From this standpoint the limit past which spatial aliasing begins should be thought of in terms of angles at which energy is missing from the data. Taking the ray angle to be 30 instead of 90 doubles horizontal wavelengths. Because data usually has good signal above 40 Hz, wide-angle processing is often frustrated by spatial aliasing. The problem of spatial aliasing usually overshadows the difference between the 15 and the 90 equations. Aliased energy does not move between hyperbola flanks and the apex.
Aliased energy tends to stay in place.
This is illustrated on Figure 20 which shows a 90 hyperbola and a 15 hyperboloid from a finite difference equation. Overall, there is little difference. Look at the amplitude of the hyperbolic arrival. It is dropping off faster than predicted by spherical spreading and the obliquity function. This is because the dispersion curve semicircles overlap one another.