Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

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5.4. REAL DATA EXAMPLES 89 Time (s) [s] 3.8 4.0 4.2 4.4 4.6 4.8 5.0 Traces 10 20 30 40 50 60 Traces 70 80 90 100 110 120 130 140 (a) (b) Data Figure 5.11: Real Data example shot gather (closer look of removed multiples). (a) Original data. (b) Prediction of multiples. (c) Removed multiples via f − x linear prediction error filtering. (d) Removed multiples with a f − x nonlinear prediction error operator (third order Volterra series). (c) (d)
5.5. SUMMARY 90 5.5 Summary In this Chapter I have investigated the possibility of using nonlinear prediction for adaptive attenuation of multiples, so far with encouraging results. Adaptive subtraction of curved events with synthetic data examples has showed that Volterra series contributes removal of curved events. On the other hand, real data examples indicates that this method is not better than usual adaptive subtraction models based on linear prediction error filtering methods when modeling with small data windows in the f - x domain. More research, however, is needed to understand the role played by the nonlinear kernels of the Volterra expansion. In other words, the linear part has a very well understood action when written in prediction error form. It represents a notch filter that attenuates one or more linear events. The second and third-order kernels must contribute as some sort of special ”notch” operators that can model a continuous distribution of wave numbers (variable dip in the t − x domain).
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Name of Author: Soner Bekleric Univ
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University of Alberta Faculty of Gr
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Abstract Linear filter theory has p
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Contents 1 Introduction 1 1.1 Appli
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List of Tables 3.1 Filter length an
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4.4 (a) Prediction of Figure 4.2(b)
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List of symbols Symbol Name or desc
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List of abbreviations Abbreviation
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In applied seismology predictive de
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1.1. APPLICATIONS 4 applied to vide
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1.3. THESIS OUTLINE 6 • Chapter 4
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2.2. LINEAR PROCESS 8 Finally, I pr
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2.3. LINEAR PREDICTION 10 E(z) 1 X(
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2.3. LINEAR PREDICTION 12 In my the
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2.3. LINEAR PREDICTION 14 which can
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2.3. LINEAR PREDICTION 16 ∂ρ fb
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2.3. LINEAR PREDICTION 18 I have an
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2.4. 1-D SYNTHETIC AND REAL DATA EX
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2.4. 1-D SYNTHETIC AND REAL DATA EX
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2.6. SUMMARY 24 Relative PSD Relati
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Chapter 3 Nonlinear Prediction 3.1
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3.1. NONLINEAR PROCESSES VIA THE VO
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3.1. NONLINEAR PROCESSES VIA THE VO
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3.2. NONLINEAR MODELING OF TIME SER
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Page 53 and 54: 3.2. NONLINEAR MODELING OF TIME SER
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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
Page 73 and 74: RMSE 2 4.3. NONLINEAR PREDICTION OF
Page 77 and 78: 4.4. NOISE REMOVAL AND VOLTERRA SER
Page 79 and 80: 4.5. SYNTHETIC AND REAL DATA EXAMPL
Page 89 and 90: 4.6. SUMMARY 74 4.6 Summary In this
Page 91 and 92: 5.1. INTRODUCTION 76 ples remains a
Page 93 and 94: 5.3. SYNTHETIC DATA EXAMPLES 78 Not
Page 95 and 96: 5.3. SYNTHETIC DATA EXAMPLES 80 Tim
Page 97 and 98: 5.3. SYNTHETIC DATA EXAMPLES 82 Tim
Page 99 and 100: 5.4. REAL DATA EXAMPLES 84 Time [s]
Page 101 and 102: 5.4. REAL DATA EXAMPLES 86 Time [s]
Page 103: 5.4. REAL DATA EXAMPLES 88 Time [s]
Page 107 and 108: series in this thesis has been trun
Page 109 and 110: 6.1. FUTURE DIRECTIONS 94 Noise red
Page 111 and 112: BIBLIOGRAPHY 96 Canales, L. L. (198
Page 113 and 114: BIBLIOGRAPHY 98 Marple, S. L. (1980
Page 115 and 116: BIBLIOGRAPHY 100 Trad, D. (2003). I
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Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

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