Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

1.2. MOTIVATION AND GOALS OF THE THESIS 5
Applications of higher- order spectra (HOS) and Volterra series
The connection between HOS and Volterra series were investigated by researchers
under different topics namely; nonlinear ocean waves and HOS (Powers et al., 1997);
non-normal random processes (Gurley et al., 1996); nonlinearity detection (LeCail-
lec and Garello, 2004).
1.2 Motivation and Goals of the Thesis
The motivation of this thesis is to introduce nonlinear prediction to the seismic data
processing community and study the feasibility of nonlinear prediction algorithms
for problems of waveform modeling for SNR enhancement and adaptive modeling
and subtraction for the general problem of coherent noise attenuation.
The goal of this thesis is to study nonlinear prediction algorithms and their
applicability to model seismic waveforms in the f −x domain. In particular, I would
like to model signals that are not correctly represented by the linear prediction
theory. Those signals often involve seismic waveforms with hyperbolic moveout
(seismic reflections or diffractions) that are often immersed in noise and one would
like to enhance prior to imaging.
1.3 Thesis Outline
• Chapter 2 presents an introduction to linear modeling of time series.
• Chapter 3 reviews the concept of nonlinear prediction and its realization via
Volterra series.