Parameter Estimation and Inverse Problems

Ön Kapak
Academic Press, 10 Ara 2011 - 376 sayfa

Parameter Estimation and Inverse Problems, Second Edition 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, Second Edition 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.

  • Includes appendices for review of needed concepts in linear, statistics, and vector calculus.
  • Accessible to students and professionals without a highly specialized mathematical background.
 

Seçilmiş sayfalar

İçindekiler

1 Introduction
1
2 Linear Regression
25
3 Rank Deficiency and IllConditioning
55
4 Tikhonov Regularization
93
5 Discretizing Problems Using Basis Functions
129
6 Iterative Methods
141
7 Additional Regularization Techniques
169
8 Fourier Techniques
193
11 Bayesian Methods
253
12 Epilogue
281
A Review of Linear Algebra
283
B Review of Probability and Statistics
315
C Review of Vector Calculus
339
D Glossary of Notation
347
Bibliography
349
Index
355

9 Nonlinear Regression
217
10 Nonlinear Inverse Problems
239
Telif Hakkı

Diğer baskılar - Tümünü görüntüle

Parameter Estimation and Inverse Problems
Richard C. Aster,Brian Borchers,Clifford H. Thurber
Sınırlı önizleme - 2013
Parameter Estimation and Inverse Problems, 1. cilt
Richard C. Aster,Clifford H. Thurber,Brian Borchers
Sınırlı önizleme - 2005
Parameter Estimation and Inverse Problems
Richard C. Aster,Brian Borchers,Clifford H. Thurber
Sınırlı önizleme - 2005
Tümünü görüntüle »

Sık kullanılan terimler ve kelime öbekleri

algorithm apply approach approximately associated assume basis called Chapter columns compute condition consider converge corresponding covariance matrix deconvolution defined Definition density derivatives determine diagonal difference discrete discussed effect elements errors estimate Example factorization Figure forward Fourier function given gives important independent inverse problems inverse solution iterative L-curve least squares problem least squares solution linear linear system MATLAB mean measurement method minimizing model parameters multiply noise nonlinear nonzero norm normally distributed Note observations obtain operator optimal orthogonal orthogonal matrix particular plot points positive posterior distribution practice prior probability produces properties random variable range ray path regression require residual resolution resulting sample seismic shows singular values smooth solution solve space standard deviation symmetric matrix system of equations theorem Tikhonov regularization transform true model vector zero

Yazar hakkında (2011)

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.

Kaynakça bilgileri

BaşlıkParameter Estimation and Inverse Problems
90. cilt/International Geophysics
YazarlarRichard C. Aster, Brian Borchers, Clifford H. Thurber
Baskı2
YayıncıAcademic Press, 2011
ISBN0123850495, 9780123850492
Uzunluk376 sayfa
  
Alıntıyı Dışa AktarBiBTeX EndNote RefMan