Geophysical Data Analysis and Inverse Theory with MATLAB or Python, Fifth Edition is a revised and expanded introduction to inverse theory and tomography as it is practiced by geophysicists. The book demonstrates the methods needed to analyze a broad spectrum of geophysical datasets, with special attention given to those methods that generate images of the earth. Data analysis can be a mathematically complex activity, but the treatment in this volume is carefully designed to emphasize those mathematical techniques that readers will find the most familiar and to systematically introduce less-familiar ones. A series of "crib sheets" offer step-by-step summaries of methods presented.
Utilizing problems and case studies, along with MATLAB and Python computer code and summaries of methods, the book provides professional geophysicists, students, data scientists and engineers in geophysics with the tools necessary to understand and apply mathematical techniques and inverse theory.
Key Features
- Includes material on probability, including Bayesian influence, probability density function, and metropolis algorithm
- Offers detailed discussions of the application of inverse theory to seismological, gravitational, and tectonic studies
- Provides numerous examples, color figures, and end-of-chapter problems to help readers explore and further understand the presented ideas
- Includes both MATLAB and Python examples and problem sets
2. Describing inverse problems
3. Using probabilty to describe random variation
4. Solution of the linear, normal inverse problem, viewpoint 1: the length method
5. Solution of the linear, normal inverse problem, viewpoint 2: generalized inverses
6. Solution of the linear, normal inverse problem, viewpoint 3: maximum likelihood methods
7. Data assimilation methods including gaussian process regression and kalman filtering
8. Nonuniqueness and localized averages
9. Applications of vector spaces
10. Linear inverse problems with non-normal statistics
11. Nonlinear inverse problems
12. Monte carlo methods
13. Factor analysis
14. Continuous inverse theory and tomography
15. Sample inverse problems
16. Applications of inverse theory to solid earth geophysics
17. Important algorithms and method summaries
