C8411 - INVERSION OF GEOPHYSICAL DATA

Learning outcomes

At the end of the course, students acquire mathematical and computational skills to utilise atmospheric and solid Earth data to obtain information on the physical processes that generate them.

Course contents

Inverse Problems are the fundamental tool through which, given theory and experimental data, we can reconstruct the parameters that controlled the data. This means being able to reconstruct parameters, such as temperature or wave velocity, that explain how the deep Earth, the atmosphere, and the interface between the two work.

The course is structured within the framework of Bayesian approaches to find solutions to physical problems and estimate the uncertainties of the parameters that control them in a computationally efficient manner. Theoretical lectures will be followed by practical exercises with applications to the fields of Solid Earth Physics, Atmospheric Physics, and Oceanography.

Topics covered:

Definition of Inverse Problems: Data, model parameters, and exact physical theories, with references to non-uniqueness.

Bayesian Inferences and Monte Carlo Methods: Probabilistic information states and the solution of probabilistic inverse problems with corresponding search methods.

Linear Problems: Least-squares methods with concepts of resolution and stability, using a priori information and Tikhonov Theory to address the lack of observations.

Weakly Nonlinear Problems: Backus-Gilbert and optimization using linearization methods, gradient-guided searches, and Newton methods.

Adjoint Methods and Nonlinear Problem Solution: Discrete and continuous methods applied to the wave equation, including misfit and sensitivity kernel calculations.

Inverse Problem Solutions: Analytical and computational solutions, including advanced topics.

Readings/Bibliography

Reference Books and Materials

• Fichtner A., Lecture Notes on Inverse Theory https://www.cambridge.org/engage/coe/article-details/60e6a70d609d0d7fa3d893a7 oppure https://www.cambridge.org/core/books/inverse-theory/36CF63411C39626EE8BB8354B0B03505
• Aster, Borchers, Thurber. Parameter Estimation and Inverse Problems (2013). Elsevier. https://www.sciencedirect.com/book/monograph/9780123850485/parameter-estimation-and-inverse-problems#book-info

Additional Books and Materials:

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

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

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

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, the Solid Earth and their interface are added.

The course includes several computational exercises carried out in Matlab, Python and Julia environments, which allow students to be introduced to standard codes for 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.

Non-attending students are encouraged to contact the instructor, who will suggest a path based on the Menke content and exercises. The instructor will record the lectures upon request.

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.

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.

Students with specific learning disabilities (SLD) or temporary or permanent disabilities are advised to contact the relevant university office (https://site.unibo.it/studenti-con-disabilita-e-dsa/it) well in advance. That office will propose any necessary accommodations to the students concerned; these proposals must be submitted to the instructor for approval at least 15 days in advance, so that the instructor can assess their suitability in relation to the course's learning objectives.

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 Luca De Siena