# Suchergebnis: Katalogdaten im Frühjahrssemester 2021

Rechnergestützte Wissenschaften Bachelor | ||||||

Für alle Studienreglemente | ||||||

Vertiefungsgebiete | ||||||

Geophysik Empfohlene Kombinationen: Fach 1 + Fach 2 Fach 1 + Fach 3 Fach 2 + Fach 3 Fach 3 + Fach 4 Fach 5 + Fach 6 + Fach 8 Fach 4 + Fach 5 Fach 7 + Fach 8 | ||||||

Geophysik: Fach 7 | ||||||

Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
---|---|---|---|---|---|---|

651-4096-00L | Inverse Theory I: Basics | W | 3 KP | 2V | A. Fichtner | |

Kurzbeschreibung | 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. | |||||

Lernziel | 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. | |||||

Inhalt | 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 parameters 2. Representing information by probabilities 3. Bayes' theorem and mathematical scientific inference 4. Random walks and Monte Carlo Methods 5. The Metropolis-Hastings algorithm 6. Simulated Annealing 7. Linear inverse problems and the least-squares method 8. Resolution and the nullspace 9. Basic concepts of iterative nonlinear inversion methods While 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. | |||||

Skript | Presentation slides and detailed lecture notes will be provided. | |||||

Voraussetzungen / Besonderes | This course is offered as a half-semester course during the first part of the semester | |||||

651-4096-02L | Inverse Theory II: ApplicationsVoraussetzung: Erfolgreicher Abschluss von 651-4096-00L Inverse Theory I: Basics. | W | 3 KP | 2G | A. Fichtner, C. Böhm | |

Kurzbeschreibung | This second part of the course on Inverse Theory provides an introduction to the numerical solution of large-scale inverse problems. Specific examples are drawn from different areas of geophysics and image processing. Students solve various model problems using python and jupyter notebooks, and familiarize themselves with relevant open-source libraries and commercial software. | |||||

Lernziel | This course provides numerical tools and recipes to solve (non)-linear inverse problems arising in nearly all fields of science and engineering. After successful completion of the class, the students will have a thorough understanding of suitable solution algorithms, common challenges and possible mitigations to infer parameters that govern large-scale physical systems from sparse data measurements. Prerequisites for this course are (i) 651-4096-00L Inverse Theory: Basics, (ii) basic programming skills. | |||||

Inhalt | The class discusses several important concepts to solve (non)-linear inverse problems and demonstrates how to apply them to real-world data applications. All sessions are split into a lecture part in the first half, followed by tutorials using python and jupyter notebooks in the second. The range of covered topics include: 1. Regularization filters and image deblurring 2. Travel-time tomography 3. Line-search methods 4. Time reversal and Born’s approximation 5. Adjoint methods 6. Full-waveform inversion | |||||

Skript | Presentation slides and some background material will be provided. | |||||

Voraussetzungen / Besonderes | This course is offered as a half-semester course during the second part of the semester |

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