Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

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5.8 Real Data example A common offset gather (a closer look of removed multiples). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.9 Real Data example shot gather. . . . . . . . . . . . . . . . . . . . 87 5.10 Real Data example shot gather (closer look). . . . . . . . . . . . . . 88 5.11 Real Data example shot gather (a closer look of removed multiples). 89
List of symbols Symbol Name or description (·) ∗ Complex conjugate (·) b n (·) f n Backward prediction at time index n Forward prediction at time index n (·) T Matrix transpose (ˆ·) Hat denotes prediction A Filter matrix (either linear or nonlinear) ai bij c2 clms Cn Linear prediction filter coefficient at time index i Quadratic prediction filter coefficient at time index jk Second order cumulant (autocorrelation) Cubic prediction filter coefficient at time index lms n th − order spectrum d Data vector E[·] Expectation operator εn Error or innovation process of time index n e Noise vector f Temporal frequency in Herts (Hz) H1(·) Linear transfer function of Volterra series H2(·, ·) Quadratic transfer function of Volterra series H3(·, ·, ·) Cubic transfer function of Volterra series h Offset (distance between source and receiver) hk(σ1, . . . , σk) Volterra kernels of the system I Identity matrix Im Imaginary part of a complex variable J Cost function kp Prediction coefficient m Model vector µ Trade-off parameter N Number of data samples
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: 4.4 (a) Prediction of Figure 4.2(b)
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 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
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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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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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