Projektdetails
Abstract
Context
In this project, we investigate the inverse problem associated with time-harmonic wave propagation, for the quantitative identification of the medium properties. We have in mind seismic (characterization of subsurface properties) and medical (diagnostic of interior disease, elastography) imaging applications. The project cornerstone is the propagation of mechanical waves in viscoelastic materials, and we shall work with partial data.
Objectives
The project examines the different stages of inverse problems: viscoelastic modeling, reconstruction algorithm, convergence and stability properties. It is designed at the interface between mathematical analysis and large scale computational experiments. We foresee an improvement of medium characterization by building numerical tools that better describe the physics (viscosity, in accordance with experiments) and by designing decision tools that would analyze the inverse algorithm. In addition, misfit functional based upon reciprocity, which has recently been introduced in the applicant's work for seismic imaging, will be investigated. inverse wave problems will be developed, to validate and reproduce our work.
Method
We target viscous behavior in time-harmonic wave propagation, and first note that several viscosity models exist. The first task is to validate the numerical formulation from experimental measurements. Then, we use quantitative reconstruction methods, which rely on iterative minimization algorithms, for the recovery of the physical parameters. We envision to study the model parametrization in inversion, in the regularization by discretization approach. We expect to analyze the performance of methods by the joint consideration of
stability and convergence estimates.
Level or originality
The encoding and recovery of viscosity, in relation with experimentalists, is quite original, and would help to better image complex media. Several heuristics remain in iterative minimization methods (frequency progression, regularization criteria) and the design of a priori decision tools based upon stability and
convergence estimates (where both applicant and co-applicant have experience) to evaluate the performance of algorithms can produce high impact. Also, the non-collocation of observational and computational sources with the reciprocity misfit functional is totally original and we anticipate that it will lead to computational cost reduction and improved reconstruction accuracy.
Researchers involved
The project is carried by Dr. Florian Faucher, who completed his Doctoral degree in computational seismic inverse problems in France, after holding a temporary research position in the United States. He will be mentored by Prof. Otmar Scherzer at the University of Vienna, who has a long-standing and recognized
expertise in the fields investigated.
In this project, we investigate the inverse problem associated with time-harmonic wave propagation, for the quantitative identification of the medium properties. We have in mind seismic (characterization of subsurface properties) and medical (diagnostic of interior disease, elastography) imaging applications. The project cornerstone is the propagation of mechanical waves in viscoelastic materials, and we shall work with partial data.
Objectives
The project examines the different stages of inverse problems: viscoelastic modeling, reconstruction algorithm, convergence and stability properties. It is designed at the interface between mathematical analysis and large scale computational experiments. We foresee an improvement of medium characterization by building numerical tools that better describe the physics (viscosity, in accordance with experiments) and by designing decision tools that would analyze the inverse algorithm. In addition, misfit functional based upon reciprocity, which has recently been introduced in the applicant's work for seismic imaging, will be investigated. inverse wave problems will be developed, to validate and reproduce our work.
Method
We target viscous behavior in time-harmonic wave propagation, and first note that several viscosity models exist. The first task is to validate the numerical formulation from experimental measurements. Then, we use quantitative reconstruction methods, which rely on iterative minimization algorithms, for the recovery of the physical parameters. We envision to study the model parametrization in inversion, in the regularization by discretization approach. We expect to analyze the performance of methods by the joint consideration of
stability and convergence estimates.
Level or originality
The encoding and recovery of viscosity, in relation with experimentalists, is quite original, and would help to better image complex media. Several heuristics remain in iterative minimization methods (frequency progression, regularization criteria) and the design of a priori decision tools based upon stability and
convergence estimates (where both applicant and co-applicant have experience) to evaluate the performance of algorithms can produce high impact. Also, the non-collocation of observational and computational sources with the reciprocity misfit functional is totally original and we anticipate that it will lead to computational cost reduction and improved reconstruction accuracy.
Researchers involved
The project is carried by Dr. Florian Faucher, who completed his Doctoral degree in computational seismic inverse problems in France, after holding a temporary research position in the United States. He will be mentored by Prof. Otmar Scherzer at the University of Vienna, who has a long-standing and recognized
expertise in the fields investigated.
| Status | Abgeschlossen |
|---|---|
| Tatsächlicher Beginn/ -es Ende | 1/10/19 → 30/09/21 |
Projektbeteiligte
- Universität Wien (Leitung)
- Medizinische Universität Wien
- OMV
- Université de Pau et des Pays de l'Adour
- Universität Bordeaux