B2069 - INVERSIONE DEI DATI GEOFISICI

Learning outcomes

At the end of the course, the student:

- acquires competence in the use of geophysical data to obtain information on the processes and structure of the Earth;

- knows the main mathematical techniques for inverting these data to obtain descriptive parameters of the Earth system;

- acquires the basis of computational techniques for the inversion of geophysical data;

- knows the most recent lines of research for the inversion of geophysical data following non-linear theories.

Course contents

The course intends to highlight the importance of inverse problems as essential tools for finding the parameters that best reproduce experimental values following a physical theory. Therefore, we will structure the course within the framework of Bayesian approaches to finding solutions to physical problems. These approaches provide a coherent and comprehensive apparatus in which we find, as special cases, more common and better-known methods that provide convenient and widespread solutions, such as "least squares" or “Tikhonov solutions”.

We will cover general solutions that can address complex problems—often at the cost of increased computational effort. We will highlight some misconceptions and errors that can be easily overcome and that can influence a wide variety of parameter search problems.

Readings/Bibliography

• Tarantola A., Inverse problem theory, SIAM, 2005.

• Jaynes, E. T., Probability theory: the logic of Science, Cambridge University Press, 2003.

• Menke W., Geophysical Data Analysis: Discrete Inverse Theory – Matlab edition, Academic Press, Elsevier, 2012.

• Fichtner A., Lecture Notes on Inverse Theory https://www.cambridge.org/engage/coe/article-details/60e6a70d609d0d7fa3d893a7

• Teacher's notes and in-depth suggestions provided on the Virtual platform.

Teaching methods

To the cycle of frontal lessons, in which student participation is stimulated through questions and discussions of modern lines of research, analyzes and solutions of practical cases within the Physics of the Atmosphere and the Solid Earth are added.

In the second part, a review of the state of the art and current problems is carried out with reference to articles in the scientific literature. The last part of the course includes several computational laboratories carried out in Bash, Matlab, Python and Julia environments, which allow students to be introduced to standard codes in the Geophysics and Atmospheric Physics community. In the final exercises, students will develop small applications related to their chosen curriculum, with the aim of contributing to the learning necessary for the thesis.

Assessment methods

The assessment test is oral and will consist of an interview lasting a maximum of 30 minutes. It will start from an initial topic and continue with two other course topics, according to the teachers' requests for further information.[Ld1] [applewebdata://BC1AFF66-D684-4FFF-AF52-E60137A0FB0A#_msocom_1]

The commission will ensure that the student has well understood the principles and methods underlying the solution of inverse problems in Geophysics and the limits and fields of application of the different methods studied through comments and questions that test the student's understanding and help the student reconnect the conversation. Application topics will be covered, with questions on the examples covered in class.

The criteria used for the evaluation of the oral test will refer to the following indicators:

1. ability to analyze a topic in a way that is relevant to the questions, well organized, concise and exhaustive;

2. ability to clearly express theoretical themes, connecting equations and physical theories in a conceptual way using the specific language of the discipline;

3. ability to critically re-elaborate and discuss any variations with respect to the reasoning proposed in lessons and comments by the commission.

Teaching tools

The frontal lessons use visual aids such as PowerPoint, teacher handouts, and videos, which will be partially uploaded to the site.

The course includes activities that directly involve students, who will be asked to solve theoretical and computational exercises.

Optional seminar activities are held by researchers from other Research Institutes affiliated to the Department who are invited to present their recent research/publications.

Office hours

See the website of Andrea Morelli

See the website of Luca De Siena