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Book
xxx, 322 pages : illustrations ; 24 cm
  • 1. Describing Inverse Problems 2. Some Comments on Probability Theory 3. Solution of the Linear, Gaussian Inverse Problem, Viewpoint 1: The Length Method 4. Solution of the Linear, Gaussian Inverse Problem, Viewpoint 2: Generalized Inverses 5. Solution of the Linear, Gaussian Inverse Problem, Viewpoint 3: Maximum Likelihood Methods 6. Nonuniqueness and Localized Averages 7. Applications of Vector Spaces 8. Linear Inverse Problems and Non-Gaussian Statistics 9. Nonlinear Inverse Problems 10. Factor Analysis 11. Continuous Inverse Theory and Tomography 12. Sample Inverse Problems 13. Applications of Inverse Theory to Solid Earth Geophysics.
  • (source: Nielsen Book Data)9780128135556 20180924
Geophysical Data Analysis: Diverse Inverse Theory, Fourth Edition is a revised and expanded introduction to inverse theory and tomography as it is practiced by geophysicists. It demonstrates the methods needed to analyze a broad spectrum of geophysical datasets, with special attention to those methods that generate images of the earth. Data analysis can be a mathematically complex activity, but the treatment in this volume is carefully designed to emphasize those mathematical techniques that readers will find the most familiar and to systematically introduce less-familiar ones. Using problems and case studies, along with MATLAB computer code and summaries of methods, the book provides data scientists and engineers in geophysics with the tools necessary to understand and apply mathematical techniques and inverse theory.
(source: Nielsen Book Data)9780128135556 20180924
Earth Sciences Library (Branner)
GEOPHYS-281
Book
xii, 342 p. : ill. (some col.) ; 26 cm.
  • 1. The general discrete inverse problem-- 2. Monte Carol methods-- 3. The least-squares criterion-- 4. Least-absolute values criterion and minimax criterion-- 5. Functional inverse problems-- 6. Appendices-- 7. Problems-- References-- Index.
  • (source: Nielsen Book Data)9780898715729 20160528
The use of actual observations to infer the properties of a model is an inverse problem, which are often difficult as they may not have a unique solution. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. The book attempts to explain how a method of acquisition of information can be applied to actual real-world problems, including many heuristic arguments. Prompted by recent developments in inverse theory, this text is a completely rewritten version of a 1987 book by the same author, and includes many algorithmic details for Monte Carlo methods, least-squares discrete problems, and least-squares problems involving functions. In addition, some notions are clarified, the role of optimization techniques is underplayed, and Monte Carlo methods are taken much more seriously.
(source: Nielsen Book Data)9780898715729 20160528
Earth Sciences Library (Branner)
GEOPHYS-281
Book
xii, 301 p. : ill. ; 24 cm. + 1 CD-ROM (4 3/4 in.)
  • Preface 1. Introduction 2. Linear Regression 3. Discretizing Continuous Inverse Problems 4. Rank Deficiency and Ill-Conditioning 5. Tikhonov Regularization 6. Iterative Methods 7. Other Regularization Techniques 8. Fourier Techniques 9. Nonlinear Regression 10. Nonlinear Inverse Problems 11. Bayesian Methods Appendix A: Review of Linear Algebra Appendix B: Review of Probability and Statistics Appendix C: Glossary of Notation Bibliography Index.
  • (source: Nielsen Book Data)9780120656042 20160528
"Parameter Estimation and Inverse Problems" primarily serves as a textbook for advanced undergraduate and introductory graduate courses. Class notes have been developed and reside on the World Wide Web for facilitating use and feedback by teaching colleagues. The authors' treatment promotes an understanding of fundamental and practical issues associated with parameter fitting and inverse problems including basic theory of inverse problems, statistical issues, computational issues, and an understanding of how to analyze the success and limitations of solutions to these problems. The text is also a practical resource for general students and professional researchers, where techniques and concepts can be readily picked up on a chapter-by-chapter basis. "Parameter Estimation and Inverse Problems" is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who may not have an extensive mathematical background. It is accompanied by a Web site that contains Matlab code corresponding to all examples. It is designed to be accessible to graduate students and professionals in physical sciences without an extensive mathematical background. It includes three appendices for review of linear algebra and crucial concepts in statistics. It is battle-tested in courses at several universities, and MATLAB exercises facilitate exploration of material.
(source: Nielsen Book Data)9780120656042 20160528
Earth Sciences Library (Branner)
GEOPHYS-281
Book
xi, 386 p. : ill. ; 25 cm.
  • PrefaceCh. 1Mathematical PrecursorCh. 2Linear Problems with Exact DataCh. 3Linear Problems with Uncertain DataCh. 4Resolution and InferenceCh. 5Nonlinear ProblemsAppendix A: The Dilogarithm FunctionAppendix B: Table for 1-norm MisfitsReferencesIndex.
  • (source: Nielsen Book Data)9780691036342 20160528
In many physical sciences, the most natural description of a system is with a function of position or time. In principle, infinitely many numbers are needed to specify that function, but in practice only finitely many measurements can be made. Inverse theory concerns the mathematical techniques that enable researchers to use the available information to build a model of the unknown system or to determine its essential properties. In "Geophysical Inverse Theory", Robert Parker provides a systematic development of inverse theory at the graduate and professional level that emphasizes a rigorous yet practical solution of inverse problems, with examples from experimental observations in geomagnetism, seismology, gravity, electromagnetic sounding, and interpolation. Although illustrated with examples from geophysics, this book has broad implications for researchers in applied disciplines from materials science and engineering to astrophysics, oceanography, and meteorology. Parker's approach is to avoid artificial statistical constructs and to emphasize instead the reasonable assumptions researchers must make to reduce the ambiguity that inevitably arises in complex problems. The structure of the book follows a natural division in the subject into linear theory, in which the measured quantities are linear functionals of the unknown models, and nonlinear theory, which covers all other systems but is not nearly so well understood. The book covers model selection as well as techniques for drawing firm conclusions about the earth independent of any particular model.
(source: Nielsen Book Data)9780691036342 20160528
Earth Sciences Library (Branner)
GEOPHYS-281