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Information-based inversion and processing with applications
Author
Title
Information-based inversion and processing with applications / by Tadeusz J. Ulrych, Mauricio D. Sacchi.
ISBN
0080461344
9780080461342
9780080447216
008044721X
008044721X
1280641045
9781280641046
9786610641048
6610641048
Edition
1st ed.
Published
Amsterdam ; Boston : Elsevier, 2005.
Physical Description
1 online resource (xxvii, 405 pages) : illustrations.
Local Notes
Access is available to the Yale community.
Notes
English.
Access and use
Access restricted by licensing agreement.
Summary
This book examines different classical and modern aspects of geophysical data processing and inversion with emphasis on the processing of seismic records in applied seismology. Chapter 1 introduces basic concepts including: probability theory (expectation operator and ensemble statistics), elementary principles of parameter estimation, Fourier and z-transform essentials, and issues of orthogonality. In Chapter 2, the linear treatment of time series is provided. Particular attention is paid to Wold decomposition theorem and time series models (AR, MA, and ARMA) and their connection to seismic data analysis problems. Chapter 3 introduces concepts of Information theory and contains a synopsis of those topics that are used throughout the book. Examples are entropy, conditional entropy, Burg's maximum entropy spectral estimator, and mutual information. Chapter 4 provides a description of inverse problems first from a deterministic point of view, then from a probabilistic one. Chapter 5 deals with methods to improve the signal-to-noise ratio of seismic records. Concepts from previous chapters are put in practice for designing prediction error filters for noise attenuation and high-resolution Radon operators. Chapter 6 deals with the topic of deconvolution and the inversion of acoustic impedance. The first part discusses band-limited extrapolation assuming a known wavelet and considers the issue of wavelet estimation. The second part deals with sparse deconvolution using various 'entropy' type norms. Finally, Chapter 7 introduces recent topics of interest to the authors. The emphasis of this book is on applied seismology but researchers in the area of global seismology, and geophysical signal processing and inversion will find material that is relevant to the ubiquitous problem of estimating complex models from a limited number of noisy observations. * 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.
Variant and related titles
Knovel. OCLC KB.
Other formats
Print version: Ulrych, Tadeusz J. Information-based inversion and processing with applications. 1st ed. Amsterdam ; Boston : Elsevier, 2005
Format
Books / Online
Language
English
Added to Catalog
February 26, 2024
Series
Handbook of geophysical exploration. Seismic exploration ; v. 36
Bibliography
Includes bibliographical references and index.
Contents
Cover
Contents
Some Basic Concepts
Introduction
Probability Distributions, Stationarity & Ensemble Statistics
Properties of Estimators
Orthogonality
Orthogonal Vector Space
Fourier Analysis
Expectations etc.,
Lagrange Multipliers
Linear Time Series Modelling
Introduction
The Wold Decomposition Theorem
The Moving Average. MA, Model
The Autoregressive, AR, Model
The Autoregressive Moving Average, ARMA, Model
MA, AR and ARMA Models in Seismic Modelling and Processing
Extended AR Models and Applications
A Few Words About Nonlinear Time Series
Levinson's Recursion and Reflection Coefficients
Minimum Phase Property of the PEO
Information Theory and Relevant Issues
Introduction
Entropy in Time Series Analysis
The Kullback-Lciblcr Information Measure
MaxEnt and the Spectral Problem
The Akaike Information Criterion, AIC
Mutual Information and Conditional Entropy
The Inverse Problem
Introduction
The Linear (or Linearized) Inverse Formulation
Probabilistic Inversion
Minimum Relative Entropy Inversion
Bayesian Inference
Signal to Noise Enhancement
Introduction
f
x Filters
Principal Components, Eigenimages and the KL Transform
Radon Transforms
Time variant Radon Transforms
Discussion
Deconvolution with Applications to Seismology
Introduction
Layered Earth Model
Deconvolution of the Reflectivity Series
Sparse Deconvolution and Bayesian Analysis
ID Impedance Inversion
Nonminimum Phase Wavelet Estimation
Blind, Full Band Deconvolution
Discussion
A Potpourri of Some Favorite Techniques
Introduction
Physical Wavelet Frame Dcnoising
Stein Processing
The Bootstrap and the EIC
The Extended Information Criterion
Summary
Last Page.
Subjects
Genre/Form
dissertations.
Academic theses
Academic theses.
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