# Search result: Catalogue data in Spring Semester 2021

Computational Science and Engineering Master | ||||||

Fields of Specialization | ||||||

Geophysics Recommended combinations: Subject 2 + Subject 5 + Subject 6 + Subject 7 Subject 2 + Subject 4 + Subject 5 + Subject 6 + Subject 8 Subject 2 + Subject 5 + Subject 6 + (Subject 1 or Subject 3) | ||||||

Geophysics: Subject 1 offered in the autumn semester | ||||||

Geophysics: Subject 2 offered in the autumn semester | ||||||

Geophysics: Subject 3 | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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651-4008-00L | Dynamics of the Mantle and Lithosphere | W | 3 credits | 2G | A. Rozel | |

Abstract | The goal of this course is to obtain a detailed understanding of the physical properties, structure, and dynamical behavior of the mantle-lithosphere system, focusing mainly on Earth but also discussing how these processes occur differently in other terrestrial planets. | |||||

Learning objective | The goal of this course is to obtain a detailed understanding of the physical properties, structure, and dynamical behavior of the mantle-lithosphere system, focusing mainly on Earth but also discussing how these processes occur differently in other terrestrial planets. | |||||

Geophysics: Subject 4 | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

651-4094-00L | Numerical Modelling for Applied Geophysics | W | 5 credits | 2G | J. Robertsson, H. Maurer | |

Abstract | Numerical modelling in environmental and exploration geophysics. The course covers different numerical methods such as finite difference and finite element methods applied to solve PDE’s for instance governing seismic wave propagation and geoelectric problems. Prerequisites include basic knowledge of (i) signal processing and applied mathematics such as Fourier analysis and (ii) Matlab. | |||||

Learning objective | After this course students should have a good overview of numerical modelling techniques commonly used in environmental and exploration geophysics. Students should be familiar with the basic principles of the methods and how they are used to solve real problems. They should know advantages and disadvantages as well as the limitations of the individual approaches. The course includes exercises in Matlab where the stduents both should lear, understand and use existing scripts as well as carrying out some coding in Matlab themselves. | |||||

Content | During the first part of the course, the following topics are covered: - Applications of modelling - Physics of acoustic, elastic, viscoelastic wave equations as well as Maxwell's equations for electromagnetic wave propagation and diffusive problems - Recap of basic techniques in signal processing and applied mathematics - Potential field modelling - Solving PDE's, boundary conditions and initial conditions - Acoustic/elastic wave propagation I, explicit time-domain finite-difference methods - Acoustic/elastic wave propagation II, Viscoelastic, pseudospectral - Acoustic/elastic wave propagation III, spectral accuracy in time, frequency domain FD, Eikonal - Implicit finite-difference methods (geoelectric) - Finite element methods, 1D/2D (heat equation) - Finite element methods, 3D (geoelectric) - Acoustic/elastic wave propagation IV, Finite element and spectral element methods - HPC and current challenges in computational seismology - Seismic data imaging project Most of the lecture modules are accompanied by exercises Small projects will be assigned to the students. They either include a programming exercise or applications of existing modelling codes. | |||||

Lecture notes | Presentation slides and some background material will be provided. | |||||

Literature | Igel, H., 2017. Computational seismology: a practical introduction. Oxford University Press. | |||||

Prerequisites / Notice | This course is offered as a full semester course. During the second part of the semester some lecture slots will be dedicated towards working on exercises and course projects. | |||||

Geophysics: Subject 6 | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

651-4006-00L | Seismology of the Spherical Earth | W | 3 credits | 3G | M. van Driel, S. C. Stähler | |

Abstract | Brief review of continuum mechanics and the seismic wave equation; P and S waves; reciprocity and representation theorems; eikonal equation and ray tracing; Huygens and Fresnel; surface-waves; normal-modes; seismic interferometry and noise; numerical solutions. | |||||

Learning objective | After taking this course, students will have the background knowledge necessary to start an original research project in quantitative seismology. | |||||

Literature | Shearer, P., Introduction to Seismology, Cambridge University Press, 1999. Aki, K. and P. G. Richards, Quantitative Seismology, second edition, University Science Books, Sausalito, 2002. Nolet, G., A Breviary of Seismic Tomography, Cambridge University Press, 2008. | |||||

Prerequisites / Notice | This is a quantitative lecture with an emphasis on mathematical description of wave propagation phenomena on the global scale, hence basic knowledge in vector calculus, linear algebra and analysis as well as seismology (e.g. from the 'wave propagation' lecture) are essential to follow this course. | |||||

Geophysics: Subject 7 | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

651-4096-00L | Inverse Theory I: Basics | W | 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. | |||||

Learning 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 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. | |||||

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 | |||||

651-4096-02L | Inverse Theory II: ApplicationsPrerequisites: The successful completion of 651-4096-00L Inverse Theory I: Basics is mandatory. | W | 3 credits | 2G | A. Fichtner, C. Böhm | |

Abstract | 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. | |||||

Learning objective | 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. | |||||

Content | 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 | |||||

Lecture notes | Presentation slides and some background material will be provided. | |||||

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

Geophysics: Subject 8 offered in the autumn semester | ||||||

Geophysics: Seminar | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-5880-00L | Seminar in Geophysics for CSE | W | 4 credits | 2S | T. Gerya, P. Tackley | |

Abstract | ||||||

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