Geophysical data analysis: Discrete inverse theory. MATLAB edition. (Q2881388)

This is a practical book on data analysis based on numerical Matlab procedures for solving inverse problems with a special application in seismology. The book is useful both as a textbook for graduate students in geophysics and as a numerical data processing reference book for researchers not only in geophysics but also those involved in acoustic tomography and X-ray imaging data processing. Detailed descriptions of various statistical, probabilistic methods are supplied by relevant numerical codes in Matlab which enables immediate applications in practical data analyses.NEWLINENEWLINEThe book contains xxxvi+293 pages with text divided into sections: Introduction, 13 Chapters, and Appendices. Each chapter ends with typical exercise problems related to the considered subject.NEWLINENEWLINEIn the Introduction, one finds explanations of the theory of solving inverse problems in fields of pure science as well as in practical applications. This is followed by an insight into elements of programming in Matlab focused on some useful Matlab operations. Chapter 1 deals with details of describing inverse problems, their formulations and how to obtain the solutions. Some comments on probability theory are given in Chapter 2 which includes noise and random variables, correlations, and probability functions. Solutions to the linear Gaussian problem are obtained and discussed in Chapters 3-5 depending on the applied method: the length method, generalized inverses, and maximum likelihood methods respectively. Chapter 6 deals with nonuniqueness and localized averages, and with the role of information assumed a priori. Various applications of vector spaces and transformations are elaborated in Chapter 7. Linear inverse problems in non-Gaussian statistics are considered in Chapter 8 while Chapter 9 tackles the non-linear inverse problems by various statistical methods. The method of factor analysis is treated in Chapter 10 while details of continuous inverse theory and tomography are the subject of Chapter 11. Geophysical applications are considered in Chapters 12-13. In this sense, Chapter 12 involves sample inverse problems related to temperature distributions, earthquake locations, and vibration problems, among other, while Chapter 13 presents further details of application of inverse theory to solid earth geophysics. The latter includes determinations and analysis of seismic wave characteristics, tectonic plate motions, gravity and geo-magnetism, and magnetotelluric parameters. Two Appendices are on implementation of constrains with Lagrange multipliers, and on inverse theory with complex quantities respectively.