Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

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Symbol Name or description n−D n− dimensional: e.g 1-D ω Angular/radial frequency (radian/seconds) PAR(ω) AR Power spectrum estimator Pxx(ω) or C2(ω) Power spectrum estimation p Linear filter length or AR model order q Quadratic filter length or AR model order R Autocorrelation matrix Rp Autocorrelation sequence at lag p r Cubic filter length or AR model order Re Real part of a complex variable S Single waveform in f − x domain s Single waveform in t − x domain σ 2 ε σp Innovation of the system White noise variance t Travel time in seconds θ Apparent slowness Z(xn) = X(z) Z-transform of xn
List of abbreviations Abbreviation Name or description AO Arctic oscillation AR(p) Autoregressive model of order p AR(p, q, r) Autoregressive Volterra model of order p, q, r ARMA Autoregressive moving average DFT Discrete Fourier transform FSME Free surface multiple elimination FT Fourier transform IIR Infinite impulse response MA(q) Moving average model of order q PEF Prediction error filter PSD Power spectrum density RMSE Root-mean square error SNR Signal-to-noise ratio SRME Surface related multiple elimination YW Yule-Walker equations
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: List of symbols Symbol Name or desc
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
Page 63 and 64: 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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