Inverse Problems

Basics, Theory and Applications in Geophysics

Mathias Richter (Autor)

Buch | Softcover

XII, 240 Seiten

2016 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-48383-2 (ISBN)

Infos

lt;p>The overall goal of the book is to provide access to the regularized solution of inverse problems relevant in geophysics without requiring more mathematical knowledge than is taught in undergraduate math courses for scientists and engineers. From abstract analysis only the concept of functions as vectors is needed. Function spaces are introduced informally in the course of the text, when needed. Additionally, a more detailed, but still condensed introduction is given in Appendix B.

A second goal is to elaborate the single steps to be taken when solving an inverse problem: discretization, regularization and practical solution of the regularized optimization problem. These steps are shown in detail for model problems from the fields of inverse gravimetry and seismic tomography.

The intended audience is mathematicians, physicists and engineers having a good working knowledge of linear algebra and analysis at the upper undergraduate level.

Inhalt

1.Characterization of Inverse Problems.- 2.Discretization of Inverse Problems.- 3.Regularization of Linear Inverse Problems.- 4.Regularization of Nonlinear Inverse Problems.- Appendix: A.Results from Linear Algebra.- B.Function Spaces.- C.The Fourier Transform.- D.Proofs of Theorems from Chapter 3.

Produkt-Details

• Erscheinungsdatum: 06.01.2017
• Reihe/Serie: Lecture Notes in Geosystems Mathematics and Computing
• Zusatzinfo: XII, 240 p. 52 illus., 32 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Maße: 155 x 235 mm
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geophysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Schlagworte: geomathematics • Geophysics • Geophysics/Geodesy • ill-posed problems • inverse gravimetry • Inverse Problems • Mathematical Physics • Mathematics • mathematics and statistics • nonlinear least squares problems • Numerical analysis • Numerical and Computational Physics, Simulation • Regularization • Seismic tomography
• ISBN-10: 3-319-48383-8 / 3319483838
• ISBN-13: 978-3-319-48383-2 / 9783319483832
• Zustand: Neuware