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E-raamat: Parameter Estimation and Inverse Problems

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(New Mexico Institute of Mining and Technology, Socorro, USA), (New Mexico Institute of Mining and Technology, Socorro, USA), (University of Wisconsin-Madison, USA)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 10-Dec-2011
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780123850492
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Parameter Estimation and Inverse ProblemsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 10-Dec-2011
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780123850492
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Parameter Estimation and Inverse Problems, 2e provides geoscience students and professionals with answers to common questions like how one can derive a physical model from a finite set of observations containing errors, and how one may determine the quality of such a model. This book takes on these fundamental and challenging problems, introducing students and professionals to the broad range of approaches that lie in the realm of inverse theory. The authors present both the underlying theory and practical algorithms for solving inverse problems. The authors’ treatment is appropriate for geoscience graduate students and advanced undergraduates with a basic working knowledge of calculus, linear algebra, and statistics.

Parameter Estimation and Inverse Problems, 2e  introduces readers to both Classical and Bayesian approaches to linear and nonlinear problems with particular attention paid to computational, mathematical, and statistical issues related to their application to geophysical problems. The textbook includes Appendices covering essential linear algebra, statistics, and notation in the context of the subject. A companion website features computational examples (including all examples contained in the textbook) and useful subroutines using MATLAB.

  • Includes appendices for review of needed concepts in linear, statistics, and vector calculus.
  • Companion website contains comprehensive MATLAB code for all examples, which readers can reproduce, experiment with, and modify.
  • Online instructor’s guide helps professors teach, customize exercises, and select homework problems
  • Accessible to students and professionals without a highly specialized mathematical background.


Parameter Estimation and Inverse Problems, 2e provides geoscience students and professionals with answers to common questions like how one can derive a physical model from a finite set of observations containing errors, and how one may determine the quality of such a model. This book takes on these fundamental and challenging problems, introducing students and professionals to the broad range of approaches that lie in the realm of inverse theory. The authors present both the underlying theory and practical algorithms for solving inverse problems. The authors’ treatment is appropriate for geoscience graduate students and advanced undergraduates with a basic working knowledge of calculus, linear algebra, and statistics.

Parameter Estimation and Inverse Problems, 2e introduces readers to both Classical and Bayesian approaches to linear and nonlinear problems with particular attention paid to computational, mathematical, and statistical issues related to their application to geophysical problems. The textbook includes Appendices covering essential linear algebra, statistics, and notation in the context of the subject. A companion website features computational examples (including all examples contained in the textbook) and useful subroutines using MATLAB.

  • Includes appendices for review of needed concepts in linear, statistics, and vector calculus.
  • Companion website contains comprehensive MATLAB code for all examples, which readers can reproduce, experiment with, and modify.
  • Online instructor’s guide helps professors teach, customize exercises, and select homework problems
  • Accessible to students and professionals without a highly specialized mathematical background.

Arvustused

"A few years ago, it was my pleasure to review for the TLE this books first edition, published in 2005The present revised version is some 60 pages longer and contains several significant modifications. As is true of the original, the book continues to be one of the clearest as well as the most comprehensive elementary expositions of discrete geophysical inverse theory. It is ideally suited for beginners as well as a fine resource for those searching for a particular inverse problem. Each algorithm is presented in the form of pseudo-code, then backed up by a collection of MATLAB codes downloadable from an Elsevier Web siteAll examples in the book are beautifully illustrated with simple, easy to follow "cartoon" problems, and all painstakingly designed to illuminate the details of a particular numerical method." --The Leading Edge, July 2012

