In the previous sections the slanted wavefront was synthesized by using the ray parameter p. If the reflector in the subsurface is generally gentle and the lateral velocity change is small, the slanted wavefronts with constant ray parameters are enough to retrieve the angle-dependent reflectivity. However, if the reflector in the subsurface has a complex structure or the lateral velocity change is not small, a slanted wavefront with a constant ray parameter is not enough to retrieve the angle-dependent reflectivity because one need to calculate the incidence angle using the velocity of the subsurface location, which corresponds to the ray parameter of the subsurface location. We then need a plane-wave with a constant-incidence angle to reflectors instead.
In order to synthesize an areal shot record for a slanted wavefront with a constant-incidence angle at a depth level, the impulse in each trace of the predefined wavefield, , must have time lag, ,with respect to every other trace. If the trace interval is
The sign convention of the angle, , for the slanted wavefront used in this thesis is shown in Figure . Figure is the stacked section obtained by synthesizing a plane wave with 10 degrees of incidence angle at 1200 m depth (Figure ). It looks very similar to the synthesized stack with a constant ray parameter (Figure ) at the same depth level, but the difference between them becomes clear in the images shown in Figures and . The image obtained by synthesizing a constant incidence angle is readily interpretable in terms of an angle-dependent reflectivity of the reflectors where the plane-wave is synthesized, since we can easily calculate the incidence angle to reflector from the angle of synthesized plane-wave and the dip of reflector.