Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

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6.1. FUTURE DIRECTIONS 93 seismic sections. I have satisfactory results for adaptive subtraction. Limitations All methods have limitations. Volterra series produces many coefficients and cal- culation of these coefficients is computationally expensive. Also, a large number of coefficients causes overfitting of the signal and this leads to modeling both signal and noise. 6.1 Future Directions Volterra series have been implemented in nonlinear systems in a range of problems from biomedical research to communication applications. Adaptations of these methods to seismic exploration problems are presented in Chapter 4 and Chapter 5 of this thesis. The Volterra filter I developed is time-invariant; the signal is sta- tionary. However, in the future the Volterra filter presented here could be designed as a time-variant filter. The reconstruction of monochromatic complex sinusoids is a well studied prob- lem in seismic exploration in the case of regularly spaced traces in seismic sections. However, there are various interpolation methods in f − x and f − k domains; these methods can not reconstruct missing traces with events that exhibit curva- ture. There are examples of Volterra series implementation in the reconstruction of nonlinear image interpolation. For instance, Collis et al. (1997) presented an application of pixel interpolation in television images based on a nonlinear Volterra filter. Particularly, a third-order Volterra filter will be useful to interpolate missing data in seismic traces.
6.1. FUTURE DIRECTIONS 94 Noise reduction is not possible with the Volterra method because nonlinear filtering requires many coefficients for the quadratic and cubic parts of the operator resulting in signal and noise being simultaneously modeled (overfitting). The next step is to study a new inversion scheme to estimate Volterra kernels and to smooth the data to prevent overfitting the noise.
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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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2.6. 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 57 and 58: 3.3. 1-D SYNTHETIC AND REAL DATA EX
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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 73 and 74: RMSE 2 4.3. NONLINEAR PREDICTION OF
Page 77 and 78: 4.4. NOISE REMOVAL AND VOLTERRA SER
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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 107: series in this thesis has been trun
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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