Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

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Abstract Linear filter theory has proven useful in many seismic data analysis applications. However, the general development of linear filter theory is limited by the implicit approximations typically found in seismic processing; one reason for this is to avoid effects of nonlinearity. This thesis concentrates on the implementation of nonlinear time series modeling based on an autoregressive method. The developed algorithm utilizes third-order Volterra kernels to improve predictability of events that cannot be predicted using linear prediction theory. Volterra series are analyzed. The application and implementation of a nonlinear autoregressive algorithm to the problem of modeling complex waveforms in the f −x domain is studied. Problems of random noise attenuation and adaptive subtraction of multiples are reexamined by the new Volterra autoregressive algorithm. Synthetic and field data examples are used to illustrate the theory and methods presented in this thesis.
Page 1 and 2: Name of Author: Soner Bekleric Univ
Page 3: University of Alberta Faculty of Gr
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 and 20: 1.1. APPLICATIONS 4 applied to vide
Page 21 and 22: 1.3. THESIS OUTLINE 6 • Chapter 4
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 37 and 38: 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
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3.3. 1-D SYNTHETIC AND REAL DATA EX
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3.4. SUMMARY 46 3.4 Summary In this
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4.1. LINEAR PREDICTION IN THE F −
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4.2. ANALYSIS OF OPTIMUM FILTER LEN
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4.2. ANALYSIS OF OPTIMUM FILTER LEN
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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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4.4. NOISE REMOVAL AND VOLTERRA SER
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4.5. SYNTHETIC AND REAL DATA EXAMPL
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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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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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