The effect of the anti-aliasing triangle width

The anti-aliasing is performed by effectively convolving a triangle function with the output trace. The width of the triangle, $\Delta_t$, usually exceeds the time sampling rate, $\Delta t$, for the steepest dips. Therefore, the triangles overlap and produce an undesirable amplitude increase. The number of overlapping triangles is proportional to their width. Thus, a reasonable method of amplitude correction is to divide the convolution triangles by $\Delta_t$, as follows:  

$$F_{aa} = \frac{1}{\Delta_t} .$$ (7)

 

Dmo2 Figure 7 A slice in the 3-D data after DMO with Black's amplitudes, corrected for spherical spreading and the triangle effect.

Figure (7) shows the same section of the 3-D cube as Figure (6), but the DMO process now involves the two correction factors for spherical spreading and triangle width. The AVO effect along the horizontal reflector is restored, and the relative amplitude of the different reflectors is better balanced and closer to the amplitude distribution in Figure (5). The third rule is now more completely verified although some singularities occur at the near offset traces (close to x = 0).