Overview
- 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
Part of the book series: Lecture Notes in Geosystems Mathematics and Computing (LNGMC)
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Table of contents (4 chapters)
Keywords
- inverse problems geophysical applications
- inverse problems numerical analysis
- inverse problems gravimetry
- inverse gravimetry problem
- inverse problems math
- Inverse problems science engineering
- Regularization inverse problems
- Discretization inverse problems
- Full waveform inversion problem
- Nonlinear problems geophysics
- Nonlinear gravimetry problem
- Ill-posed problem
- Ill-posed problem regularization
- Geomathematics
- Seismic tomography
About this book
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.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Inverse Problems
Book Subtitle: Basics, Theory and Applications in Geophysics
Authors: Mathias Richter
Series Title: Lecture Notes in Geosystems Mathematics and Computing
DOI: https://doi.org/10.1007/978-3-030-59317-9
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-59316-2Published: 06 January 2021
eBook ISBN: 978-3-030-59317-9Published: 05 January 2021
Series ISSN: 2730-5996
Series E-ISSN: 2512-3211
Edition Number: 2
Number of Pages: XIV, 273
Number of Illustrations: 14 b/w illustrations, 43 illustrations in colour
Topics: Numerical Analysis, Mathematical Methods in Physics, Mathematical Modeling and Industrial Mathematics, Earth Sciences, general