Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

series in this thesis has been truncated to a third-order Volterra series. Prediction
coefficients are found via least squares solutions. The real and synthetic data ex-
amples showed that Volterra series modeling modeling is more versatile than linear
prediction at the time of representing signals such as those arising in the context of
exploration seismology.
Events that exhibit strong curvature cannot be modeled via linear f − x predic-
tion filters. I can model these events by implementing the Volterra algorithm. The
optimum filter length of a linear model of order (p) or a nonlinear Volterra model
of order (p, q, r) can be computed via inspection of the residuals. A more practical
method is desirable but at this stage looking for evidence of under-over fitting using
sophisticated statistical analysis method was beyond the scope of this study.
Different synthetic and real data examples showed that the modeling of events
with linear moveout can be predicted mainly via linear prediction coefficients and
cubic prediction coefficients. The contribution of quadratic parts to events with
linear moveouts is negligible. In addition to this, events that exhibit curvature
can be modeled properly with nonlinear terms of a Volterra series. Finally, it is
important to stress that waveforms that exhibit linear moveout can be predicted
with a linear system. Conversely, when waveforms exhibit nonlinear moveout, which
translates in the f − x domain as non stationary signals, the nonlinear part of the
Volterra system helps in predicting the signal.
Another application of the nonlinear Volterra model in this thesis is adaptive
subtraction of multiples. Elimination of multiples is a common problem in explo-
ration seismology. In this case the prediction coefficients have been designed as
prediction error filters (PEF). I used this algorithm to annihilate multiples from
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