- 272 pages
- English
- PDF
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Geophysical Data Analysis: Discrete Inverse Theory
About This Book
Geophysical Data Analysis: Discrete Inverse Theory is an introductory text focusing on discrete inverse theory that is concerned with parameters that either are truly discrete or can be adequately approximated as discrete. Organized into 12 chapters, the book's opening chapters provide a general background of inverse problems and their corresponding solution, as well as some of the basic concepts from probability theory that are applied throughout the text. Chapters 3-7 discuss the solution of the canonical inverse problem, that is, the linear problem with Gaussian statistics, and discussions on problems that are non-Gaussian and nonlinear are covered in Chapters 8 and 9. Chapters 10-12 present examples of the use of inverse theory and a discussion on the numerical algorithms that must be employed to solve inverse problems on a computer. This book is of value to graduate students and many college seniors in the applied sciences.
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Table of contents
- Front Cover
- Geophysical Data Analysis: Discrete Inverse Theory
- Copyright Page
- Table of Contents
- PREFACE
- INTRODUCTION
- Chapter 1. DESCRIBING INVERSE PROBLEMS
- Chapter 2. SOME COMMENTS ON PROBABILITY THEORY
- Chapter 3. SOLUTION OF THE LINEAR,GAUSSIAN INVERSE PROBLEM, VIEWPOINT 1: THE LENGTH METHOD
- Chapter 4. SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 2: GENERALIZED INVERSES
- Chapter 5. SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 3: MAXIMUM LIKELIHOOD METHODS
- Chapter 6. NONUNIQUENESS AND LOCALIZED AVERAGES
- Chapter 7. APPLICATIONS OF VECTOR SPACES
- Chapter 8. LINEAR INVERSE PROBLEMS AND NON-GAUSSIAN DISTRIBUTIONS
- Chapter 9. NONLINEAR INVERSE PROBLEMS
- Chapter 10. FACTOR ANALYSIS
- Chapter 11. SAMPLE INVERSE PROBLEMS
- Chapter 12. NUMERICAL ALGORITHMS
- APPENDIX A: Implementing Constraints with Lagrange Multipliers
- APPENDIX B: Inverse Theory with Complex Quantities
- REFERENCES
- INDEX