Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

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4.5. SYNTHETIC AND REAL DATA EXAMPLES 73 Time (s) Time (s) 0 0.5 1.0 0 0.5 1.0 Traces 20 40 60 (a) Traces 20 40 60 (d) Time (s) Time (s) 0 0.5 1.0 0 0.5 1.0 Traces 20 40 60 (b) Traces 20 40 60 (e) Time (s) Time (s) 0 0.5 1.0 0 0.5 1.0 Traces 20 40 60 (c) Traces 20 40 60 Figure 4.19: 2-D real data. (a) Original data. (b) Prediction using a third-order Volterra series with parameters p = 9, q = 9, and r = 9. (c) Contribution from the linear part. (d) Contribution from the quadratic part. (e) Contribution form the cubic part. (f) Contribution from both quadratic and cubic parts.(q = 9, and r = 9) (f)
4.6. SUMMARY 74 4.6 Summary In this chapter, I surveyed modeling methods in the f − x domain. Canales (1984) method was reviewed and extensions of this method to nonlinear problems were explored. Events with nonlinear moveouts can be modeled using nonlinear terms of a Volterra series. Events with complex waveforms need additional prediction coeffi- cients in order to properly model the data. It is clear that linear prediction fails to model data sets with curvature; nonlinear predictions can accurately model these data. I cannot claim, however, that the linear part of a Volterra series models the linear events and that the nonlinear kernels are modeling the hyperbolic events.
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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
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
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
Page 67 and 68: 4.2. ANALYSIS OF OPTIMUM FILTER LEN
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
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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 105 and 106: 5.5. SUMMARY 90 5.5 Summary In this
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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