Muu info

Check out the companion website: http://www.elsevierdirect.com/companion.jsp?ISBN=9780123850485 and the Instructor website: http://textbooks.elsevier.com/web/manuals.aspx?isbn=9780123850485
Preface ix
1 Introduction
1(24)
1.1 Classification of Parameter Estimation and Inverse Problems
1(3)
1.2 Examples of Parameter Estimation Problems
4(4)
1.3 Examples of Inverse Problems
8(6)
1.4 Discretizing Integral Equations
14(5)
1.5 Why Inverse Problems Are Difficult
19(3)
1.6 Exercises
22(1)
1.7 Notes and Further Reading
23(2)
2 Linear Regression
25(30)
2.1 Introduction to Linear Regression
25(2)
2.2 Statistical Aspects of Least Squares
27(10)
2.3 An Alternative View of the 95% Confidence Ellipsoid
37(1)
2.4 Unknown Measurement Standard Deviations
38(4)
2.5 L1 Regression
42(5)
2.6 Monte Carlo Error Propagation
47(2)
2.7 Exercises
49(3)
2.8 Notes and Further Reading
52(3)
3 Rank Deficiency and Ill-Conditioning
55(38)
3.1 The SVD and the Generalized Inverse
55(7)
3.2 Covariance and Resolution of the Generalized Inverse Solution
62(2)
3.3 Instability of the Generalized Inverse Solution
64(4)
3.4 A Rank Deficient Tomography Problem
68(6)
3.5 Discrete Ill-Posed Problems
74(13)
3.6 Exercises
87(4)
3.7 Notes and Further Reading
91(2)
4 Tikhonov Regularization
93(36)
4.1 Selecting Good Solutions to Ill-Posed Problems
93(2)
4.2 SVD Implementation of Tikhonov Regularization
95(4)
4.3 Resolution, Bias, and Uncertainty in the Tikhonov Solution
99(4)
4.4 Higher-Order Tikhonov Regularization
103(8)
4.5 Resolution in Higher-Order Tikhonov Regularization
111(2)
4.6 The TGSVD Method
113(2)
4.7 Generalized Cross-Validation
115(4)
4.8 Error Bounds
119(5)
4.9 Exercises
124(3)
4.10 Notes and Further Reading
127(2)
5 Discretizing Problems Using Basis Functions
129(12)
5.1 Discretization by Expansion of the Model
129(4)
5.2 Using Representers as Basis Functions
133(1)
5.3 The Method of Backus and Gilbert
134(5)
5.4 Exercises
139(1)
5.5 Notes and Further Reading
140(1)
6 Iterative Methods
141(28)
6.1 Introduction
141(1)
6.2 Iterative Methods for Tomography Problems
142(8)
6.3 The Conjugate Gradient Method
150(5)
6.4 The CGLS Method
155(5)
6.5 Resolution Analysis for Iterative Methods
160(6)
6.6 Exercises
166(2)
6.7 Notes and Further Reading
168(1)
7 Additional Regularization Techniques
169(24)
7.1 Using Bounds as Constraints
169(5)
7.2 Sparsity Regularization
174(2)
7.3 Using IRLS to Solve L1 Regularized Problems
176(10)
7.4 Total Variation
186(5)
7.5 Exercises
191(1)
7.6 Notes and Further Reading
192(1)
8 Fourier Techniques
193(24)
8.1 Linear Systems in the Time and Frequency Domains
193(6)
8.2 Linear Systems in Discrete Time
199(5)
8.3 Water Level Regularization
204(4)
8.4 Tikhonov Regularization in the Frequency Domain
208(6)
8.5 Exercises
214(1)
8.6 Notes and Further Reading
215(2)
9 Nonlinear Regression
217(22)
9.1 Introduction to Nonlinear Regression
217(1)
9.2 Newton's Method for Solving Nonlinear Equations
217(3)
9.3 The Gauss-Newton and Levenberg-Marquardt Methods for Solving Nonlinear Least Squares Problems
220(4)
9.4 Statistical Aspects of Nonlinear Least Squares
224(4)
9.5 Implementation Issues
228(6)
9.6 Exercises
234(3)
9.7 Notes and Further Reading
237(2)
10 Nonlinear Inverse Problems
239(14)
10.1 Regularizing Nonlinear Least Squares Problems
239(5)
10.2 Occam's Inversion
244(4)
10.3 Model Resolution in Nonlinear Inverse Problems
248(3)
10.4 Exercises
251(1)
10.5 Notes and Further Reading
252(1)
11 Bayesian Methods
253(28)
11.1 Review of the Classical Approach
253(2)
11.2 The Bayesian Approach
255(5)
11.3 The Multivariate Normal Case
260(9)
11.4 The Markov Chain Monte Carlo Method
269(4)
11.5 Analyzing MCMC Output
273(5)
11.6 Exercises
278(2)
11.7 Notes and Further Reading
280(1)
12 Epilogue
281(2)
Appendix A Review of Linear Algebra
283(32)
A.1 Systems of Linear Equations
283(3)
A.2 Matrix and Vector Algebra
286(6)
A.3 Linear Independence
292(1)
A.4 Subspaces of Rn
293(5)
A.5 Orthogonality and the Dot Product
298(4)
A.6 Eigenvalues and Eigenvectors
302(2)
A.7 Vector and Matrix Norms
304(2)
A.8 The Condition Number of a Linear System
306(2)
A.9 The QR Factorization
308(2)
A.10 Complex Matrices and Vectors
310(1)
A.11 Linear Algebra in Spaces of Functions
311(1)
A.12 Exercises
312(2)
A.13 Notes and Further Reading
314(1)
Appendix B Review of Probability and Statistics
315(24)
B.1 Probability and Random Variables
315(6)
B.2 Expected Value and Variance
321(2)
B.3 Joint Distributions
323(3)
B.4 Conditional Probability
326(3)
B.5 The Multivariate Normal Distribution
329(1)
B.6 The Central Limit Theorem
330(1)
B.7 Testing for Normality
330(2)
B.8 Estimating Means and Confidence Intervals
332(2)
B.9 Hypothesis Tests
334(2)
B.10 Exercises
336(1)
B.11 Notes and Further Reading
337(2)
Appendix C Review of Vector Calculus
339(8)
C.1 The Gradient, Hessian, and Jacobian
339(2)
C.2 Taylor's Theorem
341(1)
C.3 Lagrange Multipliers
341(3)
C.4 Exercises
344(1)
C.5 Notes and Further Reading
345(2)
Appendix D Glossary of Notation
347(2)
Bibliography 349(6)
Index 355
Professor Aster is an Earth scientist with broad interests in geophysics, seismological imaging and source studies, and Earth processes. His work has included significant field research in western North America, Italy, and Antarctica. Professor Aster also has strong teaching and research interests in geophysical inverse and signal processing methods and is the lead author on the previous two editions. Aster was on the Seismological Society of America Board of Directors, 2008-2014 and won the IRIS Leadership Award, 2014. Dr. Borchers primary research and teaching interests are in optimization and inverse problems. He teaches a number of undergraduate and graduate courses at NMT in linear programming, nonlinear programming, time series analysis, and geophysical inverse problems. Dr. Borchers research has focused on interior point methods for linear and semidefinite programming and applications of these techniques to combinatorial optimization problems. He has also done work on inverse problems in geophysics and hydrology using linear and nonlinear least squares and Tikhonov regularization. Professor Thurber is an international leader in research on three-dimensional seismic imaging ("seismic tomography") using earthquakes. His primary research interests are in the application of seismic tomography to fault zones, volcanoes, and subduction zones, with a long-term focus on the San Andreas fault in central California and volcanoes in Hawaii and Alaska. Other areas of expertise include earthquake location (the topic of a book he edited) and geophysical inverse theory.
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