Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

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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.
1.3. THESIS OUTLINE 6 • Chapter 4 provides a detailed study of linear and nonlinear prediction applied to SNR enhancement of seismic records. • Chapter 5 studies the feasibility of using nonlinear prediction for adaptive subtraction of coherent noise from seismic records. • Chapter 6 contains a summary. In addition, I provide conclusions including the limitations of nonlinear prediction theory in seismic signal processing. Finally, I provide a discussion of future research directions.
Page 1 and 2: Name of Author: Soner Bekleric Univ
Page 3 and 4: University of Alberta Faculty of Gr
Page 5 and 6: Abstract Linear filter theory has p
Page 7 and 8: Contents 1 Introduction 1 1.1 Appli
Page 9 and 10: List of Tables 3.1 Filter length an
Page 11 and 12: 4.4 (a) Prediction of Figure 4.2(b)
Page 13 and 14: List of symbols Symbol Name or desc
Page 15 and 16: List of abbreviations Abbreviation
Page 17 and 18: In applied seismology predictive de
Page 19: 1.1. APPLICATIONS 4 applied to vide
Page 23 and 24: 2.2. LINEAR PROCESS 8 Finally, I pr
Page 25 and 26: 2.3. LINEAR PREDICTION 10 E(z) 1 X(
Page 27 and 28: 2.3. LINEAR PREDICTION 12 In my the
Page 29 and 30: 2.3. LINEAR PREDICTION 14 which can
Page 31 and 32: 2.3. LINEAR PREDICTION 16 ∂ρ fb
Page 33 and 34: 2.3. LINEAR PREDICTION 18 I have an
Page 35 and 36: 2.4. 1-D SYNTHETIC AND REAL DATA EX
Page 39 and 40: 2.6. SUMMARY 24 Relative PSD Relati
Page 41 and 42: Chapter 3 Nonlinear Prediction 3.1
Page 43 and 44: 3.1. NONLINEAR PROCESSES VIA THE VO
Page 45 and 46: 3.1. NONLINEAR PROCESSES VIA THE VO
Page 47 and 48: 3.2. NONLINEAR MODELING OF TIME SER
Page 61 and 62: 3.4. SUMMARY 46 3.4 Summary In this
Page 63 and 64: 4.1. LINEAR PREDICTION IN THE F −
Page 65 and 66: 4.2. ANALYSIS OF OPTIMUM FILTER LEN
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Page 69 and 70: 4.3. NONLINEAR PREDICTION OF COMPLE
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4.3. NONLINEAR PREDICTION OF COMPLE
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RMSE 2 4.3. NONLINEAR PREDICTION OF
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4.3. NONLINEAR PREDICTION OF COMPLE
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4.4. NOISE REMOVAL AND VOLTERRA SER
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4.5. SYNTHETIC AND REAL DATA EXAMPL
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4.6. SUMMARY 74 4.6 Summary In this
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5.1. INTRODUCTION 76 ples remains a
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5.3. SYNTHETIC DATA EXAMPLES 78 Not
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5.3. SYNTHETIC DATA EXAMPLES 80 Tim
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5.3. SYNTHETIC DATA EXAMPLES 82 Tim
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5.4. REAL DATA EXAMPLES 84 Time [s]
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5.5. SUMMARY 90 5.5 Summary In this
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series in this thesis has been trun
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6.1. FUTURE DIRECTIONS 94 Noise red
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BIBLIOGRAPHY 96 Canales, L. L. (198
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BIBLIOGRAPHY 98 Marple, S. L. (1980
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BIBLIOGRAPHY 100 Trad, D. (2003). I
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Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

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