Fracture Identification in Volcanology
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General framework
The excellency laboratory ClerVolc (Centre Clermontois de Recherche sur le Volcanisme)
started in 2012. It aims at conducting interdisciplinary research in volcanology and related
fields. Several laboratories are involved in it, namely the Laboratoire Magma et Volcans (UMR
CNRS 6524), the Mathematics Laboratory (UMR CNRS 6620) and the Laboratoire d’Informatique, de Modélisation et d’Optimisation des Systèmes (UMR CNRS 6158).
The context of the post-doctorate position proposed here is a cooperation between researchers of these three laboratories.
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Objectifs scientifiques
Fractures play a major part in the earth crustal layer. In a volcanic context, magma moves
towards the earth surface via intrusions, volcanoes a created and deformed by these magmatic
intrusions and mechanical friction phenomena. The crust is a complex medium : in particular
rocks have inhomogeneous properties, yielding spatially variable mechanical properties. Openings and frictions can occur on fractures which are isolated one from another. These inner
deformations produce ground deformations which are measurable by different techniques.
Deformations of the crust are modeled by the laws of linear elasticity. The direct problem
consists in computing the deformation field, knowing the shape and localisation of the fracture. So far the most common numerical method to achieve this goal was based on boundary
elements. This technique presents several drawbacks : need to reassemble the matrices (at leat
partially) when the fracture changes, and the impossibility to take material heterogeneities
into account. Moreover the existing code used at the laboratory only allows to work with
constant (or linear with respect to depth) constraint fields along the fracture.
As a first step in the cooperation between mathematicians and geophysicists, a 3D finite
element software has been developed (programmed in C++ with the use of the Getfem library),
overcoming the previously cited drawbacks. A fictitious domain technique is implemented in
this software. The results have been published in [1].
The project proposed for this post-doctoral position deals with the inverse problem, that
is the identification of the fracture from the surface deformation measurements. A simpler
version of this problem consists in supposing that the constraints on the fracture are known.
The full problem consists in identifying both the shape of the fracture and the constraints.
1
Three steps will be followed :
— solving the simpler problem ;
— solving the full problem ;
— modify the finite element code to take the friction on the fracture into account.
Several methods will be studied for the inverse problems, in particular topological optimization.
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Candidates we look for
The candidates must have a PhD in Applied Mathematics with a good craftsmanship in
scientific computing. A good knowledge in optimization and inverse problems is also asked for.
Having some practice with the finite element library Getfem would be ideal.
The post-doctoral position is a 2 year contract and the recruited person will work in the
University of Saint-Etienne (where two of the three project managers work).
Keywords :
Elasticity, Inverse problems, Fictitious domain methods, Shape optimization.
Contacts :
— Olivier Bodart ([email protected])
— Jonas Koko ([email protected])
— Valérie Cayol ([email protected])
Bibliography
[1] O. Bodart, S. Court, V. Cayol,J. Koko. XFEM-Based Fictitious Domain Method for
Linear Elasticity Model with Crack. SIAM J. Sci. Comput. 38 (2016), no. 2, B219–B246.