Geophysical Data Analysis and Inverse Theory with MATLAB® and Python

William Menke is a Professor of Earth and Environmental Sciences at Columbia University. His research focuses on the development of data analysis algorithms for time series analysis and imaging in the earth and environmental sciences and the application of these methods to volcanoes, earthquakes, and other natural hazards. He has thirty years of experience teaching data analysis methods to both undergraduates and graduate students. Relevant courses that he has taught include, at the undergraduate level, Environmental Data Analysis and The Earth System, and at the graduate level, Geophysical Inverse Theory, Quantitative Methods of Data Analysis, Geophysical Theory and Practical Seismology.

1. Getting started with Matlab® or python 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