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Lecture Notes in Geosystems Mathematics and Computing

Inverse Problems

Basics, Theory and Applications in Geophysics

Authors: Richter, Mathias

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  • Provides an introduction to inverse problems that delivers a rigorous treatment of the area without requiring familiarity with functional analysis
  • Emphasizes numerical analysis and geophysical applications, featuring accessible examples taken from active and popular research areas
  • This second edition includes an expanded and up-to-date treatment of nonlinear problems of inverse gravimetry and seismic tomography
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eBook 42,79 €
price for Spain (gross)
  • ISBN 978-3-030-59317-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-030-59316-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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 present regularized solutions of inverse problems in finite-dimensional spaces, with Chapter Three covering linear problems and Chapter Four studying nonlinear problems. Model problems reflecting scenarios of practical interest in the geosciences, such as inverse gravimetry and full waveform inversion, are fully worked out throughout the book. They are used as test cases to illustrate all single steps of solving inverse problems, up to numerical computations. Five appendices include the mathematical foundations needed to fully understand the material.
This second edition expands upon the first, particularly regarding its up-to-date treatment of nonlinear problems. Following the author’s approach, readers will understand the relevant theory and methodology needed to pursue more complex applications. Inverse Problems is ideal for graduate students and researchers interested in geophysics and geosciences.

About the authors

Matthias Richter is Professor of Mathematics at Universität der Bundeswehr München, Faculty of Electrical Engineering and Information Technology. He has conducted industrial research with Siemens and Infineon Technologies for fourteen years.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook 42,79 €
price for Spain (gross)
  • ISBN 978-3-030-59317-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-030-59316-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Inverse Problems
Book Subtitle
Basics, Theory and Applications in Geophysics
Authors
Series Title
Lecture Notes in Geosystems Mathematics and Computing
Copyright
2020
Publisher
Birkhäuser Basel
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-59317-9
DOI
10.1007/978-3-030-59317-9
Softcover ISBN
978-3-030-59316-2
Series ISSN
2730-5996
Edition Number
2
Number of Pages
XIV, 273
Number of Illustrations
14 b/w illustrations, 43 illustrations in colour
Topics