Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

5.3. SYNTHETIC DATA EXAMPLES 79
multiples from linear and nonlinear prediction error filters in Figures 5.4(e) and
5.4(f), respectively. Linear prediction error filter eliminated less multiples than the
nonlinear prediction error filter. However, the nonlinear prediction filter removes
more multiples, but it also affects the amplitude response of the primaries.
In Figure 5.5(a) I present three primaries (linear events) and two multiples (two
multiples with sharp apexes) that cannot be properly modeled by linear events.
Figure 5.5(b) shows the distorted estimation of the multiples and Figure 5.5(c) is
the solution via classical linear prediction. Again, the method can not separate
multiples from primary and also distorts primaries. Figure 5.5(d) is the solution
with the third order Volterra series. However, the prediction error filter was able to
model the curved multiples and produce an acceptable result when applied to the
data panel.
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Figure 5.2: Synthetic data example. (a) Original data. (b) Multiples. (c) Adaptive
multiple attenuation using f − x linear prediction error operators computed from
(b).
(c)