Inverse Theory

The Art of Scientific Inference
Erscheinungsjahr 2026
ISBN: 978-1-009-55238-7
Verlag: Cambridge University Press

Buch, Englisch, 488 Seiten

How can we draw reliable conclusions from limited and imperfect data? This textbook offers a clear and accessible guide to the principles behind scientific inference, showing how a unifying framework connects fields as diverse as Earth science, medical imaging, non-destructive testing, meteorology, climate research, and machine learning. It presents both classical and modern methods for solving real-world inference problems, with practical guidance on evaluating the reliability of results and understanding their uncertainties. Designed as both a learning resource and a long-term reference, the book balances depth with clarity. Hands-on computational exercises throughout help readers translate ideas into practice, strengthen their intuition and build confidence in tackling their own data challenges. It is ideal for advanced undergraduate and postgraduate students, as well as researchers and professionals, across many disciplines, from environmental science and medical imaging to climate research, machine learning, and economics.

Autoren/Hrsg.

Fichtner, Andreas

Inhaltsverzeichnis

Preface; About this book; List of frequently used symbols; Part I. Bayesian Inference and Monte Carlo Methods: 1. Prelude; 2. Historical warm-up: how to predict the future; 3. Probabilities and information; 4. Solving probabilistic inverse problems; 5. Monte Carlo methods; Part II. Linear and Weakly Nonlinear Problems: 6. The least-squares method for linear problems; 7. Backus-Gilbert theory; 8. Weakly nonlinear problems and optimisation; 9. Adjoint methods; 10. Data assimilation; Part III. Advanced and Integrated Topics: 11. Least-squares filters; 12. Neural network solutions of inverse problems; 13. Nullspace shuttles; 14. Autotuning Monte Carlo; 15. Evidence and model selection; 16. Variational inference; 17. Alice's dilemma in Wonderland and the No-Free-Lunch theorem; Part IV. Analytically Solvable Inverse Problems: 18. Inverse scatting in 1-D and the Marchenko equation; 19. Tomography and the central slice theorem; 20. Diffraction imaging and holography; 21. Potential field extrapolation; Part V. Appendix; 22. Mathematical tools; 23. Physical and numerical models; References; Index.

Über Autor(innen)

Fichtner, Andreas
Andreas Fichtner is a professor of Seismology and Wave Physics at ETH Zürich. His research focus is on seismic tomography and fibre-optic sensing. He received the Keiiti Aki Award from the American Geophysical Union in 2011, the Early Career Scientist Award from the International Union of Geodesy and Geophysics in 2015, and the Hoffmann Prize from the Bavarian Academy of Sciences in 2018. He is the author or co-author of over 180 peer-reviewed articles, and he has authored and co-authored five books: Vector Analysis (with Sproessig, 2005, Eagle Publishing), Full-Waveform Modelling and Inversion (Springer, 2010), Exploiting Seismic Waveforms (with Kennett, 2020, Cambridge University Press); Fundamentals of Geophysics, Third Edition (with Lowrie, 2019, Cambridge University Press); and Seismic Ambient Noise (with Nakata and Gualtieri, 2019, Cambridge University Press).