complex weighting function can be computed solely by kinematic ray tracing. Further, it is shown that the phase (caustic) correction is not essential for the stack process. As a consequence, the weighted diffraction stack migration can be implemented without using dynamic ray tracing at all. In other words, the subsurface structure can be imaged without using any Green's function. Therefore, using the new formula may accelerate the performance of the Kirchhoff-type migration, especially in 3-D cases. In addition, the new formula may affect the model smoothing process necessary for using some traveltime computing methods based on ray tracing. As is known, kinematic quantities associated with a given ray are less sensitive to the velocity distribution than the dynamic ones. Thus, the new formula allows one to use a model less smoothed than that demanded for using dynamic ray tracing. As a result, less smoothing operation is needed by building a velocity model without interfaces. The latter points are vital for the accuracy and efficiency of the ray tracers for computing the traveltime of point-diffracted rays.