# Search result: Catalogue data in Spring Semester 2021

Number Title Type ECTS Hours Lecturers Earth Sciences Master Major in Geophysics Compulsory Modules Geophysics Geophysics: Methods I 651-4096-00L Inverse Theory I: Basics O 3 credits 2V A. Fichtner Abstract Inverse theory is the art of inferring properties of a physical system from noisy and sparse observations. It is used to transform observations of waves into 3D images of a medium seismic tomography, medical imaging and material science; to constrain density in the Earth from gravity; to obtain probabilities of life on exoplanets ... . Inverse theory is at the heart of many natural sciences. Objective The goal of this course is to enable students to develop a mathematical formulation of specific inference (inverse) problems that may arise anywhere in the physical sciences, and to implement suitable solution methods. Furthermore, students should become aware that nearly all relevant inverse problems are ill-posed, and that their meaningful solution requires the addition of prior knowledge in the form of expertise and physical intuition. This is what makes inverse theory an art. Content This first of two courses covers the basics needed to address (and hopefully solve) any kind of inverse problem. Starting from the description of information in terms of probabilities, we will derive Bayes' Theorem, which forms the mathematical foundation of modern scientific inference. This will allow us to formalise the process of gaining information about a physical system using new observations. Following the conceptual part of the course, we will focus on practical solutions of inverse problems, which will lead us to study Monte Carlo methods and the special case of least-squares inversion.In more detail, we aim to cover the following main topics:1. The nature of observations and physical model parameters2. Representing information by probabilities3. Bayes' theorem and mathematical scientific inference4. Random walks and Monte Carlo Methods5. The Metropolis-Hastings algorithm6. Simulated Annealing7. Linear inverse problems and the least-squares method8. Resolution and the nullspace9. Basic concepts of iterative nonlinear inversion methodsWhile the concepts introduced in this course are universal, they will be illustrated with numerous simple and intuitive examples. These will be complemented with a collection of computer and programming exercises.Prerequisites for this course include (i) basic knowledge of analysis and linear algebra, (ii) basic programming skills, for instance in Matlab or Python, and (iii) scientific curiosity. Lecture notes Presentation slides and detailed lecture notes will be provided. Prerequisites / Notice This course is offered as a half-semester course during the first part of the semester
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