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
General
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