Inverse Problems : Basics, Theory and Applications in Geophysics. 2nd ed. 2020

種類:

電子ブック

責任表示:

by Mathias Richter

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2020

著者名:

• Richter, Mathias.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Geosystems Mathematics and Computing ;

ISBN:

9783030593179 [3030593177]    

注記:

Characterization of Inverse Problems -- Discretization of Inverse Problems -- Regularization of Linear Inverse Problems -- Regularization of Nonlinear Inverse Problems -- Appendix A. Results from Linear Algebra -- Appendix B. Function Spaces -- Appendix C. The Fourier Transform -- Appendix D. Regularization Property of CGNE -- Appendix E. Existence and Uniqueness Theorems for Waveform Inversion.
This textbook is an introduction to the subject of inverse problems with an emphasis on practical solution methods and applications from geophysics. The treatment is mathematically rigorous, relying on calculus and linear algebra only; familiarity with more advanced mathematical theories like functional analysis is not required. Containing up-to-date methods, this book will provide readers with the tools necessary to compute regularized solutions of inverse problems. A variety of practical examples from geophysics are used to motivate the presentation of abstract mathematical ideas, thus assuring an accessible approach. Beginning with four examples of inverse problems, the opening chapter establishes core concepts, such as formalizing these problems as equations in vector spaces and addressing the key issue of ill-posedness. Chapter Two then moves on to the discretization of inverse problems, which is a prerequisite for solving them on computers. Readers will be well-prepared for the final chapters that prese

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