
Information-Based Inversion and Processing with Applications
Description
Key Features
- Non-conventional approaches to data processing and inversion are presented
- Important problems in the area of seismic resolution enhancement are discussed
- Contains research material that could inspire graduate students and their supervisors to undertake new research directions in applied seismology and geophysical signal processing
Readership
Table of Contents
List of Figures
Dedication
Acknowledgements
Preface
Please Read Initially
Chapter 1: Some Basic Concepts
1.1 Introduction
1.2 Probability Distributions, Stationarity & Ensemble Statistics
1.3 Properties of Estimators.
1.4 Orthogonality
1.5 Orthogonal Vector Space
1.6 Fourier Analysis
1.7 The z Transform
1.8 Dipole Filters
1.9 Discrete Convolution and Circulant Matrices
Appendices
Chapter 2: Linear Time Series Modelling
2.1 Introduction
2.2 The Wold Decomposition Theorem
2.3 The Moving Average, MA, Model
2.4 The Autoregressive, AR, Model
2.5 The Autoregressive Moving Average, ARMA, Model
2.6 MA, AR and ARMA Models in Seismic Modelling and Processing
2.7 Extended AR Models and Applications
2.8 A Few Words About Nonlinear Time Series
Appendices
Chapter 3: Information Theory and Relevant Issues
3.1 Introduction
3.2 Entropy in Time Series Analysis
3.3 The Kullback-Leibler Information Measure
3.4 MaxEnt and the Spectral Problem
3.5 The Akaike Information Criterion, AIC
3.6 Mutual Information and Conditional Entropy
Chapter 4: The Inverse Problem
4.1 Introduction
4.2 The Linear (or Linearized) Inverse Formulation
4.3 Probabilistic Inversion
4.4 Minimum Relative Entropy Inversion
4.5 Bayesian Inference
Appendix
Chapter 5: Signal to Noise Enhancement
5.1 Introduction
5.2 f − x Filters
5.3 Principal Components, Eigenimages and the KL Transform
5.4 Radon Transforms
5.5 Time variant Radon Transforms
Chapter 6: Deconvolution with Applications to Seismology
6.1 Introduction
6.2 Layered Earth Model
6.3 Deconvolution of the Reflectivity Series
6.4 Sparse Deconvolution and Bayesian Analysis
6.5 1D Impedance Inversion
6.6 Nonminimum Phase Wavelet Estimation
6.7 Blind, Full Band Deconvolution
6.8 Discussion
Chapter 7: A Potpourri of Some Favorite Techniques
7.1 Introduction
7.3 Stein Processing
7.4 Bootstrap and the EIC
7.5 Summary
Bibliography
Index
Product details
- No. of pages: 436
- Language: English
- Copyright: © Elsevier Science 2005
- Published: December 16, 2005
- Imprint: Elsevier Science
- eBook ISBN: 9780080461342
About the Authors
T.J. Ulrych
Affiliations and Expertise
M.D. Sacchi
Affiliations and Expertise
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