Study Programmes 2015-2016
Modelling and inversion in geophysics
Duration :
20h Th, 20h Pr, 15h Proj.
Number of credits :
Master in geology and mining engineering (120 ECTS)3
Lecturer :
Frédéric Nguyen
Language(s) of instruction :
French language
Organisation and examination :
Teaching in the first semester, review in January
Units courses prerequisite and corequisite :
Prerequisite or corequisite units are presented within each program
Course contents :
How does one obtain a physical model from a finite set of noisy observations? How to assess image appraisal ? How can a 2D models represent a 3D problem? The course of "Modeling and inversion in geophysics" presents the theory and algorithms necessary to find the answers to the questions raised above. The resolution of direct and inverse problems will be exposed for linear models and non-linear theory, according to a deterministic and Bayesian approach. Particular attention will be paid to numerical, mathematical and statistical aspects in relation with geophysical applications.

Many exercices will be resolved in Matlab, where students can create their own codes and test them on actual data (eg Deep Ocean Drilling vertical seismic profiling). Several practical cases will be solved through software commonly used in geophysical prospecting companies or equivalent (eg Mag3D, Grav3D, EM1DFM, Res2dinv).
Learning outcomes of the course :
The course aims to cover the following aspects:


Fundamental geophysical equations (eg wave equation, eikonal equation, Poisson equation, Laplace equation, Maxwell's equations)

Integral representation and differential methods for geophysics

Linear and nonlinear inversion:

Method of Backus and Gilbert

Singular values decomposition

Regularization (Tikhonov, Occam, maximum entropy, total variation)

Iterative methods in ray tomography

Bayesian methods

Particular attention will be paid on the concepts of resolution, sensitivity, and covariance model.
Prerequisite knowledge and skills :
GEOL0021-7 Geophysical Prospecting or equivalent
Planned learning activities and teaching methods :
The lab work will occur at each lecture after presentation of the theory. For each lab, a report must given for the following week per team of 2 students. The labs required a laptop, Matlab, as well as different geophysical softwares which will be provided.
Mode of delivery (face-to-face ; distance-learning) :
The course takes place during the first quadrimester.
Recommended or required readings :
Parameter estimation and inverse problems by Aster et al.
Assessment methods and criteria :
Lab reports: 50%, 1 grade per team
Oral exam on the reports: 50%, 1 individual grade
Work placement(s) :
Organizational remarks :
Reference textbook: Parameter estimation and inverse problems. Aster R.C., Borchers B., and Thurber C.H. Elsevier Academic Press. 2005.
Contacts :
F. Nguyen
Tel: 043663797