Data Analysis and Modeling in Geoscience and Astrophysics

• find suitable representations/parametrizations of data and models
• classify inverse problems
• solve linear inverse problems with analytical methods
• examine how noise on the data propagates into uncertainty on the solutions
• use prior information in solving an inverse problem
• use methods to avoid instability in numerical solution methods
• perform a Fourier analysis of data that are non-uniform distributed
• solve weakly non-linear problems with iterative methods based on linearization.

The course deals with methods for data representation and quality assessment, parameterization of physical systems, description of empirical and analytical relationships between data and model parameters, stochastic description of uncertainties and noise, and stochastic and deterministic quantification of prior knowledge about a physical system.

A number of analytical/numerical methods for solving linear and nonlinear inverse problems are presented. The propagation of noise in the data to uncertainty of the solutions is a major theme in the course.

02631/02632/02633/01035

Lectures, exercises, and small projects